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  • wings XIV
    folded back onto the body The flight of the representatives of this subtype is apparently most investigated and may be characterized as to be highly maneuverable and having a great store of power Biological significance of flight for the most specialized forms very great and connected with obtaining food for their larvae necessity of tranporting heavy loads and long range of flight This subtype only contains members of the Order Hymenoptera The various numerous groups of this Order illustrate the diversity of changes in the subtype the study of which changes will be an independent and broad theme The chief features of specialization boil down to a smaller or greater development of costalization and reduction of the postcostal venation and decrease of size of the hindwings Most primitive in this series are the sawflies Tenthredinoidea of the Family Lydidae The next Figure shows a more or less related species of sawfly Figure 13 Xyela julii Br Xyelidae Hymenoptera Symphyta A primitive hymenopteron After BERLAND 1951 from MALYSHEV 1966 The other end of the series of certain forms of the present subtype contains evidently the aculeate Hymenoptera for instance Vespidae wasps Another kind of change is expressed in the groups Ichneumonoidea and Braconoidea and characterized by the large size of the wings with relatively weak venation but nevertheless advanced in the sense of fairly strongly reduced Together with this characteristic for this change is a progressed lightening of the body having a small head thorax slender abdomen and long appendages of the body antennae legs and often a long ovipositor certain Pimplidae and Braconidae being comparable with the cerci of other insects as to its aerodynamic effect in flight Both first mentioned changes as in sawflies and aculeate Hymenoptera within the subtype are in contrast characterized by a short compact body long appendages are absent The present subtype is directly connected with another with me t adipterygia see below Extreme forms with utterly costalized wings as for instance Proctotrupoidea and Braconoidea form the transition to metadipterygia For Hymenoptera see second half of Fifth Part of Website See next Figures for some representatives of the subtype hymenodipterygia Figure 14 Polistes nimpha Family Vespidae Social Plaited winged wasps Suborder Aculeata 12 12 5 mm After SEVERA in ZAHRADNIK Thieme s insektengids For a typical solitary true bee see next Figure Figure 15 Halictus quadricinctus Superfamily Apoidea Family Halictidae Social bees Suborder Aculeata 15 16 mm After SEVERA in ZAHRADNIK Thieme s insektengids Figure 16 Left image Scutellista cyanea Mot Family Pteromalidae Order Hymenoptera Length of body 1 3 mm Middle image Hyaleus capitosus Sm Superfamily Apoidea bees Order Hymenoptera Length of body 10 mm Right image Trypoxylon connexum Turn Superfamily Sphecoidea Order Hymenoptera Australia Length of body 13 mm All Figures after TILLYARD in ROHDENDORF 1949 6 Megadipterygia dipterygia of large insects To this subtype not to be confused with me t adipterygia which is being dealt with further below do belong different insects themselves belonging to two Orders phylogenetically far apart from one another Lepidoptera butterflies and moths and Homoptera cicadas etc These apparently totally disparate insects are unified through a number of features Such are the large or medium size of the body and the strongly elongate wings possessing moderate costalization of the venation together with the reduction of a large part of the cross veins Hindwings relatively large usually about 3 5 of the length of the forewings more seldom shorter Wing venation fairly rich In resting position the insect folds the wings back onto or along the abdomen Thorax as a rule very massive and strongly built possessing a strong muscular apparatus The shape of the body is characteristic The front part is more or less thickened little pointed Towards the end the body is definitely thinning out pointed Legs short All these features are definite features of aerodynamic specialization of the body Size of the wing surface as compared to the weight of the body small Flight is investigated in one group only namely in hawk moths Sphingidae Oder Lepidoptera distinguishing themselves by the highest indexes of range of flight many hundreds of kilometers of all insects Megadipterygia originated on the one hand from forms of broad wingedness platypterygia of certain Lepidoptera in particular of the subtype diplatypterygia and on the other is based on the homodipterygia of cicadas The known forms of megadipterygia point to the diversity of the subtype Together with the typical representatives of the subtype characterized by large size massive aerodynamic and specialized body well developed hindwings such as the Sphingidae Lepidoptera many cicadas Homoptera and the fossil Palaeontinidae there exist smaller Lepidoptera Cuculiidae Psychidae Oiketicus and others characterized by a more elongate body Another change within the subtype is illustrated also in Lepidoptera certain Zygaenidae and Syntomididae Trichura In these insects the hindwings show a more advanced stage of reduction together with relatively insignificant elongation of the forewings and weak development of the thorax It may even be that the forms of the latter example should be placed in a special group after having studied things in more details Biological significance of flight is very diverse On the one hand for particular groups of Lepidoptera for example the Sphingidae flight realizes feeding and distribution the insects feed in flight on nectar from flowers and fly long distances other groups also Lepidoptera are apparently aphagous they do not feed Psychidae Oiketicus and flight for them has only significance in reproduction The significance of flight in sing cicadas is not known to me Rohdendorf is it for protection of for distribution See next Figures Figure 17 Acherontia atropos Family Sphingidae Order Lepidoptera Wingspan forewings 45 60 mm After SEVERA in ZAHRADNIK Thieme s insektengids 1977 Figure 18 Trichura sp Family Syntomididae Order Lepidoptera South America After SHARP in ROHDENDORF 1949 Figure 19 Cephonodes hylas L Family Sphingidae Order Lepidoptera Australia Length of body 40 mm After TILLYARD in ROHDENDORF 1949 Figure 20 Tibicen haematodes Family Cicadidae Order Homoptera 26 38 mm Wingspan 75 85 mm After SEVERA in ZAHRADNIK Thieme s insektengids 1977 7 Eudipterygia true two wingedness We begin with some Figures illustrating the subtype in the Order Diptera Figure 21 Fungivora punctata MEIG Fungivoridae general view of the insect From ROHDENDORF 1946 after JOHANNSEN 1909 Figure 22 A male adult of the New Zealand glow worm Arachnocampa luminosa Fungivoridea Ceroplatidae This is a rare photograph of an elusive fly but its appearance is typical of land midges all over the world After OLDROYD 1964 See also Figure 1 above And further Figure 23 Some representatives of the Lifting Lightly veined muscoid functional wing type in ROHDENDORF s classification 1951 of the wings of Diptera 1 Chlorops pumilionis Yellow stem fly 2 5 3 5 mm Family Chloropidae Acalyptratae 2 Oscinella frit Frit fly 1 5 2 mm Family Chloropidae Acalyptratae 3 Delia brassicae Cabbage fly 5 5 7 5 mm Family Anthomyiidae flower flies Calyptratae 6 Musca domestica House fly 7 9 mm Family Muscidae Calyptratae After SEVERA in Thieme s insektengids voor West en Midden Europa 1977 To this subtype do belong the majority of the Order Diptera and certain other insects They are morphologically the most specialized forms of dipterygia Most characteristic is the complete reduction of the hindwings with strong development of the mesothorax its skeleton and musculature together with various mechanical often very advanced adaptations of the wing venation shape of the body and other features The complete concentration of the flight function in the forewings being appendages of the metathorax caused the reduction of the other divisions of the thorax being transformed into insignificant appendages of the mesothoracic skeleton carrying merely the corresponding pairs of legs with their musculature In the structure of the whole body first of all as to its shape one observes various specializations of which the shortening of the body is the clearest expression directly related to the enlargement of the thorax But the most characteristic trait of this subtype are the structural features of the wings which acquire a special form Anterior margin of wing straight apex quite distinct termen very large See Part I Figure 1 and reaches far along the posterior wing margin The latter in its basal half gives off various membranous appendages lobes and blades often rather large Particular complexity is usually reached in the basal part of the wing its basiala in which mechanical adaptations are developed serving the wing s firmness all kinds of folds outgrowths thickening of veins hooks and bristles Position of the wings at rest fairly variable and in addition to usually folding them back onto the body they often are merely held a bit backwards Also took place the complete loss of the ability of folding the wings backwards this we see for example in the Bombyliidae bee flies among whom there exist forms that hold in resting posistion the wings sideways The subtype originated almost exclusively on the basis of the neurodipterygia of the ancestors of the Diptera Such probably were special lower mesozoic or permian groups of the order Paratrichoptera who in their evolution quickly went through the stage of neurodipterygia having lost the hind pair of wings while at the same time having strenghened the driving apparatus the thoracic skeleton and muscles The bloom of the Order Diptera and its long history effected an advanced differentiation in eudipterygia giving rise to a series of secondary groupings and even subtypes A detailed analysis of all transformations within eudipterygia lies outside the scope of the present treatise Such analysis is an independent and rather extensive task ROHDENDORF has done this a few years later 1951 establishing a large number of functional wing types in the Order Diptera which we have presented and supplemented in Fifth Part of Website Here it is relevant only to mention the chief forms of this subtype having shown us the most important features and pathways of differentiation of the flight devices in these forms The most primitive forms are those Diptera in which the process of costalization displacement and reduction of veins did not progress very far but where various adaptations nevertheless did take place strengthening the base of the wing its basiala To such forms does belong the majority of the representatives of the Rhagionoidea in the broad sense the robberflies Asilidae and the true Rhagionidae the hoverflies Syrphidae the blood sucking mosquitos Culicidae and some other Diptera The greater part of the representatives of the subtype illustrates various cases of costalization of the wings together with a simple little strengthened wing base Such we see in the majority of representatives of the very large group of muscoid flies Schizophora and of the group Nematocera Oligoneura such as fungus gnats Finally a special form of eudipterygia is probably represented by the cicadas Derbidae namely of the genus Muiria see next Figure Figure 24 Wing of Muiria sp Family Derbidae Order Homoptera Htfl rudiment of hindwing After HAUPT in ROHDENDORF 1949 characterized by elongate costalized wings with a remarkably structured wingbase The listed two groups are as we saw fairly peculiar i e being more or less forms of their own and undoubtedly will upon continued investigation show further differentiation For us it is now important to remark only the fact that this subtype of dipterygia was in turn the source of other subtypes which are in fact merely more differentiated subgroups of it Such is the subtype platydipterygia see below originated from the basis of little costalized forms of eudipterygia possessing a complex basiala On the other hand costalized representatives of eudipterygia were among the precursors of two further subtypes also to be described in due course costalized two wingedness and fan winged two wingedness 8 Metadipterygia costalized two wingedness This subtype is characterized by the extreme stage of specialization of the wing venation consisting of a small number of very strong veins at the anterior margin of the wing The remaining venation is weakly expressed reduced sometimes even totally absent Hindwings without venation more seldom with a vein carrying the coupling apparatus Sometimes the hindwings are absent So here in this subtype the shift of concentration of the flight function still further to the front is driven to its extreme This subtype is the derivative of two sources eudipterygia and hymenodipterygia The representatives of these subtypes independently acquired complex features while developing and strenghtening costalization of the wing The formation of such highly costalized wings testifying to a high wing beat frequency goes together with an enlargement of the thorax container of powerful muscles To this subtype do belong various Diptera namely midges and gnats of the families Tendipedidae especially of the group Corynoneurinae and Heleidae flies of the family Phoridae Stratiomyidae and certain Sarcophagidae for instance Nyctella and certain Hymenoptera namely various Chalcidoidea small parasitic wasps In this subtype as well as in the previous one also further subdivisions can be seen characterized by structural features of the basiala and the shape of the wings and body The subtype is the limiting phase of transformation of two wingedness and in essence its further evolution will merely boil down to regressive processes namely to the formation of special forms of ptilopterygia feather wingedness See next Figures illustrating the present subtype Figure 25 Wing venation of Forcipomyia ciliata WINN Order Diptera Family Ceratopogonidae Heleidae Superfamily Chironomidea After HENNIG 1954 Figure 26 Some more representatives of the Lifting Costalized stratiomyoid functional type of wings in ROHDENDORF s classification 1951 of the wings of Diptera Cyrtidae Acroceridae Oncodidae Order Diptera 206 Pterodontia misella O S 207 Acrocera convexa Cole 208 Philopota aenea Meig 209 Oncodes zonatus Erichs After HENNIG 1954 Figure 27 Wings of representatives of the Lifting Ultra costalized phoroid type in ROHDENDORF s classification 1951 of the wings of Diptera Top image Aphiochaeta sp Phoridae Length 3 5 mm After Rohdendorf 1951 Bottom image Palaeophora ancestrix Rohd Palaeophoridae Jurassic of Karatau Southern Kazachstan Length a little less than 2 mm After Rohdendorf 1938 In 1938 in Trudy Paleontologicheskovo Instituta Tom VII Issue 3 Rohdendorf had described this fossil nr 2452 329 as Archiphora ancestrix The name had to be changed because of the priority of the name Archiphora see next Figure From ROHDENDORF 1951 The next Figure depicts wings of Phoridae belonging to the present subtype Their derivation from clythioid wings is shown Figure 28 Venation of Phoridea compared with that of Clythiidae 246 Opetia nigra Meig Clythiidae After Schmitz 1929 Clythioid subtype of muscoid type in ROHDENDORF s classification 1951 of the wings of Diptera 247 Sciadocera Archiphora patagonica Schmitz Sciadoceridae After Schmitz 1929 Sciadoceratoid subtype of empidoid type in ROHDENDORF s classification 1951 of the wings of Diptera 248 Aneurina thoracica Meig Phoridae After Hennig 1954 Phoroid type in ROHDENDORF s classification 1951 of the wings of Diptera 249 Phora stictica Meig Phoridae After Hennig 1954 Phoroid type 246 247 248 249 forms a neat derivational line From HENNIG 1954 Further a member of the Chalcidoidea Order Hymenoptera also belonging to the present subtype Figure 29 A typical Chalcid Blastothrix sericea female Magnified After RICHARDS and DAVIES in Imms General Textbook of Entomology 1977 9 Strepsidipterygia fan winged two wingedness This subtype is characterized by the broadening of the wing blade turning the wing into a broad fan like lobe The subtype originated from two not much similar to one another sources the archidipterygia of mayflies Order Ephemeroptera and the eudipterygia of certain Nematocera midges gnats mosquitos Order Diptera Difference of origin entails a fairly great difference between the two groups composing the subtype the mayflies Brachycercidae and the blackflies Simuliidae The broad wings of the Brachycercidae are little costalized and have a radially structured venation Simuliidae on the other hand possess strongly costalized wings The body of the representatives of strepsidipterygia is short with a large thorax The mayflies moreover possess long cerci at the end of the body with their presence undoubtedly producing special aerodynamic conditions during flight This subtype as does the previous one shows it to be a peculiar extreme transformation of eudipterygia namely into the direction of increase of the surface area of the wings their posterior half See next Figures Figure 30 Wing venation of Prosimulium rufipes MEIG Order Diptera Family Simuliidae Melusinidae Superfamily Chironomidea Basal cell not drawn After HENNIG 1954 Figure 31 Wing of Simulium sericatum MEIG Order Diptera Family Simuliidae Melusinidae Superfamily Chironomidea After HENDEL from ROHDENDORF 1951 Figure 32 Simulium hirtipes Fries Family Simuliidae Order Diptera Europe After LINDNER in ROHDENDORF 1949 Figure 33 Simulium venustum female Family Simuliidae Order Diptera Wingspan about 6 7 mm N America Trustees of the British Museum in RICHARDS and DAVIES 1977 Figure 34 Wing of Ordella horaria L Family Brachycercidae Order Ephemeroptera After HANDLIRSCH in ROHDENDORF 1949 10 Kopedipterygia paddle winged two wingedness This subtype of dipterygia namely kope di pterygia only includes the characteristic craneflies Tipulidae and partly Limoniidae These insects have worked out strongly elongate moderately costalized wings with a comparably little reduced venation and what is especially characteristic with a strongly narrowed base basiala which has obtained a peculiar venation In these Diptera the basiala is formed by strong closely to one another running veins which sets of closely running veins after having in turn moved to one another form a narrow handle of the wing A section through the basiala shows the peculiar tube like structure of this organ consisting of concave and convex veins Such a structure of the basiala guarantees its strength and elasticity to be greater The venation of the wing blade is characteristic rendering craneflies directly as such recognizable also by the shift towards the distal end of the wing of cross veins and of the forks of the majority of longitudinal veins determining the special nature of the venation as a whole and of the aerodynamics of the wing The body doesn t show any adaptation to fast flight it doesn t have a streamlined shape The appendages of the body legs and antennae long and narrow abdomen

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  • wings XV
    argument of Cantor proves this by showing that the set of real numbers in which it is already sufficient when we take all numbers between zero and one cannot be counted and that means that it is impossible to index every real number i e label it with a natural number There are not enough natural numbers to label all real numbers It is said that the real numbers form a true arithmetic continuum Let us give and analyze this proof Cantor s diagonal argument Let us take because this is already enough the set of all real numbers between zero and one zero and one themselves excluded It is clear that each real number of this set begins with 0 so we can in indicating these real numbers leave this out and only write down the digits coming after the decimal point Each such a real number has in addition a countable potentially infinite set of digits which may be the same for instance in 0 2222222 or partly or completely different Now we assume that the following list represents all real numbers between zero and one And of course it is already clear that we cannot use the expression all to indicate the members of this set of real numbers between zero and one in the list mentioned We simply cannot list them all So by listing only a few of them we express the fact that we have to do with potential not actual infinity And the same goes for the infinity of digits after the decimal point in each such a real number We cannot list them all so we give only a few of them Here then the list of supposedly all real numbers between zero and one 1 3 2 2 8 8 5 0 0 2 2 2 9 9 9 7 3 1 5 0 0 0 0 0 1 9 7 7 3 2 9 0 9 7 6 9 1 0 4 4 2 1 5 5 4 0 9 0 1 1 2 2 2 2 3 3 2 2 5 9 9 7 8 5 5 1 0 0 3 8 1 1 1 5 7 4 4 2 7 3 5 7 8 1 6 0 0 2 9 1 2 3 7 1 3 3 4 9 8 8 The digits that fall in this list on the diagonal are highlighted but being not in any way special As has been said it is assumed that the above list doesn t miss any real number whatsoever between 0 and 1 And because this list is sequentional the next item comes after the previous one the members may be indexed by natural numbers So each member not excluding anyone of them of the set of real numbers between 0 and 1 is now supposedly accompanied with a natural number And this means that under the supposition of the completeness of the list the set of real numbers between 0 and 1 is countably infinite meaning further that the number of elements in the set of natural numbers is equal to the number of real numbers between 0 and 1 There is under this assumption a one to one correspondence between the members of the two sets But now if we take the digits forming the diagonal of the above supposedly complete list and add to each digit unity whereby 0 becomes 1 1 becomes 2 3 becomes 4 8 becomes 9 and 9 becomes 0 we obtain the following real number between 0 and 1 2 3 1 8 5 4 1 3 0 9 But this real number although being a number between 0 and 1 does not belong to the above assumed complete list because its first digit differs from that of the first number in the list its second digit differs from that of the second number in the list its third digit differs from that of the third number of the list and so on and so on And because we are supposed to have already used every natural number to index the members of the list we have no natural number left to index this newly formed real number between 0 and 1 So it is now proven that the real numbers between 0 and 1 let alone all real numbers cannot be exhaustively indexed by natural numbers We simply do not have enough of them to do so So there are more real numbers between 0 and 1 and by implication more real numbers anyway than there are natural numbers The set of real numbers the arithmetic continuum as it is called in mathematics contains un countably many elements Or said differently their number is uncountably infinite whereas the set of natural numbers is countably infinite In all this that is to say in the case of the countable infinite as well as in the case of the uncountable infinite we cannot produce the corresponding complete sets In both cases we operate not with the actual but with the potential infinite And a set with a potentially infinite number of elements is itself always finite but at the same time always still incomplete And that is what infinity really means there is no end So infinity as a number i e as a so called transfinite number does not exist It cannot be actually produced by some specified procedure And if such a procedure contains a guarantee that it will naturally come to an end it is then not a procedure producing infinity anymore And intuitionalistic mathematics as proposed by the school of the Dutch mathematician Brouwer does not accept the reality of some mathematical entity like infinity or mathematical state of things to be proven as long as it is not actually mathematically produced i e constructed So already in mathematics there is no actual infinity only potential infinity There are also no transfinite numbers as long as they express actual infinity Only if they express potential infinity they do really mathematically exist and may express the difference between countable and uncountable infinity end of intermezzo Let us now continue to follow HOENEN again and return to the other philosophers problem with the continuum Is it necessary that in order for the continuum to be divisible ad infinitum because of it being an extensum there must reside in it an actual multitude which is infinitely large The first reply is already very simple on the basis of our earlier results there is no actual multitude in the continuum because a continuum as an ens cannot be at the same time and in the same respect one and many and thus surely not an infinitely large one Now the philosophers dealing with the continuum problem supposed that the parts in the continuum were actual and then indeed the conclusion follows that the number of these parts must be infinitely large But their supposition is false already beforehand destroying the unity and thus the essence of the continuum No wonder that from this supposition a false conclusion follows And thus we can even from the falsity of this conclusion that the continuum cannot be indefinitely divisible find an affirmation of our first thesis saying that the parts in the whole are only potentially present We may pick up the thread of the difficulty again and this will give us more insight into it One may say OK the multitude of the continuum is only potential and only potential infinity is possible not an actual infinity But what does potential mean Surely that which may become actual If accordingly the potential infinite is present in the continuum i e if the infinite multitude is only potential then this potential as to its nature may become actual And again we are faced with the beast of the actual infinite which we had thought to have avoided The Aristotelian concept of potency does it is true solve things preliminarily but does not bring in a final solution On first inspection this difficulty Aristoteles has not failed to see it seems evident as well as decisive Yet it is only seemingly so One should not have led oneself astray by the concise expression potentially infinite multitude If it really meant something that is potentially an infinite multitude yes then the argument would be perfectly valid with every potency does correspond an actuality With the in this way taken potentially infinite multitude would correspond as actuality an actually infinite multitude And the possibility of this potentially infinite would imply the possibility of the actual infinite because it would imply the infinite But such a view is false and this falsity follows loud and clear precisely from the way in which we have found the concept and reality of the potential infinite in the continuum Let us again see how we did it In whatsoever a way the continuum is being partitioned it is only divisible into continua the line in lines being in turn divisible but again only into continua and so ad infinitum i e without the process ever to come to a natural end In whatsoever a way one divides the operation is always repeatable always a certain succession is necessary And this repeatability this succession will never become impossible So this succession can never be passed through entirely Only when this were possible repeated division could result in an actually infinite multitude But it cannot The expression potential infinite or potentionally infinite multitude thus means as evident from the way we d found this result the continuum how far whatsoever it is actualized partitioned still remains and with it still ad infinitum in further potency i e the parts having resulted from this partition are still continua and each one of these continua possesses the potency to become further divided This potency may always become further actualized but never entirely so Again this is what infinity in fact means no end to possible division The infinite refers to potency a potency which can never be completely neutralized it does not refer to actuality Strictly speaking we should say that potency in potentially infinite multitude refers to the infinite which itself is a determination of the multitude its number of elements So we maintain here that in the expression potentially infinite multitude the term infinite refers not to potency but to something that has no end and that something here is the multitude not the potency And because there is under no circumstances any end whatsoever no last member of the multitude and in an uncountable multitude there is not even a next one for e v e r y member of it the term potentially in potentially infinite is entirely superfluous because there is only one single way for something to be infinite and that is to be p o t e n t i a l l y infinite and all this is in essence what HOENEN means but now cast in a better wording than to speak of infinite referring to potency infinite potency no end to potency as he did According to Aristotle the infinite in quantity is essentially potency to apeiron dynamei on Indeed one should not be misled by the simple but dangerous term potentially infinite Correctly taken as is evident from the analysis resulting in this understanding it does not mean that what is potentially an infinite multitude but that what always remains such that it may still further increase Medievals perhaps firstly Albert of Saxonia did not therefore say the contiuum is divisible in infinity this expression might refer to the wrong meaning namely that the infinite could result from it but rather the continuum is in infimity divisible expressing clearly the infinitude i e the ever lasting incompleteness of this potency itself in fact the incompleteness of its actualization Ans so this analysis provides a deeper insight into potential being i e into potency We discover a potency which may be actualized otherwise it would not be a potency at all which even always may successively be still more actualized but never becoming exhausted So when one speaks of all points of a line or of any continuum whatsoever then one should be careful with the interpretation of the word all Does one take it to mean every point whatsoever i e the universal of scholasticism taken distributively then the expression makes sense and can be used in meainingful and true propositions for example in this one all points of the perpendicular through the center do have an equal distance to both ends of the line segment through which middle it is drawn In this sense one speaks of loci in classical geometry every potentially all Does one on the other hand mean with all the entire collection of individually determined points of a line then the expression doesn t make sense and when nevertheless used may of course result in false conclusions of which also in philosophy there are instances We will find one in Democritus later on This expression all as actual totality does not make sense because it presupposes something impossible namely that the extensionality of a line or of any other continuum could be exhausted by repeated division resulting in nothing more than a collection of inextensa points And we already observed that points originate only as boundaries when the line is divided They are not beforehand determined in and by the line they are determined not until real or mental division of the line That s why we quoted with agreement the words of Brouwer the continuum as a whole was however intuitively given to us Its construction as an operation which would create all its points individualized by mathematical intuition is unthinkable and impossible The continuum contains a disposition of multitude which can never be actualized completely The transition in the use of all from the first sense all as every each to the second all as totality also in other cases than the one above is called by Brouwer the comprehension axiom and rightfully indicated as the main error of the classical Cantorial doctrine of sets dass das Komprehensionsaxioma auf Grund dessen alle Dinge welche eine bestimmte Eigenschaft besitzen zu einer Menge vereinigt werden zur Begründung der Mengenlehre unzulässig bzw unbrauchbar sei Each considered thing having a property A now interpreted as a l l things with property A So the expression if referring to an infinite