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- Logic II

far as perception decoding information instead of damage is concerned Certainly there will be different colors in such a part of ultraviolet that is different parts of the petal will reflect different ultraviolet wavelengths But could it be that the same group of wavelengths can produce different perceived colors in different visual organs We could for example imagine that some object is green for a given individual human perceiver and is calling it green when asked while that same object is red for another person while he calls it green This could occur but cannot be demonstrated Therefore we can legitimately call the red as seen by the second person green or the green as seen by the first person red They both see the same quality that s for sure This same quality can be processed differently by different visual organs in the broad sense that is including the relevant parts of the brain either in virtue of their different structure or of some defect or malfunction All these cases are not cases of subjectivity because they can be detected as such They are cases of objective subjectivity precisely as in the case of the broken stick partly submerged in the water Sense observation ultimately never fails because when it does now or then it will sooner or later be detected by another sense observation So what we have so far is that extramental objects can and do have qualities and these qualities can be each for themselves objectively detected by the sensory apparatus of at least higher animals that is the latter can be objectively aware of sense qualities insofar as their sense organs are sensitive for that which transmits these qualities Further we know that awareness of a quality of an inspected physical body cannot just be the physical effect of the influence of the inspected physical body on the perceiver otherwise a steel bar that is heated in a fire would not only get hotter but would feel the heat and this is absurd The effect of the influence is just a genuine part of the receiver and is therefore subjective In order for a perceived quality to be objective the receiver must decode it and after this is accomplished the receiver has become in a way the quality As for sensing the blue copper sulfate crystal The blue which is actually present in the crystal is encoded we can also say enfolded in the light illuminating the crystal This light interacts with the retina of our eyes but not in such a way that the retina or other bodily parts of us become blue The neurological machinery of the faculty of vision now decodes retrieves or unfolds the blue i e it reads the blue from the coded message And in doing so we see the blue of the crystal Indeed generally nothing happens with the form blue when it is encoded transmitted and decoded that is the form is not necessarily perturbed or distorted during these processes and therefore it is perceived objectively The form is now shared by the sensing organism and the sensed thing and this is the relation of formal identity in sensory cognition it must be only formal because the sensing organism cannot become numerically identical to the sensed thing Qualities in the broad sense of formal contents and concomitantly quantities or generally mathematical relations are apprehended by te senses The proper object of any given sense organ color for the eye sound for the ear etc is infallibly and objectively known by means of these sense organs The concomitant objects of the sense organs all quantitative and mathematical features are not always infallibly perceived as we see it in the case where distant objects appear smaller but can be corrected by the cooperation of all the senses together finally resulting in these features also being apprehended objectively as they are in the external thing The origin and development of the concept It is now time to use all these findings for the characterization of the simple non complex natural sign the concept It will be a long discussion in which because of their importance we must sometimes repeat earlier findings The foregoing discussion about sensory cognition of formal contents as they exist in extramental reality as well as the ensuing discussion about the formation of the concept on the basis of these apprehended formal contents are crucial for the evaluation of an Intentional Logic as was first proposed by VEATCH If we cannot solve the problems presented there or if our findings turn out to be wrong we cannot accept such an Intentional Logic But because we intuitively feel that such a Logic has much to offer we do not avoid lengthy discussions and repetitions A concept of any extramental state of affairs is developing in te mind on the basis of repeated observations of individual extramental things It is precisely the formal contents of these things that are internalized in the mind according to the above described process of decoding information What follows is an attempt to describe the process that organizes all these internalized formal contents into one or more concepts Let us begin by stating that every sense organ has its proper object that is that to which it is naturally geared color for vision sound for hearing etc The apprehension of a quality however stops when the ultimate efficient cause of sensation namely the external thing vanishes Further when I observe a green apple I am aware of its qualities and concomitantly of its quantities But what we sense by means of having acquired the qualitative and concomitantly quantitative forms of the apple is always this green color of this say large apple at this distance from us and so on Sensation is always sensation of the individual But how do we come from here to universal statments and predications resulting in genuine science How do we acquire genuine universal concepts provided we do acquire them How do we apprehend a genuine that is not arbitrary class of individuals of which a universal formal content can be predicated Or asked differently how are we able to carry out induction Does reason has a peculiar object of its own materially identical to that of the senses of which the combined proper objects color sound etc together with the secondary objects quantitative features point to the same material individual thing but formally distinct from that of the senses as WILD p 452 believes In First Part of Website and also in Part I of the present Fifth Part of Website we have argued that scientific induction generalizing findings about individuals is based on a fundamental presupposition of natural science namely the Species Individuum Structure of material things In it it is supposed that every thing acts according to its intrinsic nature or essence the acting can be on other things and so also on our senses So when we have examined a number of seemingly similar individuals individual extramental things we generalize some of their features resulting in universal concepts like wood iron rat etc on the basis of these features observed in all investigated individuals In every single individual observation of a given individual thing we apprehend qualities and quantities as described above And having in this way investigated many such individual things we formulate a universal concept So we formulate it after detailed and prolonged empirical investigation experiments observations in Nature We do not possess a special mental faculty that directly apprehends a universal feature resulting in the formation of a universal concept Such a universal concept as it has gradually been developed empirically and stored in the brain is as such now a sign for extramental individuals that is once formed either still more or less rudimentary or already much more developed it in turn can and does point to individuals namely those which participate in the content comprehension of the concept On the basis of this we select individuals in order to place them in a certain class Any individual of which we can legitimately predicate the content of the concept this thing here is an apple will be placed by us in the corresponding class So the universal concept resulting from conscious or unconscious empirical investigation is then as such a natural sign pointing to a definite extramental formal content and with it to existing external concrete individual things possessing this content Of course such a sign is not wholly natural because it is the result of human investigation but once established it naturally signifies a certain extramental formal content and designates certain individual existing things It is itself signified conventionally by a spoken or written word conventional sign But the natural sign as such is not sufficient to characterize a concept unambiguously that is to characterize what a concept as concept is It must be further qualified in order to actually be such a concept because there are natural signs of things which signs are not concepts of these things but are things that point to other things that are either similar to these first things or are causes of them or are effects of them Such signs which are also natural signs are instrumental signs They have an objective nature of their own and do not signify these other things directly because they are different things different from those they point to and thus do not stand in a relation of formal identity with these other things as concepts do Those natural signs on the other hand which do stand in such a relation and are thus not instrumental signs we can call formal signs They have no nature of their own their nature simply consists in to be of or to be about something else they are materially different from that somthing else but formally identical to it And not only concepts are formal signs but also subject predicate propositions and syllogistic arguments demonstrations proofs All of them are formal signs or equivalently logical intentions We have seen that the observation of a singular individual thing results in relations of formal identity of sensed qualities necessarily interweaved with quantitative aspects For every such quality actually sensed there is such a relationship This having of all the sensible features is k n o w i n g the external thing but only as an individual here and now thing We do not yet know whether this thing is truly a self contained thing or just a fragment of such a thing or belonging to several different such things one or more of its parts belonging to one self contained thing other parts to other such things The picture of the status of our observed thing gradually arises after many other things have been observed and compared So it is in the case of single crystals and organisms where we more or less easily recognize them as self contained things then classify them resulting in respectively a system of minerals based on chemical composition and intrinsic total symmetry or on the way of their genesis and a taxonomic system of organisms based either on morphological or physiological similarities or on common ancestry In other cases however it turns out to be very difficult to decide whether something is a self contained thing or not such as twinned crystals mixed crystals lichens tight colonies of biological cells or of whole animals or such things as planets comets computers etc But little by little we learn to recognize self contained things and to clearly distinguish them not only from just aggregates of self contained things or from being just fragments of self contained things but also from other self contained things We try to find the essence of every such self contained thing But this can only be done by comparing them with other things In First Part of Website we have found a general characterization of the Essence of a self contained thing It is the dynamical law of that dynamical system that had generated or could have generated that thing Much philosophical research was necessary to establish this and still many problems remain And although such a dynamical law cannot in most cases be already actually formulated that is is not yet known it often is represented in the thing by a set of observable features that have resulted directly from this law Such a set of features thus can at least represent the Essence of the self contained thing An example is the Space Group symmetry PLUS Chemical Composition which characterizes a given crystal species which symmetry plus composition is a direct effect of the action of some specific dynamical law here one or another crystallization law But also such observable features chemical composition observed in chemical analysis total symmetry observed in X ray diffraction techniques able to represent the Essence which is some dynamical law such as a crystallization law of the given thing are in many other cases hard to find All this means that our idea of the Essence of given things albeit just in terms of observable representatives that is even if we are already satisfied in having found although not the Essence itself or we could say the genotypical Essence its observable representative the phenotypic Essence is only gradually formed in the knowing mind It is certainly not directly apprehended by some special cognitive faculty of ours as some philosophers assert for example WILD pp 450 In establishing essences the presupposition of the Species Individuum Structure of material beings is always albeit implicitly present and in holding that presupposition we carry out induction the generalizing of individual findings This generalizing resulting in the reinforcement or consolidation of the relevant concept s content until now formed and the determination of that concept s extension is always subject to error and can never be proved It can only be more and more strenghened by additional observations Not only things are implicitly classified in this way by every knower and explicitly by the scientist but also qualities However it usually takes a long time and much effort to characterize particular qualities as to what they are A good example is energy which is a certain state in which a thing finds itself to be in this particle has so and so much energy It has turned out hard to exactly define energy It is said that energy is the capability of doing work see our documents on Thermodynamics in Fourth Part of Website but not all energies can deliver work as was found out in the case of heat energy Only a part of it can deliver work the rest is dissipated What is needed in order to deliver work is an energy difference energy fall for example a hot and cold physical body But also with respect to other qualities it is often hard to establish their intrinsic nature for example red To characterize the latter in terms of wavelength of electromagnetic radiation is not enough because radiation itself is not colored But also in order to form the concept red the quality must be observed and investigated in many different things and in many different circumstances Therefore we cannot say as does WILD p 452 that Reason apprehends the very same thing materially which sense apprehends but it grasps something in this thing formally which sense cannot grasp either the essence alone by itself or the accident alone by itself The object of reason is not another t h i n g existing separately from the sensible thing It grasps this very thing or some accident of it a b s t r a c t l y a s i t i s i n i t s e l f with nothing else added or subtracted Sense cannot do this because it always grasps a concrete manifold materially confused together We agree that sense always grasps a concrete manifold materially confused together but have explained how one proceeds from this to universal knowledge not by means of a special faculty that has a universal essence of a thing or of a quality as its peculiar object such as the apple itself or the greenness as such with everything irrelevant or extraneous omitted but by means of repeated observation and then generalizing as best as one can unconsciously or consciously We have explained induction and indicated what is presupposed by it just presupposed not demonstrated the Species Individuum Structure of material beings As such it is the presupposition that every material being is catallel that is in every material real being self contained or not there is a formal content that permanently as long as the thing exists at all determines an indeterminate material substrate In the case of a quality or any other accident we also have to do with a formal content determining a material substrate but in this case it does not necessarily permanently determine it it can be replaced by another such content while the thing itself remains existent and the substrate is not as it was in the first case totally undetermined Also aggregates of self contained concrete things have a Species Individuum Structure SIS but then only in an analogous way Does all this mean that universals represented by the species part of the SIS do exist in extramental reality Not necessarily It is reasonable to assert that in extramental reality only individual things aggregates and substances occur The formal contents essence properties and accidents cannot exist save as residing in individual things and that makes them individual they only become universals when we imagine ourselves that we have somehow managed to actually separate the formal contents from their substrates which imagination is possible but not the actual carrying out of the separation itself So in extramental reality all formal contents are though not individuals individual What is universal is only the term denoting many individuals related to each other in some way So we do not need a special faculty that can apprehend universal essences in extramental things because such essences are not there in extramental reality With respect to formal contents there are only individual formal contents in extramental reality And these individual formal contents can be grasped by sense observation as I have explained above And now repeated observation and comparison consciously or unconsciously will render us capable of singling out groups of formal contents which groups we can call essences enabling us to form classes Such a class is a set of individual fully fledged things and constitutes the denotation of the concept that is constitute the meaning of that concept in terms of its extension The set of individuals itself is not the meaning of the concept but its range its range or domain of application in extramental reality The criterion to allow a given that is selected individual to be a member of such a named set for example animal is some individual formal content in it which can be observed If an individual possesses this particular formal content then we make it a member of the named set class If it doesn t possess it we do not allow it to be a member of that named set So again formal contents do exist in extramental reality but there they are always individual This view can be called moderate nominalism or equivalently conceptualism universals do not exist in extramental reality but they do exist in the mind in the form of certain signs The realistic theory of WILD says that reason has its own object a universal essence or a quality as such We have already shown that a universal essence and also a universal quality do not exist as such that is as universal in extramental reality The content of a given essence or of a given quality is as it exists in extramental reality individual and can thus be apprehended by the senses But this means that reason has no peculiar object in extramental reality that is it has no object whatsoever While calling it still the object of reason WILD now identifies it with the abstracting activity of reason Some formal content individually existing in some given extramental individual being is by the activity of reason abstracted from its material substrate resulting in this formal content to become a universal We have however already seen that this is not how things go The universal is not formed by abstracting it from its substrate and then predicated of many other individuals but is formed by often a long process of repeated observations and comparisons as explained above Also in this sense reason has no special peculiar object like any sense organ has When a concept which as such is a universal is finally formed it becomes a sign a natural sign itself indicated by a word or words And because such a sign is not something that came spontaneously and necessarily into existence but only after much had been done think of the concept of energy for example it can as such not it seems be a sign in the sense of a truly intentional sign because as such it doesn t seem to be a natural entity but a forged one But because it in fact entirely consists of or is reducible to the results of actual sense observations it must have the same character as the results of individual sense observations and this character is its formal identity with something in the things taken disjunctively So the concept is a natural intentional sign after all As such it always refers directly to certain formal contents in things and this means that we have to do with genuine signification that is a meaning of the sign not beforehand restricted by some context When we add such a context for example when we let the concept figure in a definite proposition which is such that it narrows down the meaning of it resulting in the concept s actual meaning in this present context we say that the intrinsic meaning of the concept becomes restricted there exist contexts which do not restrict the meaning of the term or concept When the sign figures as a subject in a proposition about things the subject term whether the applied context the proposition does restrict the meaning of the subject term or not refers to a thing as in man is an animal which expression in fact means that every man can be characterized by possessing the feature animality which implies that the term man as in the above proposition does not in fact s i g n i f y any concrete individual man because man s i g n i f i e s only the essence of these individuals but can s t a n d f o r these individuals that is we have to do here with supposition suppositio or equivalently designation And as has been said the total set of these individuals is the range domain or extension of the concept man In the present case the proposition man is an animal does not restrict the meaning of man that is does not exclude any individual from the domain or extension of the concept Here we have a case of what is called natural supposition If the context does exclude certain individuals from the extension of the concept such as in all white man live in the western hemisphere whether this assertion is true or not we have a case of so called accidental supposition with respect to the concept man because here this term does not refer to its full extension but to only a part of it as a result of the added adjective white which excludes all colored men So in summarizing I agree with the main ontological tenets of WILD that is to say the status of the universal or equivalently the concept I disagree however as regards the way a concept is formed and also how sensory awareness comes about The universal is not the result of a special ability of the intellect abstraction of a pre universal from the extramental matter form composite prime matter substantial form or substance accident and then see whether it can be predicated of many individuals resulting in a universal when it can be so predicated but the result of many awarenesses of extramental formal contents on many occasions Both for me and for WILD the universal is not a separate thing that exists by itself but is a relation which is perfectly expressed by calling it a formal sign The foundation of this relation is the formal content s l as it is found expressed in the Categories And when it is predicable of in principle an indefinite number of possible extramental material individuals it is a universal concept And it can be predicable in a number of different ways kinds of universal relations of such an individual namely as genus difference species genus and difference together necessary accident proprium or contingent accident accidens These five universal relations or predicables exist only in the mind What is related by these relations is the formal content s l belonging to one or another Category as it is formed in the way explained above in the mind AND the given individual material thing as it exists outside the mind NOTE 18 In this way the universal concept can stand for such individuals and signify some formal content in them The naturalness of a universal concept as sign stems from the many single observations and experiences that have preceded it and constituted it In language it is then finaly expressed by a word conventional sign The natural sign as conceived here can also be called formal sign distinguishing it from an instrumental sign also a natural sign or can be called an intention The difference between the opinion of mine and that of WILD as regards the formation of a universal concept is important because in my view an ontological dualism in man body and soul is avoided it was also avoided when considering sensory cognition The formal identity of content in sensory cognition is according to me describable as a retrieval or decoding of qualitative information about the external thing information that was encoded or enfolded by and in the medium electromagnetic field in the case of vision air in the case of hearing The formation on the basis of such formal identities of a universal concept is assumed to be accomplished by integrating many single sensations So no immaterial status of the mind is implied After all a process such as knowing cannot be immaterial because only material entities can interact Signs Let us now recapitulate the classification of types of signs and see where signs such as concepts propositions or demonstrations stand in this classification A sign is an entity that points to presents or represents another entity A natural sign points to an other entity simply in virtue of what it is as natural being So smoke is a natural sign of the presence of fire and the concept dog not the word dog is a natural sign signifying a mammal that often barks A conventional or artificial sign is one whose significance i e its signifying comes not from its own nature but from human convention such as words signals guideposts etc There is nothing in the spoken written or printed word dog this word considered simply as a physical fact that would naturally represent the mentioned animal Signs can be either formal or instrumental depending on their relation to the knower a knowing power All conventional signs and some natural signs are instrumental signs An instrumental sign like any other sign points to some entity other than it self But an instrumental sign presents its significatum that what it signifies to a knowing power only by being first apprehended itself The smoke is only a sign pointing to a fire when the knower is explicitly aware of the presence of smoke that is of the presence of the sign One can only know what the guidepost on the road means or signifies by first becoming aware of the guidepost The word dog must be seen before we can come to know what it means Some natural signs and no artificial signs are formal signs These are signs of which the knowing power need not be aware of in order to know what that sign signifies Such signs are all concepts all subject predicate propositions and all syllogistic arguments insofar as they are internalized that is not insofar as they are written down or spoken Let us continue with concepts while we know that the same general findings hold for S P propositions and syllogistic arguments and while we are not speaking here of the words representing them As to this concept itself it can hardly be said that we are obliged to know it as such and as a concept before we come to know what it is a concept of For instance in the case of the concept of dog one does not first become aware of the concept of dog and only afterward of what the concept signifies To be sure one must have the concept dog before one can become aware of dog But still one does not have to be aware of the concept dog in order to be aware of its significatum So all concepts S P propositions and syllogistic arguments insofar as they are internalized in the knowing power and are as such functioning as signs are formal signs A formal sign is one whose whole nature and being are simply a representing or a meaning or a signifying of something else In fact they are not things at all but relations Such signs in other words are nothing but meanings or intentions Thus if one were to ask what is it to be a formal sign the answer would be it is simply to be of or about something else See for all this VEATCH H Intentional Logic 1952 p 12 13 of the 1970 edition Formal signs It is not hard to see how such formal signs are altogether indispensable to that particular relation of cognitive identity which is a necessary corollary to a thoroughgoing philosophical realism For if there are to be signs which would make such a relation of identity possible those signs could not have definite determinate natures of their own insofar as we consider them in their significative function If they did have such a nature of their own as do instrumental signs then they could represent other things only as being similar to themselves things signified being similar to these signs or as causes of themselves things signified being causes of these signs or as effects of themselves things signified being effects of these signs or as in some way or another related to themselves But a formal sign does not signify or represent other things in these ways It does not present them as they are in relation to it but rather as those other things are in themselves The real object in short which the formal sign signifies is itself that sign s very content Only so can the relation of identity between knowledge and its object come about The whole nature of a formal sign in its significative function consists in being about something else This then is what is meant by calling such signs intentions Because of its way of formation the concept always connects us with aspects of extramental reality although some such aspects could turn out to be irrelevant which could however be detected later and which detection process amends the concept So the concept is objective Thus having said this we can still say that having a concept directly identifies something in us with some aspect or aspects of extramental reality and in this way we can still say that a concept is a formal sign despite its empirical way of formation And it to be a formal sign is indispensable for knowledge to be objective because a concept is the most basic element of discourse and that element must be intentional And of course in addition to formal signs which is a condition sine qua non absolutely necessary condition though not necessarily a sufficient condition instrumental signs turn out to be very useful indeed for scientific inquiry However we cannot do with instrumental signs alone Of course formal signs concepts internalized propositions and arguments must be certain higher level brain patterns neurological patterns But in order to know what the concept means we do not first have to be aware of these brain patterns This is not just an assertion but an experienced fact So concerning signs Words and models are instrumental signs used in science but they must always be supplemented by formal signs in order to render the knowledge objective The distinction of the logical from the real Logical entities like concepts S P propositions and syllogistic arguments are formal signs that is they are intentions while the extramental things or aspects of them are not intentions Extramental things can instrumentally signify other things but they do not intend them that is in signifying they do not involve relations of formal identity So a given crystal to take an example or a number of crystal individuals can be intended by a logical entity but they themselves do not intend anything The notion of intention can be a bit confusing so we must expound it further A given crystal or a collection of crystals not as collection but as individual crystals is as has been said not an intention Only insofar as it is intended we can call it an intention namely a first intention It is then the object of an intention it is intended and seen as intended it is an intention That by which the crystal is immediately intended is in fact the crystal as intended and so is also a first intention But this first intention can itself be intended by a second intention This means that such a first intention is the object of a second intention for example when we say that the concept crystal is a genus And because it is the object of a second intention it can also be called a second intention Again when a first intention is the object of a second intention it can also be called a second intention or again in other words when a first intention is intended by another intention a second intention it can also be called a second intention It is clear that an object as intended is itself an intention because it is intended it is then considered only insofar as it is intended but it is not an intention when this object cannot by itself intend anything that is it is not an intention insofar as it cannot intend anything On the other hand a direct object of second intention is a first intention and insofar this first intention can itself intend something else it is intended as well as intending Only an object which cannot intend anything else while it can be intended is a real object that is an extramental object and not a logical entity It is a logical entity only insofar as it is intended by some logical intention Apart from logical intentions there are other beings of reason such as fictitional things for example the concept of a phoenix Second intentions intend first intentions and only through these extramental things Intentions in the sense of intending real objects can be considered as intentions in the strict sense while intentions intending intentions first or second can be called intentions in the broader sense As we have said real objects are not and cannot be logical intentions This

