The Oxford Handbook of Metaphysics offers the most authoritative and compelling guide to this diverse and fertile field of philosophy. Twenty-four of the world's most distinguished specialists provide brand-new essays about 'what there is': what kinds of things there are, and what relations hold among entities falling under various categories. They give the latest word on such topics as identity, modality, time, causation, persons and minds, freedom, and vagueness. The Handbook's unrivaled breadth and depth make it the definitive reference work (...) for students and academics across the philosophical spectrum. (shrink)

Must we choose between reducing material substances to collections of properties, a’ la Berkeley and Hume or positing bare particulars, in the manner of Locke? Having repudiated the notion that a substance could simply be a collection of properties existing on their own, is there a viable alternative to the Lockean notion of a substratum, a being essentially devoid of character? E.J. Lowe and Michael Loux would answer here in the affirmative. Both recommend hylomorphism as an upgrade on the (...) metaphysics of the British empiricists: treating a material substance as its essential 'form,' this embodied 'substance' universal being, in turn, the substratum in which its 'accidents' inhere. Here, I evaluate this Aristotelian metaphysics, identifying the advantages it enjoys over the empiricist's alternatives pertaining to dependence, unity, identity, change, and the distinction between essential and accidental properties. I also develop solutions to the two problems that Loux sees it posing. (shrink)

Neste capítulo, Loux apresenta alguns problemas com relação às modalidades e algumas das relações entre elas e o vocabulário dos mundos possíveis, expondo as duas principais posições ontológicas com relação a tais mundos e às modalidades e com relação à natureza das modalidades, a saber, o possibilismo e o actualismo, defendidos respectivamente por Lewis e Plantinga. Essas são teorias inconsistentes entre si, que intentam nos dizer se os mundos possíveis são concretos ou abstratos e se existe algo além do (...) que é actual. (shrink)

Philosophy, that most misunderstood of intellectual pursuits, is often mocked; and no part of philosophy is as often mocked as metaphysics. The image of the ‘speculative metaphysician’ dreaming up abstract pictures of the world has been held up for ridicule by poets, playwrights, novelists, journalists as well as by other philosophers. The Logical Positivists in the first half of the 20th Century rejected all metaphysical speculations as ‘meaningless’ since they could not be verified by scientific experiment; in the later part (...) of the century, Wittgenstein criticised systematic metaphysics as being a kind of intellectual disease resulting from our reading false pictures of the world into the grammar of our language. The common suspicion underlying many of these attacks is that ultimately, all metaphysics is a kind of nonsense, and that metaphysicians don’t really know what they are talking about. This suspicion is not new. Nicolas-Sébastien Chamfort commented in 1796, ‘I am tempted to say of metaphysicians what Scaliger used to say of the Basques: they are said to understand one another, but I don’t believe a word of it.’ Some contemporary philosophers may agree. (shrink)

Initially introduced to the philosophical world as elusive, we-know-notwhats—substrata underlying the properties had or exemplified by things, but themselves bereft of properties—bare particulars have been dismissed as undetectable, unnecessary, and even incoherent. Hardly a warm welcome. It appears, however, that times are changing. In a recent series of articles, for example, J. P. Moreland has argued that “bare particulars are crucial entities in any adequate overall theory of individuation”;’ that is, concrete particulars cannot be individuated without them. In the same (...) vein, Oaklander and Rothstein,2 drawing upon elements of Moreland’s new theory, have defended bare particulars against Loux’s grounding objection’—that if the theory is correct, bare particulars are qualitatively indiscernible; in which case we either have no basis for saying that they arc numerically diverse, or we must introduce lower-level substrata to ground that diversity, thereby raising the spectre of an infinite regress of individuators. (shrink)

1. The Bundle Theory I shall discuss is a theory about the nature of substances or concrete particulars, like apples, chairs, atoms, stars and people. The point of the Bundle Theory is to avoid undesirable entities like substrata that allegedly constitute particulars. The version of the Bundle Theory I shall discuss takes particulars to be entirely constituted by the universals they instantiate.' Thus particulars are said to be just bundles of universals. Together with the claim that it is necessary that (...) particulars have constituents, the fundamental claim of the Bundle Theory is: (BT) Necessarily, for every particular x and every entity y, y constitutes x if and only ify is a universal and x instantiates y. 2 The standard and supposedly devastating objection to the Bundle Theory is that it entails or is committed to a false version of the Principle of Identity of Indiscernibles (Armstrong 1978: 91, Loux 1998: 107), namely: (Pll) Necessarily, for all particulars x and y and every universal z, if z is instantiated by x if and only if z is instantiated byy, then x is numerically identical with y. The most famous counterexample to the Identity of Indiscernibles is that put forward by Max Black, consisting of a world where there are only two iron spheres two miles apart from each other, having the same diameter, temperature, colour, shape, size, etc (Black 1952: 156). Let us from now on think of the properties of the spheres in this world as universals. The possibility of this world, which I shall hereafter refer to as 'Black's world', makes (Pll) false.' And according to common philosophical opinion this means that the Bundle Theory is false.. (shrink)