set the set of all elements being as to what they are of this particular type or having this particular property so often encountered in mathematical set theory does not in fact make any sense Indeed we often see the phrase the set N of all natural numbers or the set R of all real numbers or the set of all points in line segment L etc Various conclusions from the difficulty of the infinite The problems produced by the notion of infinity which notion is inherent in the continuum were especially living among scholastic philosophers earlier and later up into our 1947 time In modern philosophers they remain in the background Leibniz saw so little objection in them that he even demanded infinite multitudes to be present in a perfect Nature except for some So in Renouvier the leader of the neo criticists in France taking the infinite to be impossible because it would be un nombre sans nombre Nevertheless there is a big difference between the scholastics and Renouvier They wanted to save the real i e not only the mentally conceived continuum some of them even at the cost of theorems of geometry and tried to resolve the difficulties Renouvier on the other hand sacrified in order to deal with the contradiction of the infinite the reality of the continuum In reality there is no space no time i e nothing spatial and temporal no matter no motion But isn t then this very same contradiction present in our mental images of all these continua i e in the mere phenomena No replies Renouvier because there the actual infinite is avoided because there the parts are only potentially present not actually indeed although parts can as a result of being thought be present in the mind they cannot materially be so present And he fully acknowledges that Aristotle with his notion of potency solves the problems completely but holds that potency is only to be found in the mind not in objective reality And so he maintains that the ideal phenomenal continuum in our mind is free from contradiction but not so the real continuum the continuum as taken to be something real resulting in the fact that continua have merely a phenomenal existence i e as mental images or mathematical entities He holds that the parts of real continua must be actually existing things He makes the mistake against which we already warned above He confuses a row of contigua parts not confluent into each other but merely touching each other which as parts of an accidental whole do indeed actually exist with the parts of the intrinsically one continuum He eventually must take the frog embryo about which we spoke above as two individuals lying adjacent to each other We will meet the same explanation also in other idealists or semi idealists denying the reality of extensa with the same concession the continuum with its potential parts is present in the mind that the notion of potency saves the continuum Priority of parts before the whole reductionism or holism Leibniz as we said earlier did not object against an actually infinite multitude But from his metaphysics he obtained another proof against the reality of the continuum a proof which was repeated later by Kant 18th century and by Lachelier 19th century in their own ways It boils down to the following Metaphysics demands as they hold that in a composed thing a compositum and the continuum is composed of the parts into which it is divisible the parts as it is in the nature of things have priority over the whole i e the parts or elements are more fundamental than the whole they together form A composed thing that is real would have its reality only from the reality of its parts But then there must be parts that can be called first parts because a going back into infinity to find the ultimate conditions that must precede in order that the result be realized is impossible the going back trajectory must be finite in order that the corresponding going up trajectory of successive conditions can be traversed to realize the effect So there must be first parts However in the case of the continuum these parts cannot have extensionality anymore otherwise they would still contain parts and not be first parts or last parts if one prefers Accordingly these ultimate parts must be points But because mathematics rightfully denies that a concatenation of points results in an extensum we have a contradiction between the demands of metaphysics and those of mathematics reductionistic metaphysics demanding first parts guaranteeing the reality of the whole mathematics saying that these first parts are necessarily points and points cannot form a whole with extensionality As we saw above a line is in the original Cantorian doctrine of sets a set of points in this to be rejected sense If a line could indeed be so taken the antinomy would of course disappear This is the solution of B Russell 1911 working out his logic as based on this doctrine of sets But this solution cannot be accepted So the continuum cannot be real Only a phenomenal as in mathematics continuum is possible These philosophers themselves lead us to the solution They ask but the continua of our imagination the phenomenal continua do we construct them from first and consequently non extensional parts i e points No they reply in our imagination the whole is given There the whole has priority over the parts so there that reasoning doesn t hold Why the order is reversed there Because there i e in the mind the parts are potential parts only having originated as a result of partition of the whole the latter has priority over and above the parts Let us listen to Leibniz in a letter to Remond Dans l idéal ou le continu le tout est antérieur aux parties les parties ne sont que potentielles Mais dans le réel le simple est antérieur aux assemblages les parties sont actuelles sont avant le tout This rings a bell in our JB noëtic theory Here we are going to assume that all truly holistic events and structures do involve the Implicate Order which itself is noëtic and thus immaterial whereas all truly reductionistic events and structures wholly belong to the province of the Explicate Order It might be that a given structure insofar as manifesting itself in the Explicate Order is reductionistic while in manifesting itself such that also the Implicate Order is involved this same structure is holistic Kant and Lachelier reason similarly And again we arrive as we did above at the same result 1 0 where the parts are potential they do not need to have priority there are no first parts possible division never stops and the continuum is possible When the whole is actual and the parts are potential these parts may subsequently become actual therefore potential parts are not prior to the whole And as long repeated division is going on the resulting parts are no first i e ultimate parts no points And 2 0 the real compositum is called an assemblage indicating a same confusion of a continuum with a series of contigua And always the same opinion recurs A continuum is not taken to be an intrinsic unity but naively taken as a collection of parts existing next to each other So the Aristotelian notion of real potency as contrasted with potency in imagined structures is again capable to free the real continuum completely from contradiction All antinomies between mathematics and metaphysics disappear in Aristotle s metaphysics Here the real continuum is a totality The whole is earlier than the parts because the whole is actual whereas the parts are only potential For the same reason Kant is severely criticized by Schopenhauer He Kant commits himself to eine gar nicht feine petitio principii circular reasoning because he takes the compositum only in the sense dasz die Theile vor dem Ganzen da waren und zusammengetragen wurden wodurch das Ganze entstanden sei while in fact opposite from the simple the indivisible there is not the compositum in that sense i e in the sense of a reductionistic compositum but the divisible Die Theilbarkeit behauptet blosz die Theile a parte post only parts being present after division Das Zusammengesetztsein behaupted sie a parte ante parts already present Schopenhauer surely detects Kant s error precisely Finally we HOENEN want to point to one more difficulty having not detected it in the literature A difficulty that is at first sight looking to be unbreakable We saw that if the parts must be prior to the whole the reasoning of Leibniz and followers is sound implying that then first and thus non extensional parts must be assumed but from which no continuum can be constructed As to the static continuum the difficulty has undoubtedly disappeared But doesn t it return in the case of the dynamic flowing continuum of motion and time Aren t there necessarily the parts at least the first parts prior to the whole We shall face this difficulty later when discussing te nature of motion and time Then it will turn out that also there i e in motion and time the whole is prior to the parts Atoms and minima Introduction We came to know the continuum as divisible not divided ad infinitum by considering it as extensum alone After all s said and done its analysis as ens does not generate difficulty if we possess the Aristotelian notion of real potency But the continuum is not only ens not only extensum it is also something physical i e something having a specific content That such a continuum must also for us remain indefinitely divisible does not yet follow from its divisibility as extensum After all our tools may be in such a degree imperfect that there is a limit in the practically executed continued division likewise our senses are in such a degree imperfect that they cannot continue to be able to perceive the increasingly smaller while the intellect may well think the increasingly smaller even ad infinitum so Accordingly there exist minima to our senses but not to our intellect But these limits of divisibility are extrinsic Other limits may be thinkable which come from the nature of the physical continuum itself Because this is not a pure ens extensum it is an extensum that has a specific nature In this way we arrive at the philosophy of these physically indivisibles and historically we find two of them atoms and minima The first in Democritus greek philosopher 460 371 B C the second in Aristotle 384 3 322 1 B C and the peripatetici Aristotle s followers This historical exposition is most important to the philosophy of Nature Democritus and Descartes Descartes 1596 1650 Both philosophers view the essence of matter in its extensionality In Descartes this is clear enough in Democritus we must as we believe also assume this For him ens is nothing but the full no nothingness separating individual entia beings Now to Descartes matter is nevertheless indefinitely divisible sometimes as we saw divided all the way into infinity but to Democritus this is impossible Ens the atom is despite its extension not divisible even into two parts It is impossible that from one originate two and that from two originates one This not as a result of external circumstances about which we spoke above but as a result of an intrinsic impossibility Who is right Mathematically taken of course Descartes except as to an assumed actual unlimited dividedness into points After all as pure extensionality matter and every given part of it must be indefinitely divisible Every given continuum however small it may be must surely be divisible into two parts Therefore Descartes denied the existence of atoms i e of indivisible but still extensional parts or particles But on the other hand while one may rightfully take matter as pure extensionality if one refers to real matter the full of Democritus then one has to do with an ens and this has to obey the laws of ens and thus obey the laws of metaphysics Now to Democritus as well as to Descartes the ens was only the eleatic ens viz unchangeable Being In essence their metaphysics was that of Parmenides greek philosopher 540 480 B C And in applying this metaphysics to the extensum Democritus not Descartes was consequent For given this position even a division of one into two is already out of the question After all if from one two would originate or vice versa then at least one of these two would be a new ens respectively at least one of them would have been perished and then we would have genuine generation and corruption which in this metaphysics i e the eleatic metaphisics was held to be impossible Ens must be apathes it cannot undergo anything unchangeable and therefore also indivisible and impossible to construct from parts It is necessarily a tom i e indivisible So Democritus has dug deeper than Descartes by his attention to ens and to the theory of ens The fact that Descartes has not penetrated so deeply is connected with his whole attitude as regards these problems A continuum is for him already there where two bodies are at rest next to each other or performing the same motion They are contigua when they are moving along each other Yet also in Democritus one problem is left unsolved After all while Descartes had in considering the ens extensum neglected the ens and thus metaphysics and only focussed on the extensum Democritus almost entirely had focussed on the ens and did not sufficiently account for the extensum Yet this extensum as extensum would necessarily contain parts implying divisibility Especially so because all his extensa his atoms have the same nature only being the full and only differ in size and figure This difference in size is evidently a sign of the fact that this full was not confined to determined sizes and consequently that it had to be divisible into smaller extensa In this way atoms being absolutely indivisible things cannot be justified Democritus it is true had put forward an argument to justify this indivisibility of the full an argument that we also find in Zeno the Elean pupil of Parmenides If the extensum as we may reproduce his reasoning is divisible in one point i e in one plane then it must also be divisible in every point i e in every plane because in the purely extensional every point is equivalent to any other But if it is divisible in every point then it is divisible in all points This is the comprehension axiom about which we have spoken earlier To be divisible means can be divided And now realize this possibility and the result will be a multitude of inextensa i e of points But from these a continuum cannot be built i e the continuum cannot consist solely of points So the extensum cannot be divisible in even one point only In the eleatic and Democritic argument the last part read the inextensum is nothing and from nothing the ens the extensum cannot result Also here we cannot deny the acuteness of eleatic reasoning Nevertheless the reasoning is false The first part of it we have already analyzed earlier the transition from every to all i e from whatever point to the collection of all points as takes place in the argument is not in the case of an indefinite number as contrasted with a finite number of points legitimate and thus false So in the conception of Democritus the unsoved problem remains the problem in what way the full occurring in larger and smaller individuals can yet be indivisible Atoms cannot be justify in this theory And in every atomic theory one should be alert whether in it there may be hidden a similar error So we come to the following result Geometry considering in ens extensum the extensum demands that this must be always divisible however small it is Metaphysics as long as it sticks to the Parmenidean conception of Being one unchangeable and indivisible demands in its consideration of the ens in the ens extensum that it must be always indivisible how large it may be Nevertheless both sciences must be applicable to the same object the ens extensum So here we already have a seeming antinomy even before considering the infinite in the extensum The solution lies in the extension that Aristoteles had given to the eleatic metaphysics The same extension that can guarantee the changeableness of ens in general also explains the generation and corruption that is implied in being divided and united namely the introduction of the notion of real potency being in potency But such a consideration does not result in the notion of atoms or something like it If we view physical bodies as ens extensum only then they are indefinitely divisible then no minima do exist Yet Aristotle and with him the peripatetici have also justified the existence of minima But for this the physical body must not only be viewed as ens extensum Which is possible because natural bodies are indeed not only that i e they can have over and above merely being an ens and having extensionality a specific content and so they can be ens physicum Natural minima After all the bodies in Nature are not merely ens having them be subjected to the laws of metaphysics They moreover are not merely extensum in virtue of which geometry does apply to them They also have a specific nature principle of activity and passivity They are not exclusively the full The fact that they have different qualities already witnesses to the fact that they do have such a nature That they have a nature was already in the beginning so evident that this physis took part in constituting the name of a science physical science natuurkunde But then also the laws of this nature not all of them we do pitty enough know a priori most of them we do not so know must hold for the physical body which is not merely ens extensum but also physicum And these laws might modify the above derived results concerning indefinite divisibility This was already noticed and applied by Aristotle and further worked out by the peripatetici Aristotle and the minima Among the predecesors of Aristotle there was a philosopher who after and influenced by Parmenides had constructed a not consequent mechanicism Anaxogoras Of the theses characterizing his system one is interesting to us Natural bodies are indefinitely divisible Against this thesis Aristotle objects in the fourth chapter of the first book of his Physics The stagirite as Aristotle is called because he came from there who in the same Physics so strongly defends the indefinite divisibility of the continuum as such and solving the seemingly implied antinomies in so ingenious a way nevertheless opposes to the idea of indefinite divisibility of physical continua by the following reason the physical nature of these bodies resists it It admits division only up until a certain finite limit Remarkably he not only demands a lower limit a limit to continued division but also wants to derive an upper limit a limit to increase growth Not totally a priori because as to the specific nature we lack a priori insight but concludes it from experience Indeed he had observed that the size of individuals of a same animal species varies only within certain limits Below a certain minimum and above a certain maximum of course co depending on conditions no individuals of a given species exist And these limits differ in different species depending upon their specific nature their own proper nature oikeia physis So every species has its own maximal and minimal size like it indeed also possesses its own qualities Then Aristotle concludes against Anaxagoras that also the materials building up the animal body flesh and bones have their own minimum Were these materials possible in every size without upper and lower boundary then from them also an animal could be built up having any size whatsoever what militates against experience So the components of these living beings are not indefinitely divisible Absolute divisibility of the smallest possible particles of these substances in the chemical sense is evidently not excluded by this reasoning but it must be true that division if it succeeds results in fragments having a different nature being of a different kind not being flesh and bones anymore Who is here not recalling modern chemistry the molecule of a chemical compound being divisible but not into parts of the same physical kind as was the whole Succinctly formulated we find this thesis in THOMAS AQUINAS 13th century ideo est invenire minimam aquam et minimam carnem ut dicitur in I Phys quae si dividantur non erit ulterius aqua et caro therefore there must be found a minimum of water and a minimum of flesh as is stated in the first book of Physics which when further divided do not remain water and flesh And so Aristotle concludes as to the existence of minima indivisible particles not by themselves absolutely indivisible but only relatively so i e such that subsequent division must result in disintegration into other materials of a different kind

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    is of the greatest importance to natural philosophy If the Contact Theory is the right theory then a theory as that of Democritus which constructs the world from a swarm floating about in empty space of particles particles totally separated from each other not connected by any real medium is absurd and of course only when empty space is equated with nothing and not with merely some other type of ens in addition to that of the particles Between such particles no distance is possible and so also no change of distance no movement Maybe Democritus has seen this and so his thesis that also the not being exists may find an explanation Then this salto mortale in negation is in the end a shift of this absurdity or if one wants an emphasis of it If we replace in this context not being by empty space and then say with Democritus that empty space exists then we have affirmed the existence of something like the aether of Lorentz All this under the assumption that only the Contact Theory is intelligible while the Position Theory is not But the latter still has to be investigated Investigating the Position Theory So the Contact Theory says this In such relationships distance movement contact is primary And the possibility of contact is intuitively immediately evident as following from the datum of two real extensa two spatial things Thus first contact then position and that with immediate contact we get nearness through mediate contact we get distance The other theory which we had called the Position Theory says first position then either contact by nearness i e physical contact as a result of a special position or distance i e no physical contact as a result of some other position The absolute Position Theory attributing to already one single body a place in empty space and in it holding movement to be possible absolute place and absolute motion we already have found to be false Remains the relative Position Theory which does attribute to every physical body a position i e an internal ly determined though totally unknown to us determination accident or modality but letting result from it a relation only to other real bodies having their own internal ly determined position This relation then may be either contact nearness or determined distance If the possibility of distance in the absolute vacuum does exist i e without mediate contact through other real extensa existing then one surely will need the Position Theory for an explanation But does such a possibility really exist One a priori construction of this possibility was already analyzed above where it was read off from the datum of our common sense vision which apparently confirms it But analysis of this datum has teached us that this was only seemingly so What we read off from this datum is merely the complete intelligibility of what the Contact Theory teaches us From contact with a real milieu distance results This be enough One has tried out another construction Suppose that two bodies touch a third one at both its sides see Figure above They then will be at a determined distance from each other measured by the size of the third body Now suppose that this third body is annihilated while nothing else happens Then there is so one argues no reason to assume that that determined distance would vanish This argument seems to appeal to many Nevertheless it breaks down upon further analysis First we note that in the argument in the beginning the contact theory is presupposed distance has resulted from the double contact Then one lets annihilate the third body to which we make no objection and then one assumes that nothing else happens But against this we do have a certain and decisive objection If the third body is annihilated then necessarily two other things disappear namely the two contacts Then precisely that disappears which according to the supposition from which the construction departed made distance possible i e that from which it had resulted And so the distance disappears with it Of course not in such a way that now the two bodies have become near to each other that was supposed to be the case by Descartes but in such a way that no local relation exists anymore We may construct an analogous case When signaling apparatus and receiving set of a telegraph are connected with each other by a firm wire the signal will reach the receiver Now we suppose that the wire has been cut without anything else happening And now the same kind of reasoning would result in the conclusion saying now there is still no reason that the signal would fail to reach the receiver Why is here the absurdity immediately evident while in the first case for many apparently not The cause is clear In the first case the reasoning is accompanied by this view We see the three bodies in the configuration described It is easy to let the third disappear and see the two other remain at the same distance from each other But the reason is clear They are still connected by space which in our common sense vision is something real a true ens extensum But then we do not have the situation that was argued i e complete vacuum between the remaining two bodies So also this construction of the a priori possibility of a distance so conceived lacks any value Is then this possibility of distance across a vacuum derivable from the intelligibility of the elements themselves out of which the Position Theory is built as this was the case in the Contact Theory We have in the position theory the internally determined positions of the bodies at our disposal i e according to the theory they are given the nature of which positions however is totally obscure to us And when two bodies each one with its own position are given then from these data contact or distance is supposed to result as in the Contact Theory distance did result from a double contact with a medium The necessity of this latter resulting was intuitively clear to us as was also intuitively clear the capacity of the extensa for having contacts from which distance results So in the Contact Theory the primary datum contact is itself intuively clear But in the Position Theory we precisely find the opposite The nature of the internal ly determined positions escapes any understanding whatsoever i e here the theory s primary datum is in itself unintelligible and just as total is our lack of insight in distance resulting from these presupposed positions We might come up by saying that position as internally determined is as such caused by some definite movement or said differently the present position of a body is the result of previous movement or yet in other words the particular internal or intrinsic positioning of the body has resulted from a particular movement Apart from the problematic nature of these statements implied by the Position Theory movement is presupposed with respect to position But movement itself is no more than change of position So movement presupposes position And thus position presupposes position So in itself position the primary datum of the Position Theory remains unintelligible In our investigation of this theory the position theory we haven t made any progress at all down the path to intelligibility Things have become even more obscure than they were at the outset when we thought to understand things at least a little But we did not yet find the Position Theory to be impossible we did not encounter internal contradiction or contradiction with other certain data And yet this is contained in what we ve already found and described so far Deciding between the two theories Recall what we have seen from the notion of extensum necessarily follows the capacity to have contact between two extensa Of this we have intellective insight Is this merely a conviction following from certainly in this respect rich experience No it is not Examples To see this more clearly three examples may be instructive First one regarding properties of which we do not have lesser practical conviction but a conviction resting on pure experience only After that two examples of certainty based on intellective insight We suppose we have two little bars having the same shape and size one of lead one of steel The lead bar we can easily bend and after cessation of the force it retains its bent shape The steel bar for a much lesser degree of bending demands a far greater effort and after it it regains its original shape Of these facts and of the general law of which we saw a special case unfolding from such a law we will surely be convinced Why Because prolonged experience has teached us it But also after such prolonged experience we do not have from ascertaining the facts insight of the necessary following up of the properties from the nature of the two materials Let s consider an arithmetic addition We have seven things and add five and we are forgotten that the result of this operation is twelve Well we can arrive at the knowledge of this result and to the insight of its necessity by executing this operation We have the seven and add one by one the others until the supply of them is exhausted eight nine ten eleven up to twelve This procedure looks purely experimental it is almost an mechanical process But to what we want to call attention is this Our operation is accompanied with intellective insight into the necessity of the result insight originating from our understanding of the object of the operation and of the operation itself namely multitudes numbers and their addition It is not a pure experience i e it is not experience alone So we should take notice of especially that insight A third example We consider a triangle Through one of its angles and remaining within the triangle we draw a straight line We do not have to suppose a mathematical triangle but merely a certain triangle from our sensible experience The sides of the triangle are thus not lines but stripes having a certain width they are not perfectly straight but only so for mere vision as is also the line having been drawn through the vertex angular point which itself is no mathematical point In our vision this line intersects the opposite side of the triangle Also this is no pure datum of experience it is accompanied by the insight that this intersection necessarily follows from the nature of extensionality and of this particular figure realized in it Note With the origin of this insight the theory of knowledge not natural philosophy should deal In considering the foundations of Geometry another problem asks for a solution how namely from the above sketched inaccurate data of sensible experience does originate the accurate intellective knowledge And also another one how generic generality originates end of note Again to this intellective insight we must devote our attention Proof Well such an insight we find in knowing the contact between two extensa spatially extended bodies The capacity for such a contact is not a pure datum of experience but is known as necessary because it is known as following from the nature of extensa as is also the result of arithmetical additions and as it is in the case of the intersection with the opposite side by the line in the example above Such things we already have seen often But now we pay attention to something else If the Position Theory was true then the capacity of contact would not immediately follow from the nature of extensa From the latter would follow the possibility of internally determined position and only from these positions would follow contact or distance The necessity in nature of this resulting could not be denied but something else can In order to have insight into the ultimate resulting of possible contact namely by means of the mediator the position we then also should have had intellective insight of this mediator and its function otherwise we could not deduce from it the possibility