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Open archived version from archive - Logic III

that essence but also possible to consider them as related to the class of individuals that is constituted by this relation of identity which latter relationship is one of class membership In other words while the relation of identity between essence and individuals is both the prior relation and the properly intentional or cognitive relation still the relation of class membership is consequent upon this relation of identity and hence in its own way quite legitimate again because assigment by us to a class just follows i e is only then made possible from the cognitive relation of identity in which latter it is realized what a given thing is and thus what each examined individual is Hence not only is it legitimate and true to say that John Jones is a man it is also legitimate and true to say that he is a member of the class of men Note that both propositions are subject predicate propositions However even though both propositions are legitimate and true and even though the second is true if and because the first is still the first one alone intends and describes the real situation so far as Jones is concerned The second one on the other hand does not describe the real situation with respect to Jones for Jones is not a member of a class in extramental reality because Jones only acquires this property as a result of our classifying that is only as Jones as known Instead the second proposition intends indeed it does intend something only that situation with respect to Jones which results from that individual s having been brought into the context of a purely intentional or logical relation of identity In short the first proposition is to be taken in the first intention it is a proposition in the object language the second in second intention it is a proposition in the metalanguage Besides even when the proposition about Jones being a member of a class John Jones is a member of the class of men is to be understood in second intention it still does not intend as the proposition John Jones is a man does the whole or even the most important part of the intentional relation involved in the proposition John Jones is a man Instead the properly intentional relation in this latter proposition is the relation of identity the relation of class membership being only derivative and non intentional That is the relation of class membership is intended by the proposition John Jones is a member of the class of men But the relation of class membership although being an object of intention is itself not intentional VEACH p 126 7 Why then should the mathematical logicians have chosen to take this derivative and non intentional relation of class membership and have sought to understand both concepts and propositions in terms of it rather than to take the prior and properly intentional relation of identity So far as it presents itself the only explanation for this is to be found in the rather massive indifference on the part of the newer logicians to the fact of intentionality and their consequent willingness to disregard the properly intentional relation of identity in favor of relations that are non intentional and more properly fall within the sphere of mathematics VEATCH p 127 Indeed I myself am inclined to assert that mathematical Logic is just a part of mathematics like Group Theory and Set Theory for instance are or perhaps of meta mathematics that is mathematics about mathematics This part characterizes itself by firstly being very general indeed and secondly by treating of a special mathematical function which is called the truth function because it shows a certain analogy with the truth function in genuine Logic that is intentional Logic insofar as this Logic is about knowing extramental real beings a Logic that is where truth is dependent on the significata as they exist in extramental reality of the terms in a proposition As regards mathematical objects which can legitmately considered to be objective meaning that they are what they are independently of their being known they also can be the objects of logical intentions that is they can be intended by logical entities as to what they are I suppose that the truth function here will be a bit different because of the immaterial nature of mathematical objects It is probably the truth function as used in mathematical Logic endorsed with quirks as was discovered by GÖDEL and TARSKI For the intentional Logic concerning the knowledge of extramental real beings a metaphysical truth function is involved All this is however in need of further enquiry Propositional functions as substitutes for concepts In addition to substitute concepts in favor of classes we also encounter the attempt to substitute concepts in favor of so called propositional functions A propositional function is a mathematical way of expressing a property or generally a WHAT and thus a concept This WHAT is dependent on that of which it is a WHAT So if we symbolize this WHAT by f the function name and that of which it is the WHAT by x then we have f x which means that f x is ordered or related to x x f x in turn meaning that x is associated with f x Indeed such a propositional function expresses the relational character of a concept Socrates x is a human being f or Socrates x is sad f As we have intimated earlier a concept implicitly implies such relations that is relations of identity between the things and the formal content abstracted from them However many mathematical logicians do not limit labeling something as propositional function to such a relation of identity which is the concept but extent it to include relations connecting two or more relata All these are called propositional functions or universals To investigate the legitimacy of this extension within the context of an intentional Logic let us consider two examples of propositional functions given by a mathematical logician and quoted in VEATCH p 132 Cassio is sad F x one place propositional function Cassio loves Desdemona F x y two place propositional function As for Cassio is sad the concept sad is related to its subject term by a relation of identity NOTE 28 And this identity is expressed by the copula is On the other hand we cannot say this with respect to Cassio loves Desdemona While in Cassio is sad the function is predicated of Cassio that is the function term is predicated of the term Cassio and there the function was sad it is not so in Cassio loves Desdemona We cannot say Cassio is loves Desdemona and more generally we cannot say Cassio is loves The function can also not be predicated of the term Desdemona for we cannot say Desdemona is loves Of course when we reformulate the proposition Cassio loves Desdemona which is an instance of the two place function loves as Cassio is a lover of Desdemona which is an instance of the one place function lover of Desdemona we obtain a genuine relation of identity Cassio subject is copula a lover of Desdemona predicate So in order to obtain genuine relations of identity we must convert all many place propositional functions into one place propositional functions And because many mathematical logicians do not do this they confuse intentional and non intentional propositional functions because all the many place propositional functions are non intentional This again because the many place function cannot be predicated of its subjects We cannot say Cassio is loves nor Desdemona is loves and only predicability gives us the relation of identity and only a relation of identity is truly intentional because it separates and re unites again which is the very act of intention resulting in our knowing the what of things The relation between sad and Cassio does not correspond to a real relation because Cassio is not identical to sad also not in the context of classes because classes are themselves not real but beings of reason while the individuals included in these classes are The relation is just a logical intention On the other hand the relation between loves and Cassio corresponds to a real relation because Cassio really loves someone So this relation because it is real cannot be a logical intention It only becomes one if we convert it to Cassio is a lover and then like in Cassio is sad a state of Cassio is intended and thus known Also the real relation between Cassio and Desdemona namely the relation loves in no way represents or intends what Cassio is only what Cassio does but this is not a relation of identity or Desdemona or anything else for that matter To be sure either of these relations viz the relation between loves and Cassio or between loves Dedemona and Cassio for that matter and the relation between Cassio and Desdemona namely loves may be made the object of an intention but neither can themselves be an intention because Cassio loves Desdemona is not a subject predicate relation while Cassio is sad is a subject predicate relation Instead no sooner is such a relation made the object of an intention than the intention itself turns out to be nothing other than a relation of identity For instance if one wishes to consider the relation of Cassio to Desdemona and to state what that relation is one will say that it is a relation of lover to loved or that it is asymmetrical or that it is a predicamental relation etc In other words the minute the relation of Cassio to Desdemona becomes the object of a concept or the subject of a proposition NOTE 29 then 1 the relation of the universal concept to that particular relation namely loves universal concept to Cassio loves Desdemona the particular relation as expressed in Cassio loves Desdemona subject is copula an instance of loves predicate or 2 the relation of the predicate expressing a property of the proposition to that relation figuring as the subject of that same proposition Cassio loves Desdemona subject is copula asymmetrical predicate is a relation of identity that is to say it manifests what that relation is VEATCH p 135 The same goes for the relation between Cassio and loves or Cassio and loves Desdemona Also this relation is as has been said a real relation namely between Cassio and a state in which he is in NOTE 30 When we make this relation the object of an intention and thus the object of a concept or the subject of a proposition then 1 the relation of the universal concept substance state to that particular relation Cassio loves which can be expressed as The relation between Cassio and loves subject is copula an instance of the general relation between substance and state predicate or 2 the relation of the predicate expressing a property of the proposition to that relation as subject as in The relation between Cassio and loves subject is copula a transcendental relation predicate is a relation of identity that is to say it manifests what that relation is By treating one place functions on a par with many place functions the mathematical logicians have treated genuine intentional relations in the same way as they had treated non intentional relations Accordingly with propositional functions we can witness the same thing happening that happened with classes The Paradoxes VEATCH pp 138 The paradoxes have forced mathematicians and mathematical logicians to review much in these disciplines and are brought up as a critique against Aristotelian Logic and consequently also against an intentional Logic as devised by VEATCH and worked over by me First of all we will restrict ourselves of course to the genuinely logical paradoxes The principal outcome of the mathematical logician s recognition of these paradoxes is their insistence that Logic is not to be regarded as one and simple but rather as involving a hierarchy of types or a multiplicity of Logics and Metalogics VEATCH p 139 I add to this that the sequence of metalogics will not as might perhaps be expected run off into infinity because this sequence eventually ends up or bounces into the hardware of the brain and the latter does not work according to rules but according to natural laws that is according to causal necessity And for this necessity no rules are necessary See HOFSTADTER D Gödel Escher Bach 20th anniversary edition 2000 p 170 Section The Jukebox Theory of Meaning and the next Section Against the Jukebox Theory Among the logical paradoxes we have two types conceptual paradoxes and propositional paradoxes To the former belong that of the class of nonself membered classes and the paradox of the impredicable To the latter the liar paradox Following VEATCH pp 140 we will start with the conceptual paradoxes For this it suffices to treat of just one of them as representing them all namely the paradox of the impredicable Let us systematically expound this paradox As a preliminary we might note the following The term not in the linguistic sense that is not the word red is a term of first intention It intends a certain well defined state of some substances in extramental reality The term concept of red on the other hand is a term of second intention It intends the first intention red that is it intends the term red taken in first intention Or equivalently it is the term red taken in second intention All terms can be predicated of themselves For instance in red is red Many terms however cannot be applied to their objects when taken in second intention We cannot say the concept of red is red Such terms or predicates we call impredicable NOTE 30a On the other hand while as has been said all terms can be predicated of themselves there are a number of terms among them that also apply to their objects when taken in second intention For instance while we can of course say with respect to the analogous concept being a being is a being we can also legitimately say the concept of a being is a being it is namely a being of reason Such terms or predicates we call predicable And of course it seems that any term or predicate is either impredicable or predicable It is here however that the paradox appears Indeed if we now ask whether the term impredicable NOTE 31 itself is predicable or impredicable we run into a paradox because both alternatives give contradiction If we suppose that the term impredicable is impredicable first alternative then we must admit that precisely because of this assumed fact it is predicable NOTE 32 So we have a contradiction If on the other hand we suppose that the term impredicable is predicable second alternative then we must admit that it must be impredicable So again a contradiction And because both alternatives while there being no more of them lead to contradiction we have a paradox NOTE 33 While asking about the term impredicable led to paradox asking about the term predicable does not Let us see the alternatives First alternative while in all cases we can say predicable is predicable we also say the term or concept of predicable is predicable And indeed if it is predicable then it must be predicable No contradiction is apparently involved Second alternative while in all cases we can say predicable is predicable we also might say the term or concept of predicable is impredicable If this is true then we cannot say the term or concept of predicable is itself predicable but should say the term or concept of predicable is impredicable that is the term predicable taken in second intention is impredicable while taken in first intention it is predicable And this could be the case just like we could not say the term or concept of red is red So also here no contradiction is apparently involved And further investigation will reveal one of these alternatives to be true See further down VEATCH p 141 says about all this the following The mathematical logicians in the face of this paradox have proposed a cure which it would seem to me would really kill the patient They propose that since the idea of impredicable concepts or of nonself membered classes leads to paradox the thing to do is to rule out the notions of predicable concepts and of self membered classes This is done either by a theory of types or by a theory of metalanguages They both establisn by decree the illegitimacy of all notions or concepts which would seem to apply to their proper objects not only when these are taken in first intention but also when they are taken in second intention Indeed when concepts are considered to be sets of individual entities we arrive at a paradox when considering self membered sets If we say that the concept of impredicable concepts is the set of all impredicable concepts and the concept of predicable concepts is the set of all predicable concepts then we can ask Is the set of all impredicable concepts itself a member of the set of all impredicable concepts or is it a member of the set of all predicable concepts The first alternative amounts to the supposition that a set can in certain cases be a member of itself which is flatly absurd A whole can never be a part of itself certainly insofar we speak about finite wholes So it seems legitimate to rule out self membered sets which here means that we should rule out that the concept of the impredicable is itself impredicable note that in this line of reasoning we have just switched from set membership to belonging to a concept So the concept of the impredicable must be predicable but then again the concept of the impredicable must be impredicable which however was ruled out So we must abandon the whole question as to whether the concept of the 34impredicable is impredicable or predicable The question is thus according to the mathematical logicians meaningless But such a solution of the paradox is unacceptable for an intentional Logic because for it it is very natural to conceive of a logical intention which in intending its object would intend itself as well or better which would be such as to intend its object considered in second intention quite as much as in first intention the term the term red intends the form red in second intention while the term red intends the form red in first intention So the term impredicable intends impredicable concepts either the one or the other But also this term itself must be such as allowing it to be intended This we do by the term the term impredicable one or another impredicable concept is intended as second intention And we can then ask whether this term is predicable or impredicable that is we can ask whether the term the term impredicable is predicable or impredicable and this is of course a legitimate question Thus if I say the term impredicable is itself impredicable that is if I do not interpret this purely extensively in the exclusively quantitative sense then I would not have a case that the set of all impredicable concepts is a member of the set of all impredicable concepts It would seem that the conclusion to be drawn as already hinted at from this situation would be not that classes representing concepts must be ruled out as soon as they turn out to be self membered classes but that only sets in the mathematical sense that are self membered must be ruled out This can only be consistent if we differentiate between 1 classes not as mathematical sets that is not as purely quantitative collections but classes somehow interpreted as logical entities which are itentional and 2 purely quantitative mathematical sets which are not intentional Just as these viz logical classes versus mathematical classes are radically different from each other the one being intentional the other non intentional implying that ruling out the one does not necessarily entail the ruling out of the other we also should not rule out concepts that turn out to be predicable for example the concept of a being is a being because concepts are radically different from mathematical quantitative sets again because concepts are intentional while mathematical sets are not While it would seem difficult and even impossible to conceive of a whole at the same time being a part of itself it is not only not difficult but even very natural to conceive of a logical intention which in intending its object would intend itself as well But elsewhere we have said that the essence of a formal sign a logical intention lies solely in the fact that it signifies something else that is something other than itself The conclusion seems to be that a logical intention cannot intend itself However when we have the case of an intention of an intention we do not have an intention that intends itself as the next diagram illustrates Here we see that a second intention refers to a first intention and a first intention to an object So here there is no complete self reference and it appears evident that only complete self reference can generate a paradox The concept of red intends red It can however also intend itself the intention now intends itself that is bends onto itself but it must do this by means of a second intention so again the self reference is not total Moreover not only do such predicable concepts and self membered logical classes seem perfectly natural and normal from an intentional point of view but in addition they are absolutely indispensable Without such concepts the very analogy of Being itself in the sense of being can come in several distinct types such as substance accidents beings of reason etc could not be recognized since it is only in an analogous equivocal concept that such analogy of being itself can be apprehended and an analogous concept of the sort here required is indeed a predicable concept VEATCH p 142 The solution of the paradox in terms of a multiplicity of Logics or logical languages or sets of rules NOTE 34 is also because of another reason unacceptable because it destroys the unity of Logic That is without predicable concepts there is not one single Logic anymore but a multiplicity of logics and metalogics Nor is that all for even to propound such a theory to the effect that logical entities are not univocal but systematically ambiguous NOTE 35 even to enunciate such a principle would seem to violate the very principle enunciated For the principle itself is certainly about all logical entities namely that they do not form a unity but are distributed over several different logical systems different logics So this principle itself belongs to the one Logic after all The proposition not any logical proposition is about all logical propositions leads to contradiction because this is about all logical propositions Therefore there must exist at least one logical proposition that is about all logical propositions which implies that we nevertheless have something like one Logic But such a proposition which is about all logical propositions is then also about itself which means that this kind of self reference must be admitted And this is possible because here we have not a case of complete or total self reference The approach suggested by VEATCH pp 142 to a solution of the conceptual paradox of the impredicable along lines quite different from those followed by mathematical logicians To introduce this new line of approach which will later be supplemented by additional ideas let me quote VEATCH p 142 144 comments in square brackets Supposing that not only do certain predicable concepts seem natural and normal but also that their elimination seems to involve serious inconvenience and even downright contradiction then one wonders whether the solution to the paradoxes had not better be sought along some other lines than the total elimination of all predicable concepts and self membered classes As to what such an other line might be the one which most naturally suggests itself is that of showing that the paradoxes are nothing but sophisms and that so far from requiring a radical revision of the whole theory of logic they really demand nothing but a more determined use of the already recognized principles of logical analysis Can the paradoxes be shown to be mere sophisms I should like to think that they could but I have no great confidence that I have actually succeeded in doing it Nevertheless as a step in this direction I think it might be illuminating if some sort of classification could be given of the types of concept that are susceptible of this strange predicability or of classes that are capable of this so called self membership So far as I know this has never been very seriously attempted Instead logicians have seemed content with citing only random examples of such concepts and classes As a first group of such predicable concepts there might be mentioned the so called analogous or transcendental concepts concepts such as being thing one etc Indeed we have already considered some illustrations of how concepts such as these must be regarded as being predicable Thus the concept of being for instance quite obviously applies not only to any being taken in first intention but also to the concept itself of that being i e to that same being considered in second intention As a second type of such predicable concepts might be reckoned various concepts of second intentional or logical entities For instance a concept of a concept is itself a concept or a proposition about a proposition is itself a proposition So an entity here an intention of an intention intending a proposition can itself also be a proposition it can also in some cases not be a proposition but a concept or an argument designed to demonstrate something about an argument is itself an argument To be sure there is an obvious limitation that must be placed on the predicability of such concepts Thus although the concept of a concept is itself a concept the concept of a proposition is certainly not a proposition Despite such limitations predicability would certainly seem to be a fact about any number of intentions of intentions Finally as a third class of predicable concepts one might consider negative or in the more old fashioned terminology infinite concepts i e concepts like the nonred the noninflammable etc Thus the concept of the noninflammable is itself noninflammable etc But once again there is an interesting limitation on the predicability of these negative concepts Obviously if the negative concept represents a negation of any of the conceptual or second intentional characteristics that pertain to the concept itself of such a negative notion then that notion will not be predicable The concept of the nonconceptual is not itself nonconceptual Or the concept of the nonlogical or extralogical is not nonlogical Or the concept of the nonabstract is not itself nonabstract Given such a classification of the types of concept that are predicable it becomes obvious that the range of incidence of the paradoxes is very restricted indeed There is nothing paradoxical about the predicability of analogous concepts and nothing paradoxical about the predicability of logical or second intentional concepts Paradoxes arise only in the case of negative concepts e g the concept of the non predicable or the im predicable or the class of non self membered classes Nor obviously do all such negative concepts give rise to paradox but only certain ones And more specifically those certain ones would appear to be such negative concepts as involve the negation of the very character of predicability or self memberedness As I see it the possibility of thus pinpointing the area in which the paradoxes arise is not without significance for it tends to confirm my thesis that the trouble lies not with predicability or self memberedness as such On the contrary these features of certain concepts would seem both undeniable and indispensable It is only in a certain special connection and only in the case of a particular kind of concept that any paradox arises in connection with predicability Accordingly the more natural procedure would appear to be not to rule out predicability as such and a priori and as being somehow dubious per se but rather to examine more carefully the particular circumstances in which predicability apparently lead to paradox Perhaps we can here discover certain latent sources of misunderstanding and confusion which will account for this seeming paradox of predicability whenhever these particular circumstances are present As a matter of fact I venture to suggest that once such an investigation is pushed with determination the paradoxes will in each case begin increasingly to look as if they were more apparent than real Of course at this juncture such a suggestion must appear altogether incredible The paradox of the impredicable is so peculiar that the contradictions of both alternatives and hence the paradox is only an apparent one More specifically we could wonder whether when one says that the concept of the impredicable is predicable simply in virtue of its being not predicable whether one does not mean the latter in a somewhat different sense from the former and so also that the concept of the impredicable is impredicable simply in virtue of its being predicable Let us examine this more closely The starting point let us say is the initial supposition the first possible alternative that the concept of the impredicable is itself impredicable Now by this we mean that the concept of the impredicable is just not a predicable concept That is to say it is not according to this first possible alternative the kind of concept that applies both to its objects taken in first intention and to itself that is to its objects in second intention just like the fact that the concept of red is not red In other words the initial supposition is that this is simply the fact about the concept of the impredicable that is according to the first alternative it is assumed that the concept of the impredicable has this property namely that it is impredicable i e it happens to have this property if we like it or not In what way however are we going to express in the sense of intend or signify this fact about the concept of the impredicable Presumably the only way is to say that it is impredicable Yet this way of expressing the fact about the concept namely the fact the concept of the impredicable is impredicable has the effect of making that concept appear to meet the one and only criterion of being a predicable concept But can we say then that the concept is in fact a predicable concept Propbably not On the contrary the original supposition still stands namely that the concept is in fact impredicable Accordingly it would seem to be only in our mode of expressing or signifying this fact that the concept is given the appearance of being predicable whereas in fact it is of course impredicable according to the first alternative And this does not amount to a contradiction The concept of the impredicable is really and in fact impredicable according to the first alternative and is not impredicable that is predicable only in virtue of our mode of expressing or signifying what is so really and in fact NOTE 36 Indeed this conclusion would seem to be confirmed if as a result of our mode of expressing the fact about the concept of impredicability we were simply to enunciate the proposition This concept is now seen to be predicable Such a proposition would of course be true since the requirements for predicability have certainly been met in this case Yet what would we mean by this statement just given We could only mean that the concept of impredicability was really and in fact impredicable Why Because if the concept were not really impredicable we could not possibly say that is was predicable In other words its seeming predicability necessarily presupposes its real impredicability Accordingly the supposed predicability of the concept can only be interpreted as meaning that while the concept is really impredicable nevertheless in stating or intending the fact we necessarily give it the appearance of being predicable The negation of predicability as it is expressed in impredicability causes the impossibility of adequate expression in the sense of intention How can it be that apparently having only two alternatives viz impredicable and predicable as a property of the concept of the impredicable predicable and impredicable taken together do not constitute a contradiction Well a good example indicating that this can be so concerns non being If we speak about non being then our way of expressing it gives the appearance of the being of non being although we know that non being does not exist Similarly in the case of concept of the impredicable in treating of it and intending it we inevitably give it the appearance of being a predicable concept Yet this does not mean that it really is a predicable concept any more than mutatis mutandis our treating of and talking about non beings means that non being really is a being Up to now in our discussion of the solution of the paradox we have considered only the first alternative of answering the question Is the concept of the impredicable itself impredicable or predicable namely the supposition that it was impredicable Here we did following the expositions of VEATCH not encounter a contradiction which already means that there cannot be a paradox So what if our initial supposition were that the concept of the impredicable was predicable rather than impredicable Investigating this at the same time decides the question whether the concept of the impredicable is impredicable or predicable 34 See where we had mentioned this further investigation as to deciding this question namely HERE Consider what must be meant by the assertion that the concept of the impredicable is itself a predicable concept Presumably according to the present supposition one would mean by this that the concept was itself really and in fact predicable Yet is this a possible meaning after all To say that the concept of the impredicable is itself predicable means that this concept applies not only to its objects in first intention but also to these objects taken in second intention To be sure the concept of the impredicable is the concept we have of impredicable concepts So our second alternative states in fact that the concept of impredicable concepts is itself an impredicable concept But we said that our second alternative stated that the concept of impredicable concepts is a predicable concept So this second alternative is a downright contradiction and thus the first alternative which did not entail a contradiction is affirmed thereby All this means that the only way in which the concept of the impredicable could be said to be predicable would be for it really to be impredicable Vice versa were it not impredicable really there would be no possible sense in which it could be said to be predicable Apparently then supposing the concept to be predicable leads us right back to the same situation which we found to prevail when we supposed the concept to be impredicable That is to say the concept of the impredicable must be considered to be impredicable really And only secondarily and derivatively and in virtue merely of our mode of signifying or expressing this fact of its impredicability can it

