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  • General Ontology XXXIV
    Back to Part X Back to Part XI Back to Part XII Back to Part XIII Back to Part XIV Back to Part XV Back to Part XV Sequel 1 Back to Part XV Sequel 2 Back to Part XV Sequel 3 Back to Part XVI Back to Part XVII Back to Part XVIII Back to Part XIX Back to Part XX Back to Part XXI Back to Part XXII Back to Part XXIII Back to Part XXIV Back to Part XXV Back to Part XXVI Back to Part XXVII Back to Part XXVIII Back to Part XXIX Back to Part XXIX sequel 1 Back to Part XXIX sequel 2 Back to Part XXIX sequel 3 Back to Part XXIX sequel 4 Back to Part XXIX sequel 5 Back to Part XXIX sequel 6 Back to Part XXIX sequel 7 Back to Part XXIX sequel 8 Back to Part XXIX sequel 9 Back to Part XXIX sequel 10 Back to Part XXIX sequel 11 Back to Part XXIX sequel 12 Back to Part XXIX sequel 13 Back to Part XXIX sequel 14 Back to Part XXIX sequel 15 Back to Part XXIX sequel 16 Back to Part XXIX sequel 17

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  • Aristotelian metaphysics I
    does not mean separable by thought which it also is but separate in intelligible content The intelligibility of such a form is in no way dependent on its substrate as on the contrary that of an accident property or state is This form is an intelligible content in itself The matter that makes its substrate adds no intelligibility to it whatsoever So in this sense such a form is separate The accidents that follow upon it are not required for its intelligibility In itself it is a complete intelligible unit and so separate in knowable content from all else that depends upon it in the sensible thing Does separate in notion connote universality The form which is separate in notion as contrasted with absolutely separate that is a self subsistent form is the primary Entity of the sensible thing But no universal can be Entity because nothing in extra mental reality exists in a universal fashion while Entity is an instance of Being in extra mental reality Separate in notion therefore should not mean universality So when we say that the form which is Entity is separate in notion which it is we know that this separate in notion cannot mean that the form is a universal But what is separate from matter cannot be singular And because the form is separate from matter albeit only in notion it cannot be singular Said differently Because the form as it is in itself is separate from matter this is what separate in notion means it cannot be singular as it is in itself The singular always contains matter and for that reason is indefinable But the form is separate from matter at least in notion and is definable It cannot be singular The form apparently can be neither universal nor singular What is it then In Aristotelian metaphysics the form is called a this And a this is an Aristotelian equivocal applying to the matter as potency to the matter form composite in virtue of the form and to the form as such The form can be considered the primary instance of thisness just as it was the primary instance of Entity within the composite In Aristotelian metaphysics only singular things exist in the sensible world and only universals are knowable and they do not exist in this world This is a dilemma because how then can we know which we do albeit only incompletely the sensible world Does the peculiar character of the form hold the solution Wherever this precision of thought may lead us it at least is clear cut in its basic divisions The form is an Entity and a this without being of itself either singular or actually universal it is potentially universal Because it is not singular it can be knowable and can be the principle of knowability for the singular thing Knowledge of the form will be knowledge of the singular individual because the form is identified per se with that singular thing as its act and the form contains all the knowability found in the singular At the same time the form can be Entity because it is not actually universal How is such a form to be conceived It must be understood as something separate in notion but not separate without qualification It is to be conceived as a physical constituent for example as the dynamical crystallization law inherent in a supercooled volume of liquid water which law starts to operate when proper crystallization nuclei are present and which law then results in an ice crystal which is a new substance in the metaphysical sense This dynamical law then is the substantial form of this substance of a sensible thing the ice crystal of our example and not able to be found without its sensible matter the dynamical law inheres the matter of the supercooled melt as well as that of the resulting crystal except in thought It is the actual and formal principle and intrinsic formal cause of a singular thing without being of itself a singular As the act of sensible matter the form is the cause of Being to the sensible Entity which is singular In the passive mind the same form is without its physical matter It is the act of that passive mind In the l o g i c a l o r d e r it is actually universal while in the entitative order it is only potentially universal it is the act of intelligible matter and forms the logos or definition of the sensible thing and as such can be applied universally to all the individuals that are the same in form Speaking about individuals how should we assess the individual the individuum In Aristotelian philosophy the term is applied equally to the undivided singular and the undivided species It can mean either undivided in number or undivided in form To restrict the term to its English signification of a singular and to use it to translate the Aristotelian a this is to miss the two fold sense of thisness Or if the distinction is made the non singular sense of a this is relegated to the order of universality Yet Aristotelian metaphysics requires that the form of sensible things taken in itself be neither singular nor universal although it is the cause of Being and the foundation of universality When the form is in cognition applied universally to all the individuals that are the same in form we get the species In the actual cognition of a thing the form is known as it is in the one singular but after the actual cognition has passed it can still be used to know all other such singulars universally The singular and the universal accordingly are to be explained in terms of form and not vice versa All three are given as facts with form prior in knowability If the problem is posed in two terms only singularity and universality it becomes utterly insoluble If the premises are only the singular exists only the universal is known how can the Aristotelian notion of e i d o s which is both physical form in the sense of the dynamical law of that dynamical system that has generated the given Being and logical species ever be grasped It would then have to be fixed as either singular or universal or else merely catalogued as a hopeless union of the two contradictory alternatives OWENS p 393 The form must be kept as prior to and act of both composite Entity singular and logical universal that is the form as it resides in the sensible thing and appears in the passive intellect is potentially a universal The singular and the logical universal have to be explained in terms of f o r m as the primary instance of Entity which is neither singular nor universal This form is the what IS Being eternal as expressed by the IS unchangeable ungenerated As prior to the composite it is prior to the changeable singular and so prior to time for time follows upon change For that reason the form is timeless and can be rightly called the what IS Being It always and necessarily is the Being of the thing From it everything else in the thing derives Being The sensible matter form composite can be understood either singularly or universally As singular it is Entity As universal it is not Entity All this also decides the problem of the principle of individuation Because in the Aristotelian metaphysics the substantial form is in itself not universal there is no need to posit a principle of individuation in order to render the composite individual The composite is already an instance of a this From a slightly or maybe not so slightly different perspective one can assume that a principle of individuation is needed to account for the individuality of material beings See the document Principle of Individuation in the first Series of documents in First Part of Website The matter form composite as singular is a this second instance The form as separate in notion from matter and composite is likewise a this first instance A this cannot be a universal or a quality it is something determined and belonging to the first Aristotelian category while quality belongs to the third either as singular it then is the composite or as a form considered without matter it then is its primary instance The form is the cause of Being and the principle according to which things different in number are one in species The form should therefore explain Being It should be the cause sought by the science of Beings according as they are Beings It should be the basis of universality in that science Yet the form in itself is not a universal It is a this without being a singular It is the actual expression of the singular composite that is it is the act of the singular composite and so enters into a per se unity with the individual thing In this way the most fundamental aspect of the problem the relationships between individual singular form and universal is solved The relation of form and individual thing has been made clear If the English word individual may be used to render both senses of a this which senses are 1 secondary instance singular composite 2 primary instance substantial form it will allow the solution to be stated in a more modern fashion The Aristotelian form is individual in itself and is the cause of the individuality in the singular thing of which it is the act In this two fold way form and individual coincide Form and singular thing are respectively the primary and secondary senses of a this OWENS p 398 9 See also next scheme In the next section we will investigate how the above results influence the nature and interpretation of the Species Individuum Structure SIS as a structure that pervades all material reality The Species Individuum Structure of material Beings This structure was studied in the document The Species Individuum Structure in the Critical Series of documents in First Part of Website One of the presuppositions of natural science is that any form be it a nature quality quantity but also every specific event can in principle be repeated over several distinct cases in time as well as in space So we see that material reality which is studied with respect to its nearest causes by natural science is pervaded with two fundamental aspects individuality and specifity that is to say any given specific content can in principle occur in more than one cases We have after Van MELSEN A Natuurfilosfie natural philosophy 1955 called it the Species Individuum Structure of material reality It is clear that this structure is in some way strongly akin to the Matter Form Structure in Aristotelian metaphysics where matter is either prime matter carrying the substantial form or the matter form composite carrying the accidents We must therefore investigate the precise relationship between these two structures But before we do so we must once again consider the above mentioned thisness of form that is to say while above we had more or less followed the arguments of Aristotle as expounded and interpreted by OWENS we now will seek a thematic justification of the results First we speak about the difference between individual and individuum that is an individual Any given aggregate for example a solution of salt in a volume of water but also a granite pebble consisting of mineral grains is individual but it is not an individual that is it is not an individuum It is a collection of individuals molecules or mineral grains which did not come together according to a definite repeatable pattern that is they did not come together according to some intrinsic law The individuality of the aggregate is the case in virtue of the fact that the aggregate ultimately consists of true individuals molecules crystals So an aggregate is individual only per accidens In the following we will speak only of something being individual or of individuality Any existing material thing is individual Such a thing is either a genuine substance in the metaphysical sense or an aggregate of such substances so we can confine our discussion to substances that is to any given substance because as has been said an aggregate is individual wholly in virtue of its constituent substances in the metaphysical sense Such a given substance is for instance a given crystal It is metaphysically composed of prime matter informed by a substantial form necessary accidents properties and contingent accidents states and is as has been said individual in the present case it is also an individuum It is embedded in an environment and subject to environmental conditions The accidents are ontologically dependent beings which manifest the prime matter substantial form composite matter form composite for short that is to say they render this composite observable But because the necessary accidents are directly implied by the matter form composite and the contigent accidents follow from the interaction of the composite with the environment where the composite always reacts according to its nature the individuality of the thing flows from the matter form composite that is to say already the matter form composite is individual But where in the matter form composite does the individuality come from Does it come from the prime matter the substantial form or does it come only from the composite that is not until the composite has been formed Individuality means in se undividedness where in se means in itself and even per se that is in virtue of itself indivisibility and separateness dividedness from other ness Or perhaps better In se undivided and indivisible content separate from other content where separate from other content is two fold 1 separateness and 2 repetition or respectively 1 separate from different content and 2 separate from identical content So when investigating individuality and its necessary conditions we must consider in se undividedness and indivisibility and separateness from other ness both senses of otherness as just described Prime matter cannot be individual and then passing it over to the composite because prime matter has by definition no content It can therefore not form boundaries in either space or time So it cannot all by itself bring forth separateness neither qua content nor spatially or temporally because spatial or temporal separateness must involve in between contents Form as it is in itself that is the form separate in notion as well as matter in the metaphysical sense is undivided in itself but matter is divisible while form is not And when the form turns out also to be separate from other ness it would be truly individual Let s inquire into that A given form is separate from another form if the latter differs from the former according to content And two equal forms equal with respect to content can coexist and thus be separate otherwise they would be one form in space and time meaning that the form can be repeated either in space or in time o n l y when they are separated by a third form that is different from them with respect to content So here we have the beginnings of the ability possessed by the form of repetition and separateness Repetition of form A in space Repetition implies separation Separation in space is accomplished by the insertion of form B spatially between A and A where form B serves as a spatial boundary between A and A Repetition of form A in time Repetition implies separation Separation in time is accomplished by the insertion of form B temporally between A and A where form B serves as a temporal boundary between A and A But it is also clear that for all this a substrate is needed This is because we must be able to say that in the case of spatial repetition and separateness the substrate is here actualized by form A and there actualized by form B and farther there actualized by form A In the case of temporal repetition and separateness we must say that the substrate is now actualized by form A then actualized by form B and further then finally actualized by form A again And this substrate is either prime matter when the forms are substantial forms or the matter form composite when the forms are accidental forms properties states Here we have dealt with the possibility for some form to be repeated that is being separate from identical content But the conclusion equally well applies to the possibility of separate from different content because that is already implied The substrate is here actualized by form A and there actualized by form B And also The substrate is now actualized by form A then actualized by form B So to fulfil the condition for the possibility of separateness and repetition and thus of separatenes from other ness the form needs a substrate This substrate is as has been said either prime matter when the form is substantial or the matter form composite when the form is accidental a property or a state In itself the form is undivided and undivisible first condition met for individuality The possibility of repetition of one given form separate from identical content by insertion of a different content and the difference in content of the given form with respect to another form separate from different content together constitute the separate from other ness second condition met for individuality This second condition needs matter to be present as a substrate of the form So indeed a form any type of form can be individual but not wholly in virtue of itself it needs matter So when a form is said to be individual it is already a matter form composite and the individuality of the latter implies separateness from other ness which in turn means that the composite is singular And this aspect of being singular comes necessarily from matter So when something is singular it contains matter ultimately prime matter But for the composite to be indivisible and undivided in itself that is in itself to be undivided and indivisible content does not require matter It can not come from matter because matter as such is divisible When a composite is divisible it is so in virtue of the matter Its content is not divisible The form alone suffices for indivisibility and undividedness The form is in se and per se in itself and by itself undivided and indivisible content And to be undivided in itself not necessarily also to be indivisible is to be a this So the composite is a this And especially the form is a this and only a this Its in se undividedness is expressed in the strongest way The two aspects of individuality in se undividedness separate from other ness precisely correspond to a this and being singular The aspect of individuality representing a stronger instance of undividedness namely indivisibility of content is compatible with being a this but does not contribute any further for something to be a this The matter of a composite is a this only in virtue of the form so also the composite itself So the a this of the matter of the composite and the a this of the composite itself are secondary instances of a this while the a this of the form is the primary instance This form is the substantial form The same applies for any accidental form but here only per accidens Prime matter cannot all by itself be a this because it is totally indeterminate It is not undivided content Only as actualized by the form is it a this but then it is the composite And only the composite is truly individual because it is at the same time singular in virtue of the separateness made possible by the matter as substrate and a this in virtue of the in se undividedness of the form Individuation thus needs matter and form Although form separate in notion that is the form as an intelligible unit of content is already a this it is not yet individual For this it needs matter it must be actualized matter So matter is the p r i n c i p l e o f i n d i v i d u a t i o n after all And indeed because all things and that is all matter form composites are individual the form as it resides in such a composite but considered in itself cannot be a universal which means it cannot actually be a universal it is only potentially a universal But at the same time it cannot be individual either because it as such lacks matter and thus lacks singularity and so lacks as it is in itself separateness from other ness which is a necessary condition for something to be individual So the form is neutral in this respect it is just a this Above we spoke about undividedness indivisibility and sepateness from other ness as the conditions to be met for something to be individual Let us consider the condition of indivisibility in more detail because we could ask whether this condition is really necessary for something to be individual and if so we should ask in what respect it is to be indivisible The expression something is individual is equivalent to the expression some specific intelligible content is individual and any specific intelligible content is not divisible because it is immaterial This argument would be true if 1 indeed in this context the only alternative for something is some specific intelligible content and 2 if it were true that a specific intelligible content can be truly individual Above we saw that this is not the case just like that Let s dig deeper into this question Although an existing material aggregate i e a material unity per accidens is individual it is not of itself individual because it has no self The aggregate is nothing more than its elements Their aggregation has external causes and thus the aggregate has external causes So the individuality of the aggregate is not its own but comes from the individuality of its elements which ultimately are per se units possessing individuality all by themselves Each one of these elements is truly individual and carries a specific intelligible content of which it can be asked whether it is individual too So the individuality of an aggregate can be reduced to that of its ultimate elements and the per accidens intelligible content of the aggregate can be reduced to the per se intelligible content of its ultimate elements and questioned as to its individuality But to be more precise such a content or form can be called individual only in the sense of individualized and it is individualized in virtue of its being associated with a substrate that carries it And such a substrate is matter But then it is the composite not the form that is individual The form is not individual by itself but only as the act of matter Indeed as explained above it is only the composite of substrate and specific intelligible content that is truly individual Is such an individual composite then not only undivided but moreover also indivisible A prime matter substantial form composite is a structure Normally a structure is a certain definite configuration of parts like for example a given machine A machine is composed of parts which each for themselves exist independently and lie outside each other But because the cause of the machine as structure is extrinsic it is designed and made by humans it is not a true substance in the metaphysical sense not an intrinsic structure So it is an aggregate albeit of a special kind It is divisible it can be disassembled into its constituent parts As specific machine however it is not divisible because the result of such a division that is the disassembled machine is not that specific machine anymore And this indivisibility is to be expected because the specific machine is in fact the intelligible content of the aggregate that is called a machine A true substance on the other hand is first of all a prime matter substantial form structure that is a structure consisting of a configuration of matter and form But as structure it is of an entirely different type than the structure of a given machine Both matter and form are not parts lying outside each other Prime matter cannot exist without some substantial form by which it is actualized and a substantial form cannot exist without prime matter as its substrate So a matter form composite is as matter form structure inherently indivisible that is indivisible as to matter and form as its parts But it is also indivisible qua intelligible content because this content is the one substantial form which cannot be divided into parts But a prime matter substantial form composite is itself in turn a substrate thus a matter a substrate namely for the whole set of determinations accidents that make it manifest and observable It cannot exist without determinations Indeed part of the determinations properties necessarily flow directly from the prime matter substantial form composite while the other determinations states flow from it in virtue of its interaction with the prevailing environment an interaction wholly according to its nature All this results in an observable structure of the fully fledged substance in the metaphysical sense But like the prime matter substantial form composite its parts are not entities that exist ontologically independently They are just determinations The structure of the fully fledged substance is not a configuration of material parts each ontologically independent but of qualities quantities and relations It generally is a heterogeneous continuum discussed and explained in Part XXIX Sequel 33 of Fourth Part of Website And such a continuum like any other type of continuum is although undivided in itself nevertheless divisible What is not divisible however is the intelligible content of the substance like machine was in the case of human artifacts because it is immaterial That is although the fully fledged substance can be conceptually divided into say its several different determinations all the determinations can be reduced to the prime matter substantial form composite and ultimately to the substantial form and this is as established earlier intrinsically indivisible qua intelligible content So in this sense and only in this sense the substance is by itself indivisible The divisibility of the prime matter substantial form composite and of the fully fledged substance stems not from the composite as such or from the fully fledged substance as such but from its matter So the conditions for something to be per se individual are In se undividedness Per se indivisibility qua intelligible content Separateness from other ness A form as it is in itself does not meet these conditions because it is not without exception separate from other ness Complete separateness of a form includes separateness not only from a different form but also from the same form i e it includes the ability of repetition And because certainly for this latter ability a substrate for the form is needed the form does not possess this ability all by itself The form is not individual but because it cannot be a universal either it must be neutral in this respect And because a form is undivided in itself it is a this which we can now characterize as neutral with respect to individuality universality Let us now apply these findings to crystals Any given crystal is per se individual It is also a true individuum because it is a true substance in the metaphysical sense an intrinsic unity an intrinsic being Let s consider an ice crystal Such a crystal is first of all a prime matter substantial form composite The substantial form is the relevant dynamical law specific crystallization law Because the substantial