of contact Well this insight is totally lacking as is clear from our analysis So if this mediator really as such were present then we would have had of the possibility of contact only a mere certainty of experience without intellective insight And this contradicts what we already repeatedly had found out Succinctly summarized From capacity of contact as necessarily following from the nature of extensa we have intellective insight If it contact followed through a mediator the position we should have had also of this mediator intellective insight And because this is lacking the mediator as such isn t there and the Contact Theory wins Remarks We ve said that this theory of St Thomas was rather generally abandoned and apparently not known anymore It took us HOENEN years of struggling before we reached this view and only then we encountered it in St Thomas described as the most evident case in the world This is one of the many reasons why we admire the genious of the angelic Doctor who apparently has this insight without any trouble without even mentioning the alternative From this it is also understandable why he with so much assurance and so much open mindedness is used to say that local motion does not bring with it any internal change in that which is being moved a thesis that was unjustifiably abandoned also by so many of its followers We here should think of what precisely motion of a body really is And we do so by considering first of all regular motion i e rectilinear motion with constant speed What we here see is a continuous change of position of the body in motion And St Thomas thinks it to be impossible that this change of position reflects some internal qualitative change in the body in motion Later we will learn that motion is the extensional effect of a quality having come to inhere in the body But this quality the impetus is not connected with the position or successive positions of the body in motion As the body being in regular motion continually changes position its impetus remains the same as to its intensity Only an increase of impetus caused by a force newly applied to the moving body results in an increase of speed acceleration of that body After cessation of this force the increased speed remains the same as well as the increased intensity of the impetus of the body Nevertheless this insight is apparently present in all thinkers i e not only in St Thomas and the difficulty merely consists in making explicit and formulating the principle For everybody including those who deem distance to be possible in the absolute vacuum or even adhere to the possibility of absolute place and motion do place their bodies in the space of imagination which is in that vision a reality and there place and distance do indeed originate according to the Contact Theory Only later they forget the fact that this space has no reality in Nature and that the Contact Theory cannot be applied to the vacuum between physical bodies For we ve already said touching nothing is not touching and cannot lead to real distance and to its consequences Also to them who realized the imaginary nature of space we may say that initially in their imagination they unconsciously did apply the Contact Theory because in their imagination space was real But when they later realized that their space was only of an imaginary nature they forgot in admitting the non reality of space that now the Contact Theory is not working anymore That is to say they should realize that distance in a vacuum between bodies has been thrown away together with space Distance should have become unintelligible for them They have never realized that they in their imagination conceived distance according to precisely the Contact Theory Therefore they kept on believing that distance still exists in a vacuum between bodies But instead they should replace the imagined space by something like the aether of Lorentz and so restoring the possibilty of overall contact So the difficulty apparently lies only in making explicit and formulating the principle But isn t that strange Not so strange as it might look at first sight At least we have some more examples of the same phenomenon Above we gave the example of the line running through the vertex of a triangle and necessarily intersecting the opposite side This at least being a similar insight is one of the order axiomata axioms of order of Geometry Well these order axiomata have been used all the time and never formulated or as such indicated before the year 1882 In that year they were discovered by M Pasch This case is even stronger when one realizes that already for half a century investigations were going on as regards the axioms of Geometry investigations being done as a result of non Euclidean geometries investigations in which it was paramount to list all axioms Why weren t these axioms not formulated Well because they were so evident So the case of the Contact Theory does not stand alone We take it to have found a similar example in the two insights that according to us precede the insight of 7 5 12 While the Contact Theory was essentially abandoned by modern scholastics and much more so in others the more surprisingly we read it in Einstein Here are his words which we cannot interpret to represent something other than the formulation of the Contact Theory although he lacks the clarity of the angelic Doctor Ihm dem Raume geht die Bildung der objectiven Körperwelt voran Ich kann Körper durch sinnliche Merkmale wiedererkennen ohne sie bereits räumlich zu erfassen Ist in solchem Sinne der Körperbegriff gebildet so zwingt uns die sinnliche Erfahrung dazu Lagen Beziehungen zwischen den Körpern festzustellen d h Relationen der gegenseitigen Berührung Was wir als räumliche Beziehungen zwischen Körpern deuten is nichts anderes Also ohne Körperbegriff kein Begriff räumlicher Relationen zwischen Körpern und ohne den Begriff der räumlichen Relationen kein Raumbegriff A EINSTEIN in the periodical Forum Philosophicum having enjoyed according to HOENEN only a brief existence I 1930 p 173 The italics are HOENEN s As to its importance we JB translate this passage into English The formation of the objective world of bodies precedes space I can recognize bodies with the help of sensible features i e features that can be detected by the senses without them conceiving already spatially Has then in that sense the concept of body been formed then sense experience forces us to determine relations of position between the bodies i e Relations of mutual contact Indeed what we take to be spatial relations between bodies is nothing else Accordingly without a conception of body there is no conception of spatial relations between bodies and without conception of spatial relations there is no concept of space Here much is said beautifully namely 1 that the concept of space is secondary with respect to the concept of body or extensum i e the concept of physical body with all its features including its extensionality is prior to the concept of space in which the bodies are supposed to reside and 2 that local relations result from contact of these bodies and 3 that from these relationships the concept of space is constructed The positivistic slant that will be recognized by specialists in these lines i e the emphasis that all we have about reality are merely logical constructions of our investigating minds is not taken by us to be our responsibility and the special reason to express ourself in this way is clear enough from our expositions Whether this view as to contact being primary with respect to distance of Einstein in the periodical mentioned is compatible with his own theory of relativity is a different question Absolute and relative motion in a derived sense We already spoke about the concepts of absolute and relative motion in the original sense of the words In this sense all motion turned out to be necessarily relative i e motion with respect to another real extensum Absolute movement i e not with respect to some other reality or with respect to the nothing doesn t make sense Accordingly to be somewhere presupposes another reality different from that which is somewhere namely the place where the placed is and the nothing turned out to be not a place where a body might be In this sense the thesis all motion which is a continuous change of place is necessarily relative is evident Notice This thesis not merely means in order to observe motion another reality is needed No the other reality is needed for the very being of motion Symmetrical relations But we already pointed to it the term relative motion is also used in a different sense namely in this one If A is moved with respect to B then as one says one may as well say that B moves with respect to A One claims that also this follows from the concept of motion like the first mentioned sort of relativity did so follow and one adds that this expresses itself in observation in virtue of the fact that all physical laws valid in A experimentally without having changed do apply in B A rather vague criterion about which we will say some words later Now we merely see what follows from the concepts as they are intelligible to us So this one also calls the relativity of motion A with respect to B and B with respect to A A better formulation would read the relative aspect in the phenomenon of motion is mutual there is an equal or reciprocal or as it is expressed in modern logic a symmetrical relation Then motion would not be merely relative but in addition also symmetric relative Such a symmetrical relation is for instance the relation of equality If A is equal to B then B is also equal to A If then motion is symmetric relative then the last demand of Aristotle place in the strict sense is immobile only the placed may move must be dropped On the other hand the first two demands namely the place is something different a different real extensum different from the placed and place is in contact with the placed are preserved Physical consideration But is it true We already said phoronomically or kinetically seen it is clear One may equivalently describe what happens the pure passive with the words A moves with respect to B and B moves with respect to A Whereby one should notice that there is no complete symmetry the motions in both descriptions have opposite directions Of course opposite equal motions are symmetrical with respect to one another Here however symmetry is supposed to mean equivalence If A is a body and B the aether then the descriptions read A successively passes through the parts B1 B2 B3 etc of the aether and those parts successively pass through A in which there is complete symmetry body A passes through B1 and at the same time B1 passes through A Then A passes through B2 and at the same time B2 passes through A etc Tacitly it is assumed and this may become paramount that in both cases all parts of the aether with respect to one another are not subjected to shifts So there is only a difference of description not in the real aspect of the motion At least if we stick to the purely mathematical phoronomical aspect of it But motion is also something physical Added is an actual being an actual flowing contact which turns out to demand an actual cause this is the physical aspect which soon will bring with it an intensive factor the speed This is already not purely mathematical anymore Possibly then the symmetry of the relation ceases to exist Example See here an analogous case not a proof but an illustration We have two lines equal to each other A and B This relation is purely symmetrical Later we find out that they have become unequal A is longer than B In this relation there is it is true no symmetry but there nevertheless does exist a reverse relation For we may formulate the new datum also in this way B is shorter than A But how should we express the becoming of which we find the result A has become from equal longer than B B has become from equal shorter than A According to the purely mathematical proportional aspect both formulas are equivalent But they surely are not so as soon as we want to express the physical event The becoming expressed in both formulas evidently is not the same The first formula is true if for instance a segment is added onto A or also if it is stretched The second formula is true if a segment is taken away from B or when it has shrinked And there are indefinitely many other possibilities Notwithstanding the equivalence in the mathematical proportion the physical becoming is in these cases different to physically paste something onto A is different from physically take away something from B This could also be the case in the phenomenon of motion Motion physically taken is not symmetric relative At first sight however not so i e there doesn t seem to be a difference between the phoronomical and physical aspect of motion as follows from our description above about a body A moving with respect to the aether B On first inspection the symmetry of placement by contact i e from contact position follows appears equally well existing in the case of motion And purely phoronomically it is so But not so anymore as soon as one inspects things as to their physical aspect Suppose to pinpoint thought that a body A is submerged into an aether When the body starts to move of course with respect to the aether If one wishes one may assume other bodies to be present in the aether in order to be able to observe in it a coordinate system then all new distances of A or points in A to all points in that aether immediately result This is not something following from observation no of this we have intellective and immediate insight Here motion with respect to the aether is supposed to be possible If the aether were homogeneous and indeed homogeneous into the extreme meaning that it doesn t even have boundaries even when being of finite size then it is hard if not impossible to imagine the movement of some given physical body with respect to such an aether But the aether is not believed to be homogeneous It is believed to be a heterogeneous continuum as a result of locally varying qualitative determinations of it such as electric magnetic electro magnetic and gravitational fields These fields being carried by the aether But these varying qualitative determinations are caused by ponderable bodies electric or magnetic bodies light emitting bodies heavy bodies which are themselves in motion So if we take the motion of some given body to be with respect to the heterogeneity of the aether then its motion is in fact with respect to other ponderable bodies So as things stand a body cannot move with respect to the aether even when the latter is a heterogeneous continuum A way out of this dilemma may be the following Aether and ponderable bodies penetrate each other We draw an imaginary line through the aether without knowing where in the aether this line is On this line we draw an imaginary point Now we can draw another point on this line at a certain distance from the first point Indeed this distance is possible because these two points make contact with a third entity lying between them being now a genuine part of the aether measured along the imaginary line Through each of these points we draw a line perpendicular to the first line and now it is possible to draw a line precisely at equal distance from the first line It is clear that in this way we can draw an imaginary coordinate system in the aether And now having this coordinate system and using it as a reference system we can finally legitimately speak about the movement of some given physical body with respect to the aether It is good that the reader is convinced by the fact that the distances from a body that starts to move with respect to the aether distances to all points of the aether do change immediately and that this is a direct intellective insight Yet another reflection may further be instructive As a result of the change of distance also the action that may emanate from the body A submerged in the aether and starting to move and enforced upon remote points of the aether will change Does this changed action in particular its effect establish itself also immediately in all these remote points By merely reasoning we cannot come to an answer and one already sees in one s mind the difference with the change of mere distance immediate change of distance being intellectively clear immediate change of effect of action of A upon all remote points not being intellectively clear Further experience has teached us that this is not the case All action to propagate itself and then to have effect needs time So let us be clear about three things 1 the insight that distance immediately results 2 the fact that we do not have that insight as regards action its effect and 3 that experience teaches us the opposite no immediate effects of the action Well precisely because these distances at the beginning of and further during the movement of the body A change immediately we can purely phoronomically describe the movement of A with respect to the aether also in this way That aether as a whole moves with respect to A To this principle of the immediate resulting of distances we will return later and did already so in Fourth Part of Website part XXIX Sequel 5 when discussing the possibility of absolute simultaneity Here one should notice that in this we have a development and confirmation of the Contact Theory of St Thomas But beginning of motion as we assumed for body A demands if things are fully considered as to their physical aspect an active cause whatever this may be later we will see that also the continuation of a regular rectilinear motion demands such a cause albeit not a force in the technical mechanical sense and this influence of that cause is governed by the law of all material action namely that it doesn t propagate instantaneously This influence will immediately have to manifest itself there where the place relation has its origin namely at the sites of contact between the body A and parts of the aether occupied by A upon all contact sites or upon some of them If the motion the becoming is attributed to A and then the aether not being supposed to move A moving of course with respect to the aether then it will proceed as one usually describes it with a small deformation of A if A is small When A is small the influence soon reaches from one side of the body to the other and then only for a short while there is some deformation at the site where the influence began and none if A is seized upon in all its points at the same time Does one on the other hand want to ascribe the motion actually to the aether with respect to the body A then the influence must first seize upon the contact sites of the aether and then move it If the aether moves at all just like that then it may do it with respect to another body than A say to the body B The motion of the aether may then be zero with respect to A Accordingly to be sure that the aether moves with respect to A it cannot be aether movement just like that The body A must play a role And so in the aether commencing motion with respect to A not just any points of the aether can be seized upon but only its points of contact with A The remote parts of the aether will feel this influence deformation propagating from the points of contact with A that were seized upon in order to move the aether only after a certain time has elapsed perhaps only after an astronomical time The aether would be deformed and we do not have the same course of events as we had in the first case A moves with respect to the aether If the motion is exclusively attributed to the small object this resides in a much larger object the aether then only this smaller object can deform and this deformation is only very temporal The aether in this case is not deformed because it does not ex hypothesi take part in the motion If on the other hand the motion is attributed to the aether then the small object cannot be deformed but the eather can and will because of the large distance to be traveled by the internal contraction wave propagating from one or more sites of contact of the aether with the small object to the periphery of the aether if there does exist one it must be presupposed when attributing motion to the aether Indeed as long as the internal contraction wave has not entirely traversed the body the latter is deformed When it has traversed the body the latter as a whole has moved When one wants to assume the same influence on both body and aether then one obtains a third case the second case becomes different from the first case So physically motion is not symmetrical relative at least not without exceptions Here the case of the assumed existence of an aether Yet another reason for attributing asymmetry to motion The last consideration leads to yet another reflection that independently of the first reflection leads to the same result It lays bare a possibility being entirely neglected in classical mechanics There one knows Newton s law of action and reaction which reads When a body A applies a force onto a body B then B applies an equal but opposite force onto A Force must here be understood in the technical mechanical sense and is measured by the product of mass m and acceleration a F ma This law is not a priori evident it was in classical mechanics considered to be confirmed by very rich and precise observation But this observation only applies to ponderable matter Does it also apply to a body A and the aether in which it is submerged even apart from measuring this force in which the mass of the aether would of course trouble things Also here it is a priori not evident that this or a like law would apply and experience certainly doesn t teach us this Let us consider the following case There is an active cause moving A with respect to the aether and this cause should seize primarily upon the points of contact The fact that this cause will influence both A and the aether will be clear The influence on A manifests itself as motion change And when only a part of A is seized upon this influence will propagate

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    it the following property also when all bodies would be destroyed space capacity for new bodies would nevertheless remain It is indestructible It keeps on existing It is by its nature eternal and uncreated and incorruptible Space a being of reason But with this space as reality is also condemned It is a mere being of reason an ens rationis as the scholastics say And with this basically all philosophers agree But see in many of them difficulties against this thesis come up from considering other true and supposed data And if one does not have the means to solve these difficulties one arrives at desperate theories attempting nevertheless to attribute to this non real being of reason a reality of whatever sort Then they assume we using KANT s words an Unding absurdity because it only exists without something real existing to eventually contain all the real Others so KANT himself see themselves forced with the reality of space also to deny the reality of the spatial the extensum Both parties have made the error that they did not depart from the first given in all this namely from the extensum from the body from which then first and immediately as we has found above with Aristotle St Thomas and Einstein as a result of contact resting and flowing contact automatically derive the spatial relations of nearness distance and motion And then Nature does not need space as recipient anymore and when this space the notion of which has been introduced after these data turns out not to be real we avoid the desperate result of the first who yet accept a contradictory real space the Unding because we in order to understand Nature do not need real space And we avoid the error of the others because the rejection of space as real does not imply the rejection of the spatial of extensionality of nearness and distance and of motion These are prior to the notion of space do not depend on it do not become unreal when space becomes unreal This is certainly true when space is taken as an existing thing i e as a being Such a thing we do not need And if we take bodies as substances in the metaphysical sense or aggregates of them such as rocks logs etc but also planets and satellites then these are as material things prior to space because space derives from the spatiality of them If on the other hand we descend into Substance itself and consider its ontological constitution we may legitimately ask for the ontological condition of the substance s spatiality extensionality and this condition may well be space but now certainly not in its meaning as container of things but as a set of three extensional dimensions that are substrates of extensa As such space is a hartmannian category which as such i e even without its proper concretum has being in every individual material substance but is not a being Perhaps something similar is the case with time While the sizes i e volumes of all things substances or aggregates of them differ they do not result in as many different sets of space dimensions i e they cannot be conditioned by as many different sets of space dimensions They are conditioned carried by a single set of three space dimensions present in every substance And more specifically as to the length of things Longer and shorter things are carried by the same dimension present in every substance All the different cases of length are carried by the same dimension present in all substances Well perhaps analogously all the different cases and sorts of change in and of substances i e all cases and sorts of replacement of one form by another as each sort of them has its play in its own proper dimension such as the dimension of temperature change the dimension of pressure change the dimension of energy change the dimension of impetus change all the different cases and sorts of change possess a common element an element that is present in all change an element that is the very essence of all change so that there is in them i e in all cases of change something like a change as such And this commonly possessed change as such has its own play and thus its own dimension a dimension present in every substance and this dimension is time It is the dimension of the one universal time This universal time is not itself in motion does not itself flow It is the universal dimension present in every substance that carries the change as such commonly present in all cases of change In this way we JB in our own and independent speculations consider t h i n g s i e substance or substances to be prior in nature to space as well as to time because their respective dimensions reside and are sustained in every substance and thus presuppose this substance We said that time does not move not flow This is because there is nothing relative to which it might flow The only candidate we might come up with to which the flow of time would be relative is the NOW And although the NOW is itself flowing with time flowing from past to future or coming down from future to past it might be a point of reference with respect to which time flows However the NOW is as such not different from time itself and cannot therefore be an entity with respect to which time moves Moreover the NOW is a product of human perception not something objectively existing independently of being perceived Only from the ability of things that is of substances to be different from one another i e having a different content does the phenomenon of things becoming different derive and so does time returning to HOENEN s exposition Elucidation of space being a mere being of reason Let us clarify it a bit more We said basically all philosophers agree that space is not a real essence Only in human imagination it is so that if we remove all real bodies something remains that resists being removed namely our own body as a center surrounded by an extensum Precisely that is there in our imagination real because it cannot imagine the nothing There we have in fact not removed all bodies There in addition to ourselves a homogeneous background remains and the bodies are only apparently absent because we have removed precisely that what qualitatively differed from that homogeneous background If we really want to think space that what remains when all bodies have been removed then also that graphic homogeneous dark colored extensum of our imagination must be thought away intellectually removed Also the aether of course has been removed because it is a real physical extensum a body as well just like the ponderable and visible bodies are The aether is not the space that must be left over when all bodies have been removed But what then remains really is nothing And that basically is what all philosophers hold and rightfully so and therfore space is just a being of reason Newton and Clarke But the condition making possible the existence of real extensa of physical bodies still remains one might maintain And this surely is true when considering the active potency of the Creator But as to the passive potency it is merely an abstract condition not a really existing recipient having to include the bodies If one would demand such a real recipient if physical bodies real extensa in order for them to be able to exist had necessarily to be included into a real recipient this recipient should in its turn have to be included in another recipient and so ad infinitum which is absurd So a really existing recipient space is impossible But one might hold that while space itself as a result of its infinity does not need a recipient a finite body does need such a recipient because such a body has to be somewhere But this second reason to suppose a real recipient is also invalid because a finite body or group of bodies doesn t need to be somewhere Indeed the universe as a whole even cannot be somewhere The assertion that a body must be somewhere follows from a wrong interpretation of the datum of our imagination And then as already remarked by Leibniz in his famous polemics against Newton s pupil Clarke This space would then be an eternal and necessary being But only God is eternal and necessary and space is definitely not identical to God It is an attribute of God as maintained Clarke namely His Immensity which assumption however is likewise impossible Afterall to space necessarily are attributed mutually different parts It has extension it must serve as it was held to include bodies in order to be able to explain distance and nearness of them But to assume parts in God s Immensity is absurd because then these parts would be prior to God himself Nevertheless these properties of necessity and eternity together with extension do belong to the concept of this absolute space So it cannot be real It is to use Kant s expression an Unding So one now understands that as we said basically all philosophers saw space not as a reality but as a being of reason and consequently in itself as a nothing It is more difficult to understand how some of them Clarke is an instance of it came to realize space in one way or another Let s consider some more points Clarke defended in fact the ideas of Newton Well Newton thought that he was as a result of some experimental data forced to assume the existence of absolute space It concerned the phenomena in rotating bodies for example our Earth is as a result of its rotation flattened at the poles and Newton performed experiments with water in a rotating bucket letting him assume an absolute motion i e a motion that is not relative to bodies in its surroundings So such a motion was as he thought a motion relative to space itself Now Newton was well aware that absolute motion in the sense of being motion relative to nothing is absurd Therefore he wanted to grant space a certain degree of reality Once he called it the sensorium of God about which vague expression the polemics between Leibniz and Clarke blazed up furiously but in the scholium generale at the end of his great work in the edition from Amsterdam of 1723 p 483 we read that space is constituted by God s infinity which was also the position of Clarke defending the opinion of his master So it is more or less understandable that Newton came to his desperate thesis The properties of rotating bodies we now know better to explain as we saw earlier According to Mach it is a motion relative to the stars Still better is the view it is a motion relative to the aether of Lorentz And in