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is not concrete anymore And the nominalists want to found knowledge on the concrete world With respect to the past we can say There existed all kinds of individual things Now we must ask Which of these things must be subsumed under the supposition about which we are presently speaking That is which of those past individual things were such that they can be designated by the term we are presently using in a proposition This can only be done on the basis of the supposed nature or essence of those past things because stipulatively selecting them is not possible anymore So when an object does no longer exist the supposition suppositio must be based on a supposed essence or nature for example as expressed by a definition This means that the approach in this case has become an inten s ional one because an extensional approach selecting of individuals is not possible anymore So Buridanus wishes in the case of scientific propositions to speak of a natural supposition of terms A term has natural supposition so he says when it stands for all its concrete individuals supposita whether they exist at the moment the proposition is enunciated or only some time before it or after it In this way also the terms in a scientific proposition directly refer to concreta A 14th century critique against Buridanus s solution runs as follows Buridanus does something which is superfluous His natural supposition doesn t serve anything When he argues that he needs natural supposition to support the necessary truth of propositions like every triangle has three angles making up 180 0 this critique answers him Once this truth is established of one particular triangle it remains valid because later assertions of this kind are already implied in the first It is interesting to note that this latter statement about the implication of later propositions by the initially enunciated proposition is analogous to the presupposition of a Species Individuum Structure in things making it possible to generalize one or several particular finding We could say that because of this state of affairs in things we can repeat certain propositions about them Once the property of 180 0 of the angles is found in one particular triangle it can be generalized over all triangles But I would retort while this generalizing certainly takes place legitimately in the practise of natural science in the present case we are speaking about mathematicals and it is clear that in mathematics a particular triangle here and now that is a totally determined triangle is never as such the object of a mathematical enquiry What the enquiry is about is triangularity which is a formal content and from this formal content certain necessary properties can be deduced without recourse to individuals which moreover do not exist in mathematics So instead of the above example it would have been better to take one from material reality Let s consider the proposition man is rational This is clearly a generalization of a result that was obtained in only a limited number of individual instances In this way the proposition automatically implies it to be legitimately made in the future and in the past for that matter So a scientific proposition is according to this 14th century critique against Buridanus not as such a proposition in which the subject term has natural supposition here meaning that the supposition is omnitemporal but a proposition about an object existing at the time of the enunciation of the proposition while at the same time all future and now also past statements of this kind are implied by this one proposition One sees this critique is not really a devastating one against Buridanus The latter s doctrine of natural supposition is extensional syntactical that is a term in a universal proposition stands for all individuals of its extension and so has natural supposition Other syntactical contexts may restrict the reference of the term to just a certain part of its full extension I do not know what then significatio meant for Buridanus Generally significatio is inten s ionally characterized but such a procedure would be unacceptable for Buridanus as a nominalist because then an appeal has to be made to some nature or essence residing in things The doctrine of natural supposition is different again in John of St Thomas 1589 1644 He distinguishes supposition and thus also natural supposition from significatio by the fact that the former is about the use of a term for something for which it is verified in the proposition while the significatio of a term is its meaning apart from any propositional context Just as for Ferrer and Buridanus his major problem is that of propositions in which eternal truths are asserted John says that their truth is not demonstrated on the basis of the findings in a sensible entity but on the basis of an intelligible content because so he says such a proposition is verified according to the existence expressed by a verb that does not refer to a certain particular time For example consider a proposition like Petrus is a human being by Petrus is as was often the case meant the Apostle otherwise there would be no problem The term Petrus here stands for Petrus as atemporal essence and that was is and will be human nature The propositional context is according to John strictly demanded So the semantic model consists in the interpretation of the logical copula is as referring to an atemporal existence We could add An individuum is not atemporal but the Essence in Petrus namely humanity is and consequently the proposition is equivalent to humanity is humanity or also man is man So if the Essence of Petrus is humanity then the proposition Petrus is a human being is necessarily true It is clear that the approach of John of St Thomas as regards natural supposition is inten s ional rather than extensional And the only difference with significatio which is also inten s ional is that we only speak of supposition suppositio and thus also of natural supposition of a term when this term is actually used in a proposition So suppositio is in fact an operational approach to the meaning of a term in contrast to significatio But then I would add this operational approach should at the same time be extensional that is an approach being about of which individuals the term is actually predicable when finding itself in some syntactical context NOTE 41 From all this it is clear that there are many views concerning the status of supposition suppositio Very important is to distinguish between an inten s ional and extensional approach with respect to a theory of meaning of terms The comprehension of a given concept which in a proposition is represented by a term itself represented by a word NOTE 42 is understood to be the content intension of that concept that is the sum of the notions a term representing that concept evokes and of which the best expression is the definition of the term representing the concept The denotation is the scope extension of the concept that is the sum of the things to which the content of the concept applies Relationally expressed Inten s ion is a relation of a term to its content while denotation extension is the relation of a term to the concreta individual things which are referred to by it We see that not only of course in the inten s ion of a concept but also in the extension of it we need the content of the concept So where we do not arbitrarily define concepts but try to indicate to what the concept refers naturally we need its content This means that we cannot do without the significatio of a concept or term that is its natural meaning This concludes our preliminary discussion about suppositio It can serve as a preparatory background for the ensuing discussion of Veatch s revision of the theory of suppositio and the use of it for solving some logical problems for instance that of the null class The property of designation as it pertains to concepts in propositions Exposition and discussion of the theory of supposition as revised by VEATCH pp 193 After having prepared ourselves for discussing supposition we will now plunge into Veatch s revised theory of supposition of terms in propositions In order to distinguish his theory from the older ones he uses the term designation rather than supposition Indeed I think designation is the more appropriate expression My study of his theory is not aimed at a precise presentation of his views but helped by these views to set up a more or less definitive theory of supposition or designation which in effect is Veatch s theory but then amended by me here and there However I will study it only inso far as it has bearing on metaphysics The introduction to the theory of designation and the necessity for an intentinional Logic of having such a theory is so well expressed and explained by VEATCH that we cannot do better than to present his introductory exposition as he has it at p 193 196 almost litterally So far the whole discussion VEATCH having not yet mentioned the theory of designation of the proposition has been directed toward showing 1 that the function of the proposition in an intentional Logic is the intention of existence and 2 that the proper instrument for the performance of such a function is a proposition of the familiar two term subject predicate structure exhibiting the peculiarly logical or intentional relation of identity Unfortunately however no matter how plausible this discussion may have seemed as it proceeded neither of these two theses can ultimately sustain itself merely on the basis of the evidence which I have cited so far To see how readily both of them might seem to weaken and falter one has but to fall back into those ingrained habits of thought with which almost everyone nowadays Aristotelians and mathematical logicians alike tends to view ordinary subject predicate propositions No sooner does one begin again to look upon subject predicate propositions in this accustomed manner than almost immediately it would seem that such propositions neither intend existence nor involve a relation of identity For instance a subject predicate proposition must certainly involve two concepts unless that is one has only a trivially identical proposition of the form S is S But then if one s concepts are really two different concepts they will most certainly have two different meanings since concepts considered as formal signs are nothing but meanings However if the two concepts have two different meanings one could not possibly say that they mean the same thing or are related by a relation of identity Instead the much more sensible way of viewing the relation between the two terms of a subject predicate proposition would seem to be those suggested by LEWIS in the following quotation In dealing with the logic of terms in propositions either of two interpretations may frequently be chosen the proposition may be taken as asserting a relation between the concepts which the terms connote or between the classes which the terms denote Thus All men are mortal may be taken to mean The concept man includes or implies the concept mortal or it may be taken to mean The class of men is contained in the class of mortals The laws governing the relations of concepts constitute the logic of the connotation or intension of terms Those governing the relation of classes constitute the logic of the denotation or extension of terms Here certainly is a sufficient simple and straightforward statement So obvious does it seem that we might just as well forget all our elaborate analyses in support of an interpretation of propositions as involving a relation of identity and an intention of existence So far from the relation of subject and predicate being one in identity it is one of inclusion either the intensional inclusion of predicate in subject or the extensional inclusion of subject in predicate Nor is there anything about these two types of relation of inclusion that would seem to be in anywise intentional in my sense of the word On the contrary a relation of inclusion so far from being a formal sign if it is ever to be a sign at all would have to signify instrumentally i e as being like or similar to or isomorphic with some other relation Nor would a relation of inclusion be any more adapted to the intention of an actual esse existence or act of existence of anything than would be say a relation of congruence or greater than or ancestor of or whatnot Moreover when confronted with considerations of this sort which would seem quite simply but no less radically to undermine both of my major theses I must answer by conceding that such a way of regarding and interpreting propositions is quite legitimate so long as one takes account only of the meaning or signification of the terms or concepts that enter into a proposition As I have already suggested since subject and predicate are necessarily different concepts their meanings must be different What a concept means is a what i e a nature or essence This is the concept s intension or comprehension And on the basis of this what we can predicate the concept of terms indicating individuals And if we do so we obtain the full extension of the concept Accordingly given concepts with different meanings if they are in any way comparable with one another they would presumably be comparable in virtue of the overlapping of either their comprehension intension or their extension That is to say either the predicate will be included within the comprehension of the subject or the subject within the extension of the predicate and so one will have precisely the interpretation of the proposition which LEWIS suggests Yet why suppose that the terms which enter into a proposition are to be considered or compared simply with respect to their meanings After all such a comparison is already possible between concepts considered simply in themselves and quite apart from any role which they may play in a proposition Accordingly is it not conceivable and even probable that when they enter into a proposition concepts come to acquire further properties which considered just in themselves and as concepts they do not have at all Specifically what I am proposing is that when concepts enter into a proposition in addition to signifying the natures and essences and on the basis of this bring into their natural extension all individuals which have such a nature they also come to designate certain things as being or existing Moreover it is precisely in virtue of this property of designation which concepts come to have only insofar as they enter into a proposition it is in virtue of this property I think that I can now proceed to justify further my contentions that propositions intend existence and intend it through a relation of identity between subject and predicate For instance in the proposition All men are mortal it is certainly true to say that the subject in this proposition considered just as a concept does not mean the same thing as the predicate At the same time considered just in itself each of these concepts is simply a relation of identity between the abstracted essence which it signifies and the individuals in its extension Nevertheless in this proposition the subject concept man is used in such a way as to designate the items in its extension as existing in some sense or other since it is they that are said to be mortal And the predicate concept mortal is used in such a way as to designate as existing precisely the same individuals as the subject concept does In other words even though subject and predicate mean different things they are nevertheless both of them so used in the proposition as to designate exactly the same things as being or existing And it is in virtue of this that the predicate can be i d e n t i f i e d with the subject So far for VEATCH s introduction to the theory of designation Let us consider some more examples in order to make clear the distinction between signification and designation some men are wise The signification of the term men is of course still human nature explicitly given by its definition But here in this proposition the significative content human nature can only be applied to a part of the concept s extension that is only to a limited number of individuals possessing this content while excluding others in spite of their also possessing that content Here all non wise men are excluded from the concept s natural extension So the term men in the proposition some men are wise designates only a part of the concept s natural extension a man is entering the drugstore Also here the term man signifies human nature However it designates only a single individual having this nature Now consider these two propositions the robbers fled to cover the robbers numbered five in all The signification of the term robbers is given by the definition of the concept In both propositions the subject term applies this same signification to a number of individuals and these are precisely those individual robbers that are relevant in the present context which context is determined by the proposition That is the subject term robbers has exactly the same meaning or significance in the two cases Yet so far as designation is concerned what the subject term in the second proposition designates are a number of existing individuals taken collectively whereas in the first proposition these individuals are designated as existing not collectively but distributively See also further below where more is said about the different kinds of designation But having understood all this one might raise a question of this sort If designation means the use or employment of a concept to stand for something existing then what about a false proposition Do the terms that compose it designate anything i e do they stand for any existing thing To be sure they do have meaning since the falsity of a proposition by no means implies that its terms have no significance Yet with designation it might seem to be different For how in a false proposition could one be said to designate anything that is or that exists Well there can still be designated things that actually exist or have existed in false propositions because in many cases the falsity does not come from a failure of designation of the subject term but because the predicate simply does not match with the subject So for example in the Nazis captured Stalingrad where the term Nazis stands for things individuals that really existed Nevertheless the proposition is false Now consider the proposition the democracy of ancient Athens is ruthlessly imperialistic Here the subject term fails to designate anything because at present there isn t such a democracy in Athens as it is demanded by the copula is present tense Nevertheless the predicate is perfectly compatible with the subject Indeed being ruthlessly imperialistic was certainly true of the ancient Athenian democracy Here we can say that we have to do with a failure of the intended designation as determined by the copula of the proposition The true designation turns out to be just a being of reason that is what is actually designated by the subject term is a mere being of reason rather than a real potential or actual being Or perhaps the true designation is a possible being in extramental reality Anyway it is the discrepancy between intended and true designation actual real individual versus being of reason or actual real individual versus potential real individual that renders the proposition false The designation of a term in a proposition always refers to all or some existing individuals in the concept s natural extension So it is to be expected that there are at least as many kinds of designation as there are kinds of existence The existence can be actual and in extramental reality such as it is designated in a wolf was encountered in Oregon or it can be possible and in extramental reality and as such it is designated in the proposition dinosaurs are reptiles or in a dinosaur is presently encountered while eating leaves from trees in Yoshemite national park if this latter proposition is false that is if it is false then although actual existence was meant it turned out to be only possible existence the existence is actual when the proposition is true The existence can also be a mere existence in the mind as in the proposition a concept is an instrument of knowledge Indeed a concept can only exist in the mind So the term concept designates things which exist only as beings of reason as VEATCH states on p 201 However we must reflect upon how things are here with respect to the difference between signification and designation Thereby we must not forget that signification is inten s ional while designation is extensional So we can say that here the term concept signifies precisely that which is stated in its proper definition And this is some formal content What then is the designation of the term concept in the proposition a concept is an instrument of knowledge Well the designation is the total of all individual states of mind to which that formal content applies Now consider the proposition the concept of man is a universal concept Here also of course the signification of the term the concept of man is its definition This definition is not the same as the definition of the term man which is rational animal Let us restate this more precisely The signification of the subject term the concept of man is the definition of the concept the concept of man And this definition reads A simple in contrast to composed logical intention intending human nature The designation of the subject term the concept of man in the proposition the concept of man is a universal concept is all the individual mental states to which the just mentioned definition can be applied So here we accurately distinguish between the inten s ionality of signification and the extensionality of designation a distinction not always observed or acknowledged by VEATCH Now consider the proposition man has inhabited the planet Earth since the end of the Miocene period The concept man signifies human nature and perforce its definition as formal content while it designates now as a term in the above proposition all actual and possible existent men in extramental reality A being of reason is just an object before the mind that is an object only insofar as it is brought before the mind Such an object is for example the concept man but of course also the concept the concept of man This object is an individual state of mind or a decodable content in the brain It can be repeated in the same mind or in different minds Insofar as the concept man is a particular state of mind that state is not its meaning but an item in its extension The meaning or significatio of the concept man is as has been said its definition Its full extension is all the possibly or actually existing human individuals and in addition to it all the possible or actual individual states of mind to which that definition is applicable The concept of man of which we now have indicated its extension can be the subject term in a proposition and this proposition decides whether this subject term designates individuals in extramental reality if so we can then express the subject term as man or whether the subject term designates individual states of mind And if the latter we must express the subject term as the concept of man As a possibly or actually existing material individual man is a real being As a possible or actual state of mind it is a being of reason However we have a difficulty here If we want to include in addition to real beings beings of reason into the possible extension of a concept in order to be able to cope with the problem of the null class below then we view the concept itself as one of its designata Is this permissible VEATCH has not seen this problem I think it is As I said the designata of a concept consist of individuals or individual states to which its signification is applicable This signification is some formal content expressed in the definition And indeed this formal content can not only be predicated of the real beings which possess this content but also can be predicated of itself rational animal is rational animal So indeed the formal content as it is a particular mental state is one of the many legitimate and possible designata of the concept in question As such a designatum it is not a real being but only a being of reason but a being nonetheless Let us elaborate on this difficult issue a little more A concept is a formal sign which points to a certain formal content This is its signification Therefore it can stand for individuals having this content When it stands for all of such individuals it designates universally or equivalently it has natural supposition These individuals are first of all extramental things But also certain states of the brain carry this same formal content So also these brain states are individuals or items in the concept s maximal extension If the concept of say man designates e x c l u s i v e l y these corresponding brain states then the concept of man is taken insofar as it is a c o n c e p t of man which fact is then expressed in a proposition not as the term man but as the term the concept of man This latter term designates all the individual brain states that carry the content rational animal This result is necessary for the ensuing discussion of the problem of the so called null class and of the existential import of all genuine propositions A genuine proposition must always be about something that exists in some way or another otherwise the proposition is not about anything at all which means that it is not a proposition at all and is consequently neither true nor false So a proposition always must have existential import which is by the way its distinction from a mere concept But problems with the null class as in the alleged proposition the present king of France is bald where there is no present king of France or in the alleged proposition all sea serpents live in the Atlantic while we know that sea serpents do not exist at all have persuaded mathematical logicians to deny existential import of all universal propositions while still admitting it for particular and singular propositions And because the existential import of all propositions is a basic tenet of intentinal Logic we must deal with the null class from an intentional point of view For this we must admit to reside in the extension of a concept not only real beings of which the concept s content can be predicated but also beings of reason because there are cases within the problem of the null class in which subject terms do neither designate actual existents nor possible existents in extramental reality And in order for them not for that reasom to fail completely in designation we must allow beings of reason in the domain of designata Of course when a given proposition completely fixes the designation of its subject term and when at the same time this designation cannot however be realized the failure of designation is complete In that case the proposition is either false or is not a proposition at all All this we will extensively discuss in the ensuing Section on the null class The evocation of beings of reason serves for us to be able to insist that a proposition must always be about something existing in some way or another otherwise it is not distinguishable from a mere concept and is neither true nor false VEATCH p 202 distinguishes between inclusive and exclusive designation This however is according to me not correct To illustrate this distinction VEATCH considers the following three propositions man is a universal concept the reptile is a division of the animal kingdom and the opossum is a faunal section of North America I have slightly changed this last proposition to illustrate VEATCH s position better While in propositions like all men are mortal the subject term designates individuals in extramental reality the subject terms of the three above propositions do not designate respectively individual men individual reptiles or individual opossums all in extramental reality that is we cannot say this man is a universal concept neither can we say this reptile is a division of the animal kingdom nor finally can we say this opossum is a faunal section of North America VEATCH in effect says that this is so because the subject terms in the above three propositions signify it is true respectively human nature reptile nature and opossum nature as actually existing in extramental reality but that they designate only beings of reason Therefore we cannot predicate the respective predicate terms of actually existing in extramental reality individuals This is correct But what is not I think correct is that he calls this exclusive designation that is a designation excluding individuals because designation excluding individuals is not extensional and by consequence not designation To resolve this problem we need only to state the three propositions more adequately the concept of man is a universal concept the class of reptiles is a division of the animal kingdom and the class taxonomically the species of opossum is a faunal section of North America And now the apparent exclusion of individuals vanishes The term the concept of man refers to all individual states of mind such that such a state is a formal sign of human nature The term the class of reptiles is the result of a mentally grouping together of certain animals It refers to all individual cases of such mentally grouping together The term the class species of opossum is the result of a mentally grouping together of certain animals It refers to all individual cases of such mentally grouping together All these are individual states of minds and thus the relevant individuals that is the individual brain states carrying the relevant content are not excluded The concept the concept of man signifies its definition which is a state of mind such that human nature is intended In the proposition the concept of man is a universal concept it designates all the individual states of mind that intend human nature and it designates nothing else while the concept man in man is mortal designates all individuals possessing human nature individuals that is existing in extramental reality because mortal refers to the death not of human nature but to the death of extramental individuals having this nature The concept the class of reptiles signifies the mental grouping of certain animals In the proposition the class of reptiles is a division of the animal kingdom it designates all the individual cases of such a mental grouping of certain animals The concept the class species of opossum signifies the mental grouping of certain animals In the proposition the class species of opossum is a faunal section of North America it designates all the individual cases of such a mental grouping of certain animals Although looking awkward and cumbersome this interpretation is according to me correct In this way a term like reptile can either designate actually or potentially existing individuals in extramental reality or it can designate certain individual states of mind but then the term reptile designates as the concept of reptile the idea of reptile or the fiction of reptile for that matter So when we have a proposition like all sea serpents live in the Atlantic and if this proposition is not pronounced in the context of a phantasy world say in a novel then we can say that the intended designation of the subject term sea serpents are actual individuals existing in extramental reality while the true designation is in fact that of the idea of sea serpents that is sea serpents turned out to be merely an idea or being of reason which idea occurs as individual states of mind in individual minds And because of this discrepancy between intended designation and true designation the proposition is false To illustrate matters further consider the following syllogism or argument Animal is a genus I am an animal Therefore I am a genus This conclusion is absurd However it does not follow from the premises because there is in fact no middle term We see this as soon as we reformulate the first premise rendering it correct The concept animal is a genus And now the alleged argument doesn t have a middle term anymore The above interpretation of the designation of terms like the concept of man derives from our insistence that designation must always be extensional in order that it be distinct from signification Only then it can be restricted by certain syntactical contexts then certain individuals of the full extension are excluded as we have it mutatis mutandis in white men designating it is true individuals possessing human nature but excluding all colored individuals And now we see that there are several kinds of designation inasmuch either all existing individuals possessing that nature are designated by the term or just some of them or only a single one of them as dictated by the syntactical context of the term And these varying amounts of extension may in turn be designated in various ways Accordingly let us undertake to give a more exhaustive account of these varieties of designation First we have Singular designation that is designation in which the concept or term applies to only a single individual from the concept s natural maximal extension e g the single designation of tree in the proposition that tree is deciduous Common designation that is designation in which the concept or term is thought of as applying not just to a single existing individual of the concept s natural extension but rather to several of them or all of them of the concept s natural extension Common designation is consequently subdivided that is it is subdivided in universal and particular designation according to the following Universal designation This kind of designation we have already met as natural supposition Here all the individuals of the concept s natural maximal extension are designated For instance tree has universal designation in the proposition all trees are plants But VEATCH p 206 also calls the designation of the subject term in the proposition the men in the plane were five in all universal and collective designation This is correct The subject term here is not men but the men in the plane So here universal must refer to the men in the plane rather than to men The designation of men is contracted by the expression in the plane But this being so our new universe is now the plane and the proposition is about all men in that plane rendering the designation of the subject term universal We can also express all this in a somewhat different and alternative fashion which is worthwhile to think about In the proposition the men in the