In this paper I explore Michael Loux’s important distinction between “tropes” and “tropers”. First, I argue that the distinction throws into relief an ambiguity and discrepancy in the literature, revealing two fundamentally different versions of trope theory. Second, I argue that the distinction brings into focus unique challenges facing each of the resulting trope theories, thus calling into question an alleged advantage of trope theory—that by uniquely occupying the middle ground between its rivals, trope theory is able to recover (...) and preserve the insights of these views. Ultimately, the distinction suggests that trope theory is a divided house. (shrink)

The concept of universal in Aristotle’s philosophy has several aspects. 1) Universal and plurality Aristotle posits universal (καθόλου) versus particular (καθ᾿ ἕκαστον) each covering a range of elements: some elements are universal while others are particulars. Aristotle defines universal as ‘that which by nature is predicated (κατηγορεῖσθαι) of many subjects’ and particular as ‘that which is not’ so. (OI ., I, 7, 17a38-b1) The plurality of possible subjects of universal is what Aristotle insists on. The inclusion of the notion of (...) ‘plurality’ in the definition of universal might make us expect to have ‘singularity’ in the definition of particular. So, when Aristotle says that universal is that which is naturally predicable of many subjects, we expect him to define the particular as ‘that which is predicable of one subject only.’ Nonetheless, Aristotle does not and indeed cannot define it this way. We cannot find a text in which he defines particular as such simply because particulars are not predicable of any subject unless we regard their predication of themselves a predication, which Aristotle does not, at least in a genuine sense. Thus, he defines a particular only negatively. Hence, the capability of predication of a plurality is indeed the capability of predication itself because the particular cannot be predicated of anything. A particular is that which cannot be predicated of anything (or: of anything else, if saying of a thing of itself is to be considered as predication). It is ‘numerically one’ and what of which the universal is predicated (Met., B, 999b34-1000a1). Those that cannot be predicated of anything, or particulars, are of two kinds: primary substances and individual accidents. Besides Categories we can hardly find a text where Aristotle discusses individual accidents maybe because they are of much less importance for him compared with substances. However, substances are what he mentions repeatedly so that we can confine particulars to substances. In fact, it is substance that Aristotle considers so repeatedly as what cannot be predicated. As the main particulars and individuals, substances are posited as the main things that are not universal. The closeness of the two concepts of ‘substance’ and ‘unpredicability’ is to the extent that he ignores individual accidents and makes these concepts equal and as the opposite of universal: ‘what is not predicated of a subject is said a substance (οὐσία λέγετα τὸ μὴ καθ᾿ ὑποκειμένου) but what is always said of some subject is called a universal.’ (Met., Z, 1038b15-16. cf. Met., B, 1003a7-9) Therefore, since particulars cannot be predicated of any subject and, thus, every predication is necessarily a predication of a plurality of subjects, the inclusion of ‘plurality’ in the definition of universal is either i) in the sense of ‘representation’ or it must be regarded as ii) an unnecessary addition mentioned just for clarification or iii) only for avoiding cases where something is predicated of itself. By the first we mean this: though a substance is not said of anything, it represents some one thing and there is some one thing that is that substance. A universal, on the other hand, can represent a plurality of things. There is, however, a third possibility that has no essential difference with the sense of representation. Aristotle might have ‘arbitrary predication’ in mind when he suses ‘plurality’ in the definition of universal: while a particular can be the arbitrary predicate of just one thing, a universal can be predicated, both really and arbitrarily, of many things. Whatever Aristotle’s intention was, what is important for our investigation is this: Aristotle uses the notion of plurality in the definition of universal in spite of the fact that it is not necessary. What this implies is that this notion is so important for Aristotle that albeit every predictability is a predictability of a possible plurality, he adds the notion of plurality. What makes this notion important, I believe, is that he has something like a class in mind when he defines a universal because the notion of plurality is indistinguishable from a class. 2) Universal and whole; particular and part In Aristotle, the concepts of universal and whole are so close: ‘That which is true of a whole class and is said to hold good as a whole (which implies that it is a kind of whole) is true of a whole in the sense that it contains many things by being predicated of each, and that each and all of them, e.g. man, horse, god, are one because all are living things (τὸ μὲν γὰρ καθόλου καὶ τὸ ὃλως λεγόμενον ὡς πολλὰ περιέχον τῷ κατηγορεῖσθαι καθ’ ἑκάστου καὶ ἓν ἃπαντα εἶναι ὡς ἑκαστον, ...). Phil Corkum points to Aristotle’s distinction between quantitative and integral wholes in Met., 5, 26, 1023b26-33 where a quantitative whole is called homoiomerous, as the sum of animal while an integral whole, e.g. a house, is called heteromerous. He links the notion of homoiomerous to the notion of indivisibility of individuals (in 1b6-9 and 3b10-18) and indivisibility of universals. He believes that in PrA., I, 4, 25b32-26a2 it is the transitivity of mereological containment that is discussed. 