this way the desparate attempt to explain rotation as a motion relative to space which then would have to be identical to God s Immensity which it cannot be is avoided So absolute space this necessarily existing uncreated extensum indeed is only a mere being of reason In Nature it indeed is as we said nothing And this is the great difference from the notion of place This is a reality And we do need a reality as medium of localization Place may be as we saw the enveloping real surface surrounding the body to be placed according to Aristotle or it may be which is undoubtedly better the parts of the aether of Lorentz which is the ultimate medium of localization With the help of the reality place through contact the spatial relationships can be realized and not with the help of the unreal space That the notion of space as being of reason may well be used to describe these relations we shall see later on First we must touch upon several other attempts to realize space The atomists Also the ancient atomists Leucippus and Democritus ended up into an antinomy regarding the notion of space by the same reason as Newton did because they thought that they needed an absolute motion a motion relative to space to nothing They wanted to unify with the metaphysics of Parmenides the metaphysics of unity and of unchangeableness of Being yet the world of plurality and changeableness and then so constituting the real world Plurality then is there only in the form of a plurality of atoms differing in size and figure Changeableness merely consists in the motion of atoms But also this plurality and this changeableness was excluded by Parmenides For as he had argued this plurality would demand separation of things the full ness of Being by empty space Motion is hindered by the full i e by the one uninterrupted Being and so in turn demands empty space but the empty space is the nothing i e the not being and the not being does not exist Leucippus cut the knot with his famous thesis the not being does exist just as well as the being does And see also here space is delared to be nothing afterall all philosophers do it basically but at one stroke existence is attributed to this not being Joël called this desperate solution a salto mortale in negation and we can now better judge about the desperate The solution must be rejected according to what we found out above Afterall nearness and distance and motion can only derive from contact immediate and mediate resting and shifting contact of a real extensum with another real extensum But let us also salute the insight of these ancient Greeks who did understand and in distress they had to save the world of plurality and change grabbed this life line Then even this unreal extensum empty space must exist Of course this solution is unacceptable and in this way these first principles of Greek atomism as a solution of the problem of plurality and change should already as such be dismissed Descartes In an analogous fashion Descartes 1596 1650 wanted to explain change in the world with motion only But he wasn t an atomist his matter is divisible without limit Also in an other respect he differs from Democritus To him empty space is a contradiction in terms because space is an extensum and extension is to him the essence of matter So space is per se the full ness of material being Descartes had a problem presented to him If in a container the content is destroyed without becoming replaced by a new content matter then there would be realized a vacuum and thus empty space nevertheless His weird solution was No in the supposed case the walls of the container would touch one another because nothing is between them Here the thesis that space is nothing is urged too strongly or rather wrongly applied HOENEN apparently means the thesis that space is not only material but also the full i e matter everywhere is urged too strongly resulting in denying the possibility of isolated and partial gaps of contact between material bodies The supposed case seems to us perfectly possible perhaps not in our natural world in which the aether cannot be removed by natural forces And if it is realized emptying the container of its content the walls will not touch each other Yet actually there is no matter between them except for those walls connecting two other walls separated by a distance and this is essential for 1 the contact of the separate walls with the connecting walls and 2 the size of the latter determine the distance between the former and in this no space is needed only contact throughout of bodies with one another but a body of precisely the right size m a y be placed between them completely filling the container This is not an abstract possibility but a very concrete one resulting from the shape and size of the real container Here it makes real sense to speak of Between these walls there is space having this size and shape And this is a first example in what way the being of reason space can be applied to express real truths So the being of reason space is convenient in descriptions in precisely the sense that space is there first and that then things can be placed into it But space here is meant to be not completely empty space but as isolated gaps between parts of bodies otherwise touching other bodies bodies that are in real physical contact with other bodies resulting in the world being one single contiguum a whole consisting of parts bodies that touch one another As a result of Descartes space theory he was led to yet another weird conclusion The world must be infinitely big or rather indefinitely big A finite world would yet have space to be left outside it It afterall can indeed be bigger but that space again is extension and thus matter And consequently for Descartes and according to him with absolute necessity the world becomes infinitely big or rather because he allows the infinite only in God and His attributes the world becomes indefinite which is in the case of a really existing being absurd every existing essence or being is completely determined definite That s why this conclusion was said to be weird The solution of the difficulty presented by a finite world with an infinite space around it is evident The proposition beyond the world a space exists is if it be taken litterally absurd because then to space to the nothing existence would be attributed But this proposition should not be taken litterally It is a circumscription of the following truth With a finite world may per se be connected and indefinitely so newly created bodies by means of contact there is space enough for all these new bodies And in this way the being of reason space can once more be used in a proposition expressing a real truth This proposition was beyond the world a space exists The full ness of Being and the possibility of motion Concerning the possibility of motion in a world without vacuum four theories have been developed in the course of history The first one is the Eleatic denying the possibility of motion in a full y occupied world Therefore Parmenides denied motion itself and declared the impressions of our sense experience observing motions in Nature as mere appearance Democritus also defended the Eleatic theory of the impossibility of motion in a full world and this precisely was the reason why he assumed the existence of the vacuum local vacuum and constructed a world in which free atoms moved in empty space When considering the theory of distance of bodies we saw that this only becomes intelligible by mediate contact of real extensa rendering the distance between atoms in a Democritean world i e free atoms moving around in empty space impossible The three other theories construct the possibility of motion in a full world and so escape from the above difficulty Descartes did this by postulating that every motion is part of a total motion along a closed trajectory which also was already assumed by te Greeks in the antiperistasis This does not give problems as long as that total motion is one of matter contained between two perfect concentric circles which of course is only exceptionally the case When the motion is some arbitrary different one then deformations of shape must take place in matter namely generally continuous deformations Now in the system of Descartes however deformations can only occur as a result of division of matter And when consequently this deformation is continuous i e goes its way gradually from a straight plane must for example be produced a curved plane as a result of division and rearrangement of the particles in some matter particles an actually infinite division a division down to a powder of mathematical points must be assumed and from this be made up a continuum again Both operations the division and compounding are impossible Descartes himself sees the problem and in fact says that he doesn t have a solution of it Also this theory is unacceptable Indeed a division into actually infinite parts is impossible The division will never come to a conclusion and however far it has proceeded the number of resulting particles is still finite And a construction of a new particle out of dimensionless points is impossible as well A theory of a world without vacuum as Aristotle had developed it prevents these difficulties Aristotle assumes that the bodies are subjected to densification condensation and rarefaction dilution in the strict sense i e not only apparent condensation and dilution occurs as is known in classical physics which consist in coming closer respectively dispersing of separate particles which each for themselves retain their volume unchanged but one single continuous body i e without pores is not tied up to a determined volume why should it be it may potentially have different volumes It accordingly may have different volumes in different circumstances Up until neutron stars and black holes In this no penetration of parts of the body is presupposed i e it is not presupposed that parts would mutually penetrate one another but if the whole body may have a larger or smaller volume then also every infinitesimal part of it With this both changes condensation and rarefaction may be accompanied by changes in the geometric form of the body for example in the curving of the surface without division taking part therein In a theory that is able to explain intrinsic change qualitative change change of intensive quality with the doctrine of potency and act all this is simply following from that theory This theory has in modern physics found an application in the theory of electrons of Lorentz electrons in motion are subjected to a flattening the effects are observable at high speeds I am not sure whether this is still unequivocally confirmed today 2010 however which flattening includes both changes condensation along the axis of rotation rarefaction along all axes perpendicular to it It is clear that in the theory of Aristotle a world without vacuum does not exclude motion because condensation and rarefaction are motions at least insofar as geometric deformation is concerned But because geometric deformation here is supposed to take place as a result of corresponding deformations of the smallest parts the latter deformations must then be qualitative changes because they cannot be the result of again a rearrangement of still smaller constituent particles in the body The above mentioned electrons indeed are particles of smallest size they cannot divide anymore and do not consist of still smaller parts So their deformation is a qualitative change The most perfect theory rendering possible motion in a full world is the aether theory of Lorentz This it owes to the fact that it has demonstrated the existence of a real extensum the aether which is penetrable to ponderable bodies And in this way it delivers the perfect explanation of the possibility of motion in a full world The derivation of distances and motions as a result of intrinsic contact with various parts of the aether is immediately clear The aether is a perfect medium of localization The penetrability of the aether to ponderable bodies removes all obstacles to their motion That what renders the theory of Democritus and that of Descartes unacceptable is in the theory of Lorentz replaced by something from which the possibility of motion precisely becomes understandable In this aether systems of bodies can be found which are similar to the democritean world of separate atoms Discontinuous systems of ponderable bodies are possible A gas for example surely is a swarm of countless small separate particles which are as the atoms of Democritus in a state of violent motion colliding countless times with one another Now the discontinuity of these particles the molecules is no longer a difficulty They all move in a real continuous medium the aether which itself is the condition of the possibility of distances and motion This same aether also has an active function in the motion of ponderable bodies It serves as a substrate of electromagnetic and gravitational fields in which forces reside that give bodies acceleration It also appears as we saw to play an active role in motion of inertia Remarkable in the aether of Lorentz we recover a property which Aristotle also attributed to place when he declaired that this place also has an certain active capacity One more remark will be made here in passing If we will ever possess a good theory of the notion of mass making clear the ponderous and inert mass of Einstein but also the active and passive mass and the connection of these four aspects then mass in these expressions include we believe a relation with the aether For an attempt see later on Space as a well founded being of reason So space is a pure being of reason only Indeed space is not real while the spatial is spatially extended bodies extensa In Nature there can be no reality something really existing combining in itself all the properties attributed to the notion of space We said that all philosophers basically accept this but also saw that there were some who felt forced to look for real space nevertheless Others on the otherhand went too far into the opposite direction and together with the reality of space also rejected that of the fundament onto which the notion of space rests and so arrived at the denial of all what is spatial of extensa of nearness and distance and of motion Here we have one of the brands of idealism For a large part this came from the difficulties of the continuum which we have already discussed Without repeating things again we only want to recall that these difficulties have their complete solution in the potency theory of Aristotle and that the reasons to also reject the existence of bodies and motions turn out to be worthless on closer scrutinity If indeed real extensa did not exist then space not only would be a mere being of reason but would even lack any fundament in nature This not being the case the notion space does have such a fundament The difficulties of the continuum were for Leibniz the only reason to reject the reality of the spatial and with it to limit all this to the world of mere phenomena i e the world of mere sensory and or intellectual perception extensionality distance and motion Nevertheless Leibniz is not an all out idealist we rather would call him semi idealist For Leibniz still assumes that to all relationships of the phenomenal world known and derived by us there do exist analogous relationships in the real world resulting in the fact that we in our knowledge of the spatially phenomenal do possess an analogous knowledge of the non spatial real Kant went even further and in fact denied also this analogy of our knowledge For him the the thing as it is all by itself das Ding an sich remains unknown in our world In the present context it is interesting to scrutinize Kant s argument saying that he could legitimately conclude from the truth that space is a being of reason also the truth that all the spatial has no reality Here he made the mistake in viewing space as a fundament as a first datum and the spatial as the derived And this error became fatal to this thesis Indeed if the relationship were truly such then the unrealness of space would imply the unrealness of the spatial too But the relationship is the other way around The first datum and known as to be real is the extensum the spatial body And from this follows possibility of physical contact and from this in turn nearness distance and the possibility of motion And only then the notion of space appears And if on further scrutinity the latter appears to be a mere being of reason which moreover is unnecessary for deriving those allegedly secondary but in fact first known realities and relationships extensa and what follows from them contact distance motion then evidently it does not follow that the extensum and its effects are mere beings of reason for not space is the fundament of the spatial but the other way around If one installs in Kant s reasoning in the Transzendental Aesthetik this necessary correction that not space but the extensum as ens extensum is the first datum it automatically falls apart So space is a being of reason but as the scholastics declaired unanimously apart from deviations in special questions a being of reason based on Nature itself What this precisely means we above had indicated with two examples Space in itself is nothing So a proposition as this a space of three dimensions exists is litterally taken nonsense But above we saw in two cases space in an empty container space beyond a finite world that we may use this notion in propositions describing a reality Let us add some more examples The proposition that we just then called nonsense if taken litterally may be used in a good sense and is often so used One wants namely to express with it There is a world made up of bodies which are real extensa in three dimensions In mechanics one speaks of degrees of freedom of motion of a material point And thus the same proposition also means this fact In our world a freely mobile material point has a motion with three degrees of freedom The fact that some particular being of reason may nevertheless be founded in Nature and in fact is so founded now means It may in such a way be used in meaningful and true propositions Let us compare this case with another If someone denies that bodies of four dimensions are possible and so also a world composed of them cannot exist then he may express this by saying A space of three dimensions exists first proposition but there is no such space having four dimensions second proposition If one takes these propositions litterally also the first one should be denied because a nothing as space cannot exist i e departing from the thesis that space is a mere being of reason only then also of course a space with three dimensions is such a being of reason only But if one understands them in the sense given above then the first proposition must indeed be affirmative while the second if indeed no four dimensional things are possible negative In this sense n dimensional space in fact refers to n dimensional bodies A space of four dimensions would exist if our world of three dimensions were curved Because it must be curved within something i e it must be curved relative to a four dimensional space In such a case the theory of relativity deals with it a world without a boundary and nevertheless not being infinite is possible An example is delivered by an extensum having two dimensions If this is curved the surface of a sphere for instance then it may be without boundary a whole surface of a sphere h a s no boundary but it surely i s a boundary and yet it is finite If something like this holds for our world it would be curved and presuppose a space of four dimensions A curved two dimensional world must be in a three dimensional world And in the same way if our three dimensional world were curved it must be in a four dimensional world Such beings of reason also occur in other sciences but their cognitive theory has been hardly or not at all worked out So in projective geometry one speaks of the straight line at infinity a sort of horizon one might say and the straight plane at infinity These are not existing things not realizable boundaries of a plane or a space because they are supposed to lie at infinity They are litterally taken just as impossible to exist as space is They simply are just beings of reason which the figures in projective geometry are not precisely as is space But they may be introduced in propositions which one doesn t interpret litterally too expressing very real relationships between figures provided they are understood And then they are well founded beings of reason for they render formulations and reasonings to become wonderfully succinct and elegant Such a being of reason now is space But with this restriction that its usefulness is much more limited With the notion of place to which directly corresponds a reality one may without significant loss of succinctness or elegance express almost all relationships from this sphere of facts and problems And the introduction of the notion of space the history of philosophy is there to prove it may lead to disasterous errors So we may conclude Aristotle and after him St Thomas were very wise in speaking much of the reality of place and little about the being of reason space Earlier we have found out following HARTMANN that indeed space as it is in itself i e with nothing else does not really exist But this here means does not exist as a being of some kind It does exist though as a category in the Hartmannian sense but only together with its proper type of concretum As such space is an ontological condition of the spatiality of things where space itself is not spatial space is a system of three dimensions and in them things can vary in their sizes So the system of space dimensions is a category in the Hartmannian sense meaning that they do not exist without the proper type of concretum and then only really exists in each particular individual instance of an extensum a spatial body But still such a category is not a being So space in the Hartmannian sense is ontologically prior to spatially extended bodies while for Hoenen the latter are prior to space which is only a being of reason albeit founded on extended beings Motion About the Relativity of local Motion and about Motion as to what it precisely is With HOENEN we have discovered that a body in regular rectilinear motion needs for such motion to be intelligible an active cause in the body itself This cause is a genuine intensive quality of that body i e of every substance making up this body if it is an aggregate of them and was called the impetus But this finding brings us to the alleged fact that all motion is relative It is said that motion is relative In certain senses of relative this is entirely true But the presence of an impetus in a given moving body including the case where this body moves in a straight line and with constant speed an impetus itself an intensive quality that causes an extensive effect in the body motion attributes motion to that body and to that body alone This impetus has been brought in by the extrinsic cause of the beginning of motion for example a thrust W d better say that the extrinsic cause thrust has as its effect in the body to which the thrust was delivered the body now having an impetus of a certain intensity proportional to the thrust And when the thrust ceases to be applied the body

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  • wings XVc
    a reflecting wall As a result of reflection from the sun the particles will reach the Earth at its sunward side particles who would have been flown further if the sun had not been there flown further that is without reaching the Earth And the exact calculation tells us that this increase of the number of collisions neutralizes the decrease caused by the screen So in the case of elastic collisions the resultant apparent attraction is zero after the kinetic gas theory this result could have been foreseen If on the other hand the collisions are totally unelastic then an apparent attractive force can result but then such collisions will increase the internal energy of the Earth and with a catastrophic result According to the calculations of Darwin in order to accomplish the actual attractive force so much heat would be generated in the Earth as a result of the supply of energy that its temperature would increase with 10 26 degrees per second The Earth would receive 10 20 as much heat as the sun normally transmits to it by radiation If finally the collisions are semi elastic then the energy of the colliding particles is not entirely converted into heat but then also the resulting attraction becomes proportionally smaller because the impact of these particles on the Earth does not entirely result in a force pushing the Earth towards the sun and the sun although semi effective still works as a reflection wall In order to obtain the same attraction as actually observed one must suppose the number of collisions larger again and according to Poincaré 1908 the result of Darwin remains the same By all this the theory of Lesage is refuted Gravity as elementary property So with the old newtonians one takes general gravitation to be a propriété primitive essentielle à la matière at least of those elements which are called neutrons One had essentially done this already before Lesage s theory was refuted except for the fact that also great scientists had attempted to derive the gravitational force from electrical forces with which mechanicism is of course not helped Initially this thesis still corresponded to the wider mechanical view of Nature insofar as it claimed no changeability in this quality precisely as we saw it with the electric charge dependent only on the number of electrically charged particles with unit charge Indeed mass thus the gravitational force exerted by a body appeared to be intrinsically unchangeable A given body only obtains a larger mass when another body with its mass is added to it The fact that according to the data of the theory of relativity mass itself is changeable it may turn into energy we will neglect here This changeability is if it is objective of course immediately contradicting mechanicism With this one ascribed just as in the case of electrical influences also to gravity an immediate action at a distance If this is true the sun would immediately attract the Earth without changing a medium without needing time of propagation Then the only effect of the force of gravity would be motion then gravity would not demand a new intrinsic change Gravitational field But also this position did not hold out After one had given up actio in distans for electromagnetic influences and replaced it by the generation of a field a field that consists in real changes in a real medium the aether of Lorentz one finally has done the same thing also with respect to gravitation to which one attributes even the same speed of propagation as it is in the influence of electromagnetic fields the speed of light Definitive all this became not until the general theory of relativity but before it these ideas were already held anyway That a real gravitational field does exist in the light aether follows from the influence it has on the direction of light rays which was it is true first derived from the theory of relativity but also independently of it was found experimentally So we find for gravity what we found for the electric field As a result of the gravitational mass of ponderable matter an intrinsic qualitative change in the aether is formed Let us hear it from Lorentz who also has described the qualitative electric and magnetic field so acutely He says Dans un champ gravifique il y a un changement d état qui produit les effects qu on attribue à la gravitation Du reste pour établir et appliquer la théorie il n est aucunement nécessaire de nous former une idée de la nature de ce changement We again have as in electromagnetic fields a change which is known to us only generically un changement d état We know the effects caused by this state i e the motions given by the fields to the bodies We do not need to further know the nature i e the specific nature of those changes and in fact do not know them Again only the genus is known to us It is a quality it may have greater or smaller intensity strong field weak field The intensity decreases with the square of the distance of the mass causing the field i e according to Newton s law or roughly according to it So the final word of science in these matters is again a specification not the last of an Aristotelian general principle the principle of the intrinsic changeability of matter as to qualities And again mechanicism the theory of intrinsic un changeableness fails to account for the facts The notion of mass In the theory of gravitation we met the notion of mass What precisely the essence of mass is nobody knows We also will not attempt to answer this question but only venture to make a moderate attempt to approach it more or less And also this we do not without hesitating Anyone who makes an attempt to apprehend the nature of mass must realize that it is a notion of the science of mechanics which is connected with the motion of bodies and with the force which is taken to be the cause of acceleration of the increase of the impetus as we will say Inertial and gravitational mass One will further have to take into account the fact that in mechanics there are two concepts of mass which mass however as it turns out experimentally but for the time being just experimentally is perfectly proportional and thus when measured with the same units perfecty equal They are the inertial and the gravitational mass which from the finding of their being identical onwards having become the foundation of the general theory of relativity attracted attention They however are not always properly described Soon we ll see a reason And see here a very correct description of the difference between both concepts and of the experimental data that so clearly tell us their equality such that formerly one often took the concepts to be unqualifiedly identical The description is Einstein s 1914 Because of its correctness we may be excused to insert this long quotation Wenn wir von der Masse eines Körpers reden so verbinden wir mit diesem Wort zwei Definitionen die logisch gansz unabhängig von einander sind We verstehen unter der Masse einesteils die dem Körper zukommende Konstante welche den Widerstand des Körpers gegen eine Beschleunigung desselben miszt träge Masse andernteils diejenige Konstante des Körpers welche für die Grösze der Kraft massgebend ist welche der Körper in einem Schwerefelde erfährt schwere Masse Es ist a priori durchaus nicht selbstverständlich das die träge Masse und die schwere Masse eines Körpers übereinstimmen müssen Wir sind lediglich daran gewöhnt deren übereinstimmung vorauszusetzen Die Ueberzeugung von dieser Uebereinstimmung stammt von der Erfahrung dasz die Beschleunigung welche verschiedene Körper im Schwerefelde erfahren unabhängig is von deren Material Eötvös hat gezeigt dasz die träge und der schwere Masse jedenfalls mit sehr grosser Präzision übereinstimmen indem er durch Versuche mit der Drehwage eine Existenz von relativen Abweichungen beider Massen voneinander von der Gröszenordnung 10 8 ausschlosz English translation When we speak of the mass of a body we have with this word two definitions in mind which logically are totally independent of one another We mean by the mass on the one hand the constant of the body measuring the resistance of the body against its acceleration inertial mass on the other hand we mean with mass that constant of the body which is indicative of the magnitude of the force experienced by the body in a gravitational field gravitational mass It is a priori not self evident that the inertial mass and the gravitational mass of a given body have to coincide The belief in such an equality comes from the experience that the acceleration experienced by different bodies in the field of gravitation is independent of their material Eötvös has demonstrated that the inertial and gravitational mass at least with very large precision do coincide excluding on the basis of experiments with the balance Drehwage the existence of relative deviations of both masses from each other of the order of 10 8 A larger inertial mass which is the resistance against acceleration demands for getting