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being genuine subjects are really predicates x is a man so that these propositions are in each case not just one proposition but two that is a conjunction of two propositions But we should be equally insistent that by no means all propositions with determinate subject terms are to be so interpreted In many cases the designation of the subject term is clearly determined by the predicate as it was not so in the case of that man is tall because there are so many other things that are tall In contrast to particular and singular propositions the mathematical logician does not interpret a universal proposition as being in fact a conjunction of two propositions but rather as a hypothetical proposition So the proposition all men are mortal is not interpreted by him as all x s are men and are mortal but as for all x s if x is a man then x is mortal Indeed the designation of the subject term men in all men are mortal is clear as soon as we see this proposition as in fact being a hypothetical proposition So by interpreting singular and particular propositions as conjunctions and universal propositions as hypotheticals the mathematical logician unambiguously determines the designation of the subject term Accordingly the upshot of this whole discussion would seem to be that the mathematical logician is simply mistaken about the subject predicate proposition as such that is what it precisely and as such really and generally is He is mistaken in supposing that if the full meaning or intention of a subject predicate proposition as single and categorical proposition is to be disclosed the subject term and thus the concept which it expresses must in all cases be analyzed out and made the predicate of a second proposition either connected by an implication if then or by a conjunction and as if the only proper subjects of propositions were individuals completely bare of conceptual characterization completely stripped of formal content For although some propositions do stand in need of such further analysis by no means do all As for those that do not to insist upon subjecting them to such analysis is thoroughly misleading in that it tends to hide the fact that in their cases the predicate is attributed not just to some designata or other but precisely to those of that specific subject concept As we have seen the mathematical logician turns all universal propositions into hypotheticals and all particular propositions into conjunctions As such this is logically legitimate But it is as has been shown not generally necessary It might be necessary for a singular proposition such as there is a burglar in the house But such propositions do not convey general knowledge but only particular states of affairs On the other hand for propositions that do convey general knowledge and insight such as all men are mortal or some men are wise there is no need to transform or interpret them into either hypotheticals such as for all x s if x is a man then x is mortal or conjunctions such as there is an x such that x is a man and x is wise because in such propositions the designation of the subject term is clear and this subject term is therefore in no need of further analysis Moreover a hypothetical as a result of the transformation of a universal proposition is in fact less fundamental than the original universal proposition because such a hypothetical is really an enthymematic syllogism Consider the following syllogism All organisms are mortal all men are organisms therefore if x is a man then x is mortal So our hypothetical proposition is in fact the conclusion of a syllogism In fact from all organisms are mortal and all men are organisms directly follows all men are mortal and having this we can immediately say for all x s if x is a man then x is mortal So the hypothetical proposition presupposes the corresponding categorical universal proposition Now for conjunctions Particular propositions are interpreted by the mathematical logicians as conjunctions For example the proposition some men are wise is interpreted as there is an x such that x is a man and x is wise However this second proposition or conjunction of propositions does not represent an analysis of the first in the sense that it expresses clearly what the first had expressed only confusedly If it is recognized that a concept is a relation of identity to individuals and also that in a proposition the concept actually designates these individuals as existing then it is not necessary to represent the relation between a concept and its designated existents by explicitly predicating the concept of them To be sure the concept is predicable of them but actually to predicate it of them constitutes not an analysis of that concept but rather a further use or employment of it VEATCH p 242 Existential import Because according to the mathematical logicians universal propositions are really hypothetical propositions they do not assert existence Thus whether any human beings actually exist or not is quite irrelevant to the assertion if anything is human it is mortal But also according to the mathematical logicians things are different with respect to particular propositions If there were no human beings one could hardly assert that some beings are human and are wise which is the way the mathematical logician would interpret some men are wise Hence the supposition that particular propositions assert existence whereas universals do not However as we have seen for propositions conveying general knowledge they are not to be interpreted as either hypotheticals or conjunctions So the sharp difference in existential import between universal and particular propositions disappears Indeed when we acknowledge the fact that existence can come in several ways potential actual real fictitious we see that universals are particularly adapted to designate potential in the sense of possible existents So when we say dinosaurs are living mainly in warm regions the subject term designates exclusively possible existents But the designation of universal propositions is not in every case confined to mere possible existents For example consider again the universal proposition all men are mortal Here the designation includes possible as well as actual existents And it is indeed in most cases that actual existents are designated by universal propositions for example all presently living sponges are inhabiting natural waters and even more clearly all helium atoms are to have two protons in their nucleus So universal propositions do have existential import often designating even actual existents Now for particular propositions concentrating on those that convey general knowledge According to the mathematical logicians they have existential import also according to intentional Logic But because they do not seem to recognize any form of existence other than actual real existence they say that particular propositions exclusively and always designate actual real existents True particular propositions such as some men are wise are peculiarly fitted for the intention of actual existence just as universal propositions are for the intention of possible existence But just as the subjects of universal propositions may often be used so as to designate actual existents so also the subjects of particular propositions may be used to designate merely possible existents Consider the proposition some dinosaurs are warm blooded Here the subject term designates mere possible existents So particular propositions do not exclusively and in all cases designate actual existents sometimes they designate possible existents So from all this we can conclude that particular as well as universal propositions do have existential import And this is fully in line with the tenets of an intentional Logic which holds that propositions in contrast to mere concepts always have existential import But having established this we realize that it will now be a big question as to how logically evaluate all cases of propositions which involve the null class That is to say how from an intentional point of view we should interpret propositions involving the null class or again differently expressed how the theory of designation can cope with the null class and whether it can do that better or at least as good as the quantification theory of modern mathematical Logic 2 The thesis all propositions having existential import brings about the problem of the null class This problem appears when the traditional square of opposition see below is considered to be correct We will expound this square now The traditional Square of Opposition The square of opposition systematizes the types of opposition obtaining between the four types of categorical without conditions subject predicate propositions A E I and O and lays down the rules of truth and falsity in oppositions One such rule is for example that contradictory opposites cannot have the same truth value that is they cannot both be true or both be false It is these rules that are according to the mathematical logicians violated in some cases to be precise in cases that involve the null class depriving these rules of their general validity As such this looks suspicious We will show largely following VEATCH pp 249 that intentional Logic can restore things by its theory of designation But let us first expound the traditional square of opposition following BOYER Ch Handboek der Wijsbegeerte I 1947 Dutch edition p 115 119 Diagram above The Square of Oppositions In the above diagram some means one or another or at least one etc The proposition all men are black is equivalent to every man is black The proposition no man is black is equivalent to all men are not black and to every man is not black The diagram brings up four kinds of opposites Contradictory opposites the opposites between A and O and between E and I Contrary opposites the opposites between A and E Subcontrary opposites the opposites between I and O Subaltern opposites the opposites between A and I and between E and O Now we shall give the rules of truth and falsity implicitly expressed in this square Contradictory propositions A and O E and I cannot at the same time be true neither can they be at the same time false If the one is true the other must be false Indeed they cannot be both true because the one precisely denies what is affirmed in the other If it is true that all men are black it is false that one or another man is not black Neither can they be both false by ruling out one because one had found it to be false the other must be true If it is false that all men are black it is true that one or another man is not black Contrary propositions A and E cannot be both true but can be both false They cannot be both true because the one denies that what the other affirms But they can be both false because while they both affirm or deny in an all including way that is universally the truth can lie in the middle What is neither true nor false of all items in the extension of the subject term can be true of some of them So it is false to say that all men are black but it is also false to say that all men are not black And indeed it is true that some men are black that is to say both contrary propositions can be false again because there still is then a possibility that one or another man is black Therefore one can infer from the truth of one of the contrary opposites the falsity of the other while one cannot infer from the falsity of one the truth of the other Subcontrary propositions I O cannot both be false but they can both be true They cannot both be false because if we rule out what is affirmed by one with respect to special cases automatically makes true what the other affirms for special cases If it is false that one or another human being is an angel it is automatically true that one or another human being is not an angel But they can be both true because these subcontrary propositions do not necessarily assert something of the same subject Indeed it is true that some men are black while some other men are not black Therefore we can infer from the falsity of one the truth of the other But from the truth of one we cannot infer the falsity of the other Subaltern propositions A I and E O are when they are about necessary attributions both true or both false Subaltern propositions relate as universal proposition to its corresponding particular or singular propositions When something signified by the predicate essentially belongs that is necessarily belongs to something else signified by the subject term then at the same time it belongs to all individual designata of the subject term of the universal proposition and thus it belongs also to one of them So from the truth of the universal proposition A or E we can infer the truth of the corresponding subaltern propositions respectively I and O Are we on the other hand speaking about accidental states of affairs then when the universal proposition is true also the corresponding particular or singular propositions are true But if the universal proposition is false then the corresponding particular or singular proposition can be true because it was only denied that that what the predicate signifies is attributable to all designata of the subject term If we say that the proposition all men are black is false then the subaltern proposition some men are black can be true and is in fact true But if there were white men only then the proposition some men are black would be false So from the truth of a universal accidental proposition we can infer the truth of the corresponding particular or singular propositions But from the falsity of such a proposition we cannot infer the truth or falsity of the corresponding particular or singilar propositions The Square of Opposition under fire Consider the proposition all the dimes in my pocket are shiny But suppose that actually there are no dimes in my pocket If so one might naturally feel that the A proposition which asserts that they are all shiny would be false Now consider the corresponding O proposition that is its contradictory opposite some of the dimes in my pocket are not shiny It is clear that also this proposition is false in virtue of the same reason that the A proposition was false That the O proposition which is a particular proposition must be false is moreover evident from the fact that it is assumed by the mathematical logicians that all particular propositions designate actual and only actual existents And there are no dimes in my pocket We here have to do with the null class Having both the A and the O proposition false is a clear violation of one of the laws of truth and falsity as given above in connection with the square of oppositions Indeed even for a mathematical logician this same truth value of contradictories is inadmissible So this problem evoked by the null class should be solved How Well by a re interpretation of A propositions whether they involve the null class or not In what way are they to be re interpreted Obviously with respect to their alleged existential import So the mathematical logician now denies any existential import to A propositions that is affirmative universal categorical propositions while retaining it for particular propositions He shows this by interpreting all the dimes in my pocket are shiny as there are no dimes in my pocket that are not shiny This later assertion so it is argued could be true even if there were no dimes in my pocket Generally the mathematical logician interprets all S s are P s as there are no S s that are not P s whether there are null classes involved or not The particular proposition some dimes in my pocket are not shiny must be false because according to the mathematical logician all particular propositions designate actual existents and in this particular case there are no actual existents in the domain indicated and delineated by the proposition But because the corresponding A proposition interpreted as there are no dimes in my pocket that are not shiny is true indeed when there are no dimes at all in my pocket there can also not be dimes in my pocket that are not shiny we now do not have two contradictory opposites here A and O having the same truth value So a denial of existential import of A propositions solves the problem But this way of solving it not only goes against intentional Logic s contention that all genuine propositions have existential import but also markedly disrupts the various relationships in the square of opposition According to the mathematical logician the A proposition all the dimes in my pocket are shiny is true because he interprets it as there are no dimes in my pocket that are not shiny But then the corresponding E proposition that is its contrary there are no dimes in my pocket that are shiny which is supposed to be equivalent to no dimes in my pocket are shiny is also true And according to the rules in the square this cannot be Again a reason for the mathematical logician to abandon the square and its rules As has been said in this new interpretation of A propositions the relations of contradiction would be preserved since given the truth of an A proposition involving a null class the corresponding O proposition would have to be false inasmuch as particular propositions are assumed to designate actual existents And also the truth of the E proposition no dimes in my pocket are shiny would involve the falsity of the corresponding I proposition some dimes in my pocket are shiny because also here we have a particular proposition implying that actual existents are designated But because there are no dimes in my pocket the subject term fails to designate Having in our present case the A proposition true and the I false and likewise the E proposition true and the O proposition false we see that the rules of subaltern propositions would no longer hold To recapitulate according to the mathematical logician s new interpretation universal propositions no existential import particular propositions existential import but only with respect to actual existents the exemplified A proposition is true precisely because there are no dimes in my pocket therefore its contradictory opposite the O proposition must be false By the same reason the E proposition is true and thus its contradictory opposite the I proposition must be false Also having I false and O false the rules about subcontraries would have to be discarded O and I can both be true some dimes in my pocket are not shiny O and some dimes in my pocket are shiny I These latter shiny dimes are evidently different individuals from the ones in O that are not shiny But they cannot both be false If we suppose O to be false then there are no dimes in my pocket that are not shiny And if we suppose also I to be false then there are no dimes in my pocket that are shiny This is contradictory so O and I cannot both be false But in the new interpretation of the mathematical logicians we had both O and I false showing that they can both be false at the same time So also in this respect subcontraries the new interpretation clashes with certain rules of the square So generally we can say that the mathematical logician s solution of the problem of the null class where the problem consisted in the violation of the rules for contradictory opposites the only rules of the square that even the mathematical logician is not prepared to abandon namely his denial of existential import of A propositions disrupts the relationships in the square of opposition And for the mathematical logicians this is a clear sign that the Aristotle oriented Logic is inadequate to deal with new propblems The mathematical logicians think that even from the point of view of Aristotelian Logic the square cannot be defended Already we have seen how the Aristotelian logician assuming as he does that A propositions must have existential import proceeds on this basis to deny that an A proposition involving a null class could be true But then he would also be forced to deny that its contradictory opposite could be true either because some dimes in my pocket are not shiny cannot be true by reason of the fact that there are no dimes in my pocket However anticipating solutions accomplished by intentional Logic Aristotelian Logic does not get bogged down here because of the following reason The A proposition all the dimes in my pocket are shiny that is all the dimes is not a proposition at all because it not only involves a null class but also at the same time has a definite description of the subject namely all the dimes present in my pocket So the subject term is meant to designate actual existents and nothing else But in fact there are no dimes in my pocket so the designation fails completely in the same way as it does in the proposition the present king of France is bald later to be discussed Therefore the proposition is not about anything meaning that it is not a proposition at all Only when we eliminate the definite description of the subject will the resulting proposition be a genuine proposition and will not pose a problem anymore because then no null class is involved anymore So instead of all the dimes in my pocket that is instead of all those particular dimes that are in my pocket we take any dime in my pocket and thus thereby remove the definite description Indeed any dime in my pocket is shiny asserts if there are dimes in my pocket then they are shiny Here obviously even if there are no dimes in my pocket or even if there never have been the proposition still does not fail to designate because all that is called for is a designation of possible existents and not necessarily of actual ones And then there is no problem with the corresponding O proposition The A proposition then is all possible dimes in my pocket are shiny while the corresponding O proposition that is the contradictory opposite reads some possible dimes in my pocket are not shiny Now even when there are no actual dimes in my pocket the A proposition could be true and if it is taken to be true in enunciating it I have in mind certain or other dimes that are potentially in my pocket I am about to receive them as a wage and that are all shiny then the O proposition is false as it should be 3 Restatement of the problem of the null class from the point of view of an intentional Logic where all true propositions including universal propositions have existential import With the above discussion of the null class and its effect on the validity of the square of opposition we are presented with a whole parcel of considerations that must needs be appraised from the point of view of an intentional Logic Specifically the issue would seem to be this On an intentional view all true propositions must have existential import in the sense that they must designate their subjects as existing in some way or another But what is to be done then with propositions which as the mathematical logicians say involve the null class Surely such propositions would be lacking in designation and hence have to be considered false At the same time their contradictory opposites would have to be considered false too and this is certainly embarrassing Accordingly is an intentional Logic able to extricate itself from such a predicament By way of answer let us remark that the whole notion of the null class which is often claimed to be a peculiar discovery of the new Logic and which is certainly at the root of the present difficulty is really a very fuzzy notion indeed This is because generally in mathematical Logic existence is taken univocally With respect to the material world it is always considered to be actual real existence So a class consisting of mere possible existents is considered to be a null class By the way mathematical Logic as well as intentional Logic can also be about knowing mathematical objects But these are then treated as if they were objects existing in extramental reality Sticking to knowing extramental reality we then can have to do with a class that is a null class according to the mathematical logicians while it is not so for an intentional logician Corresponding to the different ways of existing we can have a designation of possible or actual existents And when an intentional logician speaks about beings of reason he does not mean mathematical objects which he treats as real objects but mere beings of reason such as phoenixes sea serpents and te like Confronted with the mentioned difficulties an intentional Logic can begin with seeing things as follows Take the proposition all sea serpents live in the Atlantic Such a proposition the mathematical logician will regard as being an example of a proposition involving a null class because sea serpents do not exist in extramental reality They then show that the rules of contraries in the square of opposites do not apply to this example For this to show they interpret all see serpents live in the Atlantic as there are no sea serpents that do not live in the Atlantic This proposition is true because there are no sea serpents at all And now its corresponding contrary there are no sea serpents that live in the Atlantic Obviously also this proposition is true So here we have an A proposition and an E proposition that both are true But according to the rules in the square of oppositions contraries cannot both be true So these rules should be abandoned because they are not universally valid What can an intentional Logic do about this situation such that the mentioned rule does not need to be abandoned Well to begin with intentional Logic holds that a proposition such as this one is about an existent something and does designate True the sea serpents which it is about exist only as beings of reason Still such designation suffices for existential import there is no null class In consequence the proposition is susceptible of either truth or falsity The proposition is thus about some fictitious aquatic organisms about which it is asserted that they inhabit the Atlantic Ocean only And whichever way one takes it all the relations in the square of opposition will hold provided only that one does not change the designation when one goes from A to E or from A to O etc If we now turn to the proposition all the dimes in my pocket are shiny while there are no dimes in my pocket and thus involving the null class we see that in all probability this proposition is not about fictitious dimes but is meant and only that counts when evaluating the proposition to be about not only real dimes but also of real dimes actually present in my pocket But because there are no dimes in my pocket we now seem to have to do with the null class and fail to designate altogether with all of the perplexing consequences that apparently follow so far as the square of opposition is concerned Even in the case of the sea serpents it could be that the proponent of the proposition being not well at home in biology actually meant real sea serpents existing in extramental reality And then also here we have to do with the null class because there aren t any sea serpents existing in extramental reality In other words the problem of the null class is simply not solved merely by pointing out that in addition to actual existents terms in propositions can sometimes be taken so as to designate mere beings of reason imaginary beings because such a proposition could be meant to be about actual real existents and when there are in fact no such existents then we have a failure of designation So how is an intentional logician with his theory of designation going to deal with the null class In his discusion about how to determine the correct designation in propositions involving the null class VEATCH pp 254 considers two propositions whose contradictory opposites do not involve a difference in quantity of the proposition as this difference is present when we go from all S s are P s to some S s are not P s phlogiston is the cause of combustion and RUSSEL s celebrated example the present king of France is bald Both propositions involve the null class There is no such substance as phlogiston and there is no present king of France Are these propositions true or false And what precisely is designated by their subject terms If we place these propositions in a purely fictitional context where the old chemistry was the chemistry and where France had a king then there is no null class involved The subject terms of both propositions designate and designate exclusively beings of reason or imaginary beings And having it all like this there will be no problem with the rules of truth and falsity in the square of opposites But this easy way out is not what we want We want that the proponent of these propositions supposes that they are about real actual beings And now the null class is back again because there is no phlogiston actually existing in extramental reality and in the same way there is no present king of France So how about designation here and what about their truth or falsity Do they involve violations of some laws in the square of opposites Let us first consider phlogiston is the cause of combustion It is perhaps useful to know that in early chemistry it was thought that combustion involved some special substance called phlogiston But later it was found that the weight of all the chemical substances involved in combustion taken together was equal before and after combustion So there is no special substance different from the known chemical elements or compounds involved in combustion that is phlogiston does not exist If we take the term phlogiston in the proposition phlogiston is the cause of combustion as meant to designate a real actual existent we must pronounce this proposition false not necessarily because the predicate fails to apply to the subject but simply because the subject term fails to designate anything Here the contradictory opposite gives no propblem If it is false to say that phlogiston is the cause of combustion it must be true to say that it is not the cause of combustion And indeed it is true With phlogiston is the cause of combustion it seems that conceding the involvement of a null class does not cause any trouble However the subject term although meant to designate something real does not designate anything Therefore the statement is not about anything and so is not a proposition at all and thus there is no susceptibility of truth or falsity Nevertheless we still want to say phlogiston is not the cause of combustion because that is an important result in chemistry If we now look to the proposition the present king of France is bald then here also we acknowledge that the proposition was meant to say something about something really and actually existing in extramental reality But because there is no present king of France the subject term completely fails to designate rendering the proposition false if we disregard the fact that also here because of failure of designation there is no proposition at all But while the contradictory opposite of the proposition phlogiston is the cause of combustion was perfectly true and thus causing no trouble the contradictory opposite of the present king of France is bald which consequently is the present king of France is not bald cannot be true either having thus a problem here because unlike the case of phlogiston being bald or not bald is totally accidental with respect to king of France We cannot say because there is no present king of France he is not bald So the proposition the present king of France is not bald cannot be seen as true because there is no present king of France And because there is no present king of France this proposition is false just like the proposition the present king of France is bald which is also false So here we have the problem of contradictory opposites having the same truth value still provided we for the time being ignore the fact that because of failure of designation it is not a proposition at all and so does not involve possible truth values that is such a statement is neither true nor false How must we solve these problems Considering again the proposition phlogiston is the cause of combustion how can we legitimately deny this proposition to be true without finding out that it is not a proposition at all That is to say how do we manage to express in a genuine proposition namely by denying its truth an important result in chemistry To begin with note once more that the reason for my insisting so strongly on the existential import of all propositions is that from the standpoint of an intentional Logic it is the precise nature and function of a proposition in contrast to a mere concept to intend things in their very acts of existing whether potentially actually fictitionally or whatnot Accordingly if a proposition is not about anything that is or exists in any sense it just is not about anything at all and is thus not a proposition Let us now then analyze carefully the precise nature of the designation or existential import that pertains to the two propositions phlogiston is the cause of combustion and phlogiston is not the cause of combustion The first one we want to deny the second one we want to affirm We have said that we can deny the affirmative proposition on the ground that its subject term fails to designate anything But yet at the same time by denying it we certainly understand something by the term phlogiston otherwise there was no proposition at all But if we by conceding that something was understood by the term phlogiston say that this term happens to designate merely a being of reason we run into trouble because then we cannot unequivocally deny the proposition phlogiston is the cause of combustion anymore It could well be true for instance in the context of some fictitious chemistry To solve this problem we can do as follows In order to be able to deny that phlogiston is the cause of combustion we must recognize on the one hand that phlogiston is no more than a being of reason an inferred entity with no basis in fact And on the other hand we must also recognize that in the proposition in question viz phologiston is the cause of combustion it is taken by the proponent as designating not a being of reason but a real being Only by this kind of comparison or contrast is it possible to deny the proposition or to recognize it as being