3) Universal is common between instances Universal is common (κοινόν) between all the plurality of subjects it can be predicated of because what belongs to more than one thing must be common between them. (Met., Z, 1038b10-12) In the Same way, what is common cannot be a particular and, thus, a substance. (Met., Z, 1040b23-24) An individual or substance is a ‘this’ and a ‘this’ cannot be what common indicates simply because it is here in ‘this’ and can be nowhere else while common must be common between several things. In fact, what can be indicated by a common is indeed a ‘such.’ (Met., B, 1003a7-9) 4) Universal is the same in its instances We have a universal i) in all of its instances and ii) in the same way (ταὐτὸ ἐπὶ πὰντων). (Met, Γ, 1005a9-10) While the first point is evident (otherwise how could it be their universal?), the second point might seem not only ambiguous but the cause of many problems. For Aristotle, therefore, a universal must be ‘one’ in number and not many. This numerically one universal is the very universal for all its instances. It is the same universal that is predicated on each of its instances. This sameness is not, however, a mere homonymous sameness or the sameness of a homonymous word. All these three points, namely oneness, sameness and rejection of mere homonymous sameness are asserted in Aristotle’s own words τι ἕν καὶ τὸ αὐτὸ ἐπὶ πλειόνων μη ὁμώνυμον. (PsA., A, 11, 77a8-9) This non-homonymous unity is asserted also in PsA., A, 24, 85b15-16. 5) Universal as predicate Contrary to substance that cannot be a predicate, universal is what cannot be prevented from being in the place of predicate. Therefore, Aristotle distinguishes universal from subject because while the latter must necessarily be capable of being a predicate, though it might take the position of subject as well, the latter does not necessarily have such a capability especially when it is a this because it cannot be a predicate in such a case: ‘For the subject and universal differ in being or not being a ‘this’; like man and body and soul are the subject of accidents while the accident is something like musical or white.’ (Met., Θ, 1049a27-30) This indicates that a universal is basically different from subject and although it can be posited in the place of subject, it is the position of predicate that is its position as a universal. In Metaphysics, Z, 13, Aristotle asserts that ‘no universal can be substance.’ The same is asserted in Met., I, 1053b16-17 cf. 1060b21. As James H. Lesher points out, Aristotle’s position is that ‘nothing predicated universally is a substance.’ 6) Universal in substance In Met., 10388b8-9 Aristotle says that no universal is a substance. While a universal cannot be a substance in the way essence (to ti en einai) is, it is, Aristotle asserts, ‘in’ it (ἐν τούτῳ δὲ ἐνυπάρχειν) (Met., Ζ, 1038b16-18). Aristotle’s examples are: animal in man and horse. A universal is ‘in’ the thing it is its universal. But in what sense a universal can be in a thing? It cannot be in it as ‘in a subject’, which is denied in Categories for secondary substances. If we check the senses of being in, we can find some other senses of ‘being in’ some of which are compatible with this sense of ‘being in.’ Michael J. Loux believes that contrary to his earlier works like Peri Ideaon and Organon in which the immanence of universals signals a reproduction of the platonic two worlds picture, in his later works like Physics and Metaphysics, when Aristotle tells us that universals are in particulars he means that they are ‘components of or ingredients in sensible particulars.’ In Metaphysics (Δ, 1014b3-9) Aristotle compares elements with universals and call them ‘the most universal things because elements are present either in all or in many things. 7) Logos is of universal Not only universals have logos (Met., Z, 1038b18-19) but ‘Every logos and every science is of universals and not of particulars.’ (Met., K, 1059b25-26) The reason is that they are the same: the logos of the unjiversal ‘circle’ is nothing but ‘being circle’ and the logos of the universal ‘soul’ is ‘being soul.’ (Met., Z, 1035b33-1036a2) The same is said about definition. (Met, Z, 1036a27-29) 8) Universal: in the soul Contrasting individuals, universals are in the soul (So., 3, 5, 417b22-23; cf. PsA., B, 19, 100a6-7). Aristotle also says that the form, i.e. the essence, of the artwork is in the soul. (met., Z, 1032a32-b2) Moreover, as Michael J. Loux points out, ‘the Peri Ideon tells us that we need universals to serve as the objects of noetic acts.’ 9) Universal: not beside individual In spite of the fact that demonstration creates the opinion that demonstrating is based on the existence of universals as existing among the existing things, they do not have existence besides individuals (PsA., A, 24, 85a31-35; Met, Λ, 1071a19-23). Aristotle believes that universals of a P-series (B203, 71) are not παρὰ τὰ εἴδη: 999a6ff. Also check De Anima, II, 3, 414b20-25 10) Primary or commensurate universal Aristotle distinguishes ‘πρῶτον καθόλού’ (PsA., B, 17, 99a33-35) literally meaning ‘primary universal’ but mostly, and truly, translated as commensurate universal. While a universal merely ‘μὴ ἀντιςτρέφει,’ a primary universal ‘ᾧ ἓκαςτον μὲν μὴ ἀντιςτρέφει’ (PsA., B, 17, 99a33-35). Aristotle mentions three conditions for a commensurate universal. It is an attribute that i) belongs to every instance of its subject (without exception!!!), and this belonging is ii) essentially and iii) qua that subject itself (ᾗ αύτό). (PsA., A, 4, 73b26-28) However, he insists that the second and the third conditions are indeed the same. (PsA., A, 4, 73b28-30) The first condition he paraphrases as ‘to belong to any random instance of that subject’ and the second and the third as ‘when the subject is the first thing to which it can be shown to belong.’ (PsA., A, 4, 73b32-74a3) Aristotle’s example is ‘the equality of its angles to two right angles’. This attribute is not a commensurate universal of figure due to the first condition: it cannot be demonstrated of any figure. Nonetheless, though it can be demonstrated of every isosceles because every isosceles has angles equal to two right angles, it is not a commensurate universal of isosceles due to the other conditions: it is not predicated of isosceles qua isosceles but qua triangle. These conditions seem to be like regulators: they organize everything to match to the right group. The method of finding commensurate universal is like test and error method based on elimination: you must eliminate each of the higher or lower universals and check if the attribute remains or not. The commensurate universal is that which remains in between eliminated universals. (cf. PsA., A, 5, 74a37-b4) Brad Inwoodpresents an understanding of commensurate universal that is different from what I have understood and, thus, must be checked: ‘These universals are propositions in which, for example, ‘all A are B’ is true and which are still true universal statements if converted: ‘all B are A’ is also true.’ -/- . (shrink)

Predication is a lingual relation. We have this relation when a term is said (λέγεται) of another term. This simple definition, however, is not Aristotle’s own definition. In fact, he does not define predication but attaches his almost in a new field used word κατηγορεῖσθαι to λέγεται. In a predication, something is said of another thing, or, more simply, we have ‘something of something’ (ἓν καθ᾿ ἑνὸς). (PsA. , A, 22, 83b17-18) Therefore, a relation in which two terms are posited (...) to each other in a way that one is said (predicated) of the other is a predication. The term of which the other term is said is called a subject (ὑποκειμένον) and the other, which is said about the subject, is called the predicate. Thus, in a predication the predicate is predicated of the subject; given that being predicated is almost as the same as being said. The relation between being said and being predicated is so close that ‘if something is said of a subject both its name and its definition are necessarily predicated of the subject.’ (Cat., 5, 2a19-26) This, however, is true only about the second genera and not the accidents. a) Nature of relation in predication What is Aristotle’s theory about the nature of the relation in a predication? How does he fundamentally understand this relation? Phil Corkum distinguishes between predication logic and traditional term logic and argues that the relation between subject and predicate in Aristotle is of the latter kind. While in predicate logic, subjects and predicates have distinct roles, they have the same role in traditional term logic. In predication logic, subjects refer, but predicates characterize. Thereupon, a sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. In traditional term logic, both subjects and predicates refer and a sentences expresses a truth if both name one and the same thing. He concludes that Aristotle ‘problematically conflates prediction and identity claims’ because while he thinks both subjects and predicates refer, he would deny that a sentence is true just in case the subject and the predicate name one and the same thing. Based on this, Corkum believes that Aristotle’s core semantic is not identity but the weaker relation of constitution, which is a mereological interpretation: ‘All men are mortal’ is true just in case the mereological sum of humans is part of the mereological sum of mortals. b) Aristotle’s theory of predication: one or two theories? Frank Lewis finds an inconsistent gap between the theory of predication in the Categories and that in the later books of the Metaphysics VII, 6. So too Joan Kung, Terry Irwin, Daniel Graham. c) Distinction of ‘being said of’ and ‘being in’ Owen enumerates the texts in which Aristotle’s distinction between ‘being said of’ and ‘being in’ is asserted: OI. 11b38-12a17; To., 127b1-4; Cat. 1a20-b9; 2a11-14; 2a27-b6; 2b15-17; 3a7-32; 9b22-24 d) Predication in Aristotle and the standard ‘S is P’ Marie De Rijk Lambertus thinks that the ‘S is P’ pattern is misleading when it comes to express predication in Aristotle. In his view, ‘The Aristotelian procedure should be described in terms of appositively assigning an attribute (κατηγορούμενον) to a substrate (ὑποκείμενον), rather than ascribing a predicate to a subject by means of a copula…. The comment should be considered an attribute which is said to fall to a substrate, without understanding this procedure in terms of sentence predication.’ e) Aristotle’s predication: bipartite or tripartite? It is a difficulty to make Aristotle’s theories of name-verb predication and tripartite predication consistent. The reason is that tripartite is not consistant with his name-verb structure based on which he says that the predicate term is the ‘verb.’ (20a31; 20b1-2; 16a13-5) The problem is that in a tripartite form like ‘Socrates is white’ we cannot take ‘is white’ as the verb because, based on Aristotle himself, no part of a verb can be significant itself. (16b6-7) However, his assertions about the equivalences between the two structures (OI. 12, 21b9-10; PrA. 51b13-16; Met., 1017b22-30) must mean that they are not inconsistent in his own view. Thus, as Allen Bāck points, ‘Aristotle seems to think that he has a single, consistent theory.’ The sense of saying or speaking as the root sense of rhema makes the relation between predication (saying something of something) and verb more interesting. The use of rhema in the sense of a long expression approves this. In Plato’s work (399ac) where Socrates claims that the name anthropos derives from anthron ha opopen (‘he who examines what he has seen’) we have an onoma from, or in place of, a rhema. 