form of our crystal inheres in matter the dynamical law inheres in the water molecules making up a volume of supercooled liquid water and later making up the ice crystal The specific crystallization law is separate in notion that is its intelligible content is apart from prime matter As such this law that is the substantial from is as is clear from the above discussion not only in se undivided but also as intelligible content per se indivisible It is however not separate from other ness because for that it needs matter So the crystallization law is not individual But because it is in se undivided and moreover residing in an individual substance the given ice crystal and thus not being a universal it is a this What about the indivisibility of the crystal The substantial form crystallization law immediately expresses itself as Space Group plus chemical composition Both are properties in the sense of necessary accidents propria They represent the crystallization law A crystal can be cleaved Each piece of cleavage still has the internal symmetry as described by the Space Group of the original crystal Also the chemical composition is the same in those pieces as it was in the original crystal So in contrast to a molecule a crystal can be divided without loosing its identity or nature thanks to its periodic structure What cannot be divided however is the crystal s specific intelligible content crystallization law even as it is expressed by its Space Group plus its chemical composition And in addition to this the crystal s intrinsic shape cannot be divided because it is an intelligible content too And if we transform this latter intelligible content which is an intrinsic intelligible content intrinsic with respect to te crystal s nature or essence into the actual intrinsic shape of the crystal that is the intrinsic shape as actually realized then the crystal is indivisible despite its periodic structure This is because also the actually realized intrinsic shape is a specific intelligible content But is indivisibility of intelligible content a necessary condition for something to be truely individual or is it either always implied or not necessary at all Let s look into this question If we look to take an example at a quartzite rock or pebble where we have in mind that variety of quartzite consisting entirely and exclusively of the mineral quartz SiO 2 which is present in the form of very small deformed crystals that is quartzite is a microcrystalline aggregate of quartz All the quartz crystals are tightly packed together that is they are interlocked and fused together but not according to some specific ordering or specific pattern We can say therefore that the quartzite pebble is in se undivided and of course it is separated from other ness Is it divisible Yes it is divisible We can divide it macroscopically without destroying its actual intrinsic shape because it has no intrinsic shape Its shape is always extrinsic The fragments resulting from such a division are still each of them volumes of quartzite like the cleavage pieces or whatever macroscopical fragments of a crystal are specifically still that crystal fragments of ice crystals are still ice crystals So the divisibility of quartzite is more complete than that of a crystal We can also say that a crystal is indivisible because is not divisible in all respects it is not divisible as to its actualized intrinsic shape while a quartzite pebble is divisible because it is divisible in all respects And this could mean that also its specific intelligible content is divisible But we know that such a content is not divisible So we can conclude that in the case of a quarzite pebble there is no genuine specific intrinsic intelligible content to be found The specific intelligible content could be divided simply by the fact that it was not such a content at all The individuality of the quartzite pebble is totally derived from that of its constituent quartz crystals And only the latter possess true individuality They are in se undivided they are in all respects indivisible including their actual intrinsic shape and separate from other ness It is important to note that the difference qua individuals the difference of say two identical drops of water is not a difference in either position or place Of course it is true that with this individual difference also a difference in place position or time is given by which we can at all distinguish between individuals that are identical in all other respects but these differences are not the cause but the effect of the difference qua individuals For if we would interchange the places of those individuals the latter would not be interchanged After all both individuals possess in virtue of the fact that they are specifically identical the same capacity to take each other s place without them ceasing to be two individuals Having considered concrete examples concerning the Singular the Individual Individuality the Form as a this or neutral entity and the Universal we are now ready to discuss the Species Individuum Structure that pervades all of material reality The Species Individuum Structure In the document The Species Individuum Structure in the Critical Series of documents in First Part of Website we discussed this structure as being a fundamental presupposition of natural science that is of its main method the inductive method which consists in generalization on the basis of singular findings It is presupposed that a given intelligible content of a material entity can in principle be exactly repeated in nature or in experiment Based on this possibility we can formulate natural laws We also discussed the possibility that any such given intelligible content of something does not and never repeat itself exactly but can repeat itself in an approximate way When this is so then natural science and its inductive method is still possible when the range of variation which must be random easily falls within the range of exactitude of observation and measurement Also we discussed the possibility that the Species Individuum Structure is not an ontological structure at all but just a cognitive structure Because 1 the Species Individuum Structure is so pervasive either in its exact form or in its approximate form 2 it provides much justification for Aristotelian metaphysics because it assumes natures and 3 it deepens our insight in individuality form the universal etc it is paramount to address the above questions and thus to dig deeper into the essence of the Species Individuum Structure And the best way to do this is by paraphrasing the text of its discoverer A van MELSEN in his book Natuurfilosofie natural philosophy in Dutch 1955 pp 14 We will do that in due course Even if we limit ourselves to material things natural science cannot cover it all which here means not because of the fact that there is such a bewildering multitude of things and processes but in principle This is so because natural science is necessarily based on certain presuppositions that is fundamental presuppositions which are such that without them natural science is not even possible in principle and which cannot therefore be discussed or questioned by natural science itself that is by natural science as empirical science which means that it starts from observation and experiments and verifies its theories again by observation and experiment Therefore there must be another science not an empirical science that must be able to deal with these fundamental presuppositions And this science is natural philosophy Van MELSEN is very clear and instructive on these points and we cannot do better than to present his views in the form of a rough translation including unannounced amendments and supplementary remarks of long portions of his text pp 14 THE INSUFFICIENCY OF NATURAL SCIENCE Natural science is based on presuppositions It is without doubt

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  • Aristotelian metaphysics II
    to something else is or is not the case Said differently whether a given property necessarily belongs to a given subject It is the question quia est It is the question is S P or is S not P When we know that indeed S P S is P we ask why this is so It is to ask for the cause or reason why a given property necessarily belongs to a given subject It is the question propter quid In addition to these composed questions we can also ask simple that is non composed questions Does S exist It concerns the existence of the subject It is the question si est or an est As soon as we know that S is that S exists we will ask What is S This is the question that asks for the Whatness or Essence of the subject It is the question quid est Quia and si est ask whether there is a cause whether there exists a corresponding cause and that means logice NOTE 9 whether there is a middle term Propter quid and quid est ask what the cause is and that means logice what the middle term is A condition that must be met in all this asking is that we know the meaning of our terms words i e before we can find out at all whether S is resp whether S P is whether S is P we must know the meanings of the terms S and P here it is about a preliminary circumscription often involving accidental items see St Thomas In II Post An lectio 8 This circumscription does not yet give the quid est It is the answer to the question quid est quod dicitur NOTE 10 REMARK As to the notion of Essence of an intrinsic being and its relationship to per se determinations properties there is a problem in Classical Metaphysics There with respect to Man his Essence is considered to be his ability to think and all what it entails Classical metaphysics says that the ability to think is an essential quale But the ability to laugh which is also considered only to occur in Man is considered to be just a property not an essential quale What then is the ontological difference between ability to think and ability to laugh Classical metaphysics does not provide an answer It just stipulates that ability to think is an essential quale of Man meaning that it belongs to his Essence in contrast to caused by his Essence and not a property not a necessary determination of Man This problem can be solved along the following lines The Essence is considered by classical metaphysics to be the intrinsic cause of the being of which it is the Essence at least the formal cause But the ability to think clearly is not a cause but an effect that is an effect of the Essence just like the ability to laugh is an effect of the Essence What then is the Essence of a given being Well it is as found out in First Part of Website the dynamical law governing the dynamical system that can generate this being out of basic elements such as atoms So both the ability to think and the ability to laugh are effects of Man s Essence that is of Man s dynamical law And indeed these two features have now the same ontological status and the problem is solved b Deductive Demonstration the Proof All these questions and their answers stand in a certain relationship to deductive demonstration proof i e the syllogism that is one of the possible formal figures of demonstration Let s dwell for a moment upon the syllogism Suppose as an example that certain chemical configurations belonging to the phenotypical expression of the Essence of a class of material bodies in whatever way cause a cellular character or texture in these bodies as a result of which these material bodies manifest themselves as individual cells or as multicellular bodies and suppose that in particular living matter in contrast to inorganic matter necessarily possesses this property and that in addition to it we know that animals consist of living matter then we can set up the following syllogism Maior 1st premise All animals are cellular Minor 2nd premise Sponges are animals Conclusio conclusion Sponges are cellular The validity of this demonstration is immediately clear when we consider the range of signification of the terms that is if we consider the terms as indicating collections or classes of things s l Then we can represent the syllogism by means of a Venn diagram Here animals is the middle term and represents a part of the definition of the subject of the conclusion and is reason or cause of that what is posed in the conclusion Cellular is the extreme superior term maius Sponges is the extreme inferior term minus The conclusion is deductively demonstrable because the range or extension of the superior and inferior term is such that a middle term can be inserted between them It is for the same reason that a strict proof of the necessary attribution of a definiens definition to the definiendum that what is to be defined is impossible because both extensions are equal so that nothing that is no middle term can be placed between them The example presented above was a syllogism of the first figure of which the conclusion is universal and affirmative where M is middle term P is predicate of conclusion and S the subject of the conclusion So far for the time being about the syllogism c Reduction of quid est of the property to propter quid Aristotle shows in the second chapter of the IInd book of the Posteriora Analytica and St Thomas in loco NOTE 11 that the what is it question is the same as the why question However this is valid in the Posteriora Analytica as epistemology only for those things s l that have a cause which is different from that thing itself and that means that the reduction is only possible in the case of properties because for these their cause indeed lies outside themselves in contrast to substances NOTE 12 When we ask what is A we do not have an answer when we reply A is A indeed it is metaphysics which nevertheless tries to answer such a question also with respect to substances However in the present discussion that is in the context of the Posterior Analytics it is not about metaphysics in the strict sense that we speak but physics in the broad sense We also do not get an anwer when we reply A is B because A is not B but A is A But if we in addition to relations of identity and non identity take into account other relations for example A has B or B is the cause of A then it is perhaps possible to obtain an answer to the question what is it which gives more information than A is A It is clear that especially the second possibility of the two just mentioned can supply an answer to the question what is it NOTE 13 Indeed an anwer could read A is what it is in virtue of B So the question what is A is asking for something different on which A is based which here is B In this way the what question is a question asking for the cause So we see that for such a reduction to be possible a duality a catallellism is needed and such a duality of essence loosely whatness and cause is only to be found in properties If we then speak about the reduction of quid est to propter quid then we for the time being that is as long as we stay within the domain of epistemology mean exclusively the quid est of a given property The treatment of the quid est of a given substance does not belong to the epistemology of the Posteriora Analytica d The sequential order of the Questions with respect to properties First of all we must know the meaning of the term that signifies the given property We ask quid est quod dicitur NOTE 14 the answer is a nominal definition Next we can ask ourselves whether this term indeed has a significatum NOTE 15 i e whether the property is on the subject the subject is presupposed to exist This is the question quia est Next we can ask what it is that est NOTE 16 and this is as we have demonstrated the same as asking why it is as it is that is why this given property is on the subject rests on the subject This is the question propter quid NOTE 17 The answer is then at the same time the answer to the what question quid est NOTE 18 regarding the property It is the quod quid est NOTE 19 of the property e The sequential order of the Questions with respect to substance With the simple i e not composed questions as regards the s u b j e c t things are different First of all we must again have at our disposal a definition quid nominis nominal definition as answer to the question quid est quod dicitur see NOTE 14 in order to be able to ask ourselves next whether the term actually has a significatum in re NOTE 20 This is the question si est This cannot be deductively demonstrated but only possibly be observed After we know that the given substance the subject of the property or properties exists we can ask what it is essentially quid est substantia that is we ask for the Essence of the given substance we could also say that we ask for the substance itself of a thing Because the cause of the Essence is here identical with that Essence we cannot in a catallel way ask for the cause that is we cannot ask in such a way as to involve a duality of the thing and its cause which here is the duality consisting of the Essence and its cause See Aristotle II Posteriora Analytica Chapter 10 NOTE 21 We cannot ask this in terms of some duality because the Essence does not within the context of science have a dual nature Within the context of science as contrasted with that of metaphysics we cannot as regards substance say what A is in terms of B the cause The Essence should be intuitively and inductively grasped as Aristotle describes in Chapter 19 of the IInd book of the Posterior Analytics NOTE 22 f Catallel transformation of quid est as regards substance AERTSEN J A in his Natura en Creatura 1982 p 22 now discusses the problem as regards the quid est of s u b s t a n c e s following the discussion of St Thomas in In VII Metaph lectio 17 that is in his commentary on the Metaphysics of Aristotle concerning a catallel transformation When we despite what has been said above nevertheless perform this transformation then the composition compositio resulting from this transformation out of these alleles is of a totally different nature than is the compositio of a subject and a necessary property The problem of the what question with respect to substance concerning what a given substance is is because it is a metaphysical problem and not a problem of natural science dealt with in Aristotle s Metaphysics especially in Book VII and also by St Thomas in loco and by AERTSEN p 30 33 The question quid est with respect to any given substance now in this metaphysical treatment also becomes a question as to the cause and this cause is the forma in materia causes of it in turn are the efficient and final causes which are both extrinsic causes But for the philosopher it is the intrinsic causes that should be looked for causes that constitute things from within AERTSEN p 31 and this intrinsic first of all refers to substance secondly to some state of affairs that is to a substance accident composite compositum substance determination composite which forms a unity secundum quid NOTE 23 Well St Thomas takes the Essence of a given substance or takes a given substance as forma totius form of the whole that is forma and materia but without matter as individualizing materia signata This forma totius is itself catallel i e dual in character but is still as such identical with its cause as a result of which we still cannot ask the why question It is clear that the question as to the Essence of a given substance thus what some given thing is cannot be the business of discursive demonstrating science It that is the whatness cannot be demonstrated from that is out of something else The only form of being catallel which is left is that of the individual suppositum NOTE 24 and the Essence residing in it NOTE 25 AERTSEN p 32 quotes St Thomas In VII Metaph lectio 17 nr 1667 Et similiter cum quaerimus quid est homo idem est ac si quaereretur propter quid hoc scilicet Socrates est homo quia scilicet inest ei quidditas hominis NOTE 26 Where Socrates should mean Socrates as pointed to with the finger So in this way the question is transformed in a catallel way Socrates as individual suppositum and whatness of man as forma totius as a result of which it will now read AERTSEN p 23 why is this namely Socrates a human being Something is asked about a thing that is pointed to with the finger and the conclusion of a syllogism would then read ergo this Socrates is a human being And this is said to be possible because a distinction is made between first and second substance That such a view of an Essence residing in a thing that is the distinction between first and second substance is not undisputed we will expound later The question what is man now reads after catallel transformation What in Socrates is the cause that he is what he is But then we already ask things about particular cases We ask for the intrinsic cause of contingent supposita that is unique things NOTE 27 Human ity is the cause of Socrates and no science asks for the cause of contingent supposita see NOTE 24 The question is thus not quid est Socrates transformed into propter quid but quid est homo NOTE 28 See for example St Thomas De ente et essentia Cap 4 Leonina edition from line 97 And this i e homo is equivalent to Socrates for example The latter is not contigent anymore because we have precisely given up Socrates Let us dwell a little on this point In Socrates for example like in homo the particular is not considered but the aspect of being individual is and acordingly Socrates for example stands for the individual Essence By cutting off the designated matter matter under designated dimensions we cut off the particular the aspect of being a here and now individual the semaphoront but not the individual If we ask about just Socrates we ask about a contingent case we ask about the particular i e just this individual pointed to with the finger But if we ask about Socrates for example we ask about a non contigent case although still individual See the documents The principle of individuation non classical series of documents and What is an individuum Part I classical series of documents in First Part of Website So we still cannot ask for the cause of the Essence That is to say that with respect to this the question what is it cannot be transformed into something catallel in order to form a why question because we gave up the individual suppositum Socrates and turned to Socrates for example or equivalently to homo and are thus left with the Essence alone It is however arguable that even the forma totius as Essence or substance which is the primary instance of the categorial for St Thomas equivocal Being the secondary instances are the accidents itself in turn refers to an even more fundamental primary instance namely the substantial form forma partis and this form we can now take as the intrinsic cause of the Essence forma totius The substantial form is the ultimate inner cause of the Essence as a result of which the question concerning this Essence as what question can now be transformed into something catallel Within Aristotle s Primary Philosophy his metaphysics we have ended up at the most fundamental We can now say The Essence forma totius materia non signata forma that is a given Essence is that what it is in virtue of the form that is the substantial form REMARK At issue here is not what Essence as Essence is but what a given Essence is For example quid est homo what is man and not quid est essentia f 1 An analysis of the Essence as forma totius We now can in our modern view take the forma totius as being the dynamical law as the latter is interpreted toward physical matter that is the dynamical law interpreted in terms of physical matter The forma partis substantial form then is the pure dynamical law thus the dynamical law as not interpreted toward physical matter We can think of this pure dynamical law as in its purely mathematical form its mathematical formulation its formal intelligible content The materia signata designated matter is the principle of individuation NOTE 29 Science can only work with dynamical laws that are interpreted toward physical reality that is with physically interpreted mathematical formulas The purely formal state of such a law i e its purely mathematical structure cannot within natural science be understood ontologically that is with respect to

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  • Aristotelian metaphysics III