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Open archived version from archive - Logic VI

formal content can in principle be repeated over several instances and is in fact often so repeated Such a formal content can then be in this supposit here and now but also in that supposit there and now or in that supposit here and then etc This supposit is the individuum part of the Species Individuum Structure while the species part symbolizes the formal content which can be repeated In this way properties propria of something which is a substance or interpreted as a substance are first of all actually found in some instances and are then generalized over all relevant possible or actual instances according to the mentioned presupposition So to take an example the property of iron to be susceptible to being magnetized is first found for a number of individual pieces of iron while no exception is found Then one will generalize these individual findings over all actual and possible pieces of iron whatsoever that is that all iron behaves like this and not only so in the present but also it had behaved so in the past and will behave so in the future Later when one will understand completely the nature of iron that is its essence one will be able to deduce this property of magnetization from this essence One has then demonstrated the property a property which initially was known only by induction To repeat in experience we observed that iron that is that what we use to call iron on the basis of some other properties and magnetizability always that is in all observed instances went together We then generalize this and claim that the two always go together in all possible and actual instances whether observed or not and whether these lie in the present past or future The greater the number of actually observed instances the more certain is the inductive conclusion And when we finally come to know the essence of iron more or less completely we are coming to be in a position to deductively verify the induction by deriving it directly from the essence of iron The argument that legitimizes the induction of the property in question of iron can be cast in the following syllogism Every formal content is repeatable over an unlimited number of instances Species Individuum Structure Magnetizability is such a content Therefore magnetizability is repeatable over an unlimited number of instances When we now experimentally find the property of magnetizability for a number of pieces of iron and have not found exceptions then we apply generalization that is induction where the instances are all pieces of iron And this induction is the conclusion of the above argument This argument shows induction to be legitimate on the basis of the presupposed Species Individuum Structure of things Induction and definition The what of some essence as asserted in a definitoric proposition say man is a rational animal cannot be proved by disclosing a cause Is then a proposition asserting a non arbitrary definiens of a definiendum the result of induction Well in retrospect we can say that the content rational animal was found in those investigated or experienced instances which we call human beings and was then generalized to include all possible and actual instances This is clearly induction The result of the induction is then that every human being is a rational animal laid down in the proposition man is a rational animal However now knowing by induction that man is a rational animal we still do not know why man is a rational animal If we re interpret man is a rational animal as a definition of the term man then it is perforce self evident But if we do not so re interpret it then we can still ask why man is a rational animal And the answer must be found in biological results Man has in organic evolution inherited animal nature so he is some sort of animal And the evolutionary development of his animal brain has been such as to endow him with rationality so he is a rational animal All this is established on the basis of individual findings in a number of particular instances generalized over all possible and actual instances Also we must find out why the evolution of the sistergroup of the Apes to which latter now belong Chimpansee Gibbon and Gorilla went that way and ended up with humans that is rational animals If we know all this then we know why the organisms which we call human beings are rational animals Again as a definition man is a rational animal we cannot find the why in terms of something extrinsic to rational animality Man is then a rational animal wholly in virtue of himself Induction and models The use of models in science is but a sophisticated version of induction as described above A model is a supposed that is supposed to be present in extramental reality structure or regular process inspired by and geared to observed facts which one wants to explain The testing of the model is in fact an application of induction to see whether the model holds in all relevant instances If it does so for a sufficient number of instances and when no exceptions are found the model is accepted if there are several models doing the job one chooses the simplest of them And such a model no matter how complex it may be is I venture to say in fact a proposition and as such a logical intention As long as the model is still rough it cannot be such a proposition but when it is refined it can be supposed to intend something in extramental reality And if it intends that something in reality that it was designed to explain then the model as proposition is true Such models are often cast in mathematical forms And as such of course they are not intentional Only when they are physically interpreted they can be intentions that is intentions of patterns in extramental reality A good general example of a model is an equation or set of equations most often differential equations that is said to be a model of some real dynamical system like the weather system for instance When such a model is supplied with an actual existing measured initial condition or state and when in addition the mathematical symbols are physically interpreted the model can make predictions as one does in weather forecasts as to subsequent states of the real dynamical system In fact what one does is mathematically solve the equation resulting in a whole set of possible trajectories of the system and when one now introduces a measured intial state or condition one such trajectory is then automatically singled out giving the predicted sequence of system states Such a prediction of a single state then boils down to being a subject predicate proposition about some real state of affairs and later observations can verify or falsify such a prediction Theoretically one now can also say that the new state of the system when it has appeared is explained by the model The model will then be refined if necessary If one speaks of an isomorphy between the mathematical form of the model and the real situation the mathematical model is not therefore intentional because a mathematical model isn t intentional at all But when the mathematical symbols are interpreted and the model supplied with an actually measured initial condition or state then the model is intentional This preliminary view of mine deviates somewhat from that of VEATCH in this respect Logical intentions as intentions and their bearing on objective knowledge A logical intention such as a concept a proposition or an argument is an entity totally dependent on but not the same as the relevant and corresponding hardware processes in the brain The logical intentions themselves are among the high level features high level beings beings of reason of these material processes All this is by the way wonderfully expounded in HOFSTADTER s book Gödel Escher Bach 1979 where he considers emergent features in material processes That is features which are only present and only visible at the higher levels of some complex material dynamical system such as the brain At the lower levels of such a system these features are absent He calls such features software features carried as it were by some hardware machinery These considerations are relatively new not yet present in VEATCH And they will have I am sure quite a bearing on what intensionality really is and with it what objective knowledge really is Concepts such as levels hardware software emergent features isomorphy and formalization play a key role in HOFSTADTER s book which is about the question whether intelligence can be mechanized In it the problem of artificial intelligence is approached from above so to say that is from high level features of the brain artificial or not taken as functional units of intelligence The more recent approach to artificial intelligence departs from artificial neural networks that is from below These networks are however deliberately not yet fully fledged neural networks They are networks that have to be trained eventually resulting in their development as a response to this training a development toward mature networks that can fulfill the cognitive function to begin with Probably the two approaches must be integrated in some way I am intended to treat of all this in later documents that is I will once more consider and investigate the nature of logical intentions as intentions If there is to be objective knowledge of any given thing s l we must know that thing and not just a n mental image of it This means that if there is to be objective knowledge there should not be any mediating entity between the knowing power and the thing known And this in turn means that there must be a formal identity between the thing known and the intending logical entity How does a logical sign such as a concept a proposition or an argument attain this formal identity with the real objects or patterns intended Or in other words what precisely is such an identity and how precisely does it as such and only as such guarantee objective knowledge REMARK Of course we have already discussed this topic because it is crucial to an acceptance of an intentional Logic However we do not pretend to have in those earlier discussions settled the issue once and for all And because now we know so much more about what an intentional Logic must look like we can supplement our earlier discussions of this important topic The formal identity between logical entity and object to be known which identity will be shown to be necessary for knowledge to be objective must in some way be equivalent to the being about of the logical entity The what of a logical entity solely consists in its being about something else and this is accomplished by actually being that something else The logical entity then intends an object And such a logical entity is first of all a concept REMARK In what follows we first of all think of empirical concepts in contrast to theoretical or hypothetical concepts such as phlogiston natural selection energy causality etc And because of this formal identity the specific formal content i e the content commonly possessed by logical entity and thing intended by it can be predicated of individuals that is the individuals of the concept extension If we name the content of a given concept A concept and the corresponding content in the individuals of the concept s extension A where A concept A then we have for every individual thing S of the concept s extension individual thing S carrying A concept individual thing S carrying A So if for example A concept being the formal content humanity then we have the identity of Socrates carrying the content of the concept humanity and Socrates carrying the form HUMANITY implicitly expressed in Socrates is human And this guarantees an immediate contact between the knowing power and the object to be known and thus guarantees objective knowledge In Socrates is human the term Socrates stands for Socrates carrying the form HUNANITY while the term human stands for Socrates carrying the content of the concept humanity These designata are identical The same goes for the concept tanned Here we have the identity of Socrates carrying the content of the concept tannedness and Socrates carrying the form TANNEDNESS implicitly expressed in Socrates is tanned Also here the immediate contact between the knowing power and the object to be known is guaranteed and thus objective knowledge is guaranteed In Socrates is tanned the term Socrates stands for Socrates carrying the form TANNEDNESS while the term tanned stands for Socrates carrying the content of the concept tannedness And also here the designata are identical When we now are actually going to use the concepts the identity reappears in the e x p l i c i t that is now actually spoken or written predications Socrates is human and Socrates is tanned which are subject predicate propositions That is to say if we want this knowledge to be objective when using the concepts we must engage in subject predicate propositions because only then we let reappear the identity already present in the concepts and thus in the mentioned implicit predications that constitute the concepts The logical entity Socrates is human which is a logical relation between terms intends the real relation as it is between a supposit and an essence The logical entity Socrates is tanned which is also a logical relation between terms intends the real relation of the inherence of an accidental form in a substance What about the proposition tannedness inheres in Socrates This proposition is not a subject predicate proposition It does not explicitly express i d e n t i t y between Socrates carrying the content of the concept tannedness and Socrates carrying the form TANNEDNESS but expresses i n h e r e n c e It does not however do this latter by having the term tannedness inhering in the term Socrates because terms cannot inhere in other terms And this means that the proposition tannedness inheres in Socrates does not really intend anything in extramental reality although it does point to something in that reality But it points to it not as a formal sign a sign that really intends but as an instrumental sign It instrumentally points to the tanned Socrates That is to say the mental counterpart of the conventional word string tannedness inheres in Socrates is some sort of image that is caused by or similar to the real tanned Socrates So this mental counterpart is a real relation pointing to another real relation In this way tannedness inheres in Socrates is a real relation a mental picture Therefore it does not intend anything And only when this mental image is isomorphic with the tanned Socrates it points to this state of affairs but only instrumentally so because the other condition for a sign to be formal that is intentional is still wanting namely the proposition to be a subject predicate proposition where the above mentioned identity naturally reappears There is no immediate contact between the mental counterpart of the verbally enunciated proposition tannedness inheres in Socrates and the tanned Socrates Consequently it does not guarantee objective knowledge We know the mental image but not the fact itself And returning to arguments as logical intentions it is now clear that if an argument is to convey objective knowledge its constituent propositions must be subject predicate propositions because only such propositions involve identity And then we automatically have to do with a syllogism All other types of arguments only instrumentally point to a causal structure and this only when there happens to be an isomorphic relationship between the argument and the causal structure to which the argument instrumentally points And we can expect such an isomorphy to be present when the subalterns of the argument turn out to be correct predictions That is when we deduce special instances of the general argument These predictions are correct when they turn out to comply with observations We now have given the conditions for knowledge to be objective knowledge But is all knowledge ultimately objective That is are the above established conditions really present Well although we can from a realistic point of view that is from the point of view of a realistic metaphysics say that the proposition some aspects of knowledge are subjective with respect to the human knowing power itself pretends to be a piece of objective knowledge implying that certainly not all knowledge is subjective it does not necessarily mean that then all knowledge is necessarily objective Statements about knowledge can be conceded to be objective but that does not exclude that some or maybe all knowledge about things could be subjective subjective that is to say with respect to the human cognitive power and subjective in the sense of all its signs being not formal but instrumental Indeed in natural science models are set up to explain things in reality Some of them are discarded later on while others are more and more improved until they indeed make the right predictions that is until they hold against observational scrutinity In our exposition we have investigated things under the supposition that ultimately all knowledge is objective But the above considerations have shown that it is certainly worth the trouble also to investigate things under the concession that some or even all aspects of knowledge of the real world is subjective in the sense that the extramental world can be cognitively approached only instrumentally that is with instrumental signs only And this renders concepts such as isomorphism model etc very important But alongside this assumption that the extramental world can be cognitively approached only instrumentally the alternative option all knowledge can in principle be come objective as is held by intentional Logic can still be entertained and held plausible according to the following lines Only in sensory observation there is a direct contact of the knower and the extramental world and this in virtue of the coding decoding process as described earlier Formal contents of the outside world are present in the knowing power in the form of high level brain features First of all these are the empirical concepts concepts consisting of the implicit predication of such a formal content of all the individuals of the concept s extension This implicit predication embodies the concept s signifucation A subject predicate proposition consists of concepts Each concept has its signification The truth of the proposition depends not only on the signification of its concepts but especially on their designation If the designation of the concepts in the proposition is such as to effect an isomorphy between the proposition as sign and the relevant segment of the extramental world where this relevance is determined by the signification of the concepts then the proposition is true And indeed only when there is such an isomorphy the subject predicate proposition actually intends In all this we must realize that for a proposition to be a genuine logical intention it must first of all be a subject predicate proposition because its explicit relation of identity as it reflects the relation of identity between things and concepts implicit predications is a first condition of knowledge to be objective But then still such a subject predicate proposition could be false because of failure of or wrong designation of its terms Only when the designation is right that is when it effects isomorphy the proposition really intends i e it then is a genuine logical intention That is to say then not only the constituent concepts are logical intentions but also the whole proposition Precisely the same holds for arguments because they solely consist of propositions In order to be a logical intention an argument must first of all consist of subject predicate propositions but in addition to that the designations of all the concepts figuring in the argument must be such that an isomorphy is resulting between the argument as logical entity on the one hand and the causal structure it is supposed to represent on the other And because in the case of propositions as well as in that of arguments in all probability such isomorphies can in principle be accomplished by the knowing power all knowledge of the extramental world can in principle be objective These two lines of approach viz conceding the mere instrumentality of logical signs and insisting that logical signs can be formal that is intentional when certain conditions during the process of acquiring knowledge are met rendering knowledge objective will be taken up again in later documents Resumption of the exposition of the argument as logical instrument Induction The logical status of the model as it is used in natural science But now let us continue our exposition of arguments in intentional Logic We must find out how explanation by hypothesis that is by a model should fit into an intentional Logic A model for example a proposed dynamical law which is supposed to govern a given dynamical system or as another example the heliocentric configuration of the solar system or another example again the principle of natural selection in organic evolution should explain certain observed facts viz the presence of an observed system state the position of the planets the fact of adaptation If the model is correct these facts can be deduced from it But what is the evidence or warrant for the model itself It cannot be those deduced facts because no deductive argument is ever a proof of its own premises it is a proof of its conclusion On the other hand as VEATCH p 330 considers the minute we recognize that what we are seeking to find a warrant for is not just the model or hypothesis all by itself but rather the hypothesis together with the explanatory deduction founded upon it then it becomes clear what the nature of the evidence is in such a case and what that evidence is an evidence of While induction normally is a generalization of a number of individual findings here we have as VEATCH proposes a new kind of induction Although a model or explanatory hypothesis is without doubt inspired by experienced facts it is as such not observable The new kind of induction leads to a recognition of a causal order underlying and making intelligible the connections between the various objects of knowledge For example with respect to the principle of natural selection in biology From what is observed i e from such things as the occurrence of variations the inheritance of variations the overproduction of offspring the struggle for existence etc from all these observable happenings one can infer that some such thing as natural selection is causing the adaptation of organisms to their environments So natural selection causing adaptation is found on the basis of observational findings This is the new kind of induction The course here in reasoning is from the sensible to the intelligible and as such it is an induction Deduction on the other hand moves entirely on the intelligible plane So hypotheses or models can perfectly well be regarded as being in a sense inductions from experience and hence intentions of experience More specifically indeed they would seem to be instruments for intending the causal order and structure of what is given in experience Accordingly such hypotheses or models are not wholly arbitrary fabrications of a sort of freewheeling mathematical intellect whose pertinence to the given data cannot be explained So in addition to inductions that lead to concepts and propositions we now also have the induction establishing a whole causal or syllogistic argument So far for induction Compound propositions and their relevance to the topic of argument The objects intended by compound propositions The categorical proposition that is a proposition that is asserting something without conditions is the final and perfect instrument of knowledge It is designed to or should we say it has biologically evolved as to represent both that things ARE and WHAT they are nor would we seem to require more for knowledge and understanding But until a proposition is seen to be true we cannot be sure whether it represents things as they really are nor is the truth of a proposition always or even usually self evident Instead evidence must be provided from outside that proposition itself and such evidence as we have seen always takes the form of other propositions which are supposed to have bearing on the proposition to be proved VEATCH p 332 Here then would seem to be the real ground for bringing other propositions into combination with a given proposition In this way we have the syllogism consisting of three subject predicate propositions And now we see what compound propositions really can be A compound proposition is a proposition in which several propositions are combined into a single one And of course such a combination could in fact be a whole argument compressed into the form of a single compound proposition As we shall see presently all so called hypothetical propositions are really syllogisms or at least involve syllogisms Therefore those compound propositions that are hypothetical propositions always intend some cause effect situation in extramental reality while as we will see compound propositions of the conjunctive type intend accidental coexistence in extramental reality In mathematical Logic the compounding of propositions is treated of in the so called propositional calculus There all the connective constants such as AND conjunction IF THEN implication OR disjunction but also constants such as NOT negation are being investigated But in contrast to how such compound propositions are treated of in intentional Logic in mathematical Logic their truth values are made dependent on the truth values of the component propositions They are laid down as rules in so called truth tables For instance the truth table for compound propositions in which the component propositions are linked together by OR resulting in a disjunctive compound proposition is where p and q are propositions and the compound proposition p or q This is the inclusive or Another way to define OR is the exclusive or Here the proposition p v q becomes implicative because we have either p or q but not both So if we want p then we must not have q and if we want q we must not have p For everyone of the above mentioned logical constants and or if then not there is a truth table The treatment is fully non intentional and it will turn out that all the theorems of the propositional calculus are compound propositions that say something not of things but of propositions for instance that a certain proposition can also be expressed in another way and still meaning the same thing So here in mathematical Logic compound propositions are treated as syntactical entities without them having any intentional function at all It is just an independent calculus where propositions are linked together and compounds are rearranged all of it according to certain rules We will return to the propositional calculus of the mathematical logicians later On the other hand in an intentional Logic such connections etc are differently treated It is asked what precisely in extramental reality or a reality just taken as if it were such a reality is intended by a given type of compound proposition Compound propositions are either categorical or hypothetical or they are conjunctive disjunctive or implicative A categorical proposition that is an unconditional proposition can be a simple that is not compound proposition then it has a simple subject predicate structure S is P If not explicitly analysed into subject copula and predicate such a proposition can be called p and another such proposition can be called q and yet another one r As such that is as p q and r they are elements of compound propositions and also for the propositional calculus they are the basic elements the logical atoms In addition to single propositions being categorical there are compound propositions that are also categorical First of all these are the conjunctional propositions A conjunctional proposition is a proposition that consists of several single propositions linked by AND When we symbolize the connective constant AND as we can have the compound proposition Here we have just a set of two categorical propositions p and q Examples Smith is tanned and Jones is ill Smith is a carpenter and he is bald Two plus two is four and New York is a large city What is intended here is an accidental coexistence of respectively two substances two accidents in a same substance and two totally disparate entities Specifically the first proposition intends the substance Smith who is tanned and the substance Jones who is ill accidentally coexisting The second proposition intends the one substance Smith who is a carpenter and bald where these two accidental forms each accidental with respect to man s essence exist accidentally together accidentally now with respect to each other and to man s essence in the one substance Smith The third proposition intends the mathematical two plus two which is four and the aggregate New York which is a large city In all such cases an accidental pattern is intended The same goes for compound propositions consisting of more than two propositions such as But there are other compound propositions that are categorical while not being conjunctions causal propositions and concessive propositions Causal propositions begin with since because consequently therefore etc As an example Because an agreement was made with Hitler the British did not declare war on Germany In this compound proposition it is categorically stated that there was made an agreement and that no war was declared So this compound proposition is categorical However the second proposition is clearly made dependent upon the first that is the second follows upon the first Were the first not true then war was declared So here we do not have to do with the intention of an accidental togetherness or coexistence of two things or events Accordingly this compound proposition is not a mere conjunction of propositions The second type of categorical compound propositions which are not conjunctional are the concessive propositions They are characterized by expressions such as although still nevertheless Example Although the British could not directly engage the Germans in Poland they did declare war on Germany Here also it is categorically stated that the British were not in a position to engage the advancing German army in Poland And also it is categorically stated that war was declared on Germany So this compound proposition is categorical In this proposition an implication is denied If the British cannot directly engage the Germans in Poland they will not yet declare war on Germany And because the implication is denied a concessive proposition is just some sort of conjunctive proposition British could not engage AND British declared war But of course the two component propositions of our original concessive proposition are not propositions that have in fact nothing to do with each other like in genuine conjunctive propositions So not only are conjunctive compound propositions categorical but also causal compound propositions and concessive compound propositions Causal compound propositions are implicative that is the second proposition in such a compound proposition is an implication of the first because p q A concessive compound proposition is we could say also implicative but here the implication is denied Although p nevertheless q Conjunctive compound propositions are clearly not implicative So far for categorical compound propositions Compound propositions that are not categorical are hypothetical propositions that is are assertions depending on some condition All hypothetical compounds are implicative in character Hypothetical compounds contain two types conditional compound propositions and disjunctive compound propositions Let us give an example of the first type viz a conditional proposition If Germany attacks Poland then the British will declare war on Germany Here it is not categorically asserted that Germany is attacking Poland nor is it categorically asserted that the British will declare war on Germany So this compound proposition is not categorical As has been said the two component propositions are not assertions What is asserted is the necessary connection between the two component propositions The second necessarily follows from the first The Germans attacking Poland has as its consequence as is asserted by the compound proposition that the British will declare war on them The second type of hypothetical compound proposition is the disjunctive proposition and of course also etc that is p or q p or q or r etc Example Germany will either be brought to its knees by a blockade or by military attack Here it is not categorically asserted that Germany will undergo a blockade nor is it categorically asserted that it will undergo military attack So this compound proposition is not categorical The two parts of the compound depend on each other as to their truth we here think of the exclusive or When Germany will unergo a blockade it will not be subjected to military attack But when it will be subjected to military attack no blockade will be set up against it Implicative compound propositions involve syllogisms In the proposition because an agreement was made with Hitler the British did not declare war on Germany a particular individual causal structure was intended And because it is an implicative proposition here an implicative causal proposition it is in fact an abbreviated syllogism However because it is a particular one off individual causal structure that is intended the syllogism cannot proceed from general to special We do not have many possible cases of the Second World War with Hitler s Chamberlain s and Churchill s So the syllogism must read If an agreement will be made with Hitler the British will not declare war on Germany An agreement was made with Hitler Therefore the British did not declare war on Germany This is the modus ponens syllogism On the other hand there are also causal propositions which intend a general causal relation such as Because towels have a capillary structure they are absorbent Also this is an abbreviated syllogism but now one that proceeds from general to special Any material that has a capillary structure is absorbent Towels have a capillary structure Therefore towels are absorbent The two implicative propositions just considered are causal and thus categorical Other implicative propositions can be conditional hypothetical such as the proposition If the British cannot directly engage the Germans in Poland then they will not declare war on Germany A conditional hypothetical proposition expresses uncertainty It expresses the uncertainty of the minor premise in the corresponding categorical and causal proposition If the British cannot directly engage the Germans in Poland then they will not declare war on Germany The British cannot directly engage the Germans in Poland Therefore the British will not declare war on Germany If we compress this syllogism we get the causal proposition Because the British cannot directly engage the Germans in Poland they will not declare war on Germany This is a categorical causal proposition Our original proposition was hypothetical rendering the minor premise of the above categorical syllogism uncertain So this premise must be removed As a result the conclusion also vanishes and only the major premise if the British cannot directly engage the Germans in Poland then they will not declare war on Germany is left which was our original proposition The above hypothetical proposition was about a particular causal situation and expressed uncertainty There are also hypothetical propositions that are about general causal structures and express uncertainty such as If towels have a capillary structure then they are absorbent It is an abbreviated syllogism that results from the