1) Subject The subject (ὑποκειμένον) is that of which another term is said or predicated. Aristotle’s own definition is of a much more philosophical value: ‘By subject I mean that which is expressed by an affirmative term (λέγω δὲ ὑποκείμενον τὸ κάταφάσει δηλούμενον).’ (Met., K, 1067b18) Throughout Aristotle’s work, three kinds of subjects can be found: possible, prime and absolute subject. a) Possible subject Those things that can take the position of a subject in a predication we call possible subjects, no matter they can or cannot take the position of predicate in any predication. All terms except the ultimate predicates are possible subjects because they can take the position of subject. b) Prime subject Those that in any predication can only take the position of a subject and not the position of a predicate are prime subjects. (Cat., 5, 3a36-b2; Met., Z, 1028b36-1029a1) This is the truest sense of subject and belongs only to substances. (Met., Z, 1029a1-2) In fact, ‘that which is not predicated of a subject, but of which all else is predicated’ is a substance. (Met., Z, 1029a7-9) In Categories, besides primary substances (Cat., 2, 1b3-6), individual qualities are also said not to be able to be said of anything else. (Cat., 2, 1a23-29) Aristotle’s examples are a certain ‘knowledge-of-grammar’ (τὶς γράμματικὴ) and ‘an individual white’ (τὸ τὶ λευκὸν). Thus, although substances are indeed in the truest sense individuals and, thereby, in the truest sense primary subjects, other individuals can take the position of subject as well. c) Absolute subject While substances are prime subjects of all other things, there is still something of which substances can be predicated and this predication is not an accidental predication: matter. (Met., Z, 1029a21-24) This predication is, indeed, the predication of a ‘form or this’ on matter and material substance. (Met., Θ, 1049a34-36) The only thing that is absolutely a subject, therefore, and can be a predicate is prime matter (πρώτη ὓλη). (Met., Θ, 1049a24-27) d) Subject and substance The most important thing in being a substance is being a subject: ‘It is because the primary substances are subjects for all the other things and all the other things are predicated of them or are in them, that they are called substances most of all.’ (Cat., 5, 2b15-17) And what is nearer to this position is more a substance as a species is more a substance than a genus.’ (Cat., 5, 2b7-8) e) Primary versus accidental subject A subject is a primary subject in a predication when the predicate is predicated of it as itself. In such a case, the subject is the subject of the predicate qua itself and not qua something else. A subject, on the one hand, is an accidental subject when it is not the primary subject of the predicate that is predicated on it. It means that a subject is an accidental subject when the predicate is predicated of it not qua itself but qua something else. An accidental subject is, therefore, anything other than a substance. 2) Predicate as universal It is evident from our discussion of kinds of subjects that except matter, primary substances (if we ignore both accidental predication and cases of absolute subjects) and other individuals, everything else can take the position of a predicate. Since primary substances are individuals, it results that everything except matter and individuals are capable to take the position of predicate. The immediate consequence of this is that the predicate must be a universal. When individuals cannot take the position of predicate, this position cannot be taken by any particular. Therefore, only universals can be predicated of others. Moreover, albeit universals can be a simple subject (for another universal), they are not prime subjects. The closeness of universal and predicate is to the extent that Aristotle differentiates universal from subject. (Met., Θ, 1049a27-30) 3) Categories or classes of predicates Aristotle distinguishes ten highest classes into one of which each predicate must necessarily fall: substance (or what a thing is), quality, quantity, relation, place, time, position, state, activity and passivity. (Cat., 4, 1b25-27; To., I, 9, 103b20- ; PsA., A, 22, 83b13-23) The substance counted among predicates must refer to secondary and not primary substances not only because Aristotle insists that primary substances cannot be predicated but also from his own examples of the category of substance: man and animal. (To., I, 9, 103b25) However, if a predicate be asserted of itself or its genus be asserted of it, the predicate signifies substance or what is; but if ‘one kind of predicate is asserted of another kind,’ it signifies one of the other nines. (To., I, 9, 103b30) These categories are so comprehensive that no predicate can remain outside them so that even non-being has as many senses as categories. (Met., M, 1089a26-30) a) That whether Aristotle’s categories are merely linguistic or fundamentally ontological is a so much controversial dispute. Some like G. E. R. Lloyd believe that ‘categories are primarily intended as a classification of reality … rather than of the signifying terms themselves.’ b) Although Aristotle’s categories have been historically regarded as a classification of predications, there are some recent commentators like Jonathan Barnes that think it is classifying predicates and not predications. 