    CARRIER ONLY subject just like that i e in an absolute sense after we have removed those determinations And this genuine carrier only the genuine subject in an absolute sense is as we found out in the mereotopological discussion identical to the HISTORICAL individual The individual taken in its whole time span of existence contains in addition to its essential determinations other determinations that are not fully specified because they vary during the individual s existence and that is equivalent to their being removed What is left is indeed the carrier only For the important argument taken from the document on Mereotopology in First Part of Website revealing not only what is precisely the carrier only that is in the case of a true Totality fully fledged substance substance in the broader sense SUBSTANCE s str but also within that carrier only the boundary between the genotypic and phenotypic domain of a true Totality see this NOTE 64a The complete set of types of determinations mentioned earlier is as we found out in the mereotopological discussion not the carrier only or subject in an absolute sense but only in a relative sense namely with respect to one or another single determination or a few such determinations when viewed without these particular determinations It i e the mentioned set is just a general precondition for the Mereo totality to exist Determinations are always determinations of something else Parts of a subsistent being can also be interpreted as determinations Everything that ontologically comes after the prime matter of such a being can be seen as a determination including the essential parts They are determinations of the prime matter The latter is the ultimate substrate the ultimate subject But as such the substrate for any possible content End of quotation from First Part of Website The next Figure summarizes all the above results about the ontological constitution of a real being Figure above The ontological constitution of a real being END of Ontological Intermezzo Above we had investigated predication and the enquiry into the ways of predication yields the following predicables praedicabilia Genus Species Differentia Proprium Accidens They are the Genus Species etc as such and consequently not one or another genus species etc in that case they would be first intentions primae intentiones They are Genus as Genus Species as Species etc and as such they are second intentions secundae intentiones that is logical entities that result from that is are as such ascertained in our way of thinking NOTE 65 In order to obtain a better understanding of the Praedicabilia we will in what follows try to indicate several distinctions whereby it automatically becomes evident that this is not so easy as seems at first sight that is when we would only consider the human example The distinction between genus and species NOTE 66 on the one hand and differentia proprium and accidens on the other consists in the fact that the first are whatnesses while the last are qualities or traits The distinction between the accidens on the one hand and proprium and difference differentia on the other is that one or another accident signified by the accidens can at one occasion be present on a given individual subject at another time not anymore This either with respect to time or to space which latter means qua extension of the qualification accident over the set of individuals of the species Some individuals have the qualification others don t This is not the case for proprium and differentia The distinction between proprium and differentia is in fact very hard to ascertain Often it can only be so ascertained in an arbitrary fashion If we ask How can a human being be typically qualified then we can say either He is capable of laughing or we can say He is rational Which one of these would be the essential quale differentia cannot be ascertained just like that Conventially one says that it is rational that is this essential quale while taking capable of laughing to represent the proprium But this is an arbitrary decision We will return to this problem later The distinction between proprium and accidens which both must be in a subject is that the accidens with respect to a given subject can vary that is replaced by another in space or time while a proprium is always present in the subject So it goes for The human being laughs that laughs is an accident because he does not always laugh while for The human being is capable of laughing capable of laughing is a proprium because he carries this capability always with him Further can and must together with a given proprium in its definition also a certain appropriate subject be mentioned wherby it applies that this appropriate subject belongs to one species or one higher genus for which it is a proprium So when we consider all individual white physical bodies then those bodies that are always white do not represent a genus or species and therefore white is not a proprium NOTE 67 In Book I of the Topica Chapter V Aristotle defines four praedicabilia Definition Proprium Genus and Accidens The Definition consists of Genus and Differentia and can therefore in the list be replaced by the Differentia So we get Genus Difference Proprium and Accidens The fact that the Species is not mentioned forms a special problem Porphyry 3rd century A D does enter the Species in his Introduction to the Categories Science is not about particulars because these are contingent but about necessities A species is only predicable of particulars like Socrates Socrates is a human being what is by definition subsumed under a species are just individuals that s why Aristotle does not enter the Species here All terms are predicated of the species For demonstrative science the Species is the ultimate subject of predication Indeed science is about species and higher generalities it is about iron and about metals it is about light and sound it is about the silk worm butterflies and insects it is about the mammoth man and mammals It is never about the dog Fido or the greek philosopher Socrates that is it is never about individuals in the sense of particulars So the predicables as 2nd intentions classify terms such as animal Homo species est animal color White ness species is a color and space A line species is a kind of space namely one dimensional into the concept of GENUS The genus is directly predicated of the s p e c i e s The predicables further classify terms such as rational A human being species is rational living A human being species is living and sensitive A human being species is sensitive into the concept of DIFFERENCE The difference is directly predicated of the s p e c i e s The predicables in addition classify terms such as capable to laugh A human being species is capable to laugh possessing three angles that together make up 180 0 See above A triangle species is possessing three angles that together make up 180 0 and possessing a vena spuria See above Hover Flies species possess a vena spuria into the concept of PROPRIUM The proprium is directly predicated of the s p e c i e s Finally the predicables classify terms such as white A human being species is white musical A human being species is musical and tabloid An Alum crystal species is tabloid into the concept of ACCIDENS The accidens is directly predicated of the s p e c i e s All this however not in virtue of the terms themselves but in virtue of these terms as they are figuring in a given predicative context that is as a result of our way of thinking Because when predicating the term capable to laugh of a given species we mean by this predication the attribution of a quale that is a formal content to the subject which quale is such that it can diagnostically replace the Essence we characterize the term capable to laugh as representing a proprium that is as belonging in the Predicable Proprium and so in the same way with respect to the other predicables So we see that by classifying a term on the basis of what is meant in a given predication in which it figures into one of the Predicables we act according to general metaphysical presuppositions about reality that is about the ontological constitution of Being In order to understand well what is coming next it is perhaps useful to give here the Categories or equivalently the Predicaments which will be treated further below Together they form the most fundamental generic diversity within the domain of Being s l Generic diversity originates by that which makes possible different types of predications about the subject as it is said by St Thomas in In Metaph V lectio 9 nr 891 2 What the subject is What the measure of the subject is What the disposition of the subject is To what the subject is related What the subject possesses has on it When the subject is Where the subject is What the pose of the subject is What the subject does What the subject undergoes This results after maximally generalizing in the ten highest Genera What then is the precise difference between these Categories Predicaments and the above considered Predicables c The difference between praedicabilia and praedicamenta and the difference between predication and signification From what has been written in the Section on Predicables it is clear that the predicables are terms of second intention that is to say terms such as genus species proprium difference definition accidens and also the term predicable while the predicaments categories are terms of first intention Recall that terms of first intention are signs signifying extra mental things A human being that is Socrates or Plato or Peter etc IS an animal collection of all sensitive organisms Terms of second intention are signs signifying other terms of first or second intention The term animal is a genus that is the term animal is a generic term In the proposition animal is a genus the term animal refers to a certain type of terms namely a genus of which animal is an instance it as 2nd intention does not refer to extra mental things like sensitive organisms This difference between predicables and predicaments gets relief in the following The term color belonging in the accidental predicament Quality and which term can be predicated in a per se manner of for example red ness i e in virtue of the essence of red ness is the genus of red ness That is to say because the predication Red ness is a color is an essential predication here predicare in quid with respect to an auxiliary being namely red ness the term color is a genus it is not a species because the subject is not individual The term color thus belongs in the Predicable Genus It is established now what kind of term the term color is namely a genus And this genus is as genus a term of second intention As a term of first intention color signifies something in extra mental reality It signifies a collection of things which are such that we can legitimately attribute the formal content color to it When we in steps generalize color we obtain a sequence of higher and higher genera And the highest genus in this sequence red color is Quality Now we know that color belongs in the Predicament Quality and because red ness is per se a color red ness also belongs in this Predicament Red as predicated in The sun is red is however the predicable accidens because here the term is used in an accidental predication the sun is not always red while red is always also a predicamental accident because it is a quality of a given individual being that is it belongs in the predicament of Quality and is as such an ontologically dependent being NOTE 68 So the various members red color in the same Predicament Quality can differ as to in which Predicable genus species difference etc they belong Color belongs to the predicable Genus Predicative context red is a color predicare in quid essential predication with respect to a qualification as subject Red belongs to the predicable Accidens Predicative context the sun is red accidental predication Capable to laugh is a quality i e not as term but in virtue of that in reality to which the term capable of laughing refers The term signifies something which cannot stand on its own feet i e which is ontologically dependent it cannot exist all by itself but must be in a subject must be carried by a substrate so this term is a predicamental accident that is the term belongs in one of the nine Predicaments that come after the Predicament of Substance in the present case the Predicament of Quality But when the term capable to laugh is predicated of human being as in a human being species is capable of laughing it is the predicable Proprium The term capable to laugh is the predicable Proprium because it can be predicated only as proprium So as a term of first intention capable to laugh is a predicamental Accident while as a term of second intention it is the Predicable Proprium Also here the difference between predicables and predicaments is evident The Predicaments Aristotelian Categories refer to the way of b e i n g Therefore they and the subordinates of each one of them are as terms terms of first intention The Predicables refer to the way of p r e d i c a t i o n Therefore they are terms of second intention St Thomas states in In VII Metaphysica nr 1331 following the Stagirite Aristotle that predicamental accidents strictly speaking do not have a true quod quid est that is a definition because in the definition of a given accident we must always include something extrinsic with respect to it namely the subject Insofar as one nevertheless wants to speak of the essence of a predicamental accident because predicaments are terms of first intention predicables do not have an essence then one can do so only by way of analogy and via an abstract term for instance the essence of whiteness and not of white which is a concrete term The predicables classify terms into groups but as we ve said only from a predicative context The term capable to laugh is in itself not a proprium but a predicamental accident But capable to laugh insofar as this is said from something in a per se way per se predication is a proprium And this is directly related to the extension of the terms or concepts a concept is a natural sign while a term or word is the corresponding conventional sign The way of predication i e the different ways in which a predicate can be appropriate for a subject is here accordingly the criterion for distinguishing the different predicables The problem with this however is that the way of predication is also called a criterion for distinguishing the different predicaments from each other Aristoteles Metaphysica V 7 and St Thomas In V Metaphysica lectio 9 nr 890 Unde oportet quod ens contrahatur ad diversa genera secundum diversum modum praedicandi qui consequitur diversum modum essendi NOTE 69 So the via praedicandi here leads according to St Thomas to an understanding of the different ways of being expressed in the Predicaments Categories William of Ockham 14th century indeed states according to the interpretation of MOODY E A The Logic of William of Ockham 1965 p 69 note 1 that the predicaments are not ways of predication but ways of signification The name predicaments suggests that it is about ways of predication but the way of predication as such does not yield a distinction among the predicaments at all Socrates is a human being Socrates is 1 70 meter long Socrates is pale Socrates is shoed Socrates is cutting etc If we look into the per se per accidens character of such predications and that is only possible after we have considered the signification meaning we can distinguish between the predicables that is we can then determine whether a term is a proprium accidens genus etc is So it is the Predicables that are distinguished on the basis of ways of predication and not the Predicaments But distinguishing between ways of predication can only take place on the basis of the signification meaning of the terms It is directly on this that the Predicaments are based So the meaning of the terms determines directly into what Predicament the term belongs while the predicative context determines to what Predicable the terms belong The Predicaments Categories are terms as incomplex signs for things that is to represent things by referring to them They are not elements of propositions predications i e no parts of complex signs propositions Signification must precede predication because the truth of propositions depends on the signification meaning of the terms The Predicaments belong in that part of Logic which deals with the simplex apprehensio that is to say the first act of reason the apprehension of the concept and not the second act the proposition The Predicaments are ways of description of a given thing in which the degree of interiority of this description varies with the predicaments Indeed the description of a thing as having shoes on belonging in the Predicament Habitus is very external while being white belonging in the Predicament of Quality is already more intrinsic while something like being a human being belonging in the Predicament of Substance is the most intrinsic way of description way of signification So in this way we get the Predicaments as highest genera of these way s of description of a thing That is to say by maximally generalizing such descriptions shoed white human being etc we arrive at the ten upper genera Habitus Quality Substance Quantity Relation etc NOTE 70 If we consider a given term in ordere to determine its logical and ontological status we first look to what this term means and that is here to what in extra mental reality it refers if it refers to that reality at all and in so doing detached from any possible propositional or predicational context That is we consider its signification If this term indeed refers to something in extra mental reality then it is a term of first intention Such terms are classified by the system of Predicaments In fact all terms of first intention can be reduced to ten types classes or highest genera the ten Predicaments As to in what Predicament a given term of first intention belongs is determined solely from its signification that is from its meaning apart from any predicational context When we now consider the given predication in which the term happens to figure we determine again on the basis of the term s signification and that is now on the basis as to in what Predicament the term belongs the present predicative context of the term that is the per se per accidens nature of the predication and in what way the term figures in the predication that is what status the content to which it refers has does this content completely or incompletely express the Essence of an intrinsic being is it the content quale that completes the incompletely expressed Essence is it the content that can diagnostically replace the Essence or is it the content that is accidentally attributed to the given thing On the basis of this we determine as to what Predicable the given term belongs For example the term rational means some qualitative content Therefore logically it belongs as a term of first intention in the Predicament Quality In the predication A human being species is rational this qualitative content is that what completes the incomplete Essence as it is expressed by the term animal That is here the term rational is as a term of second intention a difference that is it belongs to the Predicable Difference So logically the term rational belongs as term of first intention to the Predicament Quality which is an accidental predicament while as term of second intention it as figuring in the predication a human being species is rational belongs to the Predicable Difference And this means that although rational is logically an accident its significatum does not reside in the phenotypic domain but in the genotypic domain of the given thing So ontologically the significatum of the term rational as it figures in the predication a human being species is rational is not something that is generated by the Essence that is is not a phenotypic expression of the Esssence but is part of the Essence Realize that the predicational context does not influence or determine the meaning signification of the term but only its status namely its ontological status phenotypic genotypic as well as its logical status as to what Predicable it belongs In our example we assume that rational in the predication a human being species is rational stands for the completion of the incompletely expressed Essence The Essence is the specific dynamical law governing the dynamical system human being The incomplete Essence is then the general dynamical law while that what contracts this general dynamical law to our specific dynamical law is that what is supposed to be signified by the term rational We will return to this topic further below All this leads us to the question that asks what then indeed is the the distinction between predication and signification If there is a difference at all then it seems to be as follows Signification is the apprehension simplex apprehensio of the individual essence or equivalently the quod quid erat esse NOTE 71 of a thing that is the transforming of an object into a significant object which exposes its pointe Next we apprehend the quod quid erat esse of another thing and after that of another thing etc And on the basis of the character of all these individual essences we form classes and subclasses This quod quid erat esse can also mutatis mutandis refer to a quantity a quality etc The Predicaments signify the whatness and that is here the most general whatness of either an ontologically independent being substance or of an accidental or per se determination of it In fact the predicaments signify always also in the case of accidental predicates the whatness of the thing how it is determined in itself or how it is determined per accidens and in so doing they indicate the degree of interiority of this whatness description The explicit emplacement of a thing s l or a group of things in a definite class by means of an assertion is then predication Socrates is a human being Socrates is a thing belonging in the category of Substance A human being is an animal Every human being is a thing that belongs in the category of Substance Redness is a color Redness is a thing that belongs in the category of Quality Summarizing Signification is a relation implicitly having it posited between sign signum and signified significatum or equivalently between sign and the thing which corresponds to it outside the anima intellectiva reason This sign is first of all a so called natural sign intentio animae Ockham Summa Totius Logicae I 1 which has a conventional sign as an effect that is a spoken or written word Predication is a relation between terms in virtue of their signification meaning The meaning significatio of terms incomplex signs ultimately is formed by ostensive definition that is via pointing to the signified significatum while at the same time mentioning the term As soon as we know the meaning of the terms and if they are thereby univocal or considered as univocal then we have a number of descriptions of things If we make these descriptions as general as possible then we are left with a number of fundamental ways or types of description ways of signification which indicate the whatness of a thing in as general a fashion as possible These most general ways of description differ among each other with respect to as has been said the degree of interiority of the description of the thing In this way we obtain the Categories or Predicaments The supposita that for which they stand of these most general descriptions are principles of being as was stated earlier C 1 Meaning and Extension Distinction of Predicables revisited The meanings of terms also give directly their relative extensions By means of these extensions ranges of reference which are themselves thus based on the meanings significations of the terms we can determine whether a given term belongs to the Predicable accidens proprium genus species or difference In the context of discursive science the species does not belong here while according to me it does so belong in the context of metaphysics The relative extensions are however not sufficient This is so because for instance the relative extensions of accidens and species on the one hand and the relative extensions of genus and species are identical where Ext X extension of X larger than smaller than acc accidens diff difference differentia specifica Ext acc Ext species Ext genus Ext species The other extensions are the species not being accounted for Ext diff Ext genus Ext diff Ext proprium Ext diff Ext acc Ext genus Ext acc Ext genus Ext proprium Ext proprium Ext acc So here we find the following equal relative extensions Ext diff Ext genus Ext diff Ext acc Ext acc Ext proprium Ext acc Ext diff Ext genus Ext proprium Ext genus Ext diff So in order to determine whether a given term belongs in this or that Predicable the relative extension is not sufficient For to detect a distinction between say genus and accidens their extension with respect to that of the difference is of no use because Ext diff Ext genus Ext genus Ext diff Ext diff Ext acc Ext acc Ext diff but also their extension with respect to that of the proprium is of no use because Ext genus Ext proprium Ext acc Ext proprium How then must we discriminate between say genus and accidens This can only be done by considering the way of predication predication per se predication per accidens and within predication per se predication in quid and predication in quale and within predication in quale predication in quale quid predication of the difference and predication of a proprium This way of predication takes place on the basis of the signification meaning of terms From these meanings that is to say from the terms intentions the absolute extensions follow The extensions consequently are the necessary result of the intentions Nevertheless we discriminate between for instance an accidens such as white and a proprium such as capable of laughing on the basis of how their extensions turn out to be Because capable of laughing turns out to occur exclusively and always in the species MAN we call it a proprium with respect to MAN And because white turns out to occur also beyond MAN it is in any case not a proprium with respect to MAN as appropriate subject Is it in the nature of WHITE also to occur in other things than humans Probably so Is it in the nature of CAPABLE OF LAUGHING to occur exclusively and necessarily in MAN Probably so So the term white signifies some formal content and capable of laughing also signifies some other formal content implying that they both logically belong in the Predicament of Quality But their extension range of signification turns out to be different In fact WHITE is a replaceable determination and so implies a substrate on which it can be replaced by another determination in te same Predicament while CAPABLE OF LAUGHING is a non replaceable determination it is always present in any given human being and thus does not imply a direct substrate only an ultimate substrate namely prime matter In this way we decide to which Predicable a given term belongs by considering the empirically assessed extension in the case of proprium and accidens where the extension of capable of laughing suggests it to stand for a non replaceable determination while the extension of white suggests it to stand for a replaceable determination But with this we cannot ascertain whether the term capable of laughing is a proprium or a difference because the extensions of proprium and difference are equal The distinction between proprium and difference could be that a proprium refers to an ontologically dependent entity while implying an appropriate subject while the difference refers directly to the last over forming which has itself integrated as to become over formed matter integrated such that it is now over formed matter and is thus ultimately an ontologically independent entity NOTE 72 A second distinction related to the first one could be that a proprium is always and exclusively present with the Essence without however necessarily following from it while a difference is a formal content that necessarily follows from the Essence and that means here necessarily is the Essence the difference explicitly signifies the last over forming and implicitly the rest and thus it signifies the Essence However these distinctions lack sense as long as we cannot objectively ascertain whether something for instance that which represents CAPABLE OF LAUGHING does or does not comply with the mentioned criteria Does CAPABLE OF LAUGHING comply with the criterion that it is always and exclusively concurrent with the Essence and with it with MAN without necessarily following from that Essence The first part of this criterion can be empirically verified but as regards the second part we cannot indicate anything that would convince us that CAPABLE OF LAUGHING does not necessarily follow from the Essence and that RATIONAL does necessarily follow from it RATIONAL is always and exclusively present at the Essence that is always present in MAN but does it then necessarily follow from the Essence or not Whatever answer we give in the present stage of the discussion but see already NOTE 72 the answer is stipulative instead of being ascertained on the basis of enquiry Before we investigate this further we can establish that the predicables Genus Species and Accidens do not pose problems The predicable accidens has as suppositum NOTE 73 a per accidens determination replaceable determination The predicables genus and species have as suppositum the Essence The genus expresses that aspect of te Essence that commonly occurs in the subsumed Essences For example the genus animal refers to a common nature that is present in MAN as well as in DONKEY HORSE DOG etc So genus and species do not have as suppositum one or another determination but the Essence itself But as said proprium and difference give problems at least in Classical Metaphysics In my revision as has been laid down above especially in NOTE 72 and as will be expounded further below of this sproblem I have given an answer We can say that with respect to MAN but then generalizing all this the features RATIONAL and CAPABLE OF LAUGHING are ontologically equivalent Both are generated by the dynamical law both are permanent and so do not involve inherence both are phenotypic essential parts namely certain material substructures of the human body both are generated by that part of the dynamical law that we call the difference This difference is the over forming of the generic part of the dynamical law and so is a genotypic essential part In the definition of MAN we can phenotypically let represent this difference by either the feature RATIONAL or the feature CAPABLE OF LAUGHING Both are propria That to which a proprium refers is phenotypic and not replaceable That to which an accidens refers is phenotypic and replaceable That to which a difference refers is genotypic and not replaceable In the following we will precisely and in more detail go through all this We have been able to established that the Essence of a genuine intrinsic complete being is identical to the dynamical law governing the dynamical system that can generate this being from basic elements In almost all cases of such beings we are not able to explicitly formulate this dynamical law it is simply unknown But for the exposition of the status of genus species and difference this is not necessary These status we can and will illustrate with the help of a number of simple abstract dynamical laws expressed in a mathematical form These laws are fictitious i e without possibility of physical interpretation but that is no obstacle because here it is about laws as laws Such dynamical laws can come in all kinds of forms among which that of a polynomial i e a mathematical expression involving more than one term Let us give an example X n 1 3X n 2 2X n 7 Here X n and X n 1 refer to consecutive process states and X n 2 means X n multiplied by itself that is the square of X n X n X n 1 X n 2 etc are variables and that means that they are each for themselves as it were a box provided with a name that is the name of the variable as we have here for example X n or X n 1 or X n 2 and into such a box we can put one or another chosen or computed value We then have a box with the name pasted onto it say X n and a value say 5 put into it We can change that value at will So we can replace the value 5 in box X n by the value 8 We then say that the variable X n first had the value 5 while later the value 8 has been attributed to it The meaning of the above given expression which is supposed to represent a dynamical law is as follows The new process state X n 1 is generated from the previous old process state X n namely in the present case as follows The new state X n 1 becomes equal to Three times the square of the old state X n 3X n 2 plus two times that old state 2X n plus 7 If we thus start with a value for X n then we can compute the value of X n 1 as indicated above And then a new state is generated from the previous state From this new state a next state can in turn be generated and thus calculated by repeating the procedure This we do by placing the computed value of X n 1 back into X n that is we rename the value that was computed for X n 1 to X n and introduce it back into the expression X n 1 3X n 2 2X n 7 that is X n wherever it occurs in te expression gets this new value We can then calculate this next state This can be continued as far as we want to and what we get is a whole series of consecutive states And because in this procedure every time the newly obtained value is intoduced back into the expression the formula as now representing the old one this we call iterating NOTE 74 we have to do with a feedback system feedback often occurs in organisms Such type of dynamical system one calls a recursive system So here we have given an example of a polynomial dynamical law polynomial because X n 1 3X n 2 2X n 7 is a