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Open archived version from archive - Logic VII

calculus In mathematical Logic the truth of compound propositions is universally made dependent on the truth of the component propositions When we first consider conjunctions and negations this truth functionality looks natural The truth table for the conjunction which means and of the propositions p and q is defined as Indeed can only be true if both p and q are true And for negation the truth table for not p symbolized by is defined as Where p is a proposiition Also this looks fair enough But with disjunction things are already different Indeed as we saw earlier for the disjunction meaning or as in there can be given two truth tables which both seem natural This renders the truth functionality of disjunctions to be a matter of mere arbitrary agreement But when we come to implication symbolized by things go awry indeed The truth table for where p are q are propositions is defined by the mathematical logicians as This truth table says that p q is always true except when the condition is true and at the same time the conditional false On the other hand according to intentional Logic an implication should intend a possible state of affairs expressed by the proposition q that will necessarily follow from another state of affairs expressed by the proposition p were such a state p existing So the truth of p q depends not on the truth of p and q but on their meaning For instance let p mean x is a man and q mean x is mortal p q then means if x is a man then x is mortal And we know for this implication to be true that the following must be presupposed All men are mortal Now indeed when x is man is true that is when x belongs to the class signified by the subject of the presupposition then surely it follows that x is mortal that is when p is true it follows that q is true and this means that then p q is true i e it is true that q is implied by p So the truth of p q depends to be sure on the truth of p and q but it taken as just if x is a man then it is mortal p q does not depend on these truths alone for even if it is true that x is a man and that x is mortal the fact that x is a man does not necessarily entail that x is mortal This being mortal as asserted in the considered to be true proposition x is mortal could be a fact accidentally coexisting with the fact that x is a man So while the truth of the propositions x is a man p and x is mortal q is sufficient for the conjunction to be true it is not sufficient for the implication to be true while according to the truth functional interpretation it is sufficient see the first entry of the truth table for implication given above This latter truth that is the truth of p q also depends on what x is a man means that is what man means And only when we learn to know the nature of man insofar relevant for our case that is such that this nature necessarily brings with it that it is a bearer of the property being mortal and this knowledge is expressed in the presupposed and consequently to be added proposition all men are mortal we will acknowledge the proposition if x is a man then x is mortal that is p q to be true We will acknowledge it because we now know that being mortal necessarily flows from being a man we know it as long as we assume the truth of all men are mortal So it is clear that at least implication cannot be defined truth functionally which in turn means that we cannot ignore the semantic aspect or part The truth of p q depends first of all on the meaning of p and of q If we do not consider implication according to the lines just given but simply follow its truth table we see that also in it we have the implication p q true when both p and q are true But what then when p meant two plus two is four and q meant New York is a large city Here also both propositions are true But then according to mathematical Logic as long as implication is still defined in it according to the truth table given above the proposition if two plus two is four then New York is a large city is also true And this is of course nonsense But not only this proposition but also the proposition if two plus two is five then New York is a large city is according to the truth table for implication true because here p two plus two is five is false and q New York is a large city is true And also the proposition if two plus two is five then New York is a small city would be true according to the truth table because both p and q are false Here we clearly see that the truth of p q depends on the meanings of p and q and not solely on their truth or falsity The proposition if two plus two is five then New York is a large city should be false instead of true It should be false because of what p and q mean New York being a large city cannot in any way be dependent on or follow from the absence of something corresponding to two plus two is five two plus two is five being false And also it cannot be dependent on or follow from the presence of something corresponding to two plus two is four two plus two is four being true It is by its very nature that if it is to perform its proper intentional function an implicative compound proposition involves a connection in meaning between its component propositions Indeed to assert an implicative compound proposition is not to assert the truth of the component propositions in the case of a hypothetical implicative compound if p then q and not merely to assert the truth of the component propositions in the case of a categorical implicative compound because p q Rather it is to assert precisely this sequence of the one proposition upon the other or the connection in meaning between the two Accordingly by his insistence on the truth functional interpretation of such implicative compounds the mathematical logician in effect suppresses their peculiar intentional function altogether And also attempts to remedy absurdities like the ones given above by altering the truth table for implication will not tough the real issue at stake here And because there are now as we have just seen at least two connectives disjunction and implication to which truth functionality does not properly apply we should realize that truth tables have nothing intrinsically to do with compound propositions they only happen to be in accord with conjunctions and negations For every compound proposition we must ask what precisely it is supposed to intend that is what the component propositions mean and only then we can determine whether that compound proposition is true or false It is in this way that the propositional calculus must be revised in order for it to become compatible with intentional Logic This however must be qualified further Let us concentrate on implication and consider some examples When defining implication we must as we already found out take into account intentionality that is we must take into account meaning So the definition of implication cannot rely solely on some truth table Indeed we must stipulate that the implication p q means that there must be a term in the proposition q of which the significatum that what the term signifies necessarily flows from the significatum of a term in the proposition p Let s consider the following instance of p q If x is a man that is a human being then x is capable of laughing Here x is a man stands for p while x is capable of laughing stands for q Let us further reproduce here the truth table for implication In the consequent proposition of our compound hypothetical proposition If x is a man then x is capable of laughing we find the predicate term capable of laughing And it is evident that what our hypothetical proposition asserts is that the significatum of this predicate term necessarily flows from the significatum of the term man which is the predicate term of the antecedent proposition of our compound proposition Because capability of laughing necessarily flows from being a man and perhaps could flow from other essences as well we can confidently say If x is a man then x is capable of laughing So by finding out what is presupposed by the hypothetical proposition namely the truth of the proposition All men are capable of laughing we are able to d e f i n e not arbitrarily implication That what is signified by the component proposition x is a man is a sufficient condition perhaps one of the many sufficient conditions for the truth of the other component proposition x is capable of laughing While the truth of the consequent proposition x is capable of laughing depends on the truth of the antecedent proposition as signifying one of the sufficient conditions it is clear that the implication that is the whole compound proposition is still true when the proposition x is a man is false for example when x is not a man but an insect This is so because our implication only says that if x is a man then x is capable of laughing This still being true of the implication despite the falsity of its antecedent is expressed in the last two entries of the truth table of implication Indeed when the proposition x is capable of laughing is true while the proposition x is a man is not this still does not affect the truth that if x is a man then x is capable of laughing x is an insect and as it has turned out it is capable of laughing but whether this capability is rightly fourth entry of truth table or wrongly third entry assessed in the case of the insect the fact remains that if it were a man it would surely be capable of laughing This is expressed in the third and fourth entries of the truth table And of course when the proposition x is a man is true and also the proposition x is capable of laughing is true then the implication is true It is then true by definition This is expressed in the first entry of the truth table On the other hand when the proposition x is a man is true but the proposition x is capable of laughing false then the implication is false because now the definition of implication is violated Another instance of p q is If the electromagnet is switched on then iron will be attracted toward it Here also we have a real dependence of being attracted on the electromagnet being switched on And indeed whether the electromagnet is actually being swiched on or not that is whether the proposition the electromagnet is switched on is true or not the implication is true except when while it is true the electromagnet being switched on the proposition iron will be attracted toward it is false iron will not be attracted toward it because then the definition of the implication is violated From all this it should be clear that from the viewpoint of intentional Logic a truth table cannot constitute the non arbitrary definition of implication or of any other connective for that matter Things are such that the truth table as given above holds as a result of the definition of implication And the definition of implication as implication figures in the compound proposition p q where p and q are single propositions each intending some state of affairs is There is a term in the consequent proposition q of which the significatum necessarily flows from the significatum of a term in the antecedent proposition p And from this non arbitrary definition which takes meaning into account of implication the validity of the truth table for implication follows Having found how things are in the case of implication they should mutatis mutandis be the same for the other logical connectives The definition of conjunction that is of the connective and as conjunction figures in the compound proposition where p and q are single propositions each intending some state of affairs is The significatum of the component proposition q accidentally coexists with the significatum of the component proposition p And from this non arbitrary definition which takes meaning into account of conjunction the validity of the truth table for conjunction as given in mathematical Logic follows The first entry of this table expresses the definition of conjunction The other entries express the non coexistence of the states of affairs signified by the component propositions p and q Coexistence here is only an accidental coexistence otherwise i e when the coexistence is a necessary coexistence the connective would not be and but rather is equivalent to double implication We see that such a thing like accidental coexistence and also of course necessary coexistence cannot be expressed by whatever truth table all by itself We must take into account what in extramental reality or in a reality considered as if it were extramental because objective is intended by the compound proposition implying that the propositional calculus and with it the whole of Logic cannot be a self contained system Well it can be transformed into a self contained system but then it is not part of genuine Logic anymore as long as Logic is supposed to be the science about the formal instruments of knowledge of knowable things The definition of exclusive disjunction that is of the connective or as disjunction figures in the compound proposition where p and q are single propositions each intending some state of affairs is Either the significatum of the component proposition q exists or the significatum of the component proposition p exists but not both at the same time or defining equivalently If and only if the significatum of the component proposition p does not exist the significatum of the component proposition q does exist And if and only if the significatum of the component proposition q does not exist the significatum of the component proposition p does exist And from this non arbitrary definition which takes meaning into account of exclusive disjunction the validity of the truth table for disjunction follows In the light of the definition of exclusive disjunction this truth table as given in mathematical Logic speaks for itself And if want to do so we can in addition to this exclusive or define inclusive or the truth table of which was given above and is here reproduced The connective equivalence is a double implication that is an implication that goes both ways So means The significatum of a term in the component proposition q necessarily follows from the significatum of a term in the component proposition p and vice versa with respect to these same significata Because the definition of equivalence is totally based on that of implication we can derive the truth table of equivalence from that of implication by combining the implication which goes to the right with that which goes to the left resulting in the truth table of equivalence as given in mathematical Logic The table here expresses the definition of equivalence by assigning truth to a compound proposition with its component propositions which could themselves also be compound propositions connected by only if the significata of these propositions behave in the same way If one of them is actually present that is if one of these propositions is true the other is also present that is the other proposition is also true and if one of these significata is not present that is if one of these propositions is false the other is also not present that is the other proposition is also false The definition of negation as negation figures in that is not p where p is a proposition must read The significatum of the proposition p is not present And from this the truth table of negation as given in mathematical Logic follows The entries in this table speak for themselves So now we have treated of all logical connectives in the propositional calculus and have interpreted them according to the tenets of intentional Logic It turned out that when we define these connectives properly that is in accordance with intentional Logic then the truth tables as given in mathematical Logic hold And this means that we can use these tables for the derivation of the tautologies or theorems of the propositional calculus However in doing so the propositional calculus is not a self contained system anymore but involves meaning and meaning here implies things states of affairs which are signified by its propositions single or compound which in turn means that we go outside the system proper About the tautologies or theorems of the propositional calculus In the mathematical propositional calculus a number of theorems have been derived Such theorems or logical laws are tautologies that is they are certain compound propositions that are always true no matter the truth or falsity of the constituent single propositions In science explaining observed facts these facts laid down in a description is in fact to chart that description onto a tautology A tautology as such does not contain information about an object but only about certain compound propositions insofar propositions And an explanation only contains that information which was already present in the description The charting implicitly presupposes that the connections that hold together the tautology do correspond to the relations that are contained in the description A description contains information but no logic and no explanation See for this BATESON G Mind and Matter 1979 Chapter III 9 The charting or mapping of the description onto a tautology which itself can be syllogistically proved takes place by interpreting the bare tautology physically or mathematically So in this way these tautologies function as forms of inference But they are in mathematical Logic entirely based on truth tables Let us see how this works out with the tautology where is a double implication or equivalence and p and q single propositions We have changed the order of the possible truth values of p and q in this table which is of course totally immaterial Here the compound propositions and behave exactly in the same way with respect to the possible truth values of p and q so they are equivalent If we add in the truth table argument the truth table of we get So here we clearly see that is always true no matter what the truth values of p and q are Accordingly we here have a logical law or tautology And here because the tautology is about that is about it is also so acknowledged by intentional Logic by reason of the fact that the truth functional interpretation of happens to give the same results as the intentional interpretation of That is also for intentional Logic is only true when both p and q are true and demands that p behaves in exactly the same way as q does that is when p is true q must be true and vice versa and when p is false q must also be false and vice versa But we know that the case of implication is different When implication is defined merely by its truth table as the mathematical logicians do it will not in all cases comply with this truth table as far as intentional Logic is concerned As we saw earlier sometimes nonsence is produced In the light of all this we will now show how to generally re interpret the tautologies of the propositional calculus We take as an example According to respective truth tables we get So according to the truth functional interpretation is a tautology It is always true no matter what the truth values of p and q are Now we expound how such a tautology must be understood in the context of intentional Logic Clearly in order for to be true it does not make any difference for what the proposition p stands or for what q stands Nor does it in a sense about this sense see immediately below make any difference whether they be true or false The explanation of the tautological nature of our expression an explanation that is which does not make use of truth tables is as follows If we have non q then p cannot be implied by it because then we would have q because q is implied by p therefore we have when having not q not p implied And the other way around If we have p then we cannot have not q because not q implies not p therefore we must when having p have q Here we see that we did not make use of the possible meanings of p and of q Yet even though in such a formula we do abstract from the specific meanings of p and of q we nonetheless recognize that there must be something in the meaning of such propositions that provides the foundation for the relation of implication between them remember p q is the subject of the tautology in question Consequently in the propositional mold p q we do not mean just any proposition p but rather any proposition whose meaning is such this is the in a sense we spoke about above that it implies another proposition Similarly q does not stand for any proposition but rather any proposition of such a nature as to be implied by another Moreover the important thing to notice is that in the proposition taken as a whole and which is a double implication the antecedent of the implication going to the right that is all that lies at the left side of is not simply p or the consequent that is all that lies at the right side of simply q rather the antecedent is itself a conditional proposition namely and the consequent likewise viz And precisely the same applies to the other direction of the double implication namely So our tautology is in fact two implications namely and and how to interpret the truth dependency of an implication along the lines of an intentional Logic was expounded above In other words while the truth of the whole proposition is not dependent on the meaning of the propositions p and q it is dependent on the meaning of when taking of the double implication or is dependent on the meaning of when taking of the double implication And because we do not specify the meanings of p and q the s u b j e c t of the proposition that is what the proposition is about is now that is implication itself and the same is the case of the subject of Read in either direction the proposition is not about the significata of its subject term but about the subject term itself which here means about itself That is to say it is in virtue of the nature and meaning of implication as present in and in that one is able to assert In other words the proposition is not about p and q just as such but about the peculiarly logical relation of implication itself VEATCH p 382 3 It is about respectively to be sure but because p and q are not specified it is about implication as such It is along these lines that the theorems or tautologies of the mathematical propositional calculus should be re interpreted for an intentional Logic In order to demonstrate such adjudgements or re interpretations to be made in the propositional calculus let us first consider the proposition where means the negation of that over which it is placed That this is a genuine equivalence is shown in mathematical Logic by means of truth tables So indeed according to the truth functional interpretation is a tautology it is always true no matter what the truth values are of p and of q The denial of the implication of q by p is equivalent to the conjunction of p and not q From this it follows still in the truth functional context that denying such a conjunction implies the truth of the implication However we will find out that p q is not obtained as a meaningful proposition in all cases as it should according to the truth tables Suppose we giving here an example as it is presented by VEATCH let p signify the proposition I am sitting at my desk and let q signify the proposition New York is a large city Then means New York is not a large city And now means I am sitting at my desk and New York is not a large city And this compound proposition is obviously false So the compound proposition is false as soon as we consider the particular m e a n i n g s of p and q as they are given above and consequently its negation must be true Therefore because according to the truth functional interpretation we have we can say If we assume that p is true that is we have p then we have which indeed is one of the possible outcomes resulting from negating the proposition and the only outcome when having p Accordingly in our particular case at least we have So because what p and q signify can exist together I am sitting at my desk while New York is a large city we have But the latter compound proposition is nonsense because it here means If I am sitting at my desk then New York is a large city And of course the size of the city of New York cannot in any way be dependent on whether I am sitting at my desk or not That this is here nonsense that is that turns out to be nonsense evidently is because the togetherness of p and q the fact that I am sitting at my desk and the fact that New York is a large city is not imperative They can be together but need not be together When I am not sitting at my desk New York is still a large city Indeed the expression which we have arrived at viz is also not possible according to the truth tables because implication is certainly not equivalent to conjunction as their respective truth tables show So here we cannot simply rely on the truth functional interpretation because according to that interpretation we had being always true no matter what p and q signify and therefore also while we found out that in the above case turned out to be nonsense while is perfectly possible in the form of In all this we have seen that as soon as we considered the meanings as were set above for p and q the proposition is definitely false and thus its negation true and consequently leading to the truth of which when interpreted according to those meanings of p and q yields nonsense This means that the falsity of in fact turns out to imply not the truth but the falsity of because under the meanings set above for p and q the latter cannot be implied by the former and thus not the falsity of which latter should be the case according to the equivalence of and So the truth table for this latter equivalence is violated in the present case That is to say the equivalence as established in the truth table cannot be true for all meanings of p and q while it is true for all truth values of p and q That is to say it is not a tautology as soon as we involve meanings If we leave out meanings alltogether then it is a tautology Indeed in our example that state of affairs represented by the proposition p viz I am sitting at my desk cannot in any way imply that state of affairs represented by the proposition q viz New York is a large city So it is not their truth or falsity but their meaning that is decisive for the equivalence to be true that is for it to be a genuine equivalence On the other hand there are cases where the implication is not nonsense at all but absolutely necessary so that in these cases the truth table method happens to work well Consider the following negation of a conjunctive compound In line with which itself derives from the following truth table we can say Is this latter implication viz always true Yes it is It can syllogistically be proved here can legitimately be identified with is because is is at least equivalent to We can also prove the case where the central implication goes to the left having then proved the equivalence of p q and not q not p So we have proven not by means of truth tables that the proposition is always true no matter what the propositions p and q s i g n i f y and then of course also that is the implication this in contrast to the previous example where the corresponding implication was simply which indeed cannot as such be proved true because there are different propositions on either side of whereas in p q not q not p we have the same propositions on either side of the central And because of this our proposition has not yielded nonsense The negation of a conjunction here resulted in an implication that is always true Because we now know that is always true can never go with its opposite which here also means it can never go with the negation of that is the conjunction is impossible in principle i e not just in a particular case therefore its negation is true and so its equivalent In fact the difference between the first example which was about and the second example which was about is that on the one hand the compound proposition is about objects of first intention that is it is about the state of affairs that is signified by the proposition p signified in extramental reality or in a reality considered as if it were extramental and it asserts that another state of affairs signified by the proposition q is implied while on the other hand the compound proposition is about the proposition p q as such that is as compound proposition and thus as logical intention it asserts that this proposition as proposition implies the proposition not q not p as proposition i e it is about objects taken in second intention This is evident from the fact that in contrast to the first implication we here have on either side of the central implication the same propositions namely p and q at the left side and p and q at the right side In short when we interpret things in line with intentional Logic there would seem to be a marked difference between what might be called denying a conjunction in fact as we did earlier by finding out that the togetherness of p and q is not imperative but only factual that is they have intrinsically nothing to do with each other implying that their conjunction can be denied and that therefore also the conjunction can be denied yielding which however turned out to be nonsense and therefore not complying with the truth functional interpretation and what might be called denying a conjunction in principle as we just did immediately above yielding an implication that was true at all times And it is such kinds of adjustments that have to be made for bringing the propositional calculus in accord with an intentional Logic Intentional Logic thus wants there to be a distinction between accidentally being together of certain given objects of intention where such a being together should be expressed by and per se being together of certain given objects of intention where such a being together should be expressed by or per se not being together of such objects that is excluding each other expressed by exclusive As such means either p or q but not both of them together So far as regards the interpretation of the propositional calculus in the context of and according to intentional Logic Does the propositional calculus upset the claim of the syllogism to be the exclusive instrument of deductive demonstration VEATCH p 384 quotes the mathematical logician TARSKI Almost all reasonings in any scientific domain are based explicitly or implicitly upon laws of the sentential calculus Where sentential calculus means propositional calculus And in fact these laws that is the tautologies or theorems of the propositional calculus are regarded as being simply so many validating forms of inference So clearly it is claimed that the syllogism which itself is not a tautology because as a compound proposition If S is M and M is P then S is P that is its truth depends on the truth of the component propositions while the truth of tautologies is not so dependent is not the exclusive instrument of deductive demonstration or inference The following truth table shows that the syllogism is indeed not a tautology that is it is not true for all possible truth values of its component propositions p q r In intentional Logic both premises p and q must be true in order for the conclusion r to be true And only when this is the case first entry of the table the implication as such namely is true According to intentional Logic all other truth false configurations result in the falsity of the implication On the other hand the modus ponens inference If q is implied by p and if we have p then we have q is as such a tautology The inference is true for all truth values of the component propositions p and q This is so by reason of the fact that at the right side of the main implication no new proposition is produced How has it come to be that way that is why is there apparently no new proposition produced Well it appears so because the modus ponens is in fact an abbreviation of a larger structure That is something is omissed Indeed in order to be able to assert the modus ponens major premise p q something must be presupposed that is something that is not explicitly mentioned in this premise and in the whole modus ponens inference for that matter And as has already been shown earlier when we add this presupposition explicitly to the modus ponens structure we obtain a genuine syllogism Let us show this once more by means of an example p q p Therefore q This is a modus ponens inference where p and q are propositions It can be written as the compound proposition which is a tautology Let us give the component propositions p and q a possible meaning p x is a crystal q x is periodic Our modus ponens inference then becomes If x is a crystal then it is periodic x is a crystal Therefore x is periodic Now we unearth the mentioned presupposition In order to be able