the same acceleration a greater force than a smaller inertial mass does If in the same gravitational field there are two unequal masses then they nevertheless get the same acceleration while one of them must experience a greater force than does te other it is heavier But the forces experienced by both bodies in the same gravitational field are proportional to their gravitational mass So a greater force is needed for the heavier body to give it the same acceleration And thus the resistance against this same acceleration is proportional to the degree of heaviness of the body and thus when the body s weight increases the body s inertia increases from which immediately follows the proportionality between the gravitational and inertial mass of a same body and thus when measured with the same units the equality of both masses This result is obtained from experience that shows us the equality of acceleration of all bodies in the same gravitational field i e in a field with the same intensity that is in fields in which there is the same distribution of the same intensities An attempt to apprehend the notion of mass will have to explain the equality of gravitational and inertial mass The gravitational and the inertial mass are before any further interpretation of them nothing else than certain constants belonging to the body Passive and active mass The description of Einstein is correct yet not complete For in each of the two masses we can distinguish yet another aspect The mixing up of these aspects with those mentioned by Einstein sometimes may lead to confusion What Einstein describes is a passive property The resistance against acceleration evidently is nothing else than a passive capacity to receive an amount of motion or of kinetic energy of impetus It is a passive resistance It is like the resistance offered by a container with a large diameter against the rising of the water with which one wants to fill it for the wider the container is the slower the water level in it will rise But also the above mentioned gravitational mass is something passive namely proportional to the force which the body undergoes in a given gravitational field But both masses do also possess an active aspect which wasn t described above This is immediately clear in the case of the gravitational mass It not only is subjected to the influence of the gravitational field but it itself causes one And these passive and active masses are as experience shows equal again But also the inertial mass possesses an active aspect A larger inertial mass with the same speed as that of a smaller one possesses more impulse more kinetic energy it can have greater effects In F ma Newton s second law F is the force causing the acceleration a of a body with mass m One might also say that F is the force needed to give the body with mass m an acceleration a The acceleration a can be written as d dt v where v is the velocity of the body and d dt v the rate of change of v So we can write the formula F ma as F m d dt v or equivalently F d dt mv where mv is the impulse momentum and 1 2mv 2 the kinetic energy of the moving body And again there is equality between active and passive inertial mass But now having four masses that seem to be identical the problem about the nature of mass has not become easier to solve Nevertheless see here an attempt to approach the solution which we do we again say so not without hesitation Trial of the solution The idea of the solution is Mass degree of bondage to the aether If this idea is correct then from it the four masses should derive Mass is something that connects with the mobility of bodies And motion is primarily and directly motion with respect to the aether In order to be able to occupy a place in the aether it is as follows from the contact theory of place sufficient that the thing to be placed is an extensum This is also sufficient for the thing to be able to now occupy this place and later occupy another i e in oder for it to be able to move If nothing else would play a role in these matters then at the most volume might influence mobility But bodies are not merely extensa this has become clear enough against mechanicism but in addition do possess qualitative aspects Thus equal extensa not always have equal mobilities and not always equal masses Let us now suppose that mass primarily is something through which the body is bonded to that part of the localization medium the aether which it mathematically touches The notion bonded is necessarily a bit vague but sharp enough to be able to say that the bond may be stronger or weaker It is something intensive in the same object perhaps not changeable but nevertheles intensive This being bonded immediately expresses itself as follows In order to be moved the stronger bonded body demands a greater active influence which experimentally boils down to the formula For getting equal acceleration it demands a greater force In this way we find the passive aspect of the inertial mass And now the active aspect is easy to derive It is not primarily intrinsic to the inertial mass but only a consequence of its passive nature of capacity In order to be moved the inertial body must take up impetus and only the latter we return to it later is the direct cause of motion not the cause of acceleration but of speed or rather of the motion itself A body with a greater inertial mass has in the case of equal speed taken up a stronger impetus than a body with smaller inertial mass has done From this its equal speed together with stronger bondage to a place in the aether is clear Then the active aspect of the inertial mass is only the activity which the impetus can develop It is not a direct property of the inertial mass but still proportional to it And then the equality of active and passive as the latter is the inertial mass proper inertial mass is not surprising anymore Does from that bondage to the aether also the gravitational mass become clear We think it does As to the passive gravitational mass we may without becoming too speculative say the following Mass consists according to our supposition in a property which brings with it bondage to the aether A larger mass is by qualitative contact in a stronger degree bonded to the aether in a stronger degree under the influence of the aether because mass is primarily passive than a smaller mass Then we are not surprised that the larger mass in an area of aether in which there is a gravitational field also in a stronger degree experiences the influence of it of the gravitational field i e experiences a stronger force than does a smaller mass in the same area as a result of that more intensive qualitative contact We must keep in mind that a gravitational field as also the electromagnetic fields are supposed to be conditions of the aether This cannot of course strictly be derived but it is nevertheless very probable Further it is also probable that there is proportionality between bondage to the aether and that active influence of the gravitational field as this proportionality existed between the inertial mass and that bondage Then the experimental equality between both masses the inertial and the gravitational must result and the reason now is that the mass is in both cases the same Something in the body by which the latter is bonded to the aether What on the other hand can we say of the active gravitational mass This active mass is necessary for the gravitational field which in fact results i e is caused by from the presence of mass in the aether In order to be able to cause anything in this case the gravitational field the mass must be active But is it necessary for this to suppose activity as effective cause of the gravitational field in the gravitational body itself We don t think so the same passivity found above may be sufficient In this sense Let the bondage to the aether and thus the consequence of mass be something purely passive with the mass itself If the body is then immersed into the aether the aether will seize upon this passivity and bond the body But that activity of the aether may very well happen at the expense of the aether itself and its qualities Exerting of that activity namely may result in a change in the aether itself not needing a new effective cause because the sufficient reason is already there This change in the qualitative state of the aether may propagate itself and there we have the gravitional field without activity of the gravitational body only as a result of its passive capacity its passive mass which again is the same as the passive inertial mass The activity comes from the aether Remarkable in a much more fundamental setting we find again without looking for it the ancient thesis of Aristoteles that place has not only a passive but an active capacity as well In our suppositions also the changeability of mass the appearance of longitudinal and transversal mass can we will say not be derived but they will be less perplexing because mass is taken by HOENEN to be the degree of bondage to the aether of the body having that mass And this may be more or less intense making mass to be an intensive quality that may c h a n g e as to its intensivity Remark So mass will be a qualitative passive property of a body and with this we have found yet another genuine quality which quality is essentially related to the aether The body even the free atom does not necessarily have equal mass in all of its equal parts It may with respect to this property as in all qualities be heterogeneous It will not be too speculative to suppose that these different masses and thus densities A given mass may be added to another mass resulting in the sum of these two masses but not so in the case of densities i e a body may obtain more mass by addition of other bodies to it i e by accretion but its mass may also increase when the body s density increases of a same body do not need to always be connected to the same parts of it Then the displacement of two masses in a body with respect to each other not of two parts of the body because mass is a quality will be possible So two such masses in one and the same body both form part of the total mass of that body they are not necessarily masses of two particles in that body or said differently masses of two individual material parts of that body in such a case these masses are qualities of just these parts or particles and not of the body itself The two masses in one and the same body may just be two regions of it having densities differing from their surroundings in that same body and the locations of these different densities in the body may change from time to time But because then these masses move also with respect to the aether the laws of mechanics will apply to them From which follows That what is in classical physics described as displacement for example vibrations of parts of a body with respect to one another also of atoms and molecules in a body may very well be interpreted as displacement of merely masses within the one continuous body i e of mere spatial shifts of qualities of such a body instead of local displacements of constituent parts or particles in that body And also the thermic movements of particles in a warm body may be so interpreted Motions in a continuum may be such shifts That this result may have important philosophical consequences also with respect to living beings is perfectly clear For the time being this remark should be sufficient As to the density in different parts of a body The relation of gravitational mass with volume makes the result the density intensive instead of extensive The relation of mass with the aether here only the definitional involvement of the aether also turns mass into an intensive magnitude If it is really true that mass is a quality a quality of the body that has this mass then indeed moving individual material parts in such a given material body for example an organism may without sacrificing any result as to the physics or chemistry of that given body be interpreted as a quality of that body a quality unevenly distributed in it unevenly distributed that is as to the quality s intensity which is different in different regions of the body a distribution finally that may change from time to time This interpretation of mass makes possible to take a given individual organism or a free atom molecule or crystal for that matter to be a true substance in the metaphysical sense i e to be a single material entity not consisting of separate material parts or particles because that would turn it into a mere aggregate of substances instead of one single substance Such a substance then is a continuum especially a heterogeneous continuum as HOENEN calls it Its heterogeneity is not the result of it consisting of individual material parts or particles but of it having variable qualities Later we will extensively deal with this holism of substances and the part played in it by the Implicate Order Summary Mechanicism has tried to explain Nature with purely geometric elements to which also since Descartes is reckoned motion All intensive qualities were banned Among these geometric elements there is of course one which is itself qualitative the figure or external shape But this is not an intensive quality In fact the speed of a motion is a concept that also points to something qualitative namely to a genuine intensive quality the impetus But this was overlooked by mechanicism In motion itself then the principle of inertia was taken to be something that was in no need of further explanation that was a prime datum We saw that this isn t correct And the analysis of the conditions under which the principle which in fact is given to us in experience only is valid already earlier has led us to the discovery of the impetus which has all the properties of an intensively changeable quality When does the speed of a motion change Strict mechanicism accepts only one influence that may cause acceleration or deceleration of bodies the mutual collision of bodies Broader mechanicism also accepts other forces among which also attractive forces And therefore it had to be prepared to accept qualities that attractive force is certainly something qualitative but thought that it could exclude change in qualities i e intrinsic change So all change in Nature was supposed ultimately to be motion This is the general thesis of mechanicism to which also the broader system adhered These forces causes of changes of motion we have investigated First the collision accepted in all systems Also here mechanicism thought it could do it all with two primary data which should be taken as self evident with the conservation of the amount of motion and with the demand that two extensa must necessarily in virtue of the extension alone stay outside each other The amount of motion being conserved motion has to reverse direction because the extensa the colliding bodies cannot penetrate each other However analysis demonstrates that these data apart from their truth are not sufficient Also here we undoubtedly encounter a change which is not motion but which points to intensive qualitative changeability expressing itself with forces of elasticity the continually increasing restoring force Here mechanicism failed to exclude all intrinsic changeableness Elasticity of a body of course in turn derives from motion of smaller particles with respect to one another inside that body But between the two members of every pair of such particles particles colliding with each other there is still a restoring force and this force is of an electrical nature which is qualitative The broader variant of mechanicism in addition introduced electromagnetic influences and gravitational force And all this had led to fields which we have described That what here in the form of experimental data and theoretic results as final result of analysis and thus as first data for synthesis was found again has all the nature of intensively changeable qualities does not consist of motion If we here indeed have to do with first principles of Nature then we find two fundamental real variable qualities Are they once and for all last and thus for synthesis first data It is certainly out of the question that they can be reduced to pure motion to mechanical principles The probability that they may be reduced to still deeper qualitative principles seems to us low And so the development of science has automatically called back qualities and qualitative changes which had been banned by mechanicism in an a priori way and on the basis of incorrect arguments And for us it has turned out that the crisis of the mechanical view of Nature broken loose in the atomic theory of the 20st century was there already long before or if one prefers the elements of the crisis were there already namely in the 19th century in the field theories to which many physicists had already pointed to and more they were already present from the beginning of cartesian mechanicism namely in the principle of inertia and the very collision itself Intrinsic change only finds its explanation in Aristotle s theory of act and potency This then will have to be realized in Nature But these general principles are not sufficient for a specific explanation of what takes place in Nature So we need specifications of these general principles And it is experience which will largely provide them Aristotle s own experience and that of St Thomas and other medievals still was far from sufficient No wonder that we cannot accept most of their specifications anymore Thus their fundamental quality pairs warm cold and dry humid having played an important role must be rejected Only the powerful mathematical method in experiment and theory i e explanation with specified near causes of phenomena was able to provide and process the necessary exact experience These we then have to apply to specify the general Aristotelian principles of which we already know that they are found to be true out of general experience and from the failure of the mechanical view of Nature The specifications found in this way lead to the following fundamental qualities impetus cause of inertial motion elastic forces electromagnetic and gravitational qualities electric charges and mass in ponderable bodies field states in the aether Are there in inorganic Nature still other fundamental qualities or do they result from all those mentioned Today end of 20th beginning of 21st century we in addition have discovered the so called weak and strong interactional forces in atomic and subatomic dimensions as to be fundamental or semi fundamental qualities The book of HOENEN dates from before particle physics begun in the 1950 s A definite answer we cannot give We expect that all other qualitative data may be reduced to these unless impenetrability which we learned to know as an active principle refuses to be so reduced Finally we may certainly repeat what we in a study from 1928 already described Explicative physics will either be Aristotelian Thomistic or it will not And then we may ask Wouldn t science have fared better when it without having taken the detour through the failure of the mechanistic view of Nature directly had applied its beautiful mathematical method according to us the credit of Descartes for most of it to specify the principles of Aristotle The same conclusion we will find and the same question will automatically be asked in the last chapter where we will discuss atomic theory Activity in inorganic Nature Incorrect description of Mechanicism Mechanicism often is described as a system of thought that denies activity totally or partly in inorganic Nature Partial denial then consists here in the fact that mechanists only accept causes that realize local motion i e change of place while holding that other activity is impossible This splits them up into two groups The first adhering to strict mechanicism limits this activity to collisions while the second the group of broader more comprehensive mechanicism admits also other forces This description of mechanicism is only partly correct Sometimes one ascribes the total denial of all activity to Descartes Also this is erroneous Certainly Descartes does not accept any activity other than that what develops during collision as a consequence of the motion of the colliding body But this is for him a genuine active influence of that body not only a passive transition of an amount of motion from this to the other body The latter would mean the transition of an accident of a given substance to another which also for the mind of Descartes would be absurd There certainly are cartesians like Cordemoy denying all activity in Nature The denial of active causes not only in inorganic Nature but also in all living creatures is a different different from mechanicism philosophic theory occasionalism According to this system of thought all what is happening is a direct consequence of the activity of God only not of the creatures lacking all activity The name of this system derives from the following Where people usually assume that an event is to be ascribed to the active influence of a creature mind or matter there the presence of the alleged cause is nothing else than an occasion which is used by God to realize the effect only through his own activity Such a system was already adhered to in circles of arabian philosophy in the so called Mutakallimun in St Thomas Aquinas they were called loquentes in lege Maurorum Later it was further developed by Geulincx and by Malebranche Certainly Descartes does deny all other activity in inorganic Nature and this is the only distinction between his system strict mechanicism and the system which has become the fundament of classical physics broader mechanicism which as we saw accepts also other forces And this is the only difference between them For all mechanicists agree that all forces of Nature can only produce motion change of place And moreover they agree in the more fundamental thesis that matter cannot experience any other change than motion change of place This thesis is more fundamental because if it is true also other agents also a mind can effect in matter nothing else than motion and a true intrinsic unity wholeness between matter and mind as we see it in human beings and in general in all living creatures becomes then impossible Therefore Descartes had to degrade the animals into automatons More fundamentally it is also because this thesis is the reason why mechanicism has limited the activity of matter to activity of motion Where there is no other becoming than becoming moved every other activity other than to move is superfluous Mechanicism essentially consists in its denial of passivity of matter except the possibility of being moved while the denial or limitation of activity is only secondary Various activities Because now as we ve seen matter is not only movable but also intrinsic qualitatively changeable also the derived thesis of mechanicism limiting activity to one or more moving forces and excluding all other activity is incorrect In addition to moving forces there are also active causes intrinsic qualitatively changing the bodies by their influence From the various types of change found above we can easily sort out what kinds of active causes correspond to them In fact the result is remarkable Earlier we had found an active cause of motion namely of inertial motion the impetus And such that to a faster motion of a same mass does correspond a more intense impetus Are there yet other causes of motion i e activities directly causing motion change of place All other activities influencing motion forces in the technical physical sense of the word are causes of acceleration or deceleration and thus of change of impetus and so of change of quality And only by means of the change of the impetus they can cause acceleration Consequently they are no direct causes of motion causes of the initiation of motion i e by giving impetus and of the change of speed by changing the impetus There is no place anymore for a direct influence of these forces upon motion they only influence motion by means of qualitative change of impetus which they directly cause force impetus motion And even not all these forces directly influence the impetus This may be so in the case of elastic forces affecting the impetus through impenetrability but the gravitational mass first causes a gravitational field and only the tensions in this field are causes of the impetus in a body to be moved The gravitational mass of the Earth does not directly causes the fall of a body but only through the mediation of the gravitational field which is caused by the Earth and then through the mediation of the impetus of that body gravitational mass gravitational field force impetus fall of body Here HOENEN speaks of not all forces directly influence the impetus but the example which he presents is about the gravitational mass not influencing directly the impetus But the gravitational mass is not itself a force it causes the gravitational field and this field makes ponderable bodies feel a force which then causes or influences in them the impetus The same holds for positive and negative electrical charges and for magnetic forces So also here through a field So we arrive at the conclusion that the impetus which in mechanicism and in fact in classical mechanics was neglected if not denied as active principle is in fact the only directly moving activity the direct cause of motion and of its change The forces of mechanicism and consequently those of classical mechanics are activities which directly do not effect motion but

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  • wings XVd
    passed by one after the other by a moving object And because any finite space any finite length of it is constituted of only a finite amount of such non zero units motion in this space can be completed and is thus possible So this solution of the problem of motion boils down to take space to be discrete to be a discretum and not a continuum And for such a continuous motion it is thus necessary that the continuum is not merely the sum of its parts And for this in turn it is necessary that the parts of a continuum are merely potential And finally for this in turn it is necessary that a dynamic continuum is a striving for a particular end point Because only then such a continuum is a true unity is holistic Yet another expression of the same thing If an extensum were not more than a series of contigua and thus not a series of small continua touching one another but exclusively of non extensa points touching one another then this series should contain an infinite number of such contigua then all of them would be actual then they would be prior to the whole which indeed only then is the sum of its parts then motion and time had to exhaust the infinite and thus be impossible But we have already seen that then every extensum would be impossible points points do not add up to an extensum If we now see all this together then we have insight into the continuum the static and the dynamic then we see how all the antinomies of both continua find their complete solution in the aristotelian concept of potency of being in tendency Then but only then all demands of intellectual insight are satisfied and at the same time experience saved experience which so clearly reveals to us the existence of motion The arrow The third antinomy of Zeno will now not cause trouble anymore In Aristotle s text on Zeno has it is true crept in an error not however impeding the understanding and meaning of Zeno s argument The meaning is this A body that is at a place which has the same volume as the body itself is at rest Well a flying arrow is at every moment at a place that has the same volume as the arrow itself So at every moment it is at rest and so it is during the whole time After the above discussion Aristotle s short answer will be clear Zeno illegitimately supposes that time is composed of indivisible moments We may add If we consider the flying arrow here and now then the arrow is not here in the now but shoots through the here while time is running through the now So in the philosophy of Aristotle StThomas Hoenen motion i e not only local motion but also any continuous change is not being but becoming and it is apparently supposed that becoming cannot be further analyzed it is a fundamental concept Indeed by introducing this additional type of reality ingredient namely becoming i e dynamic being the essence of the continuous is metaphysically established and forms the kernel of the solution of the problem of motion as proposed by HOENEN Whatever the value of this solution will turn out to be there is as indicated earlier yet a second possible solution of this problem a solution based on the supposed discreteness of space and of motion and of time II TIME Introduction For the nature of time especially the argument in favor of its discrete structure see also part XVb of the present series at about the beginning of the 3rd third of the document Above was stated that time does not consist of indivisible moments and so refuting Zeno s argument And indeed when these moments ar infinite in number then any period of time cannot be traversed But if these ultimate indivisible moments are supposed to be non zero moments moments having a duration but nevertheless indivisible then a finite amount of time will not be constituted out of infinitely many such moments but out of finitely many And then such an amount of time can be traversed In our considerations of motion repeatedly and automatically the notion of time popped up a sign that between these two concepts there must exist an intrinsic connection So it is natural that we now focus our attention to time Difficulty of the problem The treatment of time has been described already from early on in the history of philosophy as a work of thinking bringing with it harder difficulties than those concerning other problems The existence of time was then considered as something that was utterly clear also to the man in the street But if one arrives at the question what is time then difficulties pile up even for the wise among the wise Well known are the words of Augustinus Roman patristic philosopher 354 430 A D With what are we more familiar and what is better known in our conversations than time And when we speak about it we do isn t it understand what we say and we also understand things when we hear others talk about it So what is time When nobody asks me I know it When I have to explain it to someone who asks about it I don t know Nevertheless I can confidently say that I know that if nothing went by there would be no past and if there were nothing coming there would be no future and if there were and not had been nothing at all i e no beings at all there would be no presence Nevertheless Augustinus manages to give in the series of next chapters of the book from which the quotation was taken with suppleness of mind and in wonderful language an answer to the indiscrete question of the what of time The difficulty is in the end the same as what we encounter so often in philosophy where it is about in the context of a well known set of ideas penetrating by means of precise analysis into the first concepts and data lying at the base of this set of ideas and finding a formulation of them In what comes next we shall chiefly follow the analysis of Aristotle who is working his way more sober mindedly and also more acutely than Augustinus and also chiefly accept his results Not because they are of Aristotle but because it appears to us the best analysis the only one that gives us satisfaction In certain points we shall add some corrections indicated by St Thomas Aquinas and will have to work out the theory still further such that it can give an answer also to modern formulations of the problem Time place space Apparently there exists an analogy between the ways of Being finding an expression in the ways of predication such as to be here or there and those other ways of Being which we express in words such as to happen now or then there is an analogy but not conspecifity For in all similarity there still exists a great difference between the first and the second group Evidently they belong to different categories of Being The first is to be at a place the second to happen in a moment of time What is meant by these expressions is immediately clear to anyone Analysis leading to acuteness of insight may however involve difficulties That precisely is it what