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  • Aristotelian metaphysics IIIa
    formal content and a formal content is totally homogeneous So 3 of Defintion 8 is satisfied Definition 9 X is substantial 1 X is atomic and 2 X is not specifically dependent on any other entity Specifically dependent always and only refers to the formal content of something not to efficient causality Something atomic Definition 8 can either be substantial or accidental Definition 9 defines something being substantial Commenting on Definition 8 we already dealt with something which is substantial and at the same time not a mere part of a substantial atom but the whole substantial atom and thus the whole carrier only But atomic can also mean a proper part or region of an atom and so something substantial can be just a part of a carrier only to which we now turn our attention while applying the definition to a part of a branched snow crystal as historical individual thus considered over that part of its life time in which it was branched where its branches can vary as to their lengths and shapes carrying or not carrying sectored plates etc and where all other replaceable accidents are not determined If then we consider an arm of a branched snow crystal still attached to the crystal this arm satisfies being substantial because it satisfies being atomic and is not specifically dependent on any other entity It does not need any ontological carrier It is atomic because it is not an aggregate in the mereotopological sense because any attemted partition any cut through this arm involves common boundaries Such a boundary is an individual part and this individual part is a common part and so the parts resulting from the attempted partition are not discrete and consequently they are not mutually separable because again they have a common boundary and such a boundary is dependent for its existence on both parts So 3 of Definition 8 is satisfied And because the arm is individual and if abstractly considered i e considered as the carrier of Accidents only does not involve inherence NOTE 85a 1 and 2 of Definition 8 are also satisfied And because the arm satisfies 2 of Definition 9 this still attached arm of the snow crystal is substantial i e it is a part because it is just an arm of a Mereo totality and moreover of a genuine Substance taken as a historical individual and not a part of an accident i e it is not accidental It is in short a substantial part It is a part of the carrier only But on actual separation of the arm from the snow crystal s body the arm is not a part anymore and will have a complete boundary of its own It has become mereotopologically independent it is a Mereo totality i e a Substance in its own right in the mereotopological sense But when we supplement this mereotopological treatment with considerations from the dynamical systems approach then the detached arm is only a Mereo totality it is not a genuine Totality and equivalently not a genuine Substance within that supplemented approach The next Definitions Definitions 10 10a and 11 are very important They are about genuine boundaries of or within things Definition 10 X is boundary dependent on Y 1 X is a proper individual part of Y and 2 X is necessarily such that either Y exists or there exists some part of Y properly including X and 3 each individual part of X satisfies 2 For example X is the surface of a crystal Also every facet of it can stand for X Y is the crystal itself With surface we do not here mean the skin or rind of some object but the surface in a geometric sense This surface is boundary dependent It is a genuine mereotopological relation So the surface of a crystal and also everyone of its facets if present is boundary dependent on the crystal Let us analyse the definition X is a proper individual part of Y as stated in 1 of the definition means that X is not equal to Y apart from X there is still more of Y properly including X means that X is contained in something without thereby exhausting that something So here in 2 there is a part of Y that is partly at the same time X partly not 1 and 2 of Definition 10 are satisfied by X finding itself in the following situation Here X is indeed a proper individual part of Y so 1 is satisfied Y extends beyond X where we can call it Y X which means Y insofar as it is not X Y X is discrete from X Because X is a part of Y it cannot exist without Y or at least not without some part of Y that includes X That is at least that part of Y that coincides with X is needed for X to exist But in order to satisfy 2 X must be dependent either on the whole of Y or X must be dependent on just a part of it but this part of Y is then when we want to satisfy 2 not only that part of Y that precisely coincides with X but in addition to that coinciding part some part no matter how small of Y discrete from X that is some part of Y X X cannot be just We can see that the situation of X in our first drawing satisfies 2 of Defintion 10 and it has already satisfied 1 Now in order to check 3 we look to a proper part of X Here we have a proper part of X yellow For this part let us call it X p we can say X p as it is depicted here that is existing together with the whole of Y is necessarily such that either the whole of Y exists or at least that part of Y must exist for X p to exist that coincides with X p PLUS some part of Y discrete from X p This latter part is contained in Y X p As one can see X p satisfies 2 X p is connected with at least a part of Y that is discrete from it Therefore X satisfies 3 So X as it is given in our drawing satisfies Definition 10 But although we have now illustrated the definition and demonstrated its actual content it is clear that the intended meaning of Definition 10 X is boundary dependent on Y is quite different The meaning that is the intended meaning should be that X as a proper part of Y is at the extremes of Y and also all parts of X So although I shall not definitively assert that Definition 10 as originally given by SMITH misses its intention it is not a very clear definition of the intended state of affairs Therefore I propose to replace Definition 10 by another Definition that correctly and above all clearly and still in a topological way expresses the intended meaning Definition 10a X is boundary dependent on Y 1 X is a proper individual part of Y and 2 X is such that every neighborhood no matter how small of any given part of X does contain a part of Y discrete from X In the following diagram the situation of X clearly satisfies Definition 10a Here X is indicated by the blue rim at the periphery of Y red In fact the width of this rim must be infinitely small symbolized by the next diagram Here X is the utter extreme part of Y The next diagram shows that every possible neighborhood no matter how small of any given part of X as X is given in the diagram always includes some part of Y that is not X So 2 of definition 10a is satisfied And because also here X is a proper individual part of Y 1 is satisfied too So X as depicted in the above diagram completely satisfies Definition 10a and is thus boundary dependent The surface or a facet of a crystal exactly matches this definition that is the surface and also a facet if present of a crystal is boundary dependent on that crystal When X is a point it can be the extreme of a line as can be demonstrated by a one dimensional vanishing neighborhood When X is a line or curve it can be the extreme of a plane as can be demonstrated by a two dimensional vanishing neighborhood as is in fact the case in our last two diagrams When X is a plane curved or straight it can be the extreme of a solid as can be demonstrated by a three dimensional vanishing neighborhood Indeed SMITH characterizes the intended meaning of the definition X is boundary dependent on Y as follows Roughly a boundary of dimension n can never exist alone but exists always only as part of some extended neighborhood of higher dimension There are no points lines or surfaces in the universe that is in material reality which are not the boundaries of three dimensional material things See next Definition Definition 11 X is a boundary X is boundary dependent on some individual Because the surface of a crystal or of any of its facets if present is boundary dependent on the crystal that is satisfies Definition 10a it is a boundary of that crystal So a genuine boundary of some entity X is not discrete from X because it has individual parts in common with X See Definition 2 And consequently a shell rind or rim around something else is not a genuine boundary of that something The next Figure illustrates this Figure above The object Y has a rind This rind has a proper part P yellow that is discrete from Y Therefore this rind is not a genuine boundary of Y But the rind is separated from the outside world by a genuine boundary And this boundary is an entity which indeed is boundary dependent on some individual entity namely the rind or said differently there is a part of the rind that is boundary dependent on the rind Another genuine boundary separates the rind from Y This boundary is an entity that is boundary dependent on the rind and on Y The above Figure shows two types of genuine boundaries viz involving one sided and two sided boundary dependency Their difference relates to contiguity discontinuity and continuity and involves non common and common boundaries One sided boundary dependency is about a non common boundary while two sided boundary dependency is about a common ly possessed boundary But what then in the above Figure exactly is the difference between the genuine boundary between Y s rind and the outside world on the one hand and the genuine boundary between Y and its rind on the other The rind is an object different from Y And also the outside world can be considered to represent an object different from the rind So what makes the two corresponding genuine boundaries different from each other one of them one sidedly the other two sidedly dependent The only reason we can think of is that the rind in some way belongs to Y while that what represents the outside world does not Purely physically this distinction seems arbitrary On closer inspection however it is in many cases not arbitrary Among Mereo totalities at least all single c r y s t a l s are chemically continuous that is every atom in the chemical and physical sense is at least indirectly connected and that is here chemically bonded to all other atoms of the crystal Here the all is determined by the fact that in every crystal whatsoever the number of chemical bonds is finite At some sites of the crystal the chemical bonding is not complete there are unsatisfied valences And the sum of all such sites we call the perifery of the crystal So the crystal is chemically discontinuous to some other material range We can express this by saying that the crystal shows a chemical discontinuity as we pass from it to the outside world outside with respect to that crystal Such a crystal can have a partition of it into parts as a result of a system of cleavage planes planes in the crystal containing relatively weak chemical bonds When we want to separate these parts we have to break these bonds this is what we do when we cleave a crystal that is we have to break the crystal Therefore these parts are ontologically not separable and the partition is a partition of the crystal into mutually in separable parts as such satisfying 3 of Definition 8 The same is true of the partition of a crystal resulting from substitution The entities that are presently surrounding the crystal and as such representing the crystal s outside world can be separated from the crystal without having to break something There are no chemical bonds between the crystal and the entities representing its outside world its neighborhood So when concentrating our attention to chemical continuity or discontinuity we see that in crystals the difference between internal genuine boundaries such as cleavage planes on the one hand and the external genuine boundary that is the crystal s surface is not arbitrary Could chemical continuity be a universal feature of all true substances We do not know An atom in the physical sense is not held together by chemical bonds because it is the very unity as basic element that is bonded to other such unities by chemical bonds but by strong physical forces A molecule is held together by the chemical bonds between its atomic constituents A crystal is also held together by the chemical bonds between its constituents And an organism finally is at least for a large part held together by chemical bonds between constituents But whether an organism can or cannot be considered to be one giant molecule bathing in serum we don t know Chemical continuity is at least an important auxiliary criterion to decide where two sidedly and one sidedly boundary dependent structures lie and thus determining the spatial extent and delineation of a given Mereo totality a thing a substance either as historical individual which then is a carrier only or as here and now individual which then is the fully fledged Mereo totality as such having all its accidents fully determined When we while thinking how the situation is inside atoms would add physical forces to the criterion then we have too much because everything is connected with everything else by physical forces among which can be reckoned chemical bonds but also for example gravity If we cannot interpret an organism which definitively is a genuine Mereo totality if not a genuine Substance as chemically continuous we must stipulate that there are in the organism in addition to chemical continuities some other continuities which we must metaphysically characterize by the relation belonging to So some entities although not chemically connected to the admitted Mereo totality must nevertheless belong to it And then the decision whether some given boundary is an entity that is two sidedly or one sidedly dependent that is whether we have to do with either an internal boundary distinguishing mutually inseparable parts or with an external boundary distinguishing the Mereo totality from its outside world that is from its neighborhood cannot be made anymore on the basis of purely mereotopological considerations We will return to this interesting and important topic after having given the next Definition Definition 12 X is a Mereo totality 1 X is substantial 2 X has a boundary 3 there is no Y that is boundary dependent on X and on some individual that has parts discrete from X The Defintion in fact says that a part of a Mereo totality is itself not a Mereo totality 3 excludes substantial parts i e it excludes the possibility that a substantial part is itself a Mereo totality and by implication a Substance If there were some Y that is boundary dependent on X and at the same time boundary dependent on some individual that has parts discrete from X then X would be connected with something by means of Y that itself extends spatially beyond X and so X would be just a substantial part of a larger whole comprising X and more See next Figure Figure above A mereo totality Z with substantial part X bounded by Y A zoned crystal is a single Substance and therefore a Mereo totality The zones of this zoned crystal are not themselves Substances The chemical composition of such a crystal is defined such that the possibility of substitution of explicitly specified atomic specis is accounted for Parts enclosed by the system of cleavage planes of a given crystal are not themselves substances For clarity we can give Definition 12 in its fully analysed form X is a Mereo totality X is atomic Definition 8 X is individual X does not involve inherence There is no partition of X into mutually separable parts X is substantial Definition 9 because X is atomic and X is not specifically dependent on any other entity Further X has a boundary There is no Y that is boundary dependent on X and on some individual that has parts discrete from X A fine example of an entity that is partitioned into mutually separable parts and thus not complying with 3 of Definition 8 and thus not complying with Defintion 8 consequently not with Definition 9 and thus not with 1 of Definition 12 and by consequence not with Definition 12 meaning that it is not a Mereo totality is a quarzite pebble A quartzite is a rock composed essentially of Quartz It has been derived from a sandstone by high grade metamorphism It is a compact rock of interlocking quartz grains that is of interlocked grinded quartz crystals or crystal fragments Another example is a system of two contiguous billiard balls that is two such balls that are in contact with each other This latter example was used in the document on Mereotopology in First Part of Website to expound boundaries and partitions Because of its importance we reproduce the discussion of that example as it was laid down in the mentioned document and add some extra considerations The problem is how to ontologically assess an entity that is partitioned into mutually separable parts and the conclusion is that it is not a Mereo totality SMITH argues this with the example of two billiard balls which are in contact with each other as depicted in the next Figure Figure above Two billiard balls X and Z in contact with each other Y is the boundary separating them Let us now assess the status of one billiard ball say X The boundary Y between the two billiard balls that is between X and Z is not boundary dependent on both X and Z i e it is not boundary dependent on X Z because this boundary still exists when we destroy one of the balls To separate X Z into X and Z we do not have to break the balls away from each other So X does satisfy 3 of Definition 12 Moreover X is substantial NOTE 85b and X has a boundary so X satisfies Definition 12 This implies that X is a Mereo totality also when X is in contact with another ball The same holds for ball Z Let us now assess the status of the complex of the two balls in contact that is X Z This complex does not possess a boundary or piece of boundary that is boundary dependent both on X Z and on some W that has parts discrete from X Z This is because the boundary of X Z remains when W is removed or destroyed We do not have to break the complex X Z W into X Z and W So X Z satisfies 3 of Definition 12 And because X Z is substantial and has a boundary it follows that X Z is a Mereo totality or even a Substance Because X is itself a Substance and Z is itself a Substance certainly in the case where X and Z are quartz crystals in quartzite it follows that a Substance can consist of parts which are themselves Substances which contradicts a conclusion of SMITH that is contradicts Definition 12 But wait a minute We asserted that X Z was substantial Then it must be atomic Definition 9 Let us now recall the Definition of atomic Definition 8 X is atomic 1 X is an individual 2 X does not involve inherence 3 there is no partition of X into mutually separable parts The complex of the two billiard balls i e the complex X Z is clearly partitioned into X and Z Let us recall the definition of partition and substituting some of its symbols to make it easy to read with respect to our example Definition 7 X and Z form a partition of X Z 1 X and Z are parts of X Z 2 X and Z are discrete from each other 3 no part of X Z is discrete from both X and Z Applied to our example X and Z are indeed parts of X Z 1 is satisfied X and Z are indeed discrete from each other they have no individual parts in common 2 is satisfied no part of X Z is indeed discrete from both X and Z 3 is satisfied So X and Z form indeed a partition of X Z Because the parts X and Z are mutually separable they indeed form a partition of X Z into mutual separable parts So 3 of Definition 8 is violated implying that X Z is not atomic And thus X Z is not substantial implying further that 1 of Definition 12 is violated so X Z is not a Mereo totality and by implication not a Substance So it is already 3 from Definition 8 which decides that the complex of the two contiguous billiard balls is not a Mereo totality and consequently not a genuine Substance So a whole consisting of contiguous parts would not be a Substance according to SMITH definitions But this could according to me imply that multicellular organisms are not Substances So if we nonetheless admit them to be Substances because they seem to be even the primary instances of Substance then mereotopology alone cannot decide this This is to be expected because the relation belongs to in the sense that some entity belongs to some other entity is not a purely mereotopological concept We must stipulate that the interstices between organic tissue cells belong to the organism So these interstices are then themselves also parts of that organism And then the boundary between the boundary of a cell and the interstice dividing it from another cell could it is true still be interpreted as a bona fide boundary but this boundary is boundary dependent towards both sides implying that each cell is not separable from the interstice and vice versa so condition 3 of Definition 8 is satisfied and then each cell becomes indeed just a substantial part of the organism It also implies that an organism is not a contiguum but a albeit heterogeneous continuum It is a continuum in the sense that starting from one point location within the entity we can reach every other point of that entity without ever having temporarily to leave the confines of that entity So it is a continuum by way of belonging to that is it is only a metaphysical continuum It is not a mathematical continuum because it has actual parts if the latter indeed allow themselves to be interpreted as parts In other cases we must stipulate that some cavities do not belong to the organism by means of a functional argument i e not by means of a mereotopological argument We can detect this clearly in the discussion of SMITH BROGAARD 2000 p 25 where they discuss the question whether some items like the amnionic cavity or the digestive canal do or do not belong to the organism in question Definition 12 while basing itself on the Definitions 8 9 10 and 11 pretends to define a Mereo totality and by implication a genuine Substance We should however investigate what then precisely is being defined Is it the Mereo totality insofar as it is the carrier only or is it the full fledged Mereo totality And if it defines just the carrier only what then is the nature of such a carrier only Is it contiguous or continuous and if the latter is it homogeneous or heterogeneous In order for an entity X to be a Mereo totality Definition 12 demands X to be substantial and that means according to Definition 9 that X must be atomic and not specifically dependent on any other entity So X is the substantial part of the Substance Accident composite which means that X as finally defined in Definition 12 should be the carrier only A substance accident composite is not atomic The mereototality as carrier only is only generically dependent on its accidents This carrier only X should then have the following three important characteristics 1 There is no partition of X into mutually separable parts Definition 8 This means that the carrier only must be a complete unity and this in turn means that it is not a contiguum like the two billiard balls or the quartzite pebble even not a tight contiguum A partition of non separable parts is admitted though 2 X does not involve inherence Definition 8 3 X is not a substantial part Definition 12 i e it is not a proper part of a carrier only These are then the characteristics of the Mereo totality insofar as it is the carrier only that is the historical individual A fully fledged Mereo totality on the other hand is the here and now individual having all its accidents with it and these accidents are fully determined If there exist in such a fully fledged Mereo totality partitions into mutually separable parts and if such partitions are replaceable then they are genuine determinations that is they are then mere accidents And that means that these parts are not parts at all because accidents are not parts they are virtual parts or equivalently they are actual determinations So also such a fully fledged Mereo totality is still a continuum So if partitions of mutually separable parts are just replaceable determinations meaning that these parts are not parts at all then a fully fledged Mereo totality having these partitions also complies with Definition 12 It is perhaps useful to reproduce Definition 12 in its fully analysed form X is a Mereo totality X is atomic Definition 8 X is individual X does not involve inherence There is no partition of X into mutually separable parts X is substantial Definition 9 because X is atomic and X is not specifically dependent on any other entity Further X has a boundary There is no Y that is boundary dependent on X and on some individual that has parts discrete from X Let s proceed to the next Definition If an atomic entity is specifically dependent on a whole Mereo totality or Substance then this entity is an Accident See the relevant definitions below It needs a carrier for it to be able to exist It is a DEPENDENT ATOM because it can only co exist Definition 13 X is an accidental 1 X is