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Open archived version from archive - nomos I

such a sequence of events as a particular dynamical system is relatively stable we can for scientific or practical purposes conceptually insulate it and treat it as if it were not perturbed by any extraneous factors or other dynamical systems operating at the same time In such cases we can more or less accurately predict future states of the system But when the system is a so called chaotic but nevertheless deterministic dynamical system already the very smallest perturbation of the system is sufficient to confuse the initial order and to make impossible any more or less long term predictions This means that such systems are extremely sensitive to changes in initial conditions or any state or condition somewhere along the system s dynamical trajectory that is very small perturbations can deflect the system s original course dramatically All this means that at least ontologically seen everything is determinatively one could say causally connected with everything else in the universe Although many such connections are weak and indirect and therefore insignificant for everyday life and even for natural science they are there nevertheless and ontology must take that into account All the foregoing indicates that in fact no isolated processes exist in the space time world implying that there is in fact only one process that is one single overall world process a process whose dynamical states together form a successive series of world collocations Every such particular collocation or particular state of the world system is a pattern of simultaneous co existence of beings of whatever sort A main characteristic and determining factor of such a collocation that is what it must or can be and what it cannot be is the fact that the beings in it are such that they indeed can co exist together at least at that particular point in time They may vanish in the next state of the world system And as we have already said despite the fact that there is in reality only one dynamical system the world system some subsystems can be conceptually insulated for the purposes of science and everyday life because at many places the determinative cross connections connecting systems causally with other systems turn out to be very weak The world process consists as has been said of a successive series of world collocations each of them being a simultaneity section through the whole universe Each such a section is produced by the previous section because such sections are the successive states or stages of the one world process And in every next moment in Time a new state is formed And each such a world state is a spatial pattern of all beings co existing simultaneously at the moment when the state was created So the world process shows two types of determination viz a simultaneous determination which is about the compatibility of many different simultaneous beings with each other in order to be able to co exist and a successive determination that is the determination of one world state by the previous one where then the previous one disappears The simultaneous part involves three dimensional space i e it is along the space dimensions while the successive part involves the time dimension that is it is along that dimension This latter dimension is perpendicular to all three space dimensions The next figure diagrammatically depicts the determinative structure the world system that is the one all encompassing world dynamical system Figure 1 Diagrammatic picture of the world process The world process is a succession of spatial simultaneity sections blue lines through the whole world Each such a section is generated by the previous one The time dimension and direction is indicated The three space dimensions are perpendicular to the one time dimension They are symbolized by each blue transverse line A number of successive world states are symbolized by the letters A B C D E F and G Every such symbol refers to the whole transverse line present at both sides of the line expressing the successivity We have just depicted the world process But in fact at least along its successive dimension it is composed of still smaller determinative units or elements Let us explain If we look for example to world state C we can say that this state is the cause of the next state which is state D And at the same time state C is the effect of the previous state state B which is its cause And of course state D is not only the effect of state C but at the same time the cause of state E and so on But this was already expressed by the above diagram As has been said there are still smaller determinative elements not depicted by the diagram If we say in the context of the above diagram that say C is the cause of D then we mean the c o m p l e t e cause of D Every being thing or event present in the universe at time C is taken into account when considering the whole world process in which everything is stronger or weaker causally connected with everything else and that means that all partial causes of state D are taken into account Not any such partial cause is left out of consideration The important lesson from this is that we realize that every complete cause consists of partial causes each one of them producing some coresponding partial effect somewhere in the overall complete effect This is illustrated in the next Figure Figure 2 Blow up of a part world states B C D of Figure 1 revealing the determinative fine structure World state B is the complete cause of world state C and world state C is the complete cause of world state D Every complete cause consists of a number of partial causes and to each such a partial cause of a given complete cause corresponds a partial effect in the next world state which itself is the complete effect Accordingly the complete cause B consists of a number of partial causes of which six are depicted as examples b 1 b 2 b 3 b 4 b 5 and b 6 These partial causes produce their corresponding partial effects in world state C c 2 c 5 c 1 c 3 c 4 and c 6 These latter in turn are partial causes constituting the complete cause C And these partial causes produce their corresponding partial effects in world state D d 2 d 3 d 5 d 4 d 1 and d 6 Roughly the same type of fine structure will be found between all other world states If Then constants In Figure 2 we see that the determination between any two world states is made up of many more elementary determinative elements where such an element is seen to be the connection of a partial cause with its corresponding effect For the world states B C D 12 such elementary determinative connections or links were depicted From world state B to world state C b 1 c 2 b 2 c 5 b 3 c 1 b 4 c 3 b 5 c 4 b 6 c 6 From world state C to world state D c 2 d 2 c 5 d 3 c 1 d 5 c 3 d 4 c 4 d 1 c 6 d 6 It could be that the discussed and listed partial causes and their corresponding partial effects themselves have a fine structure in turn resulting in still more elementary determinative connections If we however for simplicity s sake assume that the just discussed determinative connections are already the most elementary determinative connections then we have to do with the very basic or last determinative elements in the sense of the ultimate elementary and therefore smallest determinative steps here as such distinguished only insofar as they are so elementary which elements together with many more such in the same degree basic determinative elements constitute the total and complete determinative structure of the space time world What precisely are these elementary determinative elements Have we met them before In a way we have In Part I of Fourth Part of Website we have discussed the theory of If Then constants the reader should consult this Part There they were interpreted as principles of determinative connections Such a principle then determines that if the sufficient ground for some specified feature or pattern X does exist in the space time world then X necessarily exists We have listed many such If Then constants Together they were supposed to constitute the determinative structure Nomos of the world Cosmos In the present exposition however we will take these constants in a slightly different way First of all we take as the very genuine and true If Then constants only those that represent or are at least meant to represent the above discussed elementary determinative connections All other sometimes so called If Then constants are here considered not as genuine If Then constants but as determinative connections that are not yet elementary but composed of still more basic determinative connections Only when we arrive at determinative connections that are absolutely elementary and thus are not composed anymore of still more basic determinative connections we have arrived at genuine If Then constants In practice it is in most cases not possible to unearth such genuine constants so we will once and for all agree that when we in the present discussion and in all that comes after it speak about and give examples of If Then constants we MEAN the genuine If Then constants representing the absolutely elementary determinative elements connections links whatever the examples used Further we will ascribe a certain degree of generality to our If Then constants that is they are principles that do not determine any being or event completely all the way down to individuality but only precisely and as such completely determine that for which their Then term that is their consequent stands and this term does not stand for something individual True individuality and one offness is only the result of many different such constants applying together for a given case And things features or events can only exist in the space time world when they are individuated Any If Then constant consists of three parts viz an If term that is an antecedent an implication and a Then term that is a consequent If that for which the antecedent stands exists then that for which the consequent stands must also exist As has been said every If Then constant has a certain degree of generality which first of all means that it is in fact the Then term which has that degree of generality which in turn means that the Then term can only be realized as existing in the space time world when other If Then terms also apply and together result in individual existence And it is because of this degree of generality of the Then term that the If term can and must be disjunctive Indeed a not yet completely determined feature or thing let us call it A can have several or even many possible different sufficient grounds say the grounds a b c d e f g h implying that is guaranteeing its existence The corresponding If Then constant then reads If a or b or c or d or e or f or g or h exists then A must exist So the condition a existing alone is already sufficient for A to exist And in the same way b existing alone is also already sufficient for A to exist The same goes for the other conditions c d e f g and h Well each determinative connection considered to be absolutely basic depicted in Figure 2 is a special case of an ontological that is natural and automatical application of a particular If Then constant Let us give this Figure again and work things out further Figure 2 Blow up of a part world states B C D of Figure 1 revealing the determinative fine structure Each red line leading from one world state to the next stands for the application of a certain If Then constant to the existence of one condition out of the constant s set of possible conditions See below The basic determinative connection basic elementary determinative link b 1 c 2 to take just an example is here a special case of an application of the following If Then constant which could read If a or b 1 or c or d or e or f exists then c 2 must exist In the context of Figure 2 the condition b 1 is supposed to exist And this means that the just given If Then constant applies this is the mentioned special case of an application It would also have applied when one of the other conditions a c d e or f existed For the other basic determinative connections given in Figure 2 we can say precisely the same Also each one of them is a special application of a certain If Then constant And as such it represents such an If Then constant But if this If Then constant is fully expressed then of course the disjunctivity of the If term must be expressed that is all the possible conditions or sufficient grounds must be included If we do not want to do this explicitly for example because alternative sufficient grounds are not completely known then we could in the case of the If Then constant If a or b 1 or c or d or e or f exists then c 2 must exist simply refer to this constant as the If Then constant for c 2 In the context of Figure 2 one of the possible sufficient grounds namely b 1 exists which then according to the If Then constant guarantees the existence of c 2 All the other basic determinative connections of Figure 2 red lines we can treat in the same way Each one of them is an application of the If Then constant to a particular existing individual case that is the actual existence of one out of the constant s set of possible sufficient grounds or conditions So we can say From world state B to world state C we have the following determinative connections links b 1 c 2 which is an application of the If Then constant for c 2 to the particular case of the existence of the condition b 1 b 2 c 5 which is an application of the If Then constant for c 5 to the particular case of the existence of the condition b 2 b 3 c 1 which is an application of the If Then constant for c 1 to the particular case of the existence of the condition b 3 b 4 c 3 which is an application of the If Then constant for c 3 to the particular case of the existence of the condition b 4 b 5 c 4 which is an application of the If Then constant for c 4 to the particular case of the existence of the condition b 5 b 6 c 6 which is an application of the If Then constant for c 6 to the particular case of the existence of the condition b 6 From world state C to world state D we have the following determinative connections links c 2 d 2 which is an application of the If Then constant for d 2 to the particular case of the existence of the condition c 2 c 5 d 3 which is an application of the If Then constant for d 3 to the particular case of the existence of the condition c 5 c 1 d 5 which is an application of the If Then constant for d 5 to the particular case of the existence of the condition c 1 c 3 d 4 which is an application of the If Then constant for d 4 to the particular case of the existence of the condition c 3 c 4 d 1 which is an application of the If Then constant for d 1 to the particular case of the existence of the condition c 4 c 6 d 6 which is an application of the If Then constant for d 6 to the particular case of the existence of the condition c 6 This kind of situation obtains between every two successive world states Generally the If Then constant for X has as its antecedent that is the If term the disjunctive list of all possible sufficient grounds or conditions for the existence of X Such conditions can be all sorts of features things or patterns each one of them alone already guaranteeing the existence of X A condition or sufficient ground for X insofar as that ground figures dynamically is a cause of X and a partial cause of the corresponding world state in which X resides This cause of X resides not somewhere in the world state in which X resides but somewhere in the previous world state And having said this the world process world dynamical system consisting of a succession of world states could be such that a small part of some given world state is repeated in a limited number of world states that come next And it could be that our X is such a small part or part of the latter that is repeated in the next world state repeated again in the next next world state and so on for a number of times An explanation for this could be that to begin with at some time X is generated from W The complete world state WS n is the complete cause of the next complete world state WS n 1 If we assume that W resides in world state WS n then W is a partial cause of world state WS n 1 that is of the next world state which itself is the complete effect of the previous world state And then X is a partial effect of that previous world state Now it could be that the world state which comes after WS n 1 which contains X that is the world state WS n 2 also contains X at the corresponding location of this word state So X is repeated in the next world state This could go on indefinitely or only a finite number of times the last repetition then taking place say in world state WS n 583 The next world state WS n 584 does not have X anymore but say Y Thus we have embedded within the succession of complete world states the sequence W X X X X X X Y And this means that we have for a number of times X X And where we have W X W must be the cause of X and this cause must consist of two elements or aspects viz a generating cause and a sustaining cause This is so because in order for X to exist at a certain location it must not only once be generated at that location or generated else and then moved to this location but it must at the same time be sustained in order to remain that is tend to remain existent At least it must have the tendency to remain existent For example if an ice crystal is to exist at some location it must have been generated there and for this generation freen water molecules must have been present in sufficient numbers In addition the ambient temperature must have been below zero during crystalization But for the ice crystal not just to exist only for a split second but having at least the tendency to remain existent the ambient temperature must remain below zero and other conditions must be such that the crystal will not directly evaporate again These are what we would like to call sustaining causes the crystal may it is true not grow larger anymore but it keeps on existing or at least tends to do so When we now consider the sequence X X X X we can say that that sequence does not need the presence or existence of the generating cause for X but it does need and thus implies the sustaining cause of X to be present at the corresponding location in all the complete world states that correspond to the members of the sequence X X X X As long as this sustaining cause is not annihilated by the system being perturbed from outside X will be repeated That is everytime it will reappear in the corresponding location of the next world state Now we must interpret this in terms of the If Then constant for X As we have said the antecedent that is the If term of the If Then constant for X is a disjunctive list of all possible sufficient grounds or conditions for the existence of X Now we know that one of these possible sufficient grounds or conditions is the presence of X itself plus one or another of its possible sustaining causes So with the event X X we have not discovered a new type of If Then constant where the If term equaled the Then term but only a new type of member of the disjunctive list of possible sufficient grounds or conditions for the existence of that for which the constant s Then term stands The actual event X X is just an application of the one If Then constant which could read If A or D or W or D or E or X and its sustaining cause exists then X must exist and indeed we get X because X exists That is X will appear at the corresponding location of the next world state because it and its sustaining cause was present in the previous world state Determinative interwoveness and If Then constants Earlier we spoke about the dependence of all dynamical systems discernable in the space time world upon each other that is their causally being connected with each other How do If Then constants as defined above fit in this picture And how must we understand this dependence As we have already said there is in fact but one dynamical system the world process Nevertheless some subsystems can conceptually more or less be insulated from their environment That is to say within the overall world process as the one dynamical system some subsystems can be discerned These latter are not independent from each other or from their environment but their dependence is relatively weak meaning their sensitivity to perturbation of one or more of their states is relatively low allowing them to be conceptually insulated for the sake of natural science or even of everyday life Some such subsystems are relatively stable meaning that most perturbations do not have an enduring effect on the perturbed system because the latter quickly restores its original course But other subsystems are more or less unstable by reason of which they will either definitively follow a new course after having been even only lightly perturbed or even totally disintegrate The causal connection between two different subsystems consists in the application of one or more If Then constants that have their If component in a state of one dynamical subsystem and their Then component in a state of the other dynamical subsystem The following diagrams try to depict all this Figure 3 World states blue lines A B C D E F G H I J K L M N O P Q R S T U V W and more as successive states stadia stages of the world dynamical system Each such a state stadium stage is a simultaneity section through the whole universe The determinative fine structure applications of If Then constants not yet drawn Before we analyze this one dynamical system world system into a number of different dynamical subsystems that can more or less be insulated we first depict what it exactly means that two subsystems are interacting with each other Figure 3a Two dynamical subsystems following their course and finally strongly interacting with each other resulting in them to merge together The vertical blue lines represent the successive world states that is the states of the one overall world dynamical system These world states are the simultaneity sections through the whole universe The thin sections of the blue lines representing the world states indicate where they are drawn the initial low degree of dependence of the one subsystem from the other as a result of a low degree of interaction Also the distance as drawn between the two subsystems symbolizes the degree of interaction between them large distance low degree of interaction Any continuous thick part of a given blue line represents the state of one sub system The other continuous thick part of the same line represents the state of the other sub system Both states belong to the same world state and are therefore simultaneous Any red line drawn between two successive world states successive from left to right blue lines is here considered to represent the application of a particular If Then constant At the right side of the diagram the two subsystems are beginning to perturb each other that is interact with each other This happens by virtue of some If Then constants in fact their particular applications spanning the two subsystems That is to say the antecedent of such an If Then constant lies in a state of one of the subsystems while the consequent of that same If Then constant lies in a state of the other subsystem which state is a partial state of the next in time world state The next Figure shows this again but now involving the world system that is its succession of states Figure 3 Here we depict several interacting dynamical subsystems In order to emphasize the fact that these subsystems although interdependent stand more or less out and thus allowing to be conceptually insulated from each other and from their environment we have omitted the thin sections as drawn in the previous Figure each one connecting a state of a given subsystem with a simultameous state of another subsystem resulting in one continuous world state Figure 4 A number of subsystems emphasized by black lines is discernible within the one overall world system itself consisting of the successive world states A W Such subsystems actually are never completely isolated from each other but interact more or less strongly with each other at several places After such interactions or perturbations original courses of involved subsystems can be deflected either temporarily or definitively Every red line drawn between two consecutive world states i e between one given state and the immediately next one stands for the application of one or another If Then constant to some particular existing member of the set of possible sufficient grounds for that for which the constant s Then term stands Here only those applications are depicted red lines that are involved in the courses of the considered subsystems and their interactions Natural laws and If Then constants From what has been said so far it is now clear that every subsystem is in fact a succession of states which are in fact partial states of the corresponding complete states of the one world process but which partial states are nevertheless such that they can conceptually be insulated from the rest and with them the subsystem itself which now is one of the many more or less particular dynamical systems or natural processes distinguished by natural science The latter describes these dynamical systems as obeying so called natural laws Generally such a law dictates the quantitative relation between any two successive states one state and the next state And then given some one state the states that went before and those which will come after it can be predicted Application of such a law is not restricted to one particular case It can be applied wherever and whenever it is relevant This is not epistemologically meant that is it is not meant in the sense that scientists can apply such a law wherever and whenever it seems relevant to them but ontologically For instance the law of gravitational attraction applies anywhere as long as there are material bodies present And it is precisely because of the inherent possibility of repeated application that we speak about lawfulness in the sense of regularity In fact the many different natural laws as they have been found by natural science express as laws the classification typification of dynamical courses trajectories of subsystems And we know that a course of a given dynamical system as subsystem of the world system is the succession of its states and that allways the next state is determined by the previous state And we know further that this determination consists of the application of a number of If Then constants which span between any two consecutive states Figure 5 Two consecutive states blue vertical lines of a subsystem The next state i e the one on the right is completely determined by the application in an ontological sense of several If Then constants red lines having their antecedent in one state i e the one on the left and their consequent in the next state So the relation between any two consecutive states of a given dynamical system that is the production of one state out of the previous state is completely determined by the application of a number of certain If Then constants And because If Then constants have the general character of If A or B or C or exists then in all cases where indeed A or B or C or exists X will exist it is clear that natural laws are indeed laws that is they can be repeatedly applied And this also means that a natural law is not as such a determining entity Its lawfulness can be completely reduced to the nature of If Then constants Modality of the space time world Before we discuss in an introductory way modality we should state the following In contrast to what we did in Fourth Part of Website we here that is in the present investigation do not consider the real world in the sense of just the world around us including ourselves to consist of ontologically different layers If we can discern layers at all these are only complexity layers Indeed organisms are more complex than inorganic things and conscious living beings are more complex than mere animals But now these differences are not considered anymore to be brought about by the appearance of something ontologically new but only by a difference in the degree of material complexity So according to this view the whole real world including inorganic things organisms human beings is ontologically homogeneous And this homogeneous real world is meant when we spoke above and will speak below about the space time world which is only to be contrasted with something like the mathematical world We can also call it the material world This is not meant to refute the theory of ontological Layers as it was laid down in Fourth Part of Website and inspired by HARTMANN 1940 but only to present an alternative view Things like this we have done earlier and the intention simply is to provide the reader with a number of possible different views which he or she then can compare with each other and with his or her own views Only in this way and not by defending during one s whole life only a single view one can I think go forward in philosophy Indeed philosophy should remain a dialogue not an ideology Now let us say something preliminary with respect to the modality or modal structure of the space time world Generally the modality of some given defined world is saying something about the determinative status of its existents which means whether a given existing being feature or event in this world exists by necessity or exists by pure chance that is by coincidence and what it means that a certain being feature or event is possible or impossible for that matter and finally what it means that a certain being feature or event is real or not real for that matter This determinative status is here meant in an ontological sense not in a mathematical sense not in a logical sense not in the everyday sense and also not in an epistemological sense When we speak about the m o d a l i t y here that is in the present investigation we have in mind the modality of the space time world as it and its modality actually is or turns out to be all by itself and totally independent of any knowledge of the things in this world First of all modality refers to here and now existing things features or patterns Such a thing feature or pattern need not to be something having a certain degree of generality here and now existing but can be any thing feature or pattern whether general specific or one off here and now existing in the space time world Of such an existing thing feature or pattern we then ask 1 whether it must then be also possible or 2 whether it exists by pure chance that is without having a cause ground or condition or 3 whether it exists necessarily Discussing the modality of the space time world in a strict philosophical and ontological way is not having in mind a certain thing feature or pattern without pointing to it as existing and then ask 1 whether in the space time world such an imagined thing feature or pattern is possible or 2 whether it can come to exist in the space time world just by pure chance without being caused or conditioned or 3 whether if it is for the sake of theory just taken to exist somewhere in the space time world it exists there necessarily This way of considering modality belongs to everyday life and human planning activities There it is perfectly legitimate and natural But philosophically and especially ontologically discussing and investigating the modality of the space time world means that our point of departure and point of reference is always a thing feature or pattern here and now existing in the space time world where here can be at any one specified location in the universe and now can be any one specified point in time whether in the present in a particular past or in a particular future When in the present the whole discussion sets itself in this present When in the past the whole discussion sets itself in this past When in the future the whole discussion sets itself in this future The following situation is perfectly compatible with the space time world Some specified thing feature or pattern exists somewhere in the space time world while it is not present at some other specified location at the same time This legitimate situation makes it possible to consider not existing as just another modality state in addition to the other ones viz existing possibility necessity and fortuitousness And indeed now having not existing as a modality state we also have impossibility as yet another modality state So the modalities that could presumably be encountered in the space time world are 1 Necessity 2 Existing to be real 3 Possibility 4 Fortuitousness 5 Not existing to be unreal 6 Impossibility We must now investigate whether indeed all six listed modality states can in principle apply in the space time world and what