Augustinus expressed above Real way of Being Both categories are apparently groups of real ways of Being Therefore we earlier had to find a reality which could fulfill the function of place The same we now have to do with the concept time Indeed it is immediately clear that a real difference in time is indicated when we say that the Flood happened before the Trojan war and the latter before the life of Aristotle precisely as a real difference is indicated when we say that Democritus was born in Abdera and Aristotle in Stagira Also we indicate a real difference by the words Aristotle reached the age of 62 years and he died in the year 323 before the beginning of our Christian Era We then indicate quantitatively the duration of a motion namely the life of the philosopher or the distance in time separating two events namely his death and the birth of Christ We here may insert a good preliminary characterization of time as contrasted with space taken from PETRONIEVICS 1904 p 131 where he already established that time is not some existing essence alongside real events In space we have a togetherness of things while in time we have an after each other of things This means that in space things or parts of space are given together and thus simultaneously and in time its parts are given only one after the another i e only successively What then is the essence of this after one another in contrast with to be together Because these relations are very simple i e not composed they cannot be reduced to more fundamental things and therefore they cannot be defined Only with respect to the way of existence which Being has in these relations they may be further distinguished and described Being i e the things that exist is in the pure to be together at complete rest while in the pure after one another in perfect motion and change When parts of Being i e parts of Being in general are together then they are stationary when they are after one another they are in motion sensu lato or when they are together they remain unchanged when they are after one another they are changeable Rest and motion unchangeableness and changeableness are the two only possible states of Being which immediately connect with the two orders of to be together and after one another of Being Without rest the to be together without change the after one another is unthinkable and the other way around without to be together rest without after one another change and motion is unthinkable Topological and metric structure And thus we already immediately find in time a twofold structure First a real order the order of before or after or of simultaneity Then we find a measure for the duration of events or for the difference in the order of appearance how long before it how long after it This twofold structure we will in terms of modern mathematics call here the topological structure indicating the order of before and after and the metric structure providing a measure of the duration In a similar way we can in the case of static extension and place find a twofold structure but as will become clear later on in time the topological structure is deeper more essential than in extension or place Something extrinsic There is yet another thing that place and time have in common Earlier we established that place is something else than that what has been placed in it it is extrinsic to the placed And it was also clear that that what has been placed has in the extension of the place of its own place a measure Likewise in time The time in which an event takes place the time which is a measure for that event s duration taken topologically and metrically is something else than the event itself or its duration so again it is extrinsic place is extrinsic to the placed and time is extrinsic to the event That what is in this way determined and measured by time is of course intrinsic it is the event itself and the flowing duration of its existence Indeed to the question When and how long did Aristotle live one cannot other than joking answer he lived in the duration of his life The answer should involve something extrinsic to Aristotle s life something in which his life took place and this is the general time frame independent of the philosopher s life and the measure for that life it provides This precisely as we saw it also with place Time is thus something extrinsic to that what takes place in it and measured by it like place to the placed Imginary time Alongside the concept place we earlier have met in the same order of things the concept space as being an extensum a recipient which as one says would remain when the whole extensive world would be destroyed which recipient was already there before the world was created We have found out that space is not an existing essence not something existing on its own but a mere product of thought And so we had found out that the word space can at most be applied in one or another sentential connection to describe some other real thing connected with placing Only in our imagination there remains something when we expel the bodies in it not so in reality Something similar is also in our imagination with respect to time If we in our imagination expel all motion of real bodies then nevertheless irresistably the impression remains of a flowing continuum the time of our imagination However it will turn out to be a mere being of reason just like space No real entity whatsoever corresponds to that imagination So as we have alongside the reality place the being of reason space we have alongside the real time also an imaginary time It is pitty that we do not possess two words signifying the dynamic continuum to distinguish the real from the imaginary as we can distinguish place from space So we have a time which is the analogue of place and a time which is the anologue of space The latter we shall call the imaginary time Later we will mention a difference between both beings of reason space imaginary time But first we shall focus our attention to real time We thus know that time must be something real in such a way that the real content of sayings like this or that happened in that time so and so long before or after that other event and lasted so and so long is justified And time must moreover be something that is extrinsic to these events taking place in it We shall have to further determine the nature of time first as to its general nature and then also more specifically Topological structure of time Motion and time That time must be connected with motion was already clear That this connection must be intrinsic is evident from the fact that our mind in order for it to form the concept time must observe or imagine a motion local or otherwise This is shown by simple introspection Also the other way around If we conceive a motion then the idea of time will easily be formed So there is a connection One might be inclined to simply assume an identity between the two This would however take things too far Already because of the following reasons There are as we saw earlier motions of different kinds Each one of them may be the datum from which we read off the concept of time Not only local motion but also increase in quantity and qualitative change Time however is not multifarious But also motion in general is not identical with time After all motion is in the moved and thus is multiplied with it Not so time Two motions running alongside each other take place in the same time Also motions may differ in speed and one and the same motion may be accelerated or decelerated Not so with time which ever and ever flows uniformly which cannot however be objectively determined According to the theory of relativity the speed of time in some region depends on the strenght of the gravitational field in that region Perhaps the demonstration of the objective existence of absulute simultaneity in fact following from the theory of relativity itself and given in Fourth Part of Website part XXIX sequel 5 may force us to accept one single universal time But we still cannot determine whether this one universal time is accelerated or decelerated in some regions of physical space although it seems to us very improbable Let this for the time being be sufficient to establish a difference Complete insight must follow from total analysis Direction Thus time is not simply identical with motion but must nevertheless be connected with it We already established When we imagine a motion the concept time will often emerge in our mind To what then in motion must we focus our attention in order to arrive at this result Let us consider an arbitrary motion For convenience we take a local motion Time undoubtedly shares with motion the fact that it is a flowing continuum and this property it extracts from motion Motion in turn extracts its continuity from its trajectory traced out by the object being moved So in the trajectory we find the origin of continuity of parts which we recover in motion and in time They extract yet more from this trajectory Indeed the trajectory is not simply an extensum a line or curve It is a line with a direction It is not simply the distance connecting Athens and Thebe it is the path from Athens to Thebe Considering merely the static continuum the line the path then the path from Athens to Thebe is one and the same thing as is the path from Thebe to Athens it is the one path between both cities The two opposite directions are merely aspects of the same reality Things become different when we consider motion To go from Athens to Thebe is a different motion from that of going from Thebe to Athens So direction is to motion to the dynamic continuum more essential than it is for the static continuum To the latter the two opposite directions are merely two different aspects of one and the same thing while motions in these two opposite directions are different motions This distinction becomes yet even more fundamental in the concept of time Indeed motions in different directions are certainly possible but the idea of a reversed course of time is absurd So direction is certainly something very essential in that flowing continuum which is time Before we continue with HOENEN s text it is perhaps instructive to present in fact repeat a quotation with remarks from PETRONIEVICS 1904 p 134 who argues that time is not a continuum but a discretum If the parts of time in contrast to the parts of space are after one another and indeed they are as contrasted with the coexistence of the parts of space embodied in the extension of simultaneously existing material bodies then there can be no simultaneous parts of time i e only a single part of time can be really given For if more than one part of time could be given then they would no longer be after one another but coexistent because only that is really given what is given simultaneously in the after one another the past part is not given anymore while the future part is not yet given and only the present part the NOW part is given i e only the present really given part But if the one given part of time contained in itself parts i e if it were composed of still more simple parts we may ask whether these parts are coexistent or are after one another They cannot be coexistent because there is no coexistence in time only in space They also cannot be after one another because then they could not all of them be real always only one of them can be really given the others are past or future So in the one really given part of time there can be no still simpler parts it must itself be simple and indivisible In another part of this text p 136 PETRONIEVICS demonstrates that these last parts are really there and that they are not merely points in time but genuine non zero parts of time One might say that the above argument only demonstrates the indivisibility of the last constituents of time but that it doesn t show that there cannot be an infinite number of such indivisible parts in a finite amount of time these parts would then be points However in this one forgets that as soon as one admits a division of a finite magnitude into a first order infinite number of parts one then further has to admit in virtue of the same necessity the division of every such first order infinitely small part into an infinite number of second order infinitely small parts and so on into the infinity of all infinities and that one in so doing lets completely vanish the last indivisible parts of time because then there are no last parts which after all is so clearly demonstrated by the above argument From this it follows that a finite amount of time can consist only of a finite number of these simple parts of time implying that these simple parts have non zero size that thus time is not indefinitely divisible Further in yet another part of this text p 137 PETRONIEVICS shows that especially time because it is interrupted every time when a NOW moment subsides into the past and a future moment enters the present cannot be a continuum he does not consider the possibility of the dynamic flowing continuum as HOENEN does The present moment of time is the only one that is really given while the past moment is not anymore and the future moment is not yet How then one can speak of a continuous time when the essence of time is precisely to always consist of one part only The after one another necessarily excludes continuity because it completely excludes the simultaneous existence of the many time parts and as a result the after one another divides time into real parts of which always only one at a time is given The after one another as negation that past part is not this present part and vice versa and also this present part is not that future part actually separates one part of time from another implying that time cannot be a continuum Wherever in Reality there is negation and separation it is in the case of time where the one part is really removed by the negation and so only as being removed makes possible the appearance of another And how can it be precisely there where separation where breaking up into parts is so evident one dares to speak of a continuum Continuing with HOENEN s text again Before and after The notion of direction in a continuum has some consequences which are especially to time of great importance In addition to starting point and end point which are not two equivalent boundaries anymore there are intermediate parts and points in such a way that between two arbitrary different parts there exists an order On the directed line the one part or point lies closer to the starting point of the line than another The one part lies before the other or at the rear of the other the other after it or in front of it There exists a topological difference in rank order between all consecutive parts And to motion it is more essential than it is to its trajectory Reversal of order for the latter brings with it only a difference in aspect while for the dynamic continuum such a reversal means the origin of a new different motion And in a corresponding way time with its continuity takes over the topological order of its parts from motion but now this order is in such a high degree essential that reversal would be absurd To every two parts lying qua spatial position before and after on the trajectory do correspond in motion parts which are earlier and later in it So this order of earlier and later is something essential to time Indeed we have found something that is characteristic of time We asked the question to what must we focus our attention in order to let originate from the idea of motion the concept of time We find as reply we must focus attention to the topological order of the parts of a given motion according to the earlier and later of these parts This temporal order of earlier and later of the parts of a motion is determined and defined by the order of the spatial before and after of the parts in the directed trajectory which in turn is determined when the direction is given or equivalently when the trajectory s starting and end point are determined Indexing of motion So in order to apprehend the concept of time the mind must focus its attention to the natural topological consecutivity of the parts of a motion It must discover a first second third etc part and must discover in each of these parts in turn a same consecutivity of sub parts a first second etc Thus we can with Aristotle say In order to arrive at the concept time the mind must discover in a given motion the natural disposition towards an indexing corresponding to the consecutive i e to the earlier and later parts being objectively present in the motion Time will be something like a possible indexing of a given motion according to its topological structure Aristotle used to express this the word arithmos of which the general translation reads number This English word is however little fit to express the idea of the philosopher Four and five are numbers Time is not a number Time is much more a system of numbers namely of numbers which first of all but not exclusively so as we shall see are ordinal numbers or indexes the first second third etc After all it is about a topological structure Such a system is better described by the word system of indexation or indexing And then with the number or numbers of this system abstract numbers are not meant numbers that is which only exist in the mind but concrete numbers i e the system of multitude of consecutive parts insofar as they are fit to be indexed according to the series of consecutive numbers Hence the other expression of Aristotle time thus is not simply motion but motion insofar as it can be indexed A possible indexing is like a possible observation So time can be observed by means of indexing Therefore time remains a continuum that a series of abstract numbers can never become After a chief indexing of parts each one of these can be subdivided and according to the consecutiveness of the resulting sub parts be indexed and so on and so on This is expressed in technical terms by the scholastics time is not numerus numerans i e an abstract number by which we count but a numerus numeratus i e a concrete number or a multitude which has been counted indexed If we realize all this then the solution of a difficulty brought against Aristotle s theory becomes easy One says If time is an indexing it cannot exist in Nature independently of an observing and counting mind After all only the mind can count can index The indexing can only exist in the mind at least not independently of it The solution is evident If in the definition to be set up of time and if with indexing were meant abstract numbers the difficulty would be unassailable They can only exist in the mind But the indexing of motion is concrete as is especially evident in cyclic motion Moreover time exists independently of the observing mind because indexing which is necessary and sufficient is not an indexing that is actually executed this would demand the work of the observing mind it is merely a succession of parts bringing with it a possible indexing And we add whose indexing is already indicated by facts in Nature itself such as the daily motion of the heavens of which the individual complete revolutions are indicated by the passing of a same star through the meridian of a same location That the mind must focus on this succession as possible indexing in order as we described above to extract the concept of time from motion presents no difficulty Of course this concept as concept depends on the mind and exists in the mind Might someone think that this result of our analysis which views time as an indexing or a system of concrete numbers would stand rather far away from the ordinary notion of time in daily life as it is not analysed living in humans then he should think of the answer that we return to a question when a question as to a certain time To the question when did St Thomas Aquinas die the answer is on the 7th of March 1274 It surely is a question as to a certain time when And the answer is nothing more than a numeral a number an ordinal number from the indexing of a certain motion That motion is the daily motion of the heavens of which each revolution one day is indicated by one of the consecutive ordinal numbers while groups of days are united into months and years It will be clear even more if we formulate the answer as we do when writing down the date in a letter 7 III 1274 This certainly is a pure number indicating the time Metric structure of time Introduction Time not only has a topological structure but must also possess a metric structure Time also serves as a measure of the duration of motions and of the distance in succession of events We not only say that Vondel lived in the Golden Century but precisely from 1587 1679 and these numbers give a measure of the duration of his life rendering it comparable with others We not only say that Shakespeare was born before Vondel but precisely the one in 1564 the other in 1587 And again with these numbers we have a measure of the distance in succession of both events The actual indexing of a motion which as to the topological structure of time only has to satisfy the condition that later parts obtain a higher ordinal number will moreover have to be such that from the difference in ordinal number the duration of the motion between these numbers can be read off The most simple case is then that equal differences in number correspond to equal parts The indexing not only representing a system of ordinal numbers must also obtain cardinal value meaning that in indexing of a motion to obtain time we not only have to do with a succession of the indexing numbers numbers in every step increasing by one a unit resulting in these numbers to express their ordinal aspect but also have to do with quantities arithmetic quantities obtained by addition or subtraction of any of the indexing numbers And while the ordinal aspect of these numbers express the topological structure of time the cardinal aspect of them expresses its metric structure and thus allows to determine measure temporal duration and distance in succession Equality of duration But when precisely is a duration equal to another or longer or shorter than it In a few cases this is immediately clear Suppose two motions are carried out together i e parallel to each other They start and end simultaneously The duration of both is equal they take place in one single identical part of time Here not any concept also not that of simultaneity with which we will deal later is not immediately clear But what if they are carried out after one another or if we enquire into the duration of two successive parts of one single motion The first attempt for a solution would be this one The motion derives its continuity as to its parts from its trajectory A division of the motion also when it is not interrupted can only be accomplished by dividing the trajectory Well let us assume that equal parts of the trajectory correspond with equal parts of duration and so with equal parts of time But then we run into troubles and even into contradiction Suppose a case like the one just given but then such that in the beginning one body lags behind the other one but catching up again precisely at the end point Initially one motion is faster later the other is If we now want to divide this identical time the identical duration of the two motions into equal parts by dividing the trajectory into equal parts and then transpose this division onto the motions and thus indexing them the we obtain from both operations contradicting results At least one of the two motions was accelerated decelarated maybe both not uniform So this attempt to define equal parts of time is incorrect It will have to be amended Uniform motion One might think to amend things quickly maybe too quickly A uniform motion must be taken one will say And then equal parts of the trajectory will correspond to equal parts of duration and thus of time And in this way one has a definition of equal parts of time This is certainly true but one should be careful After all then one can and should ask What is a uniform motion And one could be inclined to come up with a very common definition from elementary mechanics which reads motion is uniform if in arbitrarily chosen equal parts of time equal distances have been traversed But if one then defines equal parts of time with the help of uniform motion we need equal parts of time again So we have to arrive at a sharp concept of uniform motion in some other way because this concept is prior to the concept of time like the concept of motion is prior to that of time Correct definition of uniform motion This is indeed possible We began our analysis with the consideration of two bodies which simultaneously started their motion and simultaneously stopped it To this we shall now add bodies that always remain together i e in their motion the two bodies remain at rest with respect to each other Evidently such a case is possible Let us call these two motions congruent It is also immediately evident that these two motions may be performed after one another that two congruent motions after one another are possible The only difference with the first case is then in that case it could easily be observed that the motions are congruent In the second case such an observation such an empirical finding already presupposes an entire theory and a knowledge of natural laws But that is besides our point In our present discussion it is not about observation but about certain concepts and these are clear The possibility of the second case derives from the fact that the successive continuum just like the static extension is what one calls a principle of individuation In this sense it is immediately clear that a figure which is here in some extensum realized could also be realized in exactly the same way in a different extensum or in another right part of the same extensum which may when needed be expanded meaning that congruent figures can exist Such figures only differ as to their position differing purely individually purely numerically This is what one means when saying extension is a principle of individuation This is

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    too can appear to be a very recondite and mysterious statement but in fact it is saying nothing more than that things tend to happen in the most probable way there is simply a greater probability that things will become disordered than the reverse The Second Law is therefore actually a statistical law which does not prohibit absolutely the possibility of a change that induces a decrease in entropy but says only that such a change is overwhelmingly unlikely when we are considering huge numbers of molecules because these admit of many different configurations and most of them are disordered Uphill or downhill Although the Second Law of thermodynamics provides a universal arrow for specifying the direction in which change chemical or otherwise will occur it is not actually of very much practical use to chemists The problem is that the Second Law considers only the entropy of the entire Universe which as you might imagine is not an easy thing to measure In order to predict which way a chemical reaction will go we need to know not just how the entropy of the reactants differs from that of the products but also how the heat given off or consumed changes the entropy of the surroundings How heat produced in a reaction changes the surroundings is hard to establish in detail it will depend on the nature of the surroundings themselves But fortunately we do not need to worry about these details the entropic effect of heat dished out to the surroundings depends just on how much of this heat there is If the loss or gain of heat by the chemical system is accompanied by a change in volume if a gas is given off for example this also has an effect on the entropy of the surroundings When there is a volume change of this sort the chemical system is said to do work on the surroundings this work can be harnessed for example by allowing the change in volume to drive a piston and this work must also be taken into account in determining the total entropy change We can therefore determine the direction of a chemical change as specified by the Second Law on the basis of just the change in entropy of the reactants the amount of heat consumed or evolved and the work done on the surroundings All of these can in principle be measured Willard Gibbs expressed the directionality criterion in terms of a quantity called the Gibbs free energy which quantifies the net effect of these various contributions on the total change in entropy during the transformation The Gibbs free energy represents the balance in the bookkeeping sense between the change in entropy of the system and the change in entropy of the surroundings The latter is represented by a quantity called the enthalpy which is the sum of the heat change due largely to the making and breaking of chemical bonds and the work done due to a change in volume A chemical reaction is feasable if there is an overall increase in entropy of the system and its surroundings the latter being an effective representation of the rest of the Universe This means that for example if the products have less entropy than the reactants this decrease must be more than balanced by an increase in entropy of the surroundings due to the heat given out or the work done via volume changes This translates into the rule that the Gibbs free energy must decrease Strictly speaking this is true only when the temperature and pressure of the system are held constant In phase transitions i e transitions from solid to liquid or to vapor and vice versa the temperature and pressure is constant if all has free play Under different conditions other kinds of free energy must be considered instead of that defined by Gibbs The change in Gibbs free energy therefore defines the downhill direction for the reaction i e its spontaneous direction In the same way that a ball is perched atop a hill will run down it thereby reducing its potential energy the value of which depends on the ball s height above the ground a chemical reaction will tend to proceed in that direction in which it loses free energy However not every reaction will spontaneously take place when the above thermodynamic conditions are met I mean that these thermodynamic conditions are still incompletely described The vast majority of chemical reactions that are downhill processes turn out to be hindered by a barrier that prevents them from occurring at least at any significant rate What determines the feasibility of the reaction is the thermodynamics considerations of enthalpy entropy and free energy But what hinders the reaction from proceeding is the so called kinetics of the transformation The initial step of a reaction is generally an uphill process energy must be supplied to overcome the initial peak of free energy So here then were sketched the main thermodynamic settings that determine whether a chemical reaction and any other macroscopic transformation is possible in principle and in what direction it will go Of course first and foremost i e before even thermodynamic conditions are going to play a role the products of the reaction must formally be derivable from the reactants tin and chlorine atoms will not combine to iron carbonate or any other compound not containing tin and chlorine even if these products have lower free energy as compared to the reactants tin and chlorine Further it is also known that many complex chemical compounds cannot directly originate from their corresponding elements but only through a number of intermediate stages because the product does not formally derive uniquely from the reactants a larger but defined number of carbon oxygen nitrogen and hydrogen atoms may formally combine into a large number of ways resulting in different possible species of molecules But apart from these formal demands it is the thermodynamic conditions that determine feasability and direction of any chemical transformation So thermodynamics can teach us about all at least macroscopic changes in the World It determines what Substances do exist here and now there and then It describes the dynamics between volumes of Substances be they volumes of atoms or molecules On the other hand though the discussion of the present document is about Substances as to their static aspects only It enquires into the general nature of the constitution of material things and decides upon