atomic and 2 X is specifically dependent on some individual Y Examples Two ajacent arms of the six equivalent arms of a branched snow crystal have a length of say 1 0 mm while the other four arms have a length of say 0 6 mm that is two of the six arms happen to be longer than the other arms The content length of 1 0 mm is per accidens with respect to the Essence of a snow crystal and is confined to a certain region of the crystal Therefore it is an accidental not yet an accident See HERE to see such a crystal A snow crystal happens to be sectored plated See HERE to see such a crystal the crystal shown in connection with the previous example also was sectored plated Here the content sector plated refers to the whole crystal and is therefore not only accidental but also an accident see next Definition A given uniformly grown crystal has a diameter of 2 cm In all crystals their actual size is per accidens because within limits they can keep on growing The content diameter of 2 cm refers to the whole crystal and is therefore not only accidental but also an accident see next Definition As is clear from the examples an accidental could be a determination of only a part of a Mereo totality or Substance and as such it actualizes a potential part of the latter If we interpret non essential parts of a Mereo totality and especially of a Substance as mere regions i e as virtual parts then an accidental can actualize just a quality in a certain region of the Substance Definition 14 X is an accident of Y 1 X is an accidental of Y 2 Y is a Mereo totality 3 there is no substantial proper part Z of Y such that X is an accidental of Z Examples A given snow crystal happens to be sectored plated A given crystal has a diameter of 1 cm A given snow crystal happens to be tabloid shaped In snow crystals the habitus is not intrinsic because it can vary with external conditions such as ambient temperature Definition 15 X is an atom X is either a Mereo totality or Substance as carrier only or X is an Accident Examples A historical individual of a crystal species carrier only Sector plateness of a snow crystal accident Actual size of a crystal say a diameter of 1 cm accident The relation of specific dependence is the bond which holds atoms together in molecules of different sorts Such molecules are the referents of simple empirical judgments such as Socrates is tanned John is kissing Mary etc To capture the notion of molecule SMITH defines Definition 16 X is closed under specific dependence no part of X is specifically dependent on any entity discrete from X no part of X can also mean X itself So X can be a Mereo totality as carrier only a Substance as carrier only See Remark or a Mereo totality Substance Accident composite It cannot be an accidental implying that it cannot be an Accident Remark A carrier only is only generically dependent on its being determined by a complete set of types of replaceable determinations Ontologically it does not matter precisely which determination here which Accident represents each type Although definition 16 is meant to rule out accidentals on closer scrutinity it turns out not to do so An accidental is just like the carrier only not specifically dependent on a carrier it is only generically dependent on its having a carrier Thus something being an accidental is not ruled out by that Definition as given by SMITH If however we hold with SMITH that the dependence of Accidents on their carriers substrates is specific i e a one sided specific dependence then accidentals and Accidents are indeed ruled out by something that is closed under specific dependence Indeed on p 4 of the Internet version of his article SMITH states My headache for example is specifically dependent on me as also on my head Of course in this case my headache is not just dependent on one or another human substrate but is dependent on a certain individual namely me It is an individual Accident However this is because the Accident headache is qualified by my But my is extrinsic to a headache as such so it should not be included in a term which purports to signify an Accident Headache as such can occur in several species of head and referring to a genuine and complete Substance in several species of animal An Accident needs an appropriate substrate in order to exist but this still leaves open several possibilities for a substrate and thus an Accident and also an accidental is just generically dependent on a substrate If it were specifically dependent then it is either a per se proprium such as Space Group PLUS Chemical Composition in crystals or a per accidens proprium such as RATIONAL or CAPABLE OF LAUGHING in humans but such a per accidens proprium is only in a very special and very weak sense per accidens For all intents and purposes it is a per se determination and consequently not a genuine accidens but a proprium So it seems that indeed all true accidents are only generically dependent on a substrate just like a substrate is only generically dependent on its having accidents Although I will not once and for all rule out the possible asymmetry between on the one hand the dependence of a carrier only substrate on Accidents which is generic and on the other hand the dependence specific of an Accident on its carrier I for the time being and preferably will stick to the generic nature of the dependence of Accidents on their having a carrier substrate and should change the relevant Definition accordingly REMARK With respect to the example of a complex molecule namely the molecule John is kissing Mary I would like to state the following kissing as such is not exclusively dependent on John and being kissed as such is not exclusively dependent on Mary If the act of kissing can only occur in one particular species of organisms then it is specifically dependent on a carrier substrate So generally we must say that accidents are either specifically or generically dependent Consequently we must always take a possible generic dependence of accidents into account and thus the asymmetry must be indicated by upward and downward dependency As a result of the foregoing I will propose to amend Definition 16 in order to properly exclude accidentals and consequently Accidents The dependence relation between an Accident and its having a carrier is an asymmetric relation in the following way The carrier only is upwardly dependent on its having Accidents The dependence is a generic one The Accident is downwardly dependent on its having a carrier The dependence is also of a generic nature So if we want to rule out Accidents we should exclude downward dependence If we do so then we exclude accidentals and Accidents but admit Mereototality Substance Accident composites and also carriers only So we define Definition 16a X is closed under downward dependence no part of X is downwardly dependent on any entity discrete from X Examples A historical individual of a crystal species is closed under downward dependence We here have a carrier only A here and now individual of a crystal species is closed under downward dependence We here have the fully fledged substance The next definition defining a molecule should rule out carriers only Definition 17 X is a molecule 1 X is closed under downward dependence 2 X has discrete parts 3 all atoms Y Z which are parts of X are connected directly or indirectly by relations of specific or generic dependence In 1 we have replaced specific in SMITH definition with downward In 3 we have added or generic All those dependencies are meant to be ontological which means that they are not referring to efficient causality 1

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  • Aristotelian metaphysics IV
    on the other A genus is only one in virtue of its indifference as regards the various further determinations thus as regards the various species For when it is further determined then it is a plurality It only then has unity when we disregard the further determinations Matter on the other hand is one and remains one when it is further determined by the form so St Thomas says in De Ente et Essentia Cap II line 230 However it is according to me such that prime matter as soon as it is actualized by various forms substantial forms it is at once varous things that is to say that also matter is only one in virtue of its being undetermined and is also many like it was in the case of the genus after its being determined especially since St Thomas holds that every being possesses only one substantial form So here we had not been able to distinguish between a logical entity genus and an ontological entity matter Another attempt to indicate the difference between logical and ontological composition St Thomas makes from line 202 onwards by saying that man does not consist of animal and rationale terms of the definition but of body and soul matter and form and these together constitute the one thing For St Thomas but still more for those who lived since DARWIN the body and soul form a tight unity whereby the latter even do not accept a principal difference anymore on the basis of the very plausible theory of organic transmutation evolution of 1 man from other organisms for the first time deemed possible by DARWIN in 1859 and subsequently asserted by him in 1871 and 2 evolution of the first organisms from non living materials for the first time as theory proposed by HAECKEL in 1866 in Cap VI of volume I of his Generelle Morphologie der Organismen and further in its first step confirmed by the experiment of Stanley MILLER in 1953 and yet further investigated by his followers and subsequently by molecular biologists This continuity of the inorganic to the organic and from here to rational organic is nothing else than an ever progressing physico chemical determination of matter by differentiation and integration of parts that in all sorts of cases compose themselves into holistic wholes with an ever increasing diversity in work functions From this datum we can nowadays say that matter including all its forms such as wave phenomena the energies induced fields etc in itself already contains all those possibilities of evolution all the way up to generating the human species Consequently man has not originated from two sources physical matter and spirit but from one source only This implies that he is an absolute unity just like genus difference constitutes a unity for genus as well as difference indicate the species albeit in different ways Indeed e volving means unrolling the actualization of a potency The difference between matter body and form soul now even in the case of man turns out to be of the same nature as the difference between genus and difference for body is the determinable substrate and soul is the determination which latter is here a historically developed emergent high level phenomenon This determination wholly comes from the body itself just like the possible differences are already implicitly present in the genus So also here we fail to distinguish between logical and ontological entities If all this is correct then it might be that the celebrated matter form composition is nothing else than a not yet fully reasoned reification thing i fication of a way of human thinking which could end up in a dialectical or Hegelian metaphysics NOTE 124 It is clear that for all this much more enquiry is necessary and that up to date we cannot yet decide for a definite position In fact we will never decide on it this to keep the dialogue open because we do not pretend to have found the final solution What we do realize is that the standard example of the ontological constitution of MAN so often used by Aristotle and his Latin and Arabic pupils and from which example they have it is true learned so much must be looked at again especially in the light of new knowledge we have done this in First Part of Website and that also other examples must be given in order to see whether or not the metaphysical position is valid throughout we have done this but far from exhaustively so in First and Fourth Part of Website In a thematic treatment of a metaphysics along the lines of Aristotle further extended by St Thomas and some modern writers such as P HOENEN A Van MELSEN B SMITH we cannot avoid the theory of organic evolution when dealing with for example the ontological status and composition of MAN and also of living beings in general as compared to inorganic beings At least at the phenomenological level in the Explicate Order of Reality we could say it is almost certain that there is material continuity if we go from inorganic to organic to intelligence At this level the intelligent beings seem to have originated from earlier organic beings and the first organic beings seem to have originated from inorganic beings If however Reality has in addition to this phenomenological level yet another level which is more concealed an Implicate Order of Reality we could say then what we observe does not need to be all there is in Reality What we indirectly observe is a transmutation of inorganic matter into organic and finally into intelligent matter But in fact we can only observe horizontally that is along the time dimension within the Explicate Order Maybe the observable sequence of inorganic organic intelligent is just a superficial effect of a much more fundamental process taking place in the Implicate Order and which stepwise becomes manifest by ascending vertically into the Explicate Order All this we discussed in Third Part of Website and Fourth Part of Website Where on the other hand philosophy is dealing with creation not only in the theological sense the theory of organic evolution becomes irrelevant because creation is about the transition from non being to being and therefore is about the resulting ontological constitution of beings while the theory of organic evolution presupposes pre existing materials from which the origin of life and organic evolution proceed that is which pre existing material only changes into other material The theory of evolution is important for coming to know for example what MAN precisely is as to his qualitative content But this is a task belonging to Natural Science However a number of relevant results obtained from the latter will be important for Philosophy too because MAN plays such an important role there not only with respect to Ethics for example with respect to his ability think and the necessary structure of his thinking but also with respect to his alledged composition of Body and Soul In these respects the theory of evolution and its conclusions are of crucial importance to Philosophy For the time being we conclude that St Thomas at least in his De Ente et Essentia has not yet succeeded to indicate the distinction between the logical differentiation in the Definition on the one hand and the possible ontological differentiation in a finite being that is a material being on the other Of course the one is in the mind in mente while the other is outside the mind extra mentem but having only this difference at our disposal the metaphysical expositions about the ontological constitution of beings look little more than not yet well argued thingifications of the structure of thinking and language and thus in fact some brand of Neo platonism as we see it for example in Proklos NOTE 125 It is generally precisely this problem namely the problem of purifying metaphysics from exclusively logical entities which occupied William of Ockham and he shouldn t therefore be called anti metaphysical For Ockham the matter form distinction and consequently also the potency act distinction is no more than a logical distinction it figures in a propositional context of modalities namely of being possible and being real as we already have said earlier NOTE 126 f Idea as Essence Platonism St Thomas following Aristotle criticises at many places in his works the Doctrine of Ideas of Plato There are however many indications that their interpretation of Plato In the case of St Thomas the doctrine largely came down on him via Aristotle and Neoplatonism and thus not much of it directly from Plato himself is not correct in all respects and even if it were correct this doctrine of Ideas may still be a possible point of departure in an attempt to interpret Reality ontologically The fact is whatever possible metaphysics we consider sooner or later we will find out that a certain amount of Platonism cannot be avoided Aristotle sees in the Doctrine of Ideas some sort of unnecessary doubling of beings but we doubt whether Plato meant it that way NOTE 127 The being of 1 Idea and of 2 observable entity probably involves an analogy or is perhaps more or less comparable with the ways of being distinguishing Kant s noumena and phenomena Anyway they do not belong to the same order of Reality in the same way that say the sign insofar as it is sign not insofar as it is a physical thing or structure and the signified do not belong to the same reality order NOTE 128 Something comparable we find in Ockham s critique with respect to among others the Categories except Substance and Quality Also here Ockham denies for instance the reality of Quantity Two substances do not constitute a per accidens compositum of 1 the pair of substances which then would be a carrier and 2 the really existing accident twoness This is a kind of Platonism that he refutes convincingly The twoness is not something apart from the pair of substances i e we do not have a single general independently existing twoness that sometimes goes out to find possible substrates to land on The twoness must already be anticipated by each one of the mentioned substances totally in virtue of those substances own content NOTE 129 But the view of a really and independently existing accident as refuted by Ockham is as we ve said earlier not so much the view of St Thomas NOTE 130 because he has weakened the reality of accidents by means of the concept of equivocity in scholastic writings called analogy something that Ockham does know to be sure implying that his critique is in fact not directly aimed at St Thomas with respect to these matters but at others such as Duns Scotus So St Thomas holds a peculiar intermediate position between those of say Scotus and Ockham Therefore it is of no surprise to us when it turns out that the metaphysics of St Thomas Aquinas precisely because of this intermediate position has a large survival value g Predication In the following discussion we hope to gain still further insight into the Categories Predicaments and the Predicables because it looks as if philosophers in a more or less unconstrained way invent all kinds of concepts and constructions so that they are subsequently perplexed about them and then go to investigate the next 2000 years as to what then they in fact are as if they were given by God as natural structures Nevertheless in philosophy things go that way with respect to such constructions One feels that there must be something like that Theoretical considerations together with observation almost inevitably lead to them But as evident they initially appear to be in rerum natura NOTE 131 so un detectable they turn out to be as soon as they either are of a very fundamental nature or just plain mistakes We must continue to critically investigate these traditional and for a long time cherished constructions and concepts with the preparedness to reject them all if necessary After all isn t it all about the verum that is the truth May the next discussion contribute to obtaining this verum AERTSEN p 56 Natura en Creatura 1982 writes that a per se predication NOTE 132 is based upon a causal relation between the subject or a part of it and the predicate It is evident that here a logical relation is thought as it to be also ontological subject and predicate causally connected that is the relation between a subject and a predicate which is a logical relation is supposed to be based on a causal relationship between subject and predicate which must therefore necessarily be re interpreted as substrate and determination and the relation between a substrate and its determination is evidently ontological And as far as we know all this is asserted without being demonstrated something which indeed was not the task or intention of the book Natura en Creatura Indeed predication is a relation between terms not without qualification between things That it is not just like that a relation between things can be shown with the following accidental predication NOTE 133 We do not show this in the sense of an established truth concerning these matters but we show that ontologization of parts of a predication is not undisputed even already in the Middle Ages If we say This stone is spherically formed then it may be argued that the term spherically formed does not signify something that would be different from that stone For why could a substance itself not be spherically formed also without that particular entity spherically formed that is an entity apart and distinct from that substance Said a bit differently Couldn t we imagine that a substance can all by itself and thus not by involving something else be spherically formed Couldn t the content spherically formedness be already be an integrated part of the given substance which part cannot be different from the substance s content because it also belongs to this content NOTE 134 Ockham determines this as follows The term spherically formed is as concrete term connotative It signifies primarily one or another substance i e individual real thing and secondarily i e connotes the truth of a certain proposition That which is connoted is consequently not something in extramental reality but a meta object Truth of a proposition is a term of the meta language NOTE 135 a term of second intention not a term of the object language see previous NOTE not a term of first intention This connoted proposition puts that the conditions for attributing the term spherically formed are satisfied for example in virtue of an observation And indeed all this refers to a here and now individual Only when considering the historical individual can spherically formed be predicated of the carrier substrate logically of the subject because the historic individual is the carrier The abstract counterpart of spherically formed namely spherically formedness is a so called incomplete symbol just like the term humanitas in the category of Substance and is analyzable in terms of a context which involves necessity spherically formed ness is spherically formed qua spherically formed what being spherically formed simply as spherically formed necessarily entails So the abstract term is reducible to a concrete term This whole treatment of spherically formed is if taken maximally general resulting in the supreme genus Quality thus as qualitative property as such a description of a transcendental term sensible substance is coexistent with quality that is to say with to be a quale and this latter therefore is also coexistent convertible with Being We here give up on possible non sensible substances substances nevertheless expressible by the object language because their existence is far from demonstrated At most we can presuppose them within a broadened speculative perspective NOTE 136 So we see that the parts of a predication do not necessarily stand for corresponding parts in extramental reality NOTE 137 In the mentioned example spherically formedness did not have separated reality with respect of the thing which was spherically formed that is to say did not enjoy an existence apart from the thing which was spherically formed There only was a distinction secundum rationem a distinction which as distinction was formed by our intellect ratio and thus referring not to things or states of affairs in extramental reality but to our way of knowing So the distinction is not ontological but logical This must be understood as follows It is not spherically formed that is only secundum rationem but the distinction in the sense of separation of stone and spherically formed is found out to be only secundum rationem NOTE 138 And this forces us to think more about the pretense of the VIA PRAEDICATIONIS to providing knowledge of extramental reality As a preparation we must consider the following A Being ens whether it be a substance or an accident weakened being is always one is always an unum An unum as can be found in extramental reality is always a being an ens whether it be a substance or an accident an unum is a holistic totality of whatever elements UNUM is consequently a transcendental term that is it transcends every classification whatsoever of types of Being especially the classification expressed in the Table of Categories Predicaments The same applies to all other traditionally conceived transcendentals such as VERUM true BONUM good RES thing etc According to Ockham QUANTITY is also a transcendental term This for him with respect to created Being and this thematically means with respect to Real Being especially when the immaterial angels are created beings material beings sensible beings because every being is quantitatively determined or said better is quantitative and of course not only quantitative which means that every being whatsoever has a certain size involves certain numbers etc We might add that this is only correct if all other accidental categories are also not considered to be beings because say quality is with respect to its very formal content not quantitative it at most involves quantity in the sense that it must be co existent with quantity and if it were a being then we would have a being that is not quantitative ly determined So in denying being that is denying to be a being for all accidental categories making them to be no Categories of Being anymore there is only one Category of Being left Substance And then of course QUANTITY transcends all categories So as such QUANTITY is transcendental NOTE 139 NOTE 140 But this is according to me not the case with respect to the species lowest subgenera of Quantity that is to say according to me no species of Quantity is transcendental and also no species of any other accidental Category is transcendental One or another substance can be 1 50 long But not every substance is 1 50 long and with respect to Quality A substance can be spherically formed but not every substance is spherically formed And also A substance can be red but not every substance is red So 1 50 long spherically formed and red are not transcendental terms We could hold that Quantity is a principle of Being one among many such principles where we limit Being in the expression principle of Being to real Being which in the present context is material being This principle guarantees that every material being is quantitatively determined A same type of consideration can be applied to Quality and a number of other transcendental determinations So here we find a number of principles of Being which horizontally pervade all real and full fledged beings In this way we come close to Nicolai HARTMANN s doctrine of Categories and if we take those principles to be a priori categories of reason then we come close to KANT s epistemological theory And thus an Aristotelian Scholastic study of transcendentals could lead to a variant of the Hartmannian ontological doctrine of categories or to a Kantian epistemological doctrine of a priori categories In a doctrine such as Hartmann s the Gebilde the Totality individuum is not central anymore The many Totalities together make up one single domain of Being possibly consisting of several Layers of being which is pervaded and thus held together by universal principles of Being In Fourth Part of Website we have expounded this Hartmannian doctrine Here however that is in the present Fifth Part of Website our point of view lies elsewhere It lies at the Totality that is at the thing as thing A given Substance can have at the same time several quantitative