Original URL path: http://www.metafysica.nl/nature/nomos_1.html (2016-02-01)

Open archived version from archive - nomos II

system as it appears in the Explicate Order How must we visualize such a stabilization Well the initially unstable dynamical system becomes a stable one because the original bundle of sequences of activation of If Then constants as this bundle resides in the Implicate Order comes to lie at the bottom of a valley which has about the shape of a river valley which is rather narrow and when not exactly the same chain of such activations is followed on different occasions but nevertheless closely similar ones then not a particular definite dynamical system and its particular product is stabilized but one or another morphological or physiological type of dynamical system and its product The valley then will look like one that was originally carved out not by a river or stream but by a glacier And such a valley is much broader leaving room for a number of alternative but closely similar dynamical courses together constituting a certain type see next document In dynamical systems theory such a valley narrow or broad is known by the name chreode Of course this is just a metaphor or analogy because in the Implicate Order there are no spatial dimensions and consequently no valleys and the like But the metaphor is powerful and helps us to visualize stability We imagine the bottom of the valley itself gradually sloping down till it reaches the sea When a ball rolls down this valley bottom it will follow it and finally arrive at the sea Moreover when a ball starting to move somewhere up on one of the valley s side walls it will roll down to the bottom of the valley and then following this bottom reach the sea And even when a ball initially rolling neatly over the valley bottom gets a kick causing it to roll sidewards and thus climbing one of the valley s side walls it will quickly return to the valley bottom and proceed its original course that is proceed its course to the sea So the dynamical system has become a stable system because now its course in the Implicate Order lies at the bottom of a valley Said differently but equivalently the system now lies in a chreode The next Figure illustrates such a valley or chreode Figure 5a Several sub chreodes as canalized pathways of change The chreodes correspond to the valleys and lead to more or less particular developmental end points The successive positions of the ball stand for the successive states or substates of a dynamical system Depending on prevailing conditions the system will follow one sub chreode or another According to the ideas developed here the chreodes reside in the Implicate Order but of course not in a spatial form After WADDINGTON 1957 and reproduced in SHELDRAKE 1988 And naturally when the valley is not deep enough or the perturbation is too strong the system will deviate and will not regain its original course And also before the chreode was formed at all the system was unstable when then some state had popped up which although very similar to the corresponding potential state of system A was nevertheless different from that state we would see a different dynamical system let us call it dynamical system B that is different from dynamical system A going its way But as long as the chreode is deep enough and the perturbations not too strong the system will take up its original course and reach its proper end state that is the system will be stable So we have now established that repetition of a bundle of sequences of activation of If Then constants in the Implicate Order that is having this bundle repeatedly visited and passed over has the effect of sinking it down onto the bottom of a valley or chreode and so of making the system stable Now we must investigate how precisely such a chreode or valley is formed in the Implicate Order from an initially flat but slightly sloping landscape completely in terms of If Then constants which we believe to be the ultimate and most basic determinative entities Let us begin with four dynamical states One state is state A n which is a state of dynamical system A The second state to be considered lies on the same world state but is slightly different from the first one It is state B n which is a state of dynamical system B The third state is state A n 1 which is a state of dynamical system A and which comes next to state A n The fourth state to be considered is state B n 1 which is a state of dynamical system B and which comes next to state B n Figure 6 A sequence of consecutive states of dynamical system A and a sequence of conscutive states of dynamical system B Each state consists of a number of conditions and each condition triggers the activation an If Then constant in the Implicate Order leading to its application red line in the Explicate Order Four states are highlighted A n A n 1 B n and B n 1 Each system state activates many different If Then constants simultaneously We will now first follow the fate of only two If Then constants that are activated by corresponding conditions lying somewhere on the states A n and B n Figure 7 The four highlighted system states of the previous Figure A n A n 1 B n and B n 1 Of each of these system states only one condition is highlighted Condition p in system state B n Condition q in system state B n 1 Condition r in system state A n Condition s in system state A n 1 Condition p triggers the activation and application red line of the If Then constant ALPHA resulting in the condition q Condition r triggers the activation and application red line of the If Then constant BETA resulting in the condition s The If Then constant ALPHA could look like this Figure 8 The If Then constant ALPHA If one of the conditions listed in the If term discs drawn on a circle happens to exist in the Explicate Order then the If Then constant ALPHA is activated and applied and the condition q appears in the Explicate Order And thus more specifically when condition p happens to exist in the Explicate Order the If Then constant ALPHA is indeed activated and applied resulting in the condition q appearing in the Explicate Order The If Then constant BETA could look like this Figure 9 The If Then constant BETA If one of the conditions listed in the If term discs drawn on a circle happens to exist in the Explicate Order then the If Then constant BETA is activated and applied and the condition s appears in the Explicate Order And thus more specifically when condition r happens to exist in the Explicate Order the If Then constant BETA is indeed activated and applied resulting in the condition s appearing in the Explicate Order If these two If Then constants remain what they are then the existence of condition r of state A n of dynamical system A will lead to the appearance of condition s of state A n 1 of that same dynamical system A Further the existence of condition p of state B n of dynamical system B will lead to the appearance of condition q of state B n 1 of that same dynamical system B So in this setting dynamical system A and also dynamical system B is unstable when we imagine that all remaining If Then constants involved in states A n and B n behave in the same way that is in a completely comparable way However things become different when If Then constants are allowed to change Let us first consider If Then constant ALPHA We assume that condition p has disappeared from that constant s list of conditions So the If Then constant now looks like this Figure 10 The If Then constant ALPHA after it has changed The condition p has disappeared from the If term s disjunctive list of conditions So when condition p happens to exist in the Explicate Order it will at least as it concerns this particular If Then constant not lead to the appearance of condition q in the Explicate Order Let us further consider If Then constant BETA Here we assume that condition p is added to the constant s list of conditions So the If Then constant now looks like this Figure 11 The If Then constant BETA after it has changed To the constant s list of conditions the condition p is added So when the condition p happens to exist in the Explicate Order then If Then constant BETA instead of ALPHA is activated leading to the appearance in the Explicate Order of condition s Said in a more detailed way when the condition p which is a condition lying on state B n which state lies outside the series of states of the original dynamical system A exists in the Explicate Order it will nevertheless not lead to the appearance of condition q but to the appearance in the Explicate Order of condition s which lies on the state A n 1 And this state belongs to the original series of states of dynamical system A And of course when condition r comes to exist in the Explicate Order instead of condition p the condition s will also appear in the Explicate Order because condition r is still listed in the constant s If term So here as far as one If then constant is reckoned with we can say when a condition p deviating from the corresponding condition r in state A n and so deviating from the original state series of dynamical system A appears instead of condition r in the Explicate Order the dynamics nevertheless returns to this original series The system is stable See next Figure Figure 12 Determinational activity of the original If Then constants ALPHA and BETA left half of Figure and of the changed If Then constants right half of Figure After these constants have changed as specified above condition p no longer leads to condition q but to condition s And if instead of condition p condition r prevails or any other of the conditions listed in the If term of the changed BETA constant then also condition s will appear in the Explicate Order But of course a system state that is any one system state does not involve only one If Then constant but many of them When one such a system state comes to exist in the Explicate Order a whole set of If Then constants is activated and applied Now if we assume that also these other relevant If Then constants change in a corresponding way then indeed when instead of state A n state B n comes to exist the dynamics nevertheless returns to the original series of states of dynamical system A Dynamical system A has become stable We illustrate this by adding in Figure 12 another pair of If Then constants an original one and this one as changed Figure 13 Determinational activity of original If Then constants left half of Figure and of changed If Then constants right half of Figure The Figure is the same as Figure 12 but now a second pair of If Then constants is added We here only consider the second pair After these two constants have changed in the same way as the original pair discussed earlier condition d no longer leads to condition e but to condition g And if instead of condition d condition f prevails or any other of the conditions listed in the If term of the changed If Then constant then also condition g will appear in the Explicate Order Having shown the stabilization of the dynamical system with respect to a single deviating state in terms of just four If Then constants it is clear how to deal with it in terms of the complete set of If Then constants involved in such a single deviating state and consequently at the same time also in terms of all the If Then constants involved in the complete set of all possible deviating states Where does such a deviating state come from In the context of the original series of states together forming the original unstable dynamical system we can say that the deviating state is a local perturbation of that original dynamical system If for this dynamical system already a chreode has been formed as a result of alteration of the If Then constants involved the system will return from the deviating state to its original series of states that is the system will recover from the perturbation We now will attempt to describe the event of perturbation itself that is to describe from where such a perturbation actually came completely in terms of If Then constants A perturbation of dynamical system A just to give that system a label must be seen as a fusion of one particular state of that dynamical system with some particular state of another dynamical system B At first the systems A and B were running relatively on their own that is relatively independently of each other they are never completely independent of each other nevertheless they will more or less gradually approach each other and when they actually meet or collide their respective system states fuse Such a gradual approaching followed by a fusion of two systems might be illustrated with the case of two material bodies moving in space and approaching each other until they meet Figure 14 The encounter of two moving material bodies in space representing two dynamical systems A and B as a model of perturbation Following this Figure dynamical system A consists of a successive series of system states of which state A n A n 1 A n 2 A n 3 are depicted Each such a state is a state or condition in which the material body pictured by a green disc finds itself at a certain point in time namely 1 the velocity speed and direction of motion of that body at that point in time and 2 its spatial position at that same point in time In the same way dynamical system B consists of a successive series of system states of which state B n B n 1 B n 2 B n 3 are depicted Each such a state is a state or condition in which the second material body pictured by a blue disc finds itself at a certain point in time namely 1 the velocity speed and direction of motion of that body at that point in time and 2 its spatial position at that same point in time Further each state is a part of the corresponding complete world state state A n and state B n are among the many parts of the world state W m state A n 1 and state B n 1 are among the many parts of the world state W m 1 state A n 2 and state B n 2 are among the many parts of the world state W m 2 state A n 3 and state B n 3 are among the many parts of the world state W m 3 and so on Despite the fact that state A n is just a mere part of world state W n and also despite the fact that state B n which is simultaneous with A n is also just a mere part of that same world state these simultaneous states A n and B n are ex hypothesi relatively independent of each other Approximately the same goes for the simultaneous states A n 1 and B n 1 the simultaneous states A n 2 and B n 2 and the simultaneous states A n 3 and B n 3 although during this sequence of pairs of states the mutual dependency between every two simultaneous states gradually increases until finally the two states merge into one single state A n 4 B n 4 The perturbation of dynamical system A by the dynamical system B which we can also describe as the perturbation of dynamical system B by dynamical system A is precisely embodied by this fusion of two simultaneous states into one single state In all this we must realize that the earlier pairs of simultaneous states are in a way also fused because they are part of the same world state but this fusion is fairly weak In contrast with that the final fusion namely that of the states A n 4 and B n 4 is not just some loose or weak fusion but a strong fusion that is a complete integration of the two states resulting in one single new state What state comes next is totally dependent on this single new state In fact we can express things in a more compact way Until the point in time corresponding with the production of the simultaneous states A n 4 and B n 4 and thus corresponding with world state W m 4 we have two dynamical systems A and B both consisting of one moving material body So in total we have two moving material bodies But at the point in time corresponding to the world state W m 4 we have in total only one moving material body because the original two have dynamically fused and integrated in such a degree that one single dynamic entity embodying one single dynamic state has resulted With this model of perturbation in mind we will now attempt to describe the perturbation of one dynamical system by another in terms of If Then constants For this we must analyze each system

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