whether these material things are aggregates physically defined Substances or metaphysically defined Substances So it is about the formal physical and chemical relationships between the elements among themselves of some already presupposed total of them and between these elements and that total Or said a bit differently we here following HOENEN investigate already existing material things as to the nature of their composition And in this no thermodynamics is involved III ANALYSIS OF ATOMIC THEORY Introduction The problem that we investigate concerns the constitution of inorganic materials Are all composed materials in the inorganic world all mixta in a broader sense merely aggregates in which the components remain substantially unchanged i e remain to exist actually as it is in a mixture of sand and sugar or also in an externally homogeneous mixture such as air or do there exist among the composed materials also ones that are not merely an aggregate of components but a totality i e a substantial unity a mixtum perfectum in which thus the components exist only virtually materials whose becoming from and disintegration into the compoments are substantial changes For HOENEN the only alternative for something to be an aggregate is for it to be a Substance metaphysically defined He does not at all distinguish between 1 a purely physically defined Substance a constant and repeatable qualitative quantitative pattern which as such allows for such a Substance to consist of several other Substances forming such a pattern but without resulting in an absolute unity and 2 a metaphysically defined Substance which is an absolute unity one single ens and therefore not consisting of other such Substances and thus one Substance of which the components must exist merely virtually Here there are several problems that do not necessarily demand the same solution The problem of the chemical compound as to its chemical elements the problem of the atom of these elements as to its smaller components and the problem of macroscopic inorganic bodies crystals liquids and gasses For if the molecule of a chemical compound is one single Substance then also as to macroscopic bodies the question must be asked whether they are aggregates of molecules and so actual multiplicities of Substances with merely accidental unity or that among them there do exist substantial unities totalities rendering the constituent molecules totalities virtual In a physically defined Substance its unity resulting from the coexistence of spatially contiguous constituent Substances may either be accidentally but then it is not a Substance at all but an aggregate of Substances or that unity is not at all merely by accident but per se It is so for example when it is the necessary result of some definite dynamical system and certain initial conditions It is then a physically defined Substance which as has been said HOENEN does not consider The problem of the chemical compound should first of all have our attention Classical atomic theory of the 19th century thought to have solved this problem definitively already long before the end of that century According to this solution the chemical compound every molecule was nothing else than an aggregate of the chemical atoms actually existing in the molecule being held together into one single not necessarily static whole by mutual attraction It classical atomic theory in addition held that the chemical elements were true elements not divisible anymore true atoms It had as Prout had them its suspicions but no proofs as to the contrary That the chemical compounds could not be anything else than aggregates classical atomic theory had a priori assumed as told earlier because it departed from the mechanistic view of Nature In virtue of its principles it had to view all change and thus also the generation and destruction of a chemical compound as a purely local displacement of particles Giving up the Cartesian theory of the infinite divisibility of matter those particles had to be the atoms That s why all these theories had a democritean slant So the chemical molecule had to be the aggregate of atoms But during the course of the 19th century this philosophic fundament of science seemed to be confirmed very reliably by the truly wonderful results of classical atomic theory Indeed the latter consisted of a series of specifications all the time specifications of the general democritean principles These specifications indeed showed evident from the remarkable success they had the nearest causes of the phenomena for whose explanation they were assumed And because the specifications turned out to be true also the general principles of which they are specifications had to be necessarily true Hence the conviction of classical chemistry that compounds were just aggregates of atoms of the elements the conviction that this was sufficiently proved by classical atomic theory But nevertheless one was forced to introduce corrections but initially these didn t seem to affect the essence of the theory Indeed the chemical elements turned out not to be true elements the chemical atoms not atoms Earlier we heard Poincaré about it Now this wasn t yet a definitive failure for Democritus It merely was a shift of the problem toward smaller components than chemical molecules and atoms but and this is what was meant by Poincaré it precisely took place at a time at which also doubters of the success of Democritus became convinced Now the next problem had to be solved Is the composed atom of the chemical elements a totality in which then the components exist only virtually or is it in its turn an aggregate of its components So the composed nature of the atom does not yet necessarily bring with it the fiasco of the mechanical view of Nature Maybe only the displacement of the limit of its smallest particles Hence the attempts to continue along the spirit and methods of classical physics and constitute the chemical atom from its components more or less like the solar system from a central body and planets Precisely here the famous crisis of the mechanical view of Nature and thus of classical physics broke loose a crisis provoking the words of Bavink 1935 Darüber sind sich jedenfalls heute alle genaueren Kenner der modernen Physic mit wenigen Ausnahmen einig dass der alte primitive Substanzbegriff i e the substantially unchangeable matter nicht zu halten ist Leider können wir wie schon bemerkt nur nicht präzis heute sagen was an seiner Stelle zu treten hat Das soll ja noch erst herausgefunden werden Translation At least today all experts of modern physics with only a few exceptions agree that the ancient primitive concept of substance cannot be accepted Unfortunately today we as remarked earlier cannot yet say precisely what should replace it This has yet to be determined Now we think that it need not be determined anymore which theory should replace the mechanical view of Nature This view collapsed as Bavink describes correctly because its fundamental demand of the intrinsic unchangeableness of matter now also as Substance turned out to be false Then it must be replaced by the theory having proved the possibility of such a changeability having discovered the conditions that have to be satisfied by a substantially changeable matter the theory of Aristotle But also as to this theory one must enquire whether its general principles can also be specified satisfying the demands of the new and sophisticated experience Demands that could not be satisfied by the mechanistic view of Nature But the crisis does not remain to be limited to atoms only It also affects apparently definitive results obtained earlier Also the molecule of the chemical compound seems not to be as the mechanical view had it a mere aggregate but a totality also here the mechanical view seems fo fail In these discussions it is interesting to realize what precisely is the consequence of abandoning the mechanical view of Nature Does it imply the giving up of the reductionistic view of Nature i e is the philosophy of reductionism deriving the whole from its parts or equivalently reducing the whole to its parts identical to the mechanistic view of Nature Apparently it is And what then must take its place Apparently it is the philosophy of holism in which the parts are derived from the whole Indeed in aggregates the whole derives from the parts and also in physical defined substances the whole ultimately follows from the initial conditions of the dynamical system generating that whole and of course from the dynamical law of that system So also here the whole has a derived status i e derived from its elements according to the dynamical law connecting every two consecutive system states So if indeed non mechanical means holistic then as to at least atoms we have to do with true totalities i e Substances in the metaphysical sense In atoms it will be the necessary imposition of quantum conditions that turn the atom into a non mechanical object And indeed at least many of the properties of the electron often being a component of an atom can only be understood from the whole the atom of which it is a part So especially the amount of energy an electon can have at all is determined by the discrete energy levels of the atom and these energy levels are a direct consequence of the imposition of the mentioned quantum conditions So we have the following implications quantum conditions holism quantum conditions non mechanical constitution holistic constitution And if all this is correct then also molecules are true totalities Substances in the metaphysical sense because at least covalent chemical bonds between atoms of a chemical compound demand quantum conditions But we sometimes have the impression that many physicists and chemists do not detect the influence of the crisis in this problem the status of molecules and in line with classical atomic theory keep assuming the actual presence of atoms in molecules This attitude is understandable First of all remains valid to them what Bavink has said One doesn t know what has to replace the mechanical view of Nature And this is because virtual as opposed to actual presence of elements in the mixtum is unknown to them And secondly the wonderful results of atomic theory in its explanation of chemical compounds will of course definitively remain valid No error is detected in them The case is analogous with the undulation theory of light The periodic nature of light experimentally proved so well has not disappeared after one came to realize that it was no periodic change of place periodic local motion but a periodic change of quality Atomic theory contains like classical light theory true elements The only thing to do is to separate them from the superfluous and as follows from the crisis separate them from false elements So there is good reason to also subject classical atomic theory to an enquiry with the help of the principle of elimination of superfluous elements with the well based expectation that the specifications which as nearest causes of phenomena could explain so much can be taken up into a new non mechanical theory These specifications by which the classical theory had so much success will then not have to be sacrificed Also here the crisis will not cause ruins In order to introduce the Aristotelian theory also in the case of the chemical compound as a true mixtum we will have to demand that the general aristotelian theory is able to take up the specifications having caused the success of atomic theory In the investigation of this problem the aristotelian principles of natural minima and the principle of the heterogeneous virtual conservation of elements already making up the first specifications of the general principles will be further worked out by the application of the modern exact quantitative experience See here then what we must investigate in this analysis of atomic theory Atomic theory as an explanation of the stoechiometric laws The term stoechiometric may also be written as stoichiometric We must find the point of departure of classical atomic theory in the explanation it could since Dalton at the beginning of the 19th century offer of the stoechiometric laws especially of the laws of weight which we shall mention in due course We begin with a short consideration of the earlier discovered law of weight Lavoisier s Law of the conservation of mass Law of Lavoisier We may formulate this law as follows The mass of a given chemical compound is equal to the sum of the masses of the composing elements This law is as especially follows from the investigation of Landolt in such a high degree exact that experimentally no deviation can be detected Certainly the thesis of the theory of relativity that energy brings with it mass has cast doubt as to the absolute correctness of the law indeed in the case of a compound i e its generation or disintegration generally there will be a heat effect and thus import or export of energy but this deviation is surely in all cases too little to be directly detected experimentally And what is more this deviation if there is one is of no influence over our analysis to come Already in this law one saw a demonstration of atomism with this word we will in what follows refer to the atomic doctrine in democritean sense i e a doctrin supposing that the atoms are necessarily actually present in the chemical compound a demonstration of the actual continued existence of the atoms in the compound The proof may look like this in line with the physical theories We suppose atomism to be the fundament and derive the law from it Then the generation of a compound is nothing else than a change of place of atoms Change of place one assumes does not entail a change of mass So the mass will remain constant in the generation of a compound This proof is without value because of two or three reasons First it is supposed that mass does not change during change of place also not in atoms approaching one another Now if one precisely knew what mass really is it might be a reasonable supposition Now it is pure hypothesis One may call it a probable hypothesis which it is for us but it remains a hypothesis So there is no proof unless one demonstrates that it is the only hypothesis Of course one may proceed reasoning the other way around From the law experimentally follows that the approaching of atoms towards one another does not cause a change of mass but this cannot form a link in this proof This brings us to the second and third objection against the claim that Lavoisier s Law proves atomism the thesis of the actual continued existence of the atoms in the compound A similar hypothesis can be set up on a cartesian basis which has to deny the existence of atoms as a result of the indefinite divisibility So the constancy of mass also when displaced cannot form a proof in favor of the atomic theory But this is yet the lightest objection for one cannot derive anything from it even favoring mere mechanicism in general Indeed also in the Aristotelian theory i e if we suppose that the elements are not actually present in the compound an equally probable hypothesis can be formed from which also does follow the conservation of mass and even more than one hypothesis here we give one Because mass is something that is found in all ponderable bodies a property of the genus i e all species of mass possess this property namely the property of being present in all ponderable bodies it is natural to suppose that it is a property coming forth from a common principle of all ponderable bodies That principle is prime matter only So where there is the same prime matter we can expect equal masses If our earlier hypothesis of the originally passive nature of mass is true then we have yet another reason to derive this property from prime matter But at the transition from elements into a compound the same prime matter remains So from this the Law of Lavoisier immediately follows And thus is this law compatible also with a non atomistic theory From the hypothesis we made this law follows just as well as it follows from the hypothesis mass of moving atoms doesn t change implicitly held in atomism And here we thus see an experimental confirmation of the thesis that also in substantial change the mass remains the same Also in generation and corruption of living beings no change in mass has been established So we may safely conclude Lavoisier s Law does not favor mechanicism in a higher degree than it favors a theory viewing the generation and corruption of chemical compounds as substantial change Laws of proportionality So classical atomic theory of the 19th century has its point of departure in the other stoechiometric laws of weight In chemical textbooks usually two are mentioned viz that of Proust i e the law of constant proportions or of constant composition and that of Dalton i e the law of multiple proportions If the same quantity of weight of a given element combines with different amounts of some other element then these different amounts relate to one another as a proportion of small whole numbers See Van MELSEN Van Atomos naar Atoom 1949 p 133 4 To these we must add a third of which that of Dalton is just a special case Ostwald calls it the law of the weight of compounds Elsewhere we had called it the law of proportional numbers We may formulate it One can attribute to every substance in the chemical sense not only to elements a proportional weight of compound having the following property all chemical reactions proceed in such proportions of mass or weight that these can be expressed by the weight of compounds or by small whole multiples of them Closer characterization of the laws First of all we must note that here it is everywhere supposed that we have to do with pure substances substances in the chemical sense or after Ostwald with hylotropic substances about which one may consult textbooks of chemistry To one point we direct our attention the determination of these substances depends on purely experimental criteria independent of any theory the complication which the existence of isotopes brings with it does not need to be discussed here It does not mess up the theoretical picture of our analysis The law of constant proportions is a purely experimental law Some among which Ostwald 1904 have tried to deduce it Others seem to be of the opinion that it is en empty tautology a determined compound has a determined composition And this of course also holds for every mixture it holds even for every physical body such as a watch otherwise it wouldn t be this particular thing The meaning of the law is this in the case of pure substances still in the chemical sense there does not exist a continuous or practically continuous series of compounds made up of the same elements and differing in proportional composition Precisely because of this the chemical compound sharply contrasts with the mixture the latter admitting practically continuous differences in composition This we cannot deduce it is an experimental datum So if we have more than one chemical compound made up from the same elements and being not isomers then according to the Law of Proust they must differ abruptly as to their composition Isomers compounds consisting of the same elements in the same proportion differ only as to their structure and they do so abruptly Now the Law of Dalton determines the magnitude of this abruptness this gap It is as to proportional composition always expressible by small whole numbers It will be clear to the reader that the second and third laws would carry no sense when the Law of Proust wouldn t hold Dalton would not be able to determine the magnitude of the gap if there weren t any gap And because the second law is a special case of the third a theory explaining the third law automatically explains the first two It should further be realized that these laws belong to the most exact laws we possess in the physical sciences Experimentally no deviation can be found If energy has mass or is in some sense equivalent to mass according to the relation E mc 2 there will be a small but experimentally undetectable deviation Also the existence of isotopes atoms with the same number of protons in the nucleus and thus chemically of the same chemical element but with a different number of neutrons in the nucleus forces us to a more or less sharper formulation except when one very strictly defines pure or hylotropic substances As was already said we may neglect this complication having no influence on our analysis Classical explanation of the laws by atomic theory For this explanation we could refer to textbooks of chemistry but usually there is a lack of necessary acuteness and sometimes even one cannot find there essential parts of the derivation Dalton to whose insight we owe the theory took as his point of departure the atomism of Democritus But this like other metaphysical theories provides general principles only from which we cannot deduce and thus explain the stoechiometric laws Such general principles must like in other theories be specified Dalton did this by means of adding two auxiliary hypotheses as specifications to the fundamental principles So this was the foundation of Dalton s theory Bodies elements as well as compounds consist of smallest particles Dalton called them atoms in the case of elements as well as of compounds If we for indicating both species of smallest particles use the common term m i n i m a then we further may call where needed according to modern use the minima of elements atoms those of compounds molecules So physical bodies consist according to Dalton of minima This is nothing else than the atomism of Democritus the point of departure of Dalton But he now specifies it by two auxiliary hypotheses The first auxiliary hypothesis is the minima of a same body have among themselves the same properties first of all the same weight The minimum of the one sort differs from the minimum of another again first of all as to their weight So the atoms of one and the same element are completely equal among themselves So also the molecules of one and the same compound And thus individuals of such a compound have a completely equal composition out of atoms of their elements And here comes the second auxiliary hypothesis of Dalton often overlooked although it is essential One single molecule of a given compound originates from consists of a small number one two three of atoms of elements and thus not from an arbitrary number of them that this number is a whole number is not a new hypothesis it follows from the ground thesis of atomism From the so specified atomism now easily follows the derivation and thus the explanation of the stoechiometric laws provided that the law of Lavoisier holds which we in the sequel always will tacitly assume We may limit ourselves to the third law because the second is just a special case of the third and the first the law of Proust constant proportions and composition is logically implied by the second and third The stoechiometric laws are so to say macroscopic They deal with weights of bulk mass of chemical compounds or elements And then the third law comprising the others is then derived from the assumed atomic nature of the elements i e it is derived from its supposed microscopic version For convenience this doesn t devalue the generality we limit ourselves to the generation here in the sense of constitution of an arbitrary compound from arbitrary elements Then we can formulate this third stoechiometric law as follows Any given chemical compound has a proportional weight of compound later to be its molecular weight and also the composing elements have each for themselves their proportional weight of compound later to be their atomic weight with this property the weight of compound of the chemical compound is the sum of the weights of compound of the composing elements as species making up the compound each multiplied by a small whole number one two three as for instance 2 with respect to O oxygen in CO 2 carbon dioxide See now then the derivation of this third stoechiometric law from the hypotheses of Dalton According to the first auxiliary hypothesis the minima of one and the same compound have an equal composition among themselves a composition out of the same atoms From this immediately follows because the atoms of one and the same element have equal weights a chemical compound in an arbitrary quantity has the same proportional composition as to weight as any one of its molecules has a So from the assumption of minima do indeed follow the known macroscopic data of weight of bulk matter From the second auxiliary hypothesis immediately follows one single molecule of a compound has a weight that is equal to the sum of the weights of the composing atoms each multiplied with a small whole number one two three b The assumption of molecules consisting of a small number of atoms implies a corresponding relation as to the weights of these minima and then also to the proportions of weight in the corresponding bulk matter So also here we have a derivation from assumed minima to known macroscopic facts about weight From a and b follows An arbitrary chemical compound has a proportional weight of compound and the composing elements each have their proportional weight of compound with this property the weight of compound of the chemical compound is the sum of the weights of compound of the composing elements each one multiplied by a small whole number one two three and this is nothing less than the third stoechiometric law applied to the proportion of an arbitrary chemical compound to its elements From the derivation follows that the proportional weights of compound of substances in the chemical sense do relate as do the weights of the individual molecules respectively atoms From this a method may be derived for a beginning of the determination of molecular resp atomic weights namely determining these weights relative to that of Hydrogen All this is very elementary Critical analysis of Dalton s theory Analysis along the principle of elimination We re now going to investigate Daltons s theory following the previously derived principle of elimination of superfluous elements After all it has entirely the structure of theories to which the principle can be applied So let us look for superfluous elements in the earlier defined sense The first specifying hypothesis that of mutual equality of the minima of one species evidently is a necessary element of the theory If we eliminate this then the above proposition a drops out The same holds for the second hypothesis that of small numbers it is a necessary element for the derivation of the proposition b Without it the law of Proust so characteristic of the distinction between chemical compounds and mixtures would not hold And so both hypotheses of Dalton are necessary not superfluous elements But if indeed both hypotheses are necessary the same must of course go for the fundamental assumption of which they are specifications and thus the minima must be real If the minima of one and the same species are necessarily equal among themselves and bound together in small numbers into one single minimum of a compound then natural minima must exist So the fundamental hypothesis is just as necessary and therefore many scholars saw the success of Dalton s theory as a confirmation of its foundation Yet we must take a closer look at it i e that foundation And then it turns out to be composed out of two elements Indeed Dalton proceeding from atomism not only supposed that matter is divisible into minima but that it is also always divided into minima his atoms also in molecules are always actual atoms his molecules i e his atoms of chemical compounds always aggregates of atoms And so we discover that to the fundamental hypothesis of the reality of minima this is the necessary element of the derivation that we have found a second one is added the minima of the elements do always exist actually And this addition is not necessary in order to introduce both specifying hypotheses of Dalton Is it a superfluous element To decide upon this we set up a hypothesis in the Aristotelian spirit that avoids this element altogether i e the supposition that the atoms do actually exist also in the molecule and instead supposes the opposite Then the whole theory reads the bodies are divisible not however indefinitely so but until certain minima divisible not divided Division takes place as we heard it above from Toledo at or also just before the chemical reaction So just before the chemical reaction actually starts i e is realized at all the bulk matter of the reactants be they elements or compounds divides into smaller and smaller fragments and ultimately into their corresponding minima During the reaction the minima unite