determinations such as being 1 50 m long having a volume of 500 cc or consisting of three parts but these determinations can vary in Time This is evident when we in stead of the here and now individual have the historical individual in mind Only then we can speak about replaceable determinations accidents replaceable with respect to a given being The replaceable is it is true also detectable in the context of here and now individuals namely as we go from one such individual to another of the same species Socrates is now tanned while Plato is not So this replaceability appears be distinguishable also in a Nominalistic context of only here and now individuals But this is not so because speaking about replaceability of determinations in individuals of the same species necessarily implies the acceptance of an Essence that remains the same while determinations are replaced by others And such an Essence is denied by Nominalism The discussed case of some given being which was determined to be spherically formed referred to a stone with a spherical shape In the argument the stone was imagined to be a genuine Substance while it in fact isn t in order to give an analysis of the determinations that further determine this substance After all it here concerns a general exposition about determinations as such Nevertheless it is in the present context important to realize that generally a stone is not a pure being ens not an intrinsic Totality but an aggregate here a tight contiguum A stone a rock is except when it consists of one single crystal only such as a grain of sand an aggregate of crystals thus an aggregate of beings that are randomly oriented with respect to each other and are in many cases even belonging to different crystal species In the case of an aggregate such as a stone it is relatively simple and clear to speak about extrinsic determinations of this aggregate taken to be a being because a genuine but still more or less tight aggregate has few intrinsic features this in contrast to a genuine being a Totality a genuine Substance So the shape of a given aggregate and thus say the shape of a given stone is almost totally determined by external factors otherwise it wouldn t be a genuine aggregate As regards real full fledged beings intrinsic Totalities on the other hand there is a much larger proportion of intrinsic determinations which is for example obvious in the case of a molecule Here there are only very few extrinsic and therefore replaceable determinations such as position and orientation with respect to the medium in which the molecule resides We were discussing the status of determinations and found that these may only then be viewed nominalistically when they are taken as maximally generalized And if we do not do this then we must explicitly have in mind a here and now individual Quantity for instance is in this Nominalism not something that in itself has one or another form of reality alongside the reality of that something which has quantity which is quantitative Something to be quantitative is only a certain way of description by us of one or another being Viewed non nominalistically Quantity and also the other accidental supreme genera could be considered to be a principle of Being as we had found out earlier The species of Quantity such as 1 50 cm long 500 cc volume and also those of the other accidental categories cannot be viewed nominalistically because they are not transcendental are not convertible with Substance and are thus something else than Substance In a different sense they can be viewed nominalistically namely when the following conditions are satisfied Only individuals exist These individuals are always viewed as here and now individuals As consequence of 1 There doesn t exist something like an essence which remains constant under replacement of determinations Even per accidens determinations can now be viewed nominalistically because then they are descriptions directly of the substance with which we are concerned Such a description is contained in a per accidens predication such as for instance This crystal is 5 mm long And it is exactly this given crystal here and now that is totally in virtue of itself 5 mm long despite the fact that this length depends on growing conditions and elapsed time Refutation of a Nominalistic view of Reality To recap consequent Nominalism asserts that all so called accidental predicates do not refer to beings even not to mere auxiliary beings So a predication although its linguistic or syntactic form suggests it does not express that something is added to something else that to which the predicate term refers added to that to which the subject term refers On the contrary still according to Nominalism it only emphasizes some aspect of that what is signified by the subject term And this means that the accidental term is in fact not an accidental term but a transcendental term So according to Nominalism all accidents are transcendentals There exist to be sure even according to non nominalistic and therefore classical metaphysics genuine transcendental terms such as UNUM unity ALIQUID something else RES thing etc But in contrast to this non nominalistic classical metaphysics Nominalism says that in addition to these traditional transcendentals also all accidental predicates are transcendental terms A transcendental term can be characterized in two ways It is applicable to all types of Being which means that it transcends every possible classification of types of Being especially its classification into the ten types of Being derived from predication the Predicaments Categories So such a term thus not only applies to Substance but also to Quantity Quality etc It says something directly of a being that is not by adding something to it but expressing some aspect of it an aspect that is in no way apart from it These two characterizations are in fact equivalent but the first one is logical while the second is ontological NOTE 140a As one can see the term UNITY perfectly satisfies these two characterizations and thus is a transcendental term Indeed not only every Substance is a unity but also Quantity Quality etc Quantity as such doesn t have actual parts The same goes for Quality etc In the same way the other traditionally transcendental terms satisfy all this A true accidental term on the other hand says something about something else It namely adds something to Substance It adds to it by being ontologically carried by it recepted by it supervened to it inhering in it Now Nominalism as we see it for instance in Ockham asserts that to begin with also Quantity is a transcendental at variance with traditional substance accident metaphysics How can we demonstrate that Quantity is a transcendental Does it apply to all Categories Evidently it does not While it does apply to the Category of Substance it does not apply to the Category of Quality because Quality as such although necessarily entailing quantity See Van MELSEN A Natuurfilosofie 1955 p 252 is itself not Quantity because Quality can never totally be reduced to quantity See Van MELSEN A Natuurfilosofie 1955 p 249 NOTE 141 All this is of course the reason why Quantity and Quality are recognized as different categories They are obtained by maximally generalizing individual cases of quantity and quality So this shows that Quantity is not a transcendental because there is at least one Category other than itself for which it does not apply and that is Quality Of course if we deny as Nominalism does that the accidental categories in any way stand for beings of some sort then we mean by this that they in a predication do not add anything extraneous to that of which they are predicated In such a predication we just emphasize some intrinsic general aspect of that which is signified by the subject And thus denying the accidental categories to stand for beings of some sort is equivalent to saying that they are transcendentals Therefore this denial is not a demonstration that they are transcendentals and if nevertheless considered as a demonstration it is a circular argument So if and only if accidents are shown to be not beings accidental terms not signifying beings they are shown to be transcendentals which implies that transcendentals are not beings But in the document The Nominalistic Critique First Part of Website Critical Series we found out that they are indeed not beings because they are although individual not individuals individua NOTE 142 From this it would follow that they are transcendentals Only when we hold that something which is UNUM as well as ALIQUID see previous NOTE that is when it is undivided in itself and at the same time divided from the others is not necessarily already an individual but is individual then an accident satisfies being a being because an accident is individual And indeed the notion of accident as developed in Part III and Part IIIa namely as a phenotypic replaceable determination of which the content partly overlaps with that of the carrier in which it inheres where the overlapping is only implicit in the sense of an anticipation by the carrier of a possible determination by that particular accident complies very well with such a determination only being individual but not an individual It derives its individuality from the individuality of its substrate carrier Of course when one asks whether Substance which is the first Category is a being that is whether the term substance refers to a being we should perhaps reply that it cannot be a being because substance is not individual the term is general However it can be general in a disjunctive way It signifies a multitude of individuals by means of or or and so the significatum of the term substance is something individual after all The same applies to the term quantity second Category first accidental Category and to the term quality third Category second accidental Category etc The term quantity refers to this length of 1 90 cm or to that length of 200 m or to that volume of 500 cc or to So all the terms of the Categories thus including all accidental terms signify INDIVIDUAL entities while logically they are supreme genera of Being The classical definition of an individual is Something that is undivided in itself and divided from others And only if the divided from others means spatially divided from others we have defined a true individual an individuum And if the divided from others is spatial then it is always spatially separated from others whether it shares the same essential content with all other members of the same species one individual salt crystal another individual salt crystal or differs with respect to content from the others an individual sugar crystal an individual salt crystal But if on the other hand the divided from others means only qua formal content divided from others then we have not defined something to be an individual because it then is not distinguished from other members of the same species but only something which is different like redness differs from blueness And at least a n unseparable part of any given accident any given replaceable determination namely that part of it that sticks out of the substrate is in addition to undivided in itself also divided qua formal content from others which here first of all is the substrate in which that accident inheres and thus the accident complies with its being different qua formal content And only when such a something is either a part of or inheres in something individual it is itself individual Now let us see what the ontological status is of something let us call it X that is formally different and individual and only individual X then distinguishes itself qua formal content from its environment and at the same time in order for X to be individual and no more than that it must be a proper part of an individual What then is X when it satisfies these characterizations X cannot be some given Substance like an organism or a crystal which are individuals because X is not an individual for we know that a Substance is either a historical individual carrier only or a here and now individual so it is always an individual X can also not be an essential part of something because an essential part does not differ with respect to formal content from that of which it is an essential part and an essential part always only refers to an atom in the mereotopological sense not to a molecule The formal content of an essential part whether of a substance carrier only or of an accident is an all pervading content and so it indeed does not formally differ from that of which it is an essential part for instance the space group symmetry is not some qualitatively different region or part of the crystal It is not separate neither spatially nor formally What is left then for X to be is for it to be a replaceable determination that is an accident So if an entity X is formally different and at the same time individual but not an individual then X is an accident And because a concrete term signifying an accident such as the term sectored plated can be predicated of a substance as substrate for sectored plated such as in This snow crystal is sectored plated we predicate a term signifying a being of some sort let us call this term T x of another term T s signifying another being And it is then clear that the term T x cannot be a transcendental term because it adds something namely the being X to something else the substance as substrate And this means that the accidental terms quantity quality etc are not transcendental terms Every accidental term also when it is taken maximally general and then being a Predicament signifies an individual entity and this entity differs with respect to formal content from its substrate We see all this boils down whether or not we consider accidents as beings of some kind which in turn depends on whether or not we consider something that is formally different and at least individual to be a being That Quantity as an example of an accident as represented by say 1 90 cm length is individual is evident because it inheres in an individual substrate But also that which is signified by the term quantity is as we saw above individual That Quantity is formally different from the substrate or carrier is shown in Part III and Part IIIa It is different because we have shown that the formal content of any accident does by far not completely coincide with a corresponding part of the substrate Only insofar as the substrate anticipates the accident there is some overlap as regards formal content Indeed all accidents are each for themselves formally different from the substrate because they are replaceable by formally different determinations while in such a replacement the formal content of the

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  • Aristotelian metaphysics V
    at all Exact repetition in two dimensions only can be encountered in certain bryozoans But in all these cases however we have to do with colonies consisting of relatively independent organisms that is we do not have to do with genuine substances but with aggregates Each member of such an aggregate is a genuine substance and lacks a periodic structure The difference between periodic and non periodic order can be made graphic in two dimensions by considering the pattern of old fashioned wallpaper is a periodic pattern or that of many drawings of Escher also periodic and that of a persian carpet non periodic The treelet of Porphyrius in which this definition has its place looks as follows 2 The just given definitio quid rei real definition of a crystal can still better be grasped if we also try to give the definitio quid nominis nominal definition of it A crystal is a body bounded by flat faces This is of course what one always had understood a crystal to be But as it is the case with almost all concepts also those of substance accident cause essence a characterization of something by a concept quickly turns out to be insufficient or even wrong as soon as one considers the given case more closely While science progresses further the concepts become more and more theoretical that is to say much more indirect much more hidden than one originally imagined them to be It turns out that they can be unearthed in their pure form that is as truly signifying their object only after laborious analysis and observations See also further down Section g NOTE 187 Well this then also happened with the concept crystal because the possession of flat faces turned out not at all to be fundamental for crystals and already in the 17th century Steno discovered that it was the constancy of angles that is fundamental for the crystal and later one found that this was an effect of a very specific internal periodic structural pattern And only then one began to understand precisely what a crystal in fact essentially is A transition took place as seen with hindsight from the definitio quid nominis to the definitio quid rei and of course such processes are never completed In fact it is already apparent that possession of flat faces cannot perhaps be fundamental There are namely also crystal species that have curved faces such as Diamond and Siderite an iron mineral Further in nature crystal faces are seldom developed for example in many natural rocks All the observations of the crystal which we have just described lead to the unearthing of the essence and are as acts of sense and reason comparable with the very graphic example which Aristotele gives in Chapter 19 of the IInd Book of the Posteriora Analytica of the army which was fleeing and yet in the end putting itself in order again The example of a definitio quid rei which we have just given was about the definition of the term crystal And there it was left open whether the term referred to a common salt crystal a sugar crystal a mica crystal an ice crystal or to whatever sort of crystal It was a definition of a generic term namely the term crystal And this definition is correct The term crystal stands for a class of substances not for a certain kind species of substance That s why the term crystal does not signify one or another essence and if it does then it does so only in an incomplete way Completely signifying one or another essence only happens when a specific term is defined Let us give an example Common salt can be found in nature as the mineral Halite With respect to the definitio quid rei of the term halite crystal we can first remark the following We already know that it is a crystal that is to say that the term halite crystal stands for a part of the set of things which each for themselves can already be indicated by the term crystal and thus halite crystal is a logical subsumpt of crystal that is halite crystal is logically subsumed under crystal We must now define what halite crystal essentially is that is to say we must define the term halite crystal This we could do by stating its Space Group symmetry together with its Chemical Composition The Space Group NOTE 188 of Halite is F 4 m 3 2 m and the Chemical Composition is expressed by the chemical formula NaCl The crystal consists of as many sodium Na components as chlorine Cl components So here we have then a precise characterization of a Halite crystal NOTE 189 but a characterization in terms of parts which are ordered in a certain way implying the F 4 m 3 2 m symmetry while the precise distances between the components among each other are implied by the being sodium Na and the being chlorine Cl in the crystal as positively charged Na ions and negatively charged Cl ions of the crystal components And this is consequently not a metaphysical definition genus difference definition but a natural definition matter form definition where the crystal components are the matter and their periodic arrangement with the F 4 m 3 2 m symmetry the form But this matter form definition is perhaps yet not a genuine matter form definition in any case not one that refers to genuine parts because the ordering itself is not a part as it is so with body and soul when the soul is taken to be something independently existing Now the putting together of body and soul results in man Following this lead we could interpret the Chemical Composition namely NaCl as the genus and the Ordering of it as the difference But perhaps it is better to take Crystal as genus and Space Group symmetry PLUS Chemical Composition S C as the difference And so the definitio quid rei of halite crystal would then read A crystal genus that consists of Na ions and Cl ions in equal numbers which have arranged themselves into a three dimensional lattice having a symmetry according to the Space Group F 4 m 3 2 m difference True the difference is here still described in terms of consists of but this can in principle be transformed linguistically into something that ends with al as in rational resulting in A crystal genus that is al difference or equivalently A al crystal as in A rational animal which is the metaphysical definition of man This metaphysical definition of halite crystal is according to me correct but it is a definition that still refers to the phenotypic domain But a genuine metaphysical definition should refer to the genotypic domain thus to the domain of the true Essence namely the dynamical law which is in the present case the law governing the crystallization of sodium chloride NaCl either from a melt or from a solution How then would the true metaphysical definition of halite crystal read The metaphysical definition must be a term consisting of two parts genus and difference which together signify the Essence of any halite crystal whatsoever The first part of such a definition should refer to a determinable aspect of the Essence while the second part should refer to a subsequent determination of that determinable aspect This Essence is the relevant crystallization law which is applied by the NaCl crystallization system itself because the law is inherent in the elements of the system resulting in the generation of one or more halite crystals However in the case of the crystallization of sodium chloride as in the majority of the other cases the crystallization law operating in such a case is not precisely known But if it were known it could be formulated mathematically And as had already been shown ealier by using fictitious examples in such a mathematical formulation a genus and a difference can be distinguished and so it can represent the metaphysical definition of halite crystal The genus difference definition can then be predicated per se of the term signifying the dynamical law halite crystallization law NOTE 190 and with it of the term standing for halite crystal A halite crystal is The term halite crystal is the species and is equivalent to the term signifying the relevant dynamical law the halite crystallization law so the term signifies the Essence This is the intentional meaning of the term In the extensional meaning the term stands for the collection of all halite crystals One single halite crystal and thus a particular halite crystal pointed to with the finger is an instantiation of the species halite crystal It is a member of the just mentioned collection of all halite crystals or equivalently it is an individuation NOTE 191 of the corresponding Essence and that individuation particularization is an actually generated halite crystal as a result of the operation of the halite crystallization law If this individual crystal would have a proper name like Socrates is a proper name of some individual human being say Halo then we can say Halo is a halite crystal And as we saw we can then give a definio quid rei of the term halite crystal In all this it is clear that we must in almost all cases of attempts to give a genuine metaphysical definition of whatever complete being resort to all kinds of external features that is determinations and that we are thus forced to stay in the phenotypic domain because the relevant dynamical law which resides in the genotypic domain is in most cases unknown Thus in the actual practise of defining that is in a particular scientific context it is not very meaningful to say that the term halite crystal thus as a species that is to be defined refers to the dynamical law that is to the Essence and not very meaningful that that dynamical law can then be analysed into a generic and a differential aspect when we do not know that dynamical law We can alternatively signify the Essence by a term referring to the specific proprium for a halite crystal we have done this above by indicating its Space Group symmetry and its Chemical composition Or we can use a matter form definition and to give such a definition is generally less difficult However for metaphysics it is sufficient to refer to the dynamical law just as the dynamical law that is without actually formulating one such law because in metaphysics it is not about one or another given Essence in the sense of not about the Essence of halite crystals while it is about one or another given Essence in general but metaphysics is about the Essence as Essence that is Essence only insofar as it is Essence where knowledge of particular Essences such as the Essence of halite crystals is not necessarily demanded although such knowledge would certainly be instructive in that sense that as a result of actually knowing one or more such Essences the concept Essence would become less abstract for us With respect to the definitio quid nominis and quid rei of properties a same attitude as pictured above is necessary but here things are more difficult because the essence of a property in virtue of the typical relation the property has with the subject is much harder to characterize Here we should order properties under the heading states or conditions A substance is a product of a Totality generating dynamical system and enters according to the course of the system into different states successively following one after the other in time And in addition to it there are perturbations of the system that is the influence of contingent external factors We will give examples at some other occasion The three forms of definition given by Aristotle relate to demonstration as follows See SEIDL H Aristoteles ZWEITE ANALYTIKEN Mit Einleitung Übersetzung und Kommentar herausgegeben von Horst Seidl 1984 The definitio quid rei of a substance corresponds to an immediate premise of demonstration NOTE 191a The definitio quid rei of a property corresponds to the complete demonstration it is revealed through this demonstration See the syllogism above The definitio quid nominis of a property corresponds to the conclusion NOTE 192 of that demonstration that reveals the definitio quid rei See the syllogism above A definitio quid nominis of a substance that is of the subject does not play a part in the demonstration Having shown the location of the definition in demonstration it is perhaps useful to give an example see d of the way this discursive thinking is actually professed in science leading to scientific results and only then after having given this example to return to metaphysics e For only by contrasting metaphysics with other intellectual activities here empirical science we learn to apprehend what metaphysics in fact is because to answer this has turned out not so easy d Natural Science is Induction Deduction and Verification As Ernst Haeckel clearly expounds in the Chapter concerning methodology of his controversial but fascinating Generelle Morphologie der Organismen 1866 and of which Wilhelm Bölsche Ernst Haeckel in Männer der Zeit 1900 once exclaimed Philosophers should read this the process of knowing in natural science always consists of induction and deduction Namely Basing oneself on the results of a series of special experiences repeated instances of observation as regards some assumed type of behavior a general law is assumed to be at work induction and this law is now applied in the form of a prediction of the outcome deduction to a case not yet investigated i e which did not belong to the series of observations that led one to the assumption of that law to be at work A new experience or experiment can verify or fasify this deduction The more times such a verification turns out to be positive and with no exception the more certainty we obtain that this indeed is the law that actually operates In other words the more empirical verifications of predictions done by applying that law we have obtained the better that law is itself verified that is the more the induction becomes certain Let us give an example MAIOR All organisms consist of one or more cells or equivalently All organisms are cellular This guarantees that also a unicellular being distinguishes itself from say a crystal because the cell does not possess whereas the crystal does a periodically repeating structural pattern but a pattern that is directed toward a morphological center This premise could have been concluded in a previous syllogism but is in the end always found by induction It is the general law MINOR Sponges are organisms This is to be sure still the incomplete definition organisms predicated of its definiendum that is predicated of the subject sponges organisms is middle term the minor is found by induction CONCLUSIO Sponges consist of one or more cells found by deduction NOTE 193 Microscopical and optical enquiry of actual sponges can verify the conclusion verification The induction of the first premise maior has now become more strenghened however this strenghening still depending on another induction that is expressed in the minor We see by the way that natural science is a truly empirical science it begins with observation leading to induction and ends with observation experimental or observational verification The progression of natural science always proceeds through a chain of such syllogisms and thus we can continue and see that indeed progress has been made MAIOR All sponges consist of one or more cells or equivalently All sponges are cellular Conclusion of previous syllogism MINOR Scytalia spec was a sponge Namely a not further identified fossil extinct species of sponge belonging to the group Scytalia which lived from the Jurassic until the Cretaceous which means that no representatives of this group are living today The features of the fossil convince us that it was a sponge In the present syllogism sponge is middle term CONCLUSIO Scytalia spec consisted of one or more cells We have now reached the conclusion of the apparently cellular character of an organism that has left this fossil for example an impression in a rock or a petrification that is to say we are led to a conclusion concerning a state things which cannot be directly observed anymore we cannot ex hypothesi observe the cellular nature in the fossil and so this conclusion really is a step forward in our knowledge For the middle term it is sufficient to give a relevant part of the total definition NOTE 194 From all this it is also clear that the deductive aspect is just a small element in the practice of natural science It is mainly observation that delivers scientific knowledge Verification of the conclusion of the last given syllogism could be We find yet another fossil Scytalia in which the cells are indeed visible as a result of microscopic enquiry of that new fossil which in one way or another was very well preserved NOTE 195 In physics one sets up with respect to a given group of observed phenomena a mathematical model of which one hopes that it explains those phenomena and one sees whether all kinds of predictions the model gives actually come true If it does then we have an indication that the model is correct If it doesn t then the model must be modified or rejected Such a prediction always is the outcome of a possible observation or experiment The models which are thus in fact theories or hypotheses can often be very complex We have been somewhat elaborate with an example of the fundamental method of science as to its inductive and deductive aspects because examples are often scanty in the treatises on epistemology of Aristotle and St Thomas NOTE 196 Further often either the same example is put forward again and again rendering the chance of a systematic error large or sometimes as would turn out to be so inadequate examples are given And totally in the spirit of St Thomas we also say In philosophy and of course also in natural science it is not so much about the opinions of others but about the truth And this is a call for further elaborating on what was accomplished earlier e Metaphysics Definability of a given substance Having sketched the art of natural science we can now better apprehend what metaphysics is about In contrast to natural science in metaphysicis it is not about states of affairs not about the attribution of a content proprium to a subject but about this subject itself in its generality and then not first of all this subject considered as carrier of determinations accidents but as to its intrinsic relations in which metaphysics by considering the Essence qua Essence in its retrogression down along the ex structure of the thing deeper and deeper descends or if one wishes ascends perhaps all the way to the divine NOTE 197 Natural science already presupposes that there are beings at all and that they have without qualification content and consequently just asks whether these beings are in given cases for example fishes or amphibians and asks what their attributes are It does not ask what it is to be a substance that is to what in general the subject term points Induction further results in the possibility to set up a law i e a regularity of causality between A and B assumed to actually be at work between the two which means that natural science is about extrinsic causes namely the efficient cause which is the only type of cause which is accessible to natural science And this only with respect to states of affairs not with respect to things In metaphysics it is about substance and its intrinsic causes that is the intrinsic causes of Being and Content The fact that substance has in addition to intrinsic causes also an efficient and final cause gradually becomes clear during metaphysical investigations but these efficient and final causes are according to me not belonging to the subject we nowadays say object of metaphysics And in metaphysics it is not as it is in the other fields of knowledge the via demonstrationis but among others the via diffinitionis which should be entered NOTE 198 This via however will only yield results that is one or another sort of knowledge if substance is definable at all We here mean that one or another given substance allows itself to be determined we do not mean what the definition of a given substance is and also not what the definition of Substance qua Substance is Thus metaphysics is an enquiry into definiteness qua definiteness A condition for this definability is that the definition can be known completely that is that there is no infinite regress neither upwards higher generality nor downwards to the more special Aristotle investigates this in the first Book of the Posteriora Analytica Chapter 19 23 in connection with scientific proof because this must start from the definition of the subject In the category of Substance we can think of a sequence of terms in which sequence we see starting from a discrete term standing for a single individual terms that become progressively more general the higher up we go along the sequence It is this side of the sequence which we can imagine because only individuals are known to us as entities existing in extramental reality The sequence can be depicted by a Venn diagram in which the relative extensions domains of significata of the concepts where concepts are terms and are conventionally represented by words are expressed The sequence begins with a last subject that is this subject cannot in turn become a predicate for yet another subject anymore Can the sequence go up indefinitely If it can a complete definition is impossible that is a definition containing not only the difference and proximate genus but also all higher differences and genera For example that of man rational animal rational sensitive organism rational sensitive living body etc Now Aristotle holds that the sequence does not go up indefinitely and this he shows on the basis of the assumption that we are able to know at all So it is clear that with the question whether the via diffinitionis yields results the answer is already stipulated so that we have to do with a petitio principii Aristotle I Posteriora Analytica Chapter 19 asks himself 1 whether departing from a last subject there are an infinite number of predicable terms predicates before we reach a first predicate which we then would not reach and 2 whether departing from a first predicate there are infinitely many subjects before reaching the last subject He further asks whether departing from two fixed extreme terms for example this individual dog and substance they can figure in the conclusion this individual dog NOTE 199 IS a substance there are in this case or are not an infinite number of middle terms present between these two fixed extreme terms NOTE 200 For it is in principle possible to show that in this partial sequence going from dog to substance there must be a first and a last term These we may thus presuppose allowing to limit ourselves to the question whether the number of middle terms is infinite or not To investigate this latter question is however identical to an investigation whether the demonstrations themselves are or are not infinite in number for one can always prove that a more general term can in virtue of a qua degree of generality middle term be predicated of a less general term And if every term is an essential predicate then we precisely have catched sight of our above described problem the problem of the completeness of the definition And that these demonstrations themselves do not go into infinity has already been established at the beginning of the Posteriora Analytica NOTE 201 The fact that there is no infinity involved in demonstrations and consequently also not in predicates is here succinctly summarized imagined by Aristotle as follows If we depart from the assumption that scientific knowledge is possible then automatically another type of knowledge as principle of scientific knowledge must be possible and this is the definition because definitions provide us with middle terms And when we thus suppose that X is some least general term which disjunctively that is with or or points to several individual substances that is a term directly coming after the particular individuals then this term and also the more general terms must be able to serve as a definiendum that what must be defined and this implies that the number of essential predicates must be finite because knowledge is presupposed to be possible finite in the downward direction because this is presupposed since we started out from a least universal term NOTE 202 and finite in the upward direction NOTE 203 So the above reasoning in the main text purporting that in the business of defining a given substantial term the number of predicates is finite and that thus complete definition is possible has in fact not demonstrated this but presupposed this presupposition is that of Parmenides Being is intelligible But as we have seen in NOTE 201 we can demonstrate departing from an assumption different from the assumption that knowledge is possible at all that complete definition of a given substantial term is possible NOTE 203a Let us for this consider the chain of demonstrations syllogisms embodying the complete definition of a given substantial term and thus containing a sequence of middle terms that starts from some first middle term proximal definition definiens of the given substantial term to be defined completely see NOTE 203 and ends up at a last middle term proximal definition definiens of the term immediately preceding the supreme term substance and containing the latter as its genus Into this sequence of middle terms we can insert new middle terms NOTE 203b If however the present case is such that the repeated insertion of middle terms can not go on indefinitely rendering the sequence denumerable and because a denumerable sequence can still have an infinite number of elements between a first and a last element as we saw NOTE 201 for rational numbers if this insertion takes place on the basis of the degree of generality and if finally the first and last with respect to middle terms are also based on degree of generality then the complete definition neatly corresponds to a sequence of qua magnitude increasing natural numbers positive integers in an interval say the interval 1 10000 NOTE 204 from which it follows that then the number of middle terms and consequently the number of syllogisms between the given substantial term to be completely defined and the ultimate term substance is finite and thus there is only a finite number of essential predicates resulting in a complete definition to be possible And indeed in NOTE 201 we did show that middle terms cannot be inserted indefinitely so their number when going from the substantial term to be completely defined all the way up to substance is finite and a complete definition is possible When we want to present all this in terms of Dynamical Laws which should then be signified by the essential predicates we can do this in the following way Suppose that the Dynamical Law which is the Essence of the thing generated by the dynamical system governed by that particular dynamical law of the species DOG were a recursive cubic of third degree polynomial law NOTE 205 say X n 1 3X n 3 5X n 2 2X n 81 Then we can have the following consideration From this particular Dynamical Law we can ascend to ever more general dynamical laws until we have arrived at the most general cubic law X n 1 a 1 X n 3 5X n 2 2X n 81 X n 1 a 1 X n 3 a 2 X n 2 2X n 81 X n 1 a 1 X n 3 a 2 X n 2 a 3 X n 81 X n 1 a 1 X n 3 a 2 X n 2 a 3 X n a 4 But when we ascend from dog to mammal vertebrate chordate etc we will surely not have to do with only cubic dynamical laws A whale which is a mammal for instance could perhaps embody a 5th degree dynamical law A general dynamical law as the general Essence of the supposita of the term mammal the general Essence of the individuals in the extension of the concept mammal should provide for this So when we want to further ascend towards more and more general polynomial laws then we will if we want to provide for everything reach as end point the most general polynomial law which looks as follows X n 1 a 1 X n m a 2 X n m 1 a 3 X n m 2 a k 2 X n 2 a k 1 X n a k In a purely mathematical sense the number of terms of such an expression can in principle be infinite but here that is in a context in which the expression is physically interpreted this number is finite namely k m 1 and this should be so because it is not very probable that there exist physical dynamical laws with infinitely many terms The powers m m 1 m 2 etc are by definition for polynomials always exclusively integers From this it is clear that every sequence of polynomials starting with a particular polynomial that is with determined coefficients for instance a 1 X 3X powers for instance X m X 4 and a determined constant for instance a 4 73 and ascending toward the most general polynomial is finite because the number of terms in each expression is finite so the process of successively determine the coefficients powers and constant always comes to an end always reaches completion The fictitious example just given at least suggests but not of course demonstrates that no infinity is involved in the genotypic domain when we ascend from one or another completely specified dynamical law of a given Totality species say the species men to a maximally general dynamical law We must not confuse this with the number of in principle mathematically possible dynamical laws So mathematically infinitely many cubic polynomial laws are possible because in X n 1 a 1 X n 3 a 2 X n 2 a 3 X n a 4 the coefficients a 1 a 2 a 3 and the constant a 4 can vary over the set of real numbers They thus can assume every value whatsoever from this set and this set is infinitely large In reality however dynamical laws especially those of organisms cannot just like that assume every mathematically possible form The corresponding Totalities intrinsic things generated by such laws must have a certain degree of stability in order to be able to exist at all This concludes our discussion about the possible ascent from special to general with respect to the terms in the category of Substance Do we also have such an ascent and descent with respect to the terms of each of the remaining categories that is with respect to the accidental categories f Definability of the accidents With the accidents that is with the replaceable determinations we have entered the phenotypic domain of things NOTE 206 Determinations are wholly or partially generated by the dynamical law the Essence and in this way form the Totality Despite the fact that metaphysics is only concerned with substance we precisely by studying accidents obtain a good insight in what substance truly is NOTE 207 Also St Thomas devotes much attention to accidents In the problem of the Trinity he investigates Discrete Quantity and Relation and in the problem of the Eucharist he investigates Quantity and Quality As regards the accidental categories each for themselves we might think of an ascent or descent in which the subalternateness is always indicated by a predication It must be so indicated because the subalternateness is asserted The white thing IS a colored thing The thing that happened to be white IS and ascending A colored thing IS a qualitatively determined thing A thing that happened to be colored IS But here accidents are predicated of accidents and that is not a proper predication that is not a logically per se predication and such a predication that is about the accidental that is the subject here stands for an accidental state of things NOTE 208 cannot play a role in whatever process of gaining knowledge it even drops out of the province of logic and so also out of that of philosophy The same applies to a predication of a subject of an accident So in such cases no subalternateness can be asserted the white thing is a colored thing here white thing is asserted to be subsumed under colored thing but they are just accidental facts Thus as regards the accidents only the predication of an accident of a subject is relevant for us in the present context for example Socrates is tanned or men is able to laugh But after this predication we cannot in ascending proceed any further because then the logical subject of the new proposition becomes an accident tanned That is we then should get tanned is which is equivalent to the a tanned thing is so the subject has become just an accidental fact resulting in a non proper predication Descending we arrive in fact we already are at substance Socrates men and then descend further to a last subject standing for an individual thing Socrates So in the accidental categories each for themselves there is no infinity involved neither in the process of ascending nor in that of descending no infinity involved in the attribution of predicates respectively subjects Nevertheless the following predication seems to be logically per se and also per se in reality that is in quid Whiteness is a color According to Ockham whiteness is an absolute term that is a quality is signified primarily without at the same time something else being connoted In the context of this view we here indeed have to do with a logically per se predication proper predication because now the subject term does not stand for some accidental fact However we could ask whether things are seen in this way also by St Thomas For the time being our impression is that he solves the problem the problem namely whether substance and accident quality are or are not in fact detached or could be detached from each other at the Eucharist in a different way than Ockham did According to St Thomas quality can be detached from substance that is substance freed from quality but not from quantity which serves as carrier of quality So any quality is always in a carrier subject resulting in the fact that for St Thomas whiteness does not have a complete essence and thus the fact that the term whiteness as abstract term necessarily must nevertheless connote a subject NOTE 209 Further is as we know the possible independence of accidents of a substrate less strongly conceived that is less completely as it is conceived by or as it is according to Ockham Accidents in so far as their being is concerned always refer to substance So when we say whiteness is a color then according to St Thomas color is not predicated of a per se unum because whiteness although signified by an abstract expression is according to St thomas not totally independent from a carrier implying that we for the time being can assess this predication as logically accidental

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  • Logic I
    phenotypic expression of the Essence Similarly the term quality now not following Ockham is predicable universally and per se primo modo only of those terms in nominal definitions of qualitative states in which it i e quality is included For example the nominal definition of the term the red which signifies a qualitative state is something in which redness is present And indeed the term quality can be predicated per se primo modo of the term redness as in redness is a quality This predication is possible because the definition of the term redness is a color such that indicating its location in the rainbow And this definition ultimately leads to the term quality as soon as we re going to complete it by ascending from color And if we do so we will end up at the term quality But as we saw with quantity any infima species of quality say greenness or redness for that matter cannot be universally predicated of any abstract qualitative term we cannot say redness is greenness nor blueness is greenness because greenness differs from redness and from blueness Nor can we say quality is greenness because not every quality is greenness An infima species of quality can only be predicated of a substance and the term expressing this species must be concrete but then only contingently so if we dismiss Ockham s thesis that quality is exeptional among the accidental categories and if we follow him as he did with quantity An example would be Socrates is tanned And like in the case of quantity we must consider how things are when a certain quality for example the blueness of a CuSO 4 5H 2 O copper sulfate crystal is intrinsic to that here a copper sulfate crystal which has this color Indeed the blue color of a CuSO 4 5H 2 O crystal is an intrinsic feature of this crystal species pervading the whole crystal It is a generic proprium for that crystal species And we have seen that a proprium always lies completely within the carrier that is it belongs to the Essence The same was the case with the size of a given atom considered above Both must therefore be per se predicated of their subject that is predicated as propria So in the case of quantity as well as in the case of quality there ocur two possible ways of predication depending on what is signified by the subject term and by the predicate term namely per se and per accidens contigent predication And this disrupts the uniform status of quantity as well as of that of quality That is it disrupts a fixed relationship between substance and quantity and also between substance and quality We now have two ways of quantitatively or qualitatively determined In fact the above discussed feature of transcendentality cannot apply to both relationships at the same time and in the same respect namely 1 the relation of a given quantity or quality with its substance as it is expressed in per se predication and 2 the relation of a given quantity or quality with its substance as it is expressed in a per accidens predication As I said these different relationships indicate two different ways of quantitatively or qualitatively determined And this means that we cannot generally say that quantity or quality is transcendental but only that things are intrinsically or extrinsically quantitatively or qualitatively determined A given crystal being say 1 cm long is extrinsically quantitatively determined with respect to length It has grown to this length and can grow further A given atom being say 1 Angstrom in diameter is intrinsically quantitatively determined with respect to diameter Quantity can behave differently in its relation to substance on different occasions Therefore it cannot be a transcendental We see this clearly when we compare quantity with unity i e to be one which latter is a genuine transcendental Every being whatsoever is intrinsically one and always intrinsically one The same goes for quality Also it behaves differently in its relation to substance at different occasions and cannot therefore be a transcendental According to Ockham quantity quantitas is not a thing different from substance and from quality It is not a res additum a thing added Therefore we cannot say that a given substance such as an atom a molecule a crystal or an organism has quantity But we can also not say that a given substance is quantity Neither can we say it in the sense that substance is a species of quantity A species of quantity is for instance 1 70 m length nor can we say it in the sense of a given substance being the same as quantity or a quantity But a concrete quantitative term can contingently be predicated of a substantial term Socrates is happens to be 1 70 m long while we cannot say Socrates is happens to be 1 70 m length or is a length of 1 70 m The same goes for quality Among writers on Aristotelian metaphysics it hasn t occurred it seems that as we have seen above in some occasions certain quantitative terms and also certain qualitative terms when predicated of certain subjects must be predicated per se while on other occasions they can only be predicated per accidens The problem is confusing and probably demands much more study especially with respect to my assumption just made about writers on metaphysics So to reiterate a concrete connotative term whose abstract counterpart signifies something belonging to one of the accidental predicaments can in some cases be per se predicable of a subject a CuSO 4 5H 2 O copper sulfate crystal is blue meaning that this term as a result of this predicational context belongs to the Predicable Proprium while this same connotative term can in other cases only be predicated per accidens of a certain subject as in my bruise is blue a bruise can also be red and is then as a result of this predicational context belonging to the Predicable Accidens So the ontological status of that what is signified by the abstract counterpart of the concrete connotative term depends on the predicational context blueness in the one case belonging to the Essence of a copper sulfate crystal and in another case not belonging to the Essence of a given being my bruise and therefore my body which context in turn depends on the meaning of the subject term If we have say X Angstrom length of diameter where X stands for a definite number of Angstrom units such that it indicates either say the size of such small things as a given atom or an atomic nucleus or the size of say a given crystal it depends on the meaning of the subject term of which the concrete term X Angstrom long is predicated whether the significatum of the latter term s abstract counterpart X Angstrom length either resides totally within the carrier or substrate when namely the subject term indeed refers