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    non mechanical system and thus a totality despite its computability Does on the other hand the combination not have these properties but instead of them other properties then it is proved that it is not an aggregate that the resulting property originates from a higher unity than that of an aggregate i e originates from a single Substance in the metaphysical sense from a single totality Then we have accordingly a new property in a twofold sense First as above in the sense that the property was not present in the individual components and that it could not be there unless as an effect in the cause by this HOENEN might mean something like unless as enfolded in the dynamical law producing the substance from initial conditions and second in the more decisive sense that this property is in addition a different one different from the one that would result from a combination of the same components which is a true aggregate Additive properties but also aggregation resultants are not actively generated by a dynamical system but result only passively from the multitude of constituents A new property in the first sense we will call an aggregation resultant while a property which is new also in the second sense will be called a totality resultant Examples of constititive properties of a system of components properties that are aggregation resultants we had found earlier the tone of an organ pipe the revolution of a planet Orbit and period of revolution of a planet can after the fact be seen as a summation of the motion of the composing particles and is thus an aggregation resultant the pressure of a gas the blue color of the sky Also the refractive index of a liquid must be one of them The next sentence of HOENEN s to come was meant to give an example of yet another constitutive property but now one of which it is at the present point in the discussion not yet decided whether it is an aggregation resultant or a totality resultant The color of a chemical compound But because this example is according to me not very instructive I have chosen another one another constititive property which also HOENEN will use later on namely the line spectrum of hydrogen The line spectrum of the hydrogen atom also is a new property The above developed consideration about true constitutive properties can be applied also to it With this and the like properties the problem is Are they aggregation resultants or totality resultants If the first is proved then the compound is an aggregate If the second is proved that is if they differ from aggregation resultants then the compound is a totality a new Substance in the metaphysical sense So here we have discovered a true criterium of totality i e a means to distinguish totality resultants from aggregation resultants and thus to distinguish totalities from aggregates And at the present stage of the argument it is not yet shown that true totality resultants do exist at all In our discussion we have often said that atomism if the compound chemical or otherwise is a true aggregate must explain the stability of that compound as an equilibrium resulting from the forces applied to one another by the components The aggregation must in order to have that stability find its lowest energy configuration Here we see that this is a special case of a more general demand Atomism must be able to derive the new properties of the compound as aggregation resultants they may not be totality resultants In addition to the problem of unity of the compound there was the problem of novelty of properties Here the means to solve these problems unity novelty turn out more or less to coincide which is not surprising because they are aspects of the same problem that of the chemical compound the unity resulting from the specifically many Indeed if the properties of a mixtum are true totality resultants then they come from one single totality one new Substance False method of solution One should not think that the decision has already been made in the rules according to which one in organic chemistry lets correspond certain atomic groups in the structural formulae with certain properties of the materials One could already in the 19th century especially regarding the color and thus the absorption spectrum couple certain coloric properties to certain structural elements But with these constitutive properties matters are the same as in the additive properties discussed above One considers the groups always as existing in a molecule instead of considering the free groups The results apply to virtual as well as to actual groups These constitutive properties are properties that evident from observation go in a number of different molecules together with the same structural elements i e correspond to these structural elements and are equally influenced by neighboring elements from which at most may be derived the following conclusion If the constitutive properties in the one compound are aggregation resultants then also in these other compounds If they are in the one compound totality resultants then also in the other which one may safely assume by reason of the complete analogy of these compounds anyway And the issue here is still whether a given constitutive property is an aggregation resultant or a totality resultant In classically viewed structural theory the new constitutive properties necessarily had to be aggregation resultants with which it was thus demanded to detect properties of the individual atoms if need be introduce them hypothetically such that from the stable aggregate of these atoms as a molecule resulting from these properties the new property can be calculated This in order to be in line with the classical ideas should not hold for just one particular case but for all relevant cases An attempt to accomplish this should seem to be hopeless and this certainly contributed to doubt the reality value of atomic theory despite the wonderful results of the structural theory of chemistry in general The probability to obtain result indeed was rather too small Under this sceptical or desperate mood there would have been no necessity that the structural theory itself would suffer and even doubted if one would have been provided with the elaboration of the peripatetic theory leading to virtual atoms bringing with them the possibility of constitutive properties that are not aggregation resultants but totality resultants True method The investigation into the constitutive properties constitutive because the additive is about atoms or atomic groups that are already taken up into the molecule i e present in it virtually or actually be they aggregation resultants or totality resultants must bring the decision And it came when one first learned to investigate simpler cases For this one then has to know the properties of the individual components the free atoms or their parts and from them try to derive the new constitutive properties of their compounds First of all this solution was found in the chemical atoms themselves after having found out that these were not genuine elements not true atom but composed and divisible systems So then to the problem of the chemical compound discussed until now another problem is added that of the composed chemical atom The solution totality or aggregate doesn t need to be the same It may be that the molecule of the chemical compound is an aggregate and the composed atom not Before we consider the recent development of atomic theory here the structure of the atom we first must review what has been treated so far because this contains all what was known in the 19th century in classical theory and could be used to solve a problem which after sceptical and energetic tendencies had vanished was taken as to be definitively solved in an atomistic sense In natural science a possible aristotelian solution was certainly not considered one even had no inkling of it Retrospect and outlook Here as has been said an overview will be given of that what has been treated so far The very possibility not yet the actual existence of the chemical compound as a true totality metaphysical continuum has now been established and also its criterium And only after this overview in the next main Section The modern theory of the atom and its consequences the solution of the question whether there exists also in the inorganic world true Substances in the metaphysical sense will be formulated It will be found out there that for atoms as well as for molecules the necessary introduction of quantum conditions into the description of them will hold the solution every free atom and every molecule is a totality a true Substance in the metaphysical sense because these quantum conditions render them to be non mechanical composites In molecules the constituent atoms will be there in the form of qualities of the molecule meaning that these atoms in the molecules are not self contained beings anymore but grade with their electron clouds into their molecular environment i e grade into the other atomic constituents of the molecule Overview In bird s eye view we have seen the wonderful results having been reached in nineteen century atomic theory As to its classical interpretation it has originated from the atomism of Democritus and it consists of a series of still further developed specifications of this philosophy These specifications embody theories that in each case give nearest causes of newly discovered phenomena and laws In this lies the explanation of the success of this atomic theory Indeed in virtue of its specifications it can deduce a vast number of known facts from its premises and predict others and thus explain these facts After all they derive from the causes assumed by the theory It is true that the original philosophy of Democritus had to undergo many and drastic changes One had to accept the equality of the atoms of the same chemical element by which an essential principle of Democritus demanding all possible sizes and shapes of atoms had to be abandoned Further the forces expressed in the chemical compound cannot in any way be just the collision forces of strict mechanicism And one had to accept a continuum as carrier of electromagnetic and gravitational fields i e one had to abandon the notion of empty space as the medium of atoms assumed by Democritus Finally atoms as purely geometric elements are not sufficient qualitative ones had to be accepted Yet in classical theory one element of atomism apparently remained unaffected namely the supposition that the atoms are always actual that the chemical compound is an aggregate not a totality And thence classical theory is atomistic thence its successes were seen as a victory of atomism We have successively investigated the whole theory in all its parts including its atomistic principle And the result was that all the specifications expressions of nearest causes of the phenomena from which causes the latter originate had to be acknowledged as necessary and thus had to be accepted But only that one principle the atomistic principle rendering every chemical compound to be a mere aggregate and excluding it being a totality turned out again and again to be superfluous in all cases In this investigation we did not focus on the metaphysical origin of this principle only on this one question what elements of classical theory are necessary to derive the results what elements are superfluous A purely logical criterium And in this investigation the democritean element actual atoms in molecules turned out to be completely superfluous Our method was this one Everything classical theory explains could also be explained in a system viewing chemical compounds as continua in the gasses and liquids the individual molecules in the world of crystals even whole crystals But these continua cannot physically be indefinitely divisible but only up to a certain limit the minima being among themselves the same for the same material It is in fact these minima which are continua together often constituting an aggregate either of free atoms or of free molecules These minima must have a heterogeneous structure and surely a very determined one There must be heterogeneity according to properties in molecules corresponding to the chemical elements specifically to the individual minima of them in line with the demands of the chemical structural theories And because this continuum theory holding any molecule or any free atom to be a continuum in the metaphysical sense i e holding any molecule to be a single fully fledged ens explains everything that is also explained by classical atomic theory it is clear that the latter s atomistic demand of actual atoms in the molecule introducing discontinuity within the molecule is a superfluous element in classical theory which element thus according to the principle of elimination cannot obtain any confirmation whatsoever from the wonderful results having all over been accomplished by classical atomic theory But this purely logical analysis is still not sufficient A metaphysics has to be found such that its general principles allow themselves to be specified such that these continua become legitimate and intelligible We have found this metaphysics in the Aristotelian principles of prime matter and substantial form giving as general principles precisely the conditions to be satisfied by substances in the chemical sense in order that from several individuals entia beings may originate one single continuum one ens one being and vice versa and especially in order that from a body or from more than one a specifically different body or more than one may originate In this theory generally a chemical compound may be a totality having originated from different elements But do these principles allow to be specified such that precisely those continua are possible that above have been found to be necessary in an atomic theory taking chemical compounds to be totalities Indeed so we ve found the metaphysical principles of Aristotle allow them to be so specified We even didn t have to do anything else than to take up again the specifications already applied in Antiquity and Middle Ages after they were for a long time partly of even totally neglected to unite them to develop them and to test them against the rich results of modern theoretically elaborated observation The possibility of these specifications can be derived in abstracto from the general principles Their factualness was evident already in Antiquity and Middle Ages from experience and is confirmed by the new mathematical methods But these actual specifications for the time being only demonstrate the possibility within classical atomic theory of molecules to be true Substances We namely found the possibility of a potentiality prime matter which only allows itself to be realized in grades and steps so that it cannot directly be actualized to all substantial forms to which it is in potency but only as mediated by other actualizations For prime matter this is then confirmed experimentally because it is first of all in potency to the elements and only then to chemical compounds simple and more complex compounds These chemical compounds thus show genetic connection not directly with all but only with certain determined elements They also show mutual genetic connection linked to the first All this is expressed in the principle of virtual conservation of the elements in the compounds This conservation is nothing else than similarity according to their nature as principle of activity and passivity Genetic connection is just an expression a sign of that connection according to nature But with this kinship not in the usual chemical sense of the word but rather in the biological sense according to nature necessarily must go a similarity of properties between the compound and its elements and mutually between compounds containing the same elements From kinship by nature thus flows genetic connection as well as similarity of properties So these correspond to each other And thus all this is expressed by the principle of virtual conservation of properties of elements the conservation is virtual because now these properties have become properties of the compound These principles were known already in the Middle Ages Earlier we found a second specification which we clearly recognize as to be possible in aristotelian metaphysics and actually realized the possibility of heterogeneous and indeed in different ways heterogeneous continua Connecting both specifications we found the principle of heterogeneous virtual conservation of component properties in the compound Again in virtual conservation of component properties virtual refers to of component properties which properties have now become properties of the compound a principle that lets itself to be intensified as the equal principle of the heterogeneous conservation of element properties in the mixtum which in this way becomes a principle of specific heterogeneity This was as to its first part already worked out in the Middle Ages where only poor experience didn t find it to be realized in inorganic mixta A third specification was the by Aristotle already worked out principle of limited physical divisibility of material continua from which did follow the theory of natural minima equal minima for the same species of material and thus the principle of Dalton Finally we found the principle described by Toledo which together with that of Dalton makes possible a derivation of the stoechiometric laws The same principle of Toledo combined with the already derived principle of specific heterogeneity in element properties led to the principle of specific heterogeneity as to virtual conservation of atomic properties at least of nuclear properties or for heavier elements properties of nucleus and its immediate vicinity An with this aristotelian philosophy as specified by these principles has at its disposal continua that completely satisfy the demands of the crystallographic and chemical structural theories It has at its disposal as we can now succinctly say virtual atoms because it has at its disposal molecules as metaphysical continua Logical analysis told us following the principle of elimination that such continua completely satisfy all demands of modern experience with its described in physical theories nearest causes of phenomena Elaboration of Aristotle s metaphysical principles tells us that these continua are indeed possible This elaboration organically connects nearest causes with the first deepest intrinsic causes of bodies the material and the formal An aristotelian view of these theories surely is totally equivalent to the classical view All that has been explained in natural science in classical atomic theory up to the discovery of the composition and structure of the atoms themselves the investigation of which would lead to the bankruptcy of the mechanical view of Nature all this finds an at least just as perfect intelligibility in the aristotelian continua with aristotelian minima as virtual atoms All that From which it is immediately clear that one was wrong when one was by reason of the achieved results of the opinion that the problem of the chemical compound was definitively solved along democritean atomistic lines Still more does follow from it For if further development of atomic theory refutes the mechanical view of Nature then only this view of Nature falls and not any element whatsoever of classical theory which theory did indicate a true nearest cause of the phenomena is dragged along with this fall For by our results it is perfectly clear that precisely those mechanical elements of classical theory now these elements turning out to be false are superfluous elements Precisely as we found in qualities The theory insofar as it had explicative value and that was very high indeed was independent of those superfluous elements and thus will not be abandoned with them So there remain The atoms and molecules and the gas theory and the structure of molecules and crystals All these bodies built up from virtual atoms according to the structures patterns discovered by natural science Also here the collapse of the mechanical view of Nature does not bring with it ruins of physical theories Remark After the analysis of atomic theory explaining the stoechiometric laws we have noted that one also in education also in elementary teaching should not proceed as if Daltons s theory contained a proof of the actuality of atoms in the compound and thus the proof of atomistic atomic theory Even if based on later data actuality would follow the stoechiometric laws do not contain a trace of evidence for it The same we now must hold of the entire atomic theory insofar as it is developed up to the discovery of the structure of atoms insofar that is it describes the structure of molecules and crystals Also even here there is no trace of evidence of an atomistic atomic theory So also for this theory the logical Sauberkeit of scientific reasoning demands that the successes of the theory may not be put forward as evidence of the actuality of atoms in the molecule demands that the aristotelian continua with their virtual atoms must get their place in the whole discussion The more so when it has later in quantum theory turned out that the mechanical view of Nature must be abandoned Of course by all this the level of science will not be downgraded to the level it had at the time of Aristotle or in the Middle Ages Also here one should discriminate Aristotle has general metaphysical principles of natural philosophy He had first specifications of those principles He also had that after all is the task of natural philosophy explanations intending to penetrate into the last specific details the species specialissima These last explanations have now turned out to be full of error what is of no surprise when taking into account the still poor condition of experience and the lack of mathematical methods But let us not forget this was in no less a degree the case in Democritus as far as we know details it was the same in Descartes it was the same in atomists and cartesians even still far into the eighteenth century Their explantions in detail are not better than those of Aristotle or of the scholastics To call by reason of the errors of aristotelici their system of thought to be a failure and to reject their principles as a foundation for modern specifications scientifically is in fact funny In every system the particular explanations of the ancients have to be replaced by specifications demanded by modern experience and then see whether the fundamental principles allow them to be so specified And then in the end it turns out that only Aristotle s principles survive this ordeal Whereby we yet have discovered the remarkable fact that the first three general specifications of atomic theory demanded by modern experience were already found in the Middle Ages by the scholastics as elaboration of aristotelian principles We didn t do anything else than simply to take up again these principles to combine them and work them out still further Proceeding further Our long analysis of atomic theory now also has the advantage that the method to further work out our program to come to a solution of the problem of the inorganic mixtum has been automatically set up We have succeeded to develop a decisive criterium In every composite free atom free molecule crystal there are truly new purely constitutive properties The question now has become Are they aggregation resultants or totality resultants If the properties or a sufficient set of properties of individual components are known and the purely mathematical difficulties not too big the decision can be made for each case At the same time our attention was already focussed on one particular truly constitutive property very well suited to apply that criterium The spectrum the emission as well as the absorption spectrum of composites free atoms molecules crystals Moreover it is fortunate for us that science has automatically come to investigate meticulously precisely this so exactly measurable and familiar a constitutive property and that it has attempted to derive it as an aggregation resultant Not because it 20st century natural science had in mind the two possible solutions of our problem aggregates totalities reductionism holism the aristotelian one was rather and its specifications entirely unknown but because the development of science automatically demanded to derive this constitutive property the spectrum of the composite compound from the properties of the components and then naturally see it as an aggregation resultant It thus did nothing else than simply apply the criterium we had discovered And this is not coincidental Reductionism is by definition explanation also when the explanation is not yet complete And only when then automatically turned out that the spectrum is not an aggregation resultant ideas did come up viewing the composite as a totality again albeit of course that one didn t know that one in so doing introduced aristotelian ideas Albeit that one didn t know precisely because the aristotelian theory was unknown how to explain this totality But it is nevertheless remarkable that one only as a result of the natural development of physics came to think of the aristotelian totality idea Therefore it is certainly worth the trouble to present some utterances from pure physics So M Planck 1929 declaired Eins steht fest Der Rahmen der bisherigen Physik musz erweitert werden damit die neuendeckten Tatsachen darin Platz finden und wenn ich mich nicht irre wird diese Erweiterung in der Richtung liegen dasz hinfort ein Satz fallen musz den man bisher stets stillschweigend als selbstverständlich allen physikalischen Betrachtungen zugrunde legte Das ist der Satz dasz alle physikalischen Vorgänge sich darstellen lassen als eine Aneinanderreihung von einzelnen lokalen Vorgängen Die physikalische Welt ist nicht einfach eine Summe von räumlich und zeitlich nebeneinander gelagerten Einzelwelten und manche Erscheinungen entziehen sich dem Verständnis wenn man ein physikalisches Gebilde nicht als ein Ganzes betrachtet Translation One thing it is true is certain The framework of current physics must be broadened in order that the newly discovered facts can have a place in it and if I am not mistaken this broadening must extend along that direction where from now on a thesis must fall a thesis that one up to now always had taken tacitly as self evidenty underlying all physical considerations That is the thesis that all physical events can be taken to be a concatenation of single local events The physical world is not simply a sum of spatially and temporally positioned individual worlds next to one another and many phenomena are unintelligible if one does not consider a physical construct entity body pattern to be a whole For indeed all there is in explicate reality at least all existing material things are Substances in the metaphysical sense and thus are wholes Even aggregates ultimately are aggregates of Substances wholes Here it is very aptly described that it was precisely the mechanical view of Nature that tacitly was presupposed to be self evident and which then automatically is eliminated from physics as a result of the assumption of the compound to be a Ganzes A same meaning philosophical impact of the new theories quantum physics was given by H Weyl 1928 In prägnanter Fassung gilt in der Quantentheorie der heute von Vitalisten und Gestalttheoretikern zu einem philosophischen Glaubensbekenntnis erhobene Satz dasz das Ganze mehr is als die Summe seiner Teile Translation In a terse sense in quantum theory is taken up the thesis today elevated up into a philosphical confession of faith by vitalists and gestalt theorists that the whole is more than the sum of its parts But this thesis is not simply from new philosophers it is the ancient aristotelian thesis of the possibility of a totality of a new Substance originating from an other s And there it is not an article of faith but indeed becomes intellible from the principles of the theory i e holism is implied and therefore intellibible in Aristotle s metaphysics But in order to realize that this applies to mixta chemical compounds precisely according to the demands of modern physics one has to specify the aristotelian principles as we have done in our long analysis of atomic theory and what went before A same voice we could also hear in Holland where Prof A D Fokker compares the chemical atom with an organism He says 1928 In dat grootere individu het atoom zijn de individualiteiten der opbouwende deelen opgeheven geworden Het atoom is een organisme geworden dat zijn deelen beheerschend hun eigenschappen heeft veranderd Het electron als zodanig verliest zijn eigen bestaan wanneer het zich in het atoom voegt Het heeft geen afzonderlijke beweging meer noch een afzonderlijke omloopsfrequentie Zijn beteekenis gaat op in en wordt beheerscht door de beteekenis van het geheel De elementen die in dit geheel gesynthetiseerd zijn zijn geen onveranderlijke starre identiteiten Hierin ligt een tegenstelling tot klassieke opvattingen van vroeger Translation In that overall individual the atom the individualities of the components are cancelled The atom has become an organism which while dominating its parts has changed their properties The electron as such loses its own existence as soon as it incorporates itself into the atom It has no individual motion anymore nor an individual period of revolution Its meaning merges into and is dominated by the meaning of the whole The elements making up this whole are not unchangeable rigid identities In this we have a contrast to classical views of the past It is clear that this same vision can be applied to molecules with respect to their constituent atoms Where the scene is so well prepared the rest of our enquiry can be shorter First we consider the constitution of those new composites which are the chemical atoms themselves There we find the first definitive results And from these results then automatically we find our way back to the chemical compounds The modern theory of the atom and its consequences Introduction So the crisis of the mechanical view of Nature has broken out at the time when one after the discovery of the composition of the chemical atoms was looking for a structure that could account for the properties of atoms We here are considering free atoms When here facts and results became known that had no place anymore in the mechanical view of Nature one still did not immediately clearly realize the failure of that view although one saw the overwhelming difficulties and it still took several years namely until these attempts could not proceed along that same mechanicistic line anymore before one definitively realized the bankruptcy It may suffice here to consider the first still relatively simple cases the hydrogen atom in its first analysis and what immediately connects with it because we have arrived from our analysis of the elements of atomic theory and of the specifiability of the principles of atomism and of naturalism the latter is the aristotelian view involving natures at a sharp criterium making a swift solution possible For we find in those first cases already a composite of which the properties especially the spectrum are known It originated from components of which the properties are also well known also when they the components separately exist and are so observed So we have a case in which the calculation of the properties of the composite truly new and genuinely constitutive properties is possible and demanded We now know how to sharply discriminate whether a constitutive property is an aggregation resultant or a totality resultant If it isn t the first then it necessarily is the second In the first case the composite is an aggregate in the second a totality a new Substance In the first case it is to be viewed atomistically mechanically reductionistically in the second case it is to be viewed holistically i e in an aristotelian way that is according to naturalism This was the criterium that we had found after our analysis of atomic theory and of the possible specifications of both systems of thought the atomistic and the aristotelian Therefore our enquiry may finally give a result The atom of Rutherford After many attempts to find a structure of the chemical atoms Rutherford has finally succeeded to give the general structure afterwards specified by others We here shall not dwell upon all the experimental data upon which the theory rests but only present the general results The atom then consists of a twofold area the nucleus in which almost all mass of the atom is concentrated and the surroundings of the nucleus So also here in the atom we find heterogeneity First with respect to mass to this possibility we already pointed where we tried to determine the concept of mass and further when considering the structure of crystals but there is also another heterogeneity First of all in the nucleus itself the structure of which is still 1947 less well known Then in the vicinity of the nucleus as will be evident in due course The nucleus is the carrier of a positive electrical charge And this nuclear charge shows a peculiar regularity Since the experiments of Moseley it is established that one can order the chemical elements according to their specific X ray spectra in an ascending series of ordinal numbers from 1 to 92 and further when more elements exist In this series hydrogen occupies the first entry then follow helium etc until we arrive at uranium having number 92 The meaning of these numbers is also clear they express the positive electrical charge of the nuclei Thus the nucleus of hydrogen carries a single positive elementary charge that of helium two that of uranium 92 Now in the complete atom of every element there always are just as many electrons elementary negative charges as is the ordinal number of the atom Thus in hydrogen 1 electron in uranium 92 As a result the atom electrically is overall neutral These electrons are then regularly distributed in the nucleus surroundings In these surroundings one has learned to distinguish different concentrical areas shells indicated by the letters K nearest to the nucleus L M N O P Q One distributes the electrons insofar available of the atom in its normal condition ground state over these shells according to determined rules and could in this way extend the old periodic system This is in general lines the heterogeneous structure of the vicinity of the atom s nucleus The hydrogen atom of Bohr The theory of Rutherford must in its general lines be accepted as expressing the real structure of atoms They indeed must consist of the above described nucleus and its vicinity in which in one or another way the electrons for each element in a number determined by the element s ordinal number are taken up But the theory has its great difficulties especially seen within atomism Let us consider the simplest case The hydrogen atom of which the nucleus is a single positively charged proton to which in the nuclear vicinity is connected one negatively charged electron This electron cannot be stationary It would when stationary as a result of attraction by the positive nuclear charge crash onto the nucleus meaning that as such the hydrogen atom would not be stable So the hydrogen atom s electron will be in motion and then thanks to its tangential velocity be prevented from crashing onto the nucleus like the moon doesn t fall on the Earth So in general one may compare the atom of Rutherford with a planetary system The sun is the nucleus the planets the electrons But what would be the fate of the hydrogen atom if it really had this structure According to the theory of Maxwell the electron must in its motion along a curved trajectory here resulting in a periodic motion emit electromagnetic radiation such as light or X rays The system or at least the electron will lose energy here as a result of the emission the electron will lose more and more of its kinetic energy Therefore the electron will approach the nucleus and finally crash onto it more

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