to something like a given atom or atomic nucleus or whether it resides outside the carrier or substrate when namely the subject term refers to something whose exact size is extrinsic to it like a crystal For very small things it will be hard to give an example of extrinsic size because in that range of things sizes are usually intrinsic For larger things an extrinsic size is easily given the size of a given crystal The same can be argued for quality So again Things can be quantitatively or qualitatively determined in two ways per se or per accidens And this makes the question as to whether quantity or quality and also every one of the remaining accidental predicates is a transcendental or not futile Sometimes it is a res addita something added and then it is not a transcendental sometimes it is not and then it is a transcendental In fact this boils down to the finding that the accidental predicates are not transcendentals This concludes our general thematic framework as a preparation for developing an intentional logic in which framework we have discussed more or less in the context of Ockham s philosphy the ontological status of determinations namely whether these are essential parts or replaceable determinations We will now discuss some details again more or less in the context of Ockham s philosophy that we deem important and instructive for a development of an intentional logic and especially for further vindicating a substance accident metaphysics against at least the strong version of nominalism which metaphysics can serve as a basis for an intentional logic Natural Science and Metaphysics Things like the relationship Substance Accident Matter Form and the like seem to be assessed by Ockham as principles of natural science because they are principles of material change This seems to me correct But what is not correct is saying that because they are principles of natural science they do not belong to metaphysics The principles of natural science cannot themselves belong to natural science because they cannot treated by or subjected to the very methods of natural science observation induction deduction verifying or falsifying observations because these methods already presuppose these principles The principles of natural science are therefore the metaphysische Anfangsgründe der Naturwissenschaft metaphysical bases of natural science that is the metaphysical presuppositions from which natural science can get started And of course there is no such thing as principles of metaphysics because there is nothing below metaphysics and if there were it would belong to metaphysics So it is wrong to say that the book of Categories is not a book of metaphysics MOODY p 144 note 1 because it is about substance and accident which it is and therefore about change Natural science is it is true about changeable things such as atoms molecules crystals animals and stars But it is not about changeable things only and precisely insofar as they are changeable things It is metaphysics which explains the very changeability as such of all material things And if we only recognize as real beings material beings then metaphysics is about being qua changeable which is equivalent to being qua being And not only natural science but also logic in the intentional sense is based on metaphysics Some further notes about the ontological status of the accidental Categories QUANTITY There are two main species of quantity viz continuous quantity and discrete quantity In connection with the ontological status of accidents it is instructive to separately discuss them Continuous quantity A continuum as such representing continuous quantity has parts that have common boundaries therefore the parts are no more than potential parts while in a discretum contiguum the parts are actual because they have no common boundaries So if we say that a given substance is continuous we can define the quantitative term continuous as something in which if internal boundaries are present at all only common boundaries are present In a continuous body these boundaries are straight or curved surfaces These surfaces are evidently not things that are distinct from the continuous substance the body itself and then added to that substance They are not something other than a substance or a quality as Ockham adds So continuous quantity in the sense of something being continuous does not mean that something is added to that something making it continuous We can only say that in making something continuous which initially was just a contiguum something has been removed namely the interstices of the contiguum resulting in it to become a continuum However a contiguum is not a genuine being from which we then remove something but a multitude of beings namely its actual parts to which these interstices do not belong Indeed every genuine substance must be a continuum that is must have continuous quantity per se i e all by itself And even if there are substances which are nevertheless contigua they must have ultimate parts that are continuous and they are continuous all by themselves So continuous quantity is as it seems a transcendental if we only accept as real beings material beings Continuous quantity is necessarily implied by something being a substance It is not added Line whose significatum is a one dimensional continuum is a term signifying something as determinate with respect to length or as limit of a surface But length is not something distinct from that which is long since any substance having parts with relative position to one another assuming such partitioned things in many cases at least to be substances can merely through motion of these parts rarefaction or condensation of that substance become longer or shorter without anything being added to it or subtracted from it Thus length cannot be said to stand for something distinct from that which is long but present in it just as redness does stand for something distinct from that which is red but present in it according to Ockham So length and any other quantitative term and generally the term quantity is not according to Ockham signifying a real accidental form after the mode of quality resulting in the different kinds of quantity being just so many species of quality And this means that still according to Ockham these quantitative terms are transcendentals And dismissing the special status attributed by Ockham to quality we say the same things about say redness which is a quality of which indeed a non theological Ockham would say that it does not refer to something added to the thing which is said to be red So also redness and with it all other qualitative terms are according to non theological Ockhamism transcendentals Earlier we have seen that in certain cases length or generally size is indeed a quantitative per se determination of the thing having this length or size In the same way a quality must in some cases be attributed per se to a given thing In other cases however they can only contingently being attributed to given things representing a species of substance In such cases the contingent determination cannot because it is contingent necessarily follow from the Essence of the thing It must be extrinsic and therefore it is a distinct entity distinct from the thing to which it contingently is attributed It is a replaceable determination residing as such outside the carrier substrate of such determinations Therefore it is added and is thus not a transcendental But above we said that when some substance is either rarefied for instance by heating it which means that when it is a physical body it expands or concentrated for example by cooling it which means that it then contracts it does so without anything being added Is length or size then transcendental after all I don t think so The just mentioned without anything being added refers to physical material not being added or removed However when we are speaking about transcendentals such as UNITY THING and the like the without anything being added refers to the comprehension or formal content of the relevant concept Predicating a transcendental term of the term X does not add anything to the content of the concept of X So the without anything being added in the case of rarefaction or concentration as changing the length or size of a given individual substance is not relevant to the question as to whether length or size of an individual substance are transcendentals or not Discrete quantity Numbers in the sense of how many things there are for instance in a given container is a discrete quantity Since a natural number signifies a multitude of individuals simul sumptis simultaneously taken that is coniunctim that is the individuals taken in the manner of and and and since any universal concept can determine such a multitude a number taken in itself is for Ockham as for many modern mathematicians a class of classes similar to a given class For example suppose that the given class is the set of regular polyhedra tetrahedron cube octahedron dodecahedron icosahedron Then we can point to many other classes or sets for example these stars to which I point with my finger these letters A B C D E these arms of a common starfish etc All these classes or sets are similar to the first class the given class in virtue of the fact that we can relate these classes by a one to one correspondence of their elements Signifying the elements by arbitrary symbols the one to one correspondence looks like this And the whole set consisting of all these classes we call five So with the term five we refer to the total collection of classes that can be related to the given class by this one to one correspondence of their elements So the number of elements of any one of these classes is determined by this correspondence And it is we who have made this correspondence that is if ever we have added something to such a class it is not something real Also to its elements we haven t added anything The class of objects remains precisely the same whether we bring its elements into correspondence with those of other classes or not So it having a definite number of elements does not add anything to it So five expressing the number of elements of a class or set of them considered as a single entity is not a distinct entity added to that which is five fold And moreover still thinking of five foldness as an accident of a given substance often such a collection of things five things is not a single substance Only when five refers to parts they could be parts of a single substance as in the case of the star fish consisting of five antimers counterparts The parts themselves of such a star fish are however not substances Now it is possible to hold a different view on these matters Ockham directs his criticisms as regards the status of accidental predicaments mainly to Duns Scotus And that means that he criticizes the position that accidents are genuine things But the view of St Thomas regarding these accidents is different from that of Scotus It is such that we could interpret accidents not as things but as conditions or states of genuine things In this way accidents are considered to be not beings in the full sense but just auxiliary beings Let s see how this works out in the case of discrete quantity If we have a collection of five things then we could say of each of these things that they are in a condition of co existence with four other such things the same view can be held by the way for relation between things In the case of a number of parts of one given genuine substance the accident fiveness refers to each part In a common star fish this fiveness or five foldness is per se with respect to the whole star fish that is it resides inside the carrier substrate and is therefore not a res additum a thing added But in the case of say five crystal individuals present say in some natural or artificial container it is just a condition or state that is it is a replaceable determination and as such a res additum where res does not signify a full fledged being i e an ontologically complete being but an auxiliary being wholly in line with the equivocal nature of Being NOTE 10 So of discrete quantity one cannot just like that say as Ockham does that it is not a res additum Sometimes it is Quantity of it self allows being equal or unequal to another quantity In this way 3 3 and 4 3 And quantity of itself could be equivalent to just a description of a given substance implying that the equality or inequality do not apply per se to the individual substance for no substance is of itself equal to another nor is one substance equal to another by any form or thing really distinct from it rather it is equal to the other insofar as it is signifiable by a term connoting an operation of division counting potential parts that is measuring length and the like or of enumeration of parts counting actual parts applicable to the other MOODY p 155 6 It perhaps sounds strange that two substances are equal in length say or unequal for that matter to each other insofar as it that is one of them is signifiable by a term That a substance is signifiable in a certain way must have a cause in extramental reality that is in the substance itself and or in its environment Again we agree that a substance to be equal qua length say or unequal to another is not a matter of some thing being added to that substance What is added is not a thing but a condition or equivalently state A given substance X can happen to co exist with another substance Y existing somewhere having the same length where the particular length can be a proprium or just a replaceable determination Then we can say X is equal to Y with respect to length Further we can then say that is equal to Y is a condition or state of X albeit a very extrinsic and variable state because this particular state of X already gets replaced by another as soon as the length of Y is replaced by another For substance Y we can say the same is equal to X qua length is a very extrinsic condition or state of substance Y QUALITY By Ockham quality is not considered to be on an equal ontological footing with quantity While quantity is considered to be a transcendental meaning that it has apart from substance no existence at all whatsoever quality has possible independent existence that is to say it is something that is carried and therefore distinct from its carrier implying that it could by supernatural intervention without involving contradiction be separated from its carrier and subsist ontologically independently This is equivalent to saying that quality is considered by Ockham to be a predicamental accident but still in a stronger way it to be a being than St Thomas would consider it to be and any other predicamental accident When we do not pay attention to this supposed supernatural possibility and its demand on the ontological status of quality but follow the modern Ockham then quality must be considered on an equal footing with quantity with the exception perhaps that quantity stands nearer to Substance than quality does as can be surmised from what has been found out about continuous quantity And when quantity does not refer to a thing so it is with quality A strong indication as to the ontological equivalence of quantity and quality is the fact that they cannot exist without each other Quality implies intensity and intensity has a quantitative nature of its own different from that of pure extension So quality implies quantity And quantity implies quality that is it turns out to imply at least in our world quality If this were not so all quantitative relations would not be observable but we know they are observable So quantity and quality although not being the same are ontologically equivalent The modern Ockham wants to consider quality like quantity to be not a res additum thing added but just a description of the substance itself But as we saw with quantity it is a determination that can occur in two ways As phenotypic essential part proprium as we say with blue in the case of a copper sulfate crystal or as a phenotypic replaceable determination as we say in the case of a human body whose superficial part can become temporarily and partially blue So also here that is in the case of quality the ontological status is dependent on the predicational context for example whether blue is predicated of copper sulfate crystal or of human body which is in turn dependent in addition to the meaning of the qualitative term on the meaning of the subject term as we just saw it in the examples In the case of some given quality being a replaceable determination of some given substrate it is a res additum but only in the sense of a condition or state of the given substance which comes close to the position held by St Thomas with respect to the ontological status of accidents In the Category of Quality are included those terms other than essential differentiae essential quales of substance but see below which constitute appropriate answers to questions concerning the character quale of things As Aristotle says Quality is a term that is used in many senses and hence there is no single concept or meaning corresponding to the summum genus quality that is univocally predicable of all four of the species of quality enumerated by Aristotle Said a bit more precisely There is not one single intentio animae or natural sign corresponding to the one conventional sign that is the word quality but there are many such intentions concepts However it is probable that they all can be reduced to a single sense of quality certainly if we limit ourselves to qualities that are ontologically relevant A qualitative term signifies habits or dispositions habit differing from disposition in that it is with difficulty acquired or lost while disposition is easily acquired or lost Now what can be said to be acquired or lost by a substance must be something really distinct from the substance which is said to acquire it or to lose it MOODY following his historical account of Ockham p 162 If we interpret the really distinct from the substance not as being a genuine thing distinct from any given substance but as an accident in the sense of St Thomas or better still in the sense of a condition or state but involving only a formal content and not a size a number or any other quantitative feature of a substance then we have interpreted quality as a replaceable determination of some given substance We know however that a quality as such belonging in a Predicament can sometimes be a phenotypic essential part of a substance while the substantial differentiae mentioned above and provisionally excluded from the predicament quality are genotypic essential quales like blue is in the case of a copper sulfate crystal In that case it is not just a condition or state of the substance that is it is not a replaceable determination but a permanent determination of it and as such an essential part of it So like the substantial differentiae such permanent determinations must be excluded from the predicament But of course this is not right No qualitative determination should be exclused from the Predicament Quality The differences only appear in the different predicational contexts If the predication is per se and in quid then the predicated qualitative term designates the genotypic Essence of the given substance either completely or incompletely Such a term is then called a species or a genus If the predication is still per se but now in quale then the predicated qualitative term designates either a further determination of the genotypic Essence and then such a term is called a differentia or the predicated qualitative term designates a phenotypic expression of the genotypic Essence and then such a term is called a proprium And as we have said earlier Ockham should have interpreted Quantity and all other predicates belonging in all other Predicaments as well in the same way Consequently that is continuing the just given characterization of Quality which as such cannot be defined but only circumscribed because it is a supreme genus in the Predicament of Quality there are included all those qualities which Ockham calls absolute having according to Ockham possible ontological independency which substances actually possess which qualities are signified by abstract terms such as redness that can stand disjunctively for either genotypical essential quids and quales or phenotypical essential quales or replaceable qualitative states in extramental reality Also the concrete counterparts such as red of these abstract terms are included in the Predicament of Quality RELATION An example of a relation is that between mover and moved Both the terms mover and moved are concrete meaning respectively that which moves and that which is being moved and are correlatives Each of them can stand for individual substances But for what individual substance can the term motion which is abstract stand It cannot stand for any individual substance taken alone says Ockham and it does not signify any universal thing distinct both from concepts in the mind and from individuals in re that is in extramental reality Hence if it is a term of first intention it stands conjunctively for the two individuals that are signifiable disjunctively by the concrete terms mover and moved MOODY p 157 We could of course also hold that motion is a relation between mover and moved The significatum of the term motion like that of paternity similarity is according to Ockham not a res additum that is not a thing added to a given substance However I would say that motion in the sense of in motion is not just a description of some individual substance here a physical body without something added to it It is a state of a given individual substance a state of motion which as such is a replaceable determination One could counter this by saying that motion is always relative and involves some other substance physical body with respect to which it moves As such motion allegedly is not a determination of this particular substance because it could at the same time be at rest with respect to another substance physical body But even then the given substance is in a albeit very extrinsic condition or state of motion relative to that other substance and it is in a condition of rest relative to yet another substance This complies well with what we said above namely that motion is a relation of a certain kind The substance A possesses the relation moving with respect to B and in addition to it the relation to be at rest with respect to C And moreover it could be that motion is not relative after all as is argued in the document about the impetus in Part XXIX Sequel 5 in Fourth Part of Website In that case motion is a true quality that a given substance can happen to have So the term motion does signify a res additum again only in the sense of a replaceable determination not in the sense of a fully fledged being or thing of a given substance physical body So generally although we cannot say this substance is motion we can say this replaceable determination is motion Likewise we cannot say this substance is similarity or this substance is paternity but we can say this replaceable determination is exactly specified similarity or this replaceable determination is paternity In all these cases the replaceable determination is a particular state in which some given substance might find itself In this way it is perhaps correct to say that all relations can be reduced to a state of some particular single substance and that means that relation is reducible to quality or quantity There are two main types of relation viz predicamental relations which are real relations between substances for example the relation of friend between Socrates and Plato and transcendental relations The latter relations are such that both the one relatum and also the other directly constitutes the relation such as for instance the relation between substance and accident substance is a relation to accidents accident is a relation to substance the relation between matter and form matter is a relation to form form is a relation to matter etc A predicamental relation is always just a condition of a given substance that is always a replaceable condition state or determination and never an essential part proprium of a single given substance This is because such a relation always points to another substance and thus involves an extrinsic element To say this more precisely a relation of a relatum always reaches beyond this relatum namely to the other relatum But such a condition exists really it is not just an act of a mind comparing things The term teacher also signifies a relation between at least two individual substances here two human individuals or a trainer and his pet According to Ockham teacher does not signify an entity in extramental reality distinct from the individual substances involved It is therefore concluded by him that the only things which are per se in the Category of Relation are terms namely any term which cannot be verified of anything for which it can stand without reference to some other term connected with it by a preposition or by an oblique case ending NOTE 11 this other term being called its correlative MOODY p 159 and referring to Ockham s Expositio Aurea II 64 r The fact that a certain term can only be verified as to what it means by invoking another term added to it by a preposition or by an oblique case ending must have a cause in extramental reality And this we mean that a thing a given individual substance can find itself in a certain condition state by being in a certain environment which either has resulted from its own actions as in the case of being a father or from the presence of other things which are independent of it that is happen to be present as in the case of being similar The OTHER CATEGORIES that is other than Substance Quantity Quality and Relation will be discussed elsewhere if necessary All Categories except Substance and Quality are according to Ockham modes of signifying individual substances or qualities either conjunctively or connotatively and they signify nothing per se distinct from individual substances or qualities MOODY p 172 Let us now but still in a preliminary way wrap up results MOODY p 172 5 In all this we try to get as close to Ockham s undertaking as possible We can state two points of departure All that exists in extramental reality are individual entities that is concrete entities Abstract entities such as natures do not exist in extramental reality Such an individual entity a being cannot be known completely This is because such an individual entity say a crystal or an organism has an unoverseeable multitude of intrinsic or extrinsic features and the latter are constantly being replaced by others So if the different Categories signify all possible basic types of things then of each such a type of thing we have its supreme genus And although this supreme genus is not definable because it does not have a higher genus all the lower genera down until the infima species are in principle definable For instance A mammal is a milk producing vertebrate where vertebrate is the genus and milk producing is the difference Another example is red is the first rainbow color where color is the genus and first rainbow is the difference This means that we can in principle know a thing completely or at least signify it completely namely by enumerating all the differences and all the sub genera up until the supreme genus summum genus genus generalissimum of that thing However the only things that exist are individuals So we must completely signify such an individual thing as to what it is and as to what it can become where it is etc And this is impossible because indeed individuality involves an almost infinity of relations and in the course of time an almost infinity of features and

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