4) Kinds of predicates In his introduction of Categories, as J. W. Thorp truly points out , Aristotle distinguishes between the category of substance and the other categories using μὲν ... δὲ construction. This construction illustrates that beside tenfold classification of categories, there is an even more crucial differentiation between two kinds of predicates: substance or what is on the one hand and the other nine ones on the other hand: the distinction between what is predicated of the subject as what it is and what is predicated of it as an accident. Therefore, we have three kinds of classification - a twofold, a fourfold and a tenfold-complicatedly classifying the same thing, viz. the predicate. Predicates can be divided also to four kinds: property, definition, genus and accident. (To., I, 4, 101b11-20) A property is that predicate that is convertible with its subject and does not signify its essence. A definition is that predicate that is convertible with its subject and signifies its essence. It is a genus if it is not predicated convertibly and is contained in the definition of its subject. And it is an accident if it is neither convertible nor contained in the definition of its subject. (To., I, 8, ^103b3) All of these four kinds are among categories. (To., I, 9, 103b20) It seems that there might be some kind of relation between the twofold and the fourfold distinction: whereas genus and definition are predicated as what it is, accidents are not so predicated. There seems to be some rules that determine to each of these four kinds each predicate belongs. At To., IV, 123b30ff. Aristotle asserts: ‘If B has a contrary and A does not, then B does not belong to A as its genus.’ There is a dispute around per se accidents (τὰ καθ’ αὑτὰ συμβεβηκότα) (Topics., 102a18) whether they must be regarded as either of the four kinds or as a fifth kind. Barnes (1970) argued that they ‘do not fit at all neatly into the fourfold classification.’ He argues that based on the definition of accidents at A, 5, 102b4-5, they must be accidents but based on another definition, A, 5, 102b6-7, they cannot be accidents. He also defends the view that they are not properties. Barnes concludes: ‘This shows that the two definitions are not equivalent, and hence that the ‘predicables’ are not well-defined.’ Demetris J. Hadgopoulos defends the view that the two definitions of accidents are equivalent and per se accidents are properties. 5) Five types of predications We have five kinds of predications based on our division of subjects and our discussion of predicates: simple, primary (itself divided to substantial and accident), accidental (itself divided to primary and secondary), aoincidental and absolute predication. a) Simple predication. This is a predication in which a universal is predicated of either a particular or a universal subject. This sense of predication includes all other senses except the first kind of accidental predication. b) Primary predication. This is a predication in which a universal is predicated of a primary subject, namely a substance. A primary predication is of two kinds: i) Substantial predication. A primary predication in which the predicate is part of, or is included in, the definition of the subject. The universal that is the predicate here is the definition or the genus or the species or the diferentia of the subject. It is this predication that Aristotle calls a unity: ‘A statement may be called a unity … because it exhibits a single predicate as inhering not accidentally in a single subject.’ (PsA., B, 10, 93b35-37) It is only substantial predicates that can be predicated of each other: ‘Predicates which are not substantial are not predicated of one another.’ (PsA., A, 22, 83b18-19) Aristotle defines a substantial predication also in another way. A predication in which a higher genus is predicated on a lower genus, species, a substance or an individual, (or a species is predicated on an individual) is a substantial predication. Therefore, a substantial predication is a predication in a series that has individuals on one of its ends and a general category on its other end. In fact, only substantial predicates can be predicated of one another. (PsA., A, 22, 83b17-19) This series cannot be an infinite series because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) -/- ii) Accident predication. A primary predication in which the predicate is not part of, or is not included in, the definition of its subject. The universal that is the predicate here is the property or the accident of the subject. c) Accidental predication. This is a predication in which the subject is not a primary subject and its predicate is a substance. This predication is of two kinds: i) Primary accidental predication. This is a predication in which an accident is predicated of substance. Such a predication can go ad infinitum, which is inferable from Aristotle’s assertion that the secondary accidental predication cannot go ad infinitum. ii) Secondary accidental predication. It is a predication in which an accident is predicated of another accident. Such a predication, Aristotle asserts, cannot go ad infinitum because even more than two accidents cannot be combined. Now what is the meaning of Aristotle’s assertion that we cannot continue this ad infinitum? Does it mean that we cannot continue the predication ‘The musician is white’ and say ‘The white is Athenian?’ But why not? Or maybe he means that by adding any predication, we are still in a condition of predicating two accidents of a substance on each other. -/- As primary subjects, substances can also take the position of predicate though not essentially but accidentally. In propositions like ‘the white is a log’ or ‘That big thing is a log’ we observe substance taking the position of predicate but this is only accidentally: ‘When I affirm ‘the white is a log,’ I mean that something which happens to be white is a log- not that white is the subject in which log inheres (οὐχ ὡς τὸ ὑποκείμενον τῷ ξύλῳ τὸ λευκόν ἐστι), for it was not qua white or qua a species of white that the white (thing) came to be a log (οὔτε λευκὸν ὄν οὔθ᾿ ὃπερ λευκόν τι ἐγἐνετο ξύλον), and the white (thing) is consequently not a log except incidentally.’ (PsA., 22, 83a3-9) Aristotle compares this accidental use of substance in the position of predicate with the substantial use of it in the place of a subject: ‘On the other hand, when I affirm ‘the log is white,’ I do not mean that something else, which happens to be a log, is white (οὐχ ὃτι ἓτερόν τί ἐστι λευκόν, ἐκείνῳ δὲ συμβέβηκε ξύλῳ εἶναι), (as I should if I said ‘the musician is white,’ which would mean ‘The man who happens also to be a musician is white’); on the contrary, log is here the subject- the subject which actually came to be white, and did so qua wood or qua a species of wood and qua nothing else.’ (PsA., 22, 83a8-14) Aristotle asks us not to call propositions like ‘The white is a log’ a predication at all or at least call them accidental predication instead of simple (ἁπλως) predication. (PsA., A, 22, 83a14-17) An accidental predication, in which we have a substance in the place of predicate, is different from an essential predication in that while the subject of an accidental predication is said to be the predicate not by itself but as something different with which it coincides, the subject of an essential predicate is said to be the predicate by itself and not because it is something else: ‘Since there are attributes which are predicated of a subject essentially and not accidentally- not, that is, in the sense in which we say ‘That white (thing) is a man,’ which is not the same mode of predication as when we say ‘The man is white’: the man is white not because he is something else but because he is man, but the white is man because ‘being white’ coincides with ‘humanity’ within one subject. Therefore, there are terms such as are essentially subjects of predicates. (PsA., A, 19, 81a24-29) This capability of ‘non-essentially and only accidentally’ being a subject does belong, in fact, to all sensible things. (PsA., A, 27a32-36) d) Coincidental predication. this is a predication in which none of the subject and predicate are a substance or an individual. In this predication, one of the accidents of a substance or individual is predicated of one of the other accidentals of the same substance or individual. For example, when it is said that ‘The white is musical,’ there is an individual, say Socrates, for which both of white and musical are accidents. e) Absolute predication. This is a predication in which a form or a substance is predicated of a matter or a material substance. Some commentators like Loux and Lewis regarded this predication as close to accident predication, both based on inherence. As R.M. Dancy points out, these predications make Aristotle’s theory of predication immanentist: not only accident predications are explained by the immanence of accidents in substances, some of the substantial predications, which were not explained in Categories, are also explained by the immanence of form in matter. It is interesting that in this kind of predication, it is the predicate and not the subject, which is in the strictest sense substance. As the central books of Metaphysics claim, the form is the substance. Thus, in this predication, substance gets away from the sense of ὑποκείμενον. Corkum mentiones 68a19 as the only instance where Aristotle explicitly claims that a term may be predicated of itself, a passage that is, in Corkum’s view, problematic. 6) Demonstrable predicates Those predicates are demonstrable that are so related to their subjects that there are other predicates prior to them predicable of their subjects (ἔτι δ᾿ ἄλλος, εἰ ὧν πρότερα ἄττα κατηγορεῖται). (PsA., A, 22, 83b32-34) 7) Series of predications Since it is possible for a predicate to be itself the subject of another predication, we can have a series of predications in which the predicate of a predication is the subject of the next predication. This series has the following features: a) It has a limit (in number) (PsA., A, 22, 83b14-16) on the side of subjects: there are subjects that cannot themselves be predicated (PsA., A, 27, 43a39-41), which are, as we noted, prime subjects: particulars, i.e. prime substances and other individuals. (PsA., A, 19-22) Aristotle calls them ultimate (ὓστατον). (PsA., 21, 82a36-b1) b) It has a limit (in number of kinds) (PsA., A, 22, 83b14-16) also on the side of predicates: there must be predicates that cannot be subjects. (PsA., A, 19-22; PsA., A, 27, 43a36-39) Aristotle calls them primary (πρῶτον). (PsA., A, 21, 82b1-4) These are the highest categories or the highest genera of categories. (PsA., A, 22, 83b14-16) c) The series has an escalating shape from mere subjects at its downside to mere predicates at its upside. It is Aristotle himself whos uses the words up and down in this sense. (e.g. PsA., A, 22, 83b2-3) d) The predications that lie between lowest and highest ones must be finite in number. (PsA., A, 19-22 especially: 20, 82a21-35) These have subjects and predicates, each capable of both of the roles of being subject and being predicated. A result of this fitness is that neither demonstration can go to infinity nor everything is demonstrable, the two points Aristotle always insist on. e) The upward side includes the more universal ones and the downward the more particular ones. (PsA., 20, 82a21-23) f) It follows from the above features that ‘neither the ascending nor the descending series of predications … are infinite.’ (PsA., A, 22, 83b24-25) g) Reciprocation and convertibility. Except in case of terms (i.e. subjects and predicates) that are at each of the ends of series of predications, namely ultimates and primaries, it is possible to reciprocate (ἀντιστρέφειν) terms and convert the predication. (PsA., A, 19, 82a15-20) h) Antipredication. Antipredication means that in a predication (S is P), the subject becomes the predicate of its predicate (P is S) in the same category its predicate was predicated on it. For example, if P is in the category of quality, antipredication means that S be predicated of P in the category of quality. In other words, P is a quality of S and S is a quality of P. Aristotle rejects this. (PsA., A, 22, 83a36-b3) i) Self-predication versus other-predication. Aristotle distinguishes between a predication in which a term is said of itself and a predication in which a term is said of another. (Phy., Δ, 2, 209a31-33) j) Predicablity (Cat., 5, 3a36-b2): 1) Primary substances and individuals are not predicable. 2) Secondary substances are of two kinds: genus and species i) Genus is predicable able both of the species and of the individuals. ii) Species is predicable of the individual. 3) Differentiae are predicable both of the species and of the individuals. 8) Predication as classification a) Richard Patterson believes that Aristotle’s so repeated construction using hoper (estin A hoper B) in Topics (120a23 sq., 122b19, 26sq., 123a, 124a18, 125a29, 126a21, 128a35. Also in Posterior Analytics (83a24-30) (Brunschwig’s list. ‘expresses the fact that A is a kind of B (esti A B tis), that A is a species of the genus B.’ 9) Universal predication Aristotle defines universal predication (κατὰ παντὸς κατηγορεῖσθαι) as such: ‘wherever no instance of the subject (τῶν τοῦ ὑποκειμέμνου) can be found of which the other term cannot be asserted.’ (PrA., A, 24b27-29) In this predication, the subject is included in another as in a whole (ἐν ὃλῳ εἶναι) and the predicate is predicated of all of the subject (κατὰ παντὸς κατηγορεῖσθαι). (PrA., A, 24b26-27) Attach another discussion we had about ἐν ὃλῳ here. 10) Quantity of predication A predication, truly stated, has a quantity, which is the number of objects under the name of the subject of which the predicate is predicated. The quantity of subject can be stated in four ways: a. Indefinite: when the predicate belongs or does not belong to the subject without any mark to show to haw many of the particulars under the name of the subject it does or does not belong. E.g. ‘Man is white’; ‘Man is not white.’ (PrA., A, 24a20; OI., I, 7, 17b8-12) b. Universal quantity: When the predicate belongs to all or none of the subject. E.g. ‘Every man is animal’; ‘No man is animal.’ (PrA., A, 24a18-19; OI., I, 7, 17b5-6) The contrary of a predication of a universal quality is a predication of a universal quality. E.g. the contrary of ‘Every man is white’ is ‘No man is white.’ (OI., I, 7, 17b20-23) c. Particular quantity: When the predicate belongs (or does not belong) to some of the subject. E.g. ‘Some men are white’; ‘Some men are not white.’ (PrA., A, 24a19-20) d. Single quantity: when the subject is a proper name of only one object. E.g. ‘Socrates is white’; ‘Socrates is not white.’ The contrary of this predication is of a single quantity: ‘Socrates is not white.’ (OI., I, 7, 17b38-18a4) 11) Convertibility of predication. Some predications are convertible, that is, it is possible to change the place of subject and predicate in a true proposition so that the converted proposition remains true. This is supposed to mean that given the truth of a predication, the truth of the converted predication is inferable. The convert form of a predication depends on its quantity. a. Indefinite quantity: This predication has no strictly true convert because its quantity is not stated. b. Universal quantity: It can be converted in two ways: i) A negative universal can be converted to a negative universal in which the terms are changed. E.g. ‘No pleasure is good’ can be converted to ‘No good is pleasure.’ (PrA., A, 2, 25a5-8 and a14-19) ii) An affirmative universal can be converted to an affirmative particular in which the terms are changed. E.g. ‘Every pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a7-9) c. Particular quantity: If it is negative, it cannot be converted but if it is affirmative, it can be converted to an affirmative predication with particular quantity. E.g. ‘Some pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a10-13 and a20-24) d. Single quantity: It cannot be converted. 12) Characteristics of relations between subject and predicate 1. A predicate is of a wider range than its subject. It is based on this fact that Aristotle: a) Prevents individuals to be predicate because there is nothing of which an individual be of a wider range. In other words, it is due to the fact that since an individual is only ‘one particular’ thing and, thus, cannot be of a wider extent than anything that Aristotle prevents them of being a predicate. Matthews, however, thinks we cannot use Socrates, a substance and an individual, in the place of predicate and say it of Socrates because ‘Socrates does not classify Socrates: it names him.’ b) Prevents differentia, species and things under species to be predicated of genus. (To., Z, 6, 144a27-) c) Prevents the species and the things under it to be predicated of the differentia. (To., Z, 6, 144b1-4) d) Also about the effect because it is wider than its subject. (PsA., B, 17, 99a) e) Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 2. The predicate of a predicate of a subject will be predicated of the subject too: ‘whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject too.’ (Cat., 3, 1b10-15) In fact, it is due to its predication of the subject that it is predicated of its predicate. (Cat., 5, 2a36-b1) Moreover, what is not predicated of the predicate of a subject cannot be predicated of it as well. (PrA., A, 27, 43b22-27) Thus, what, for example, is not predicated of animal, cannot be predicated of man. 3. The predicate of a subject can be predicated of its predicates as well. (Cat., 5, 3a1-6) For example, you call the individual man grammatical and, thence, you call both a man and an animal grammatical. Nonetheless, the predicate of a subject belongs to it more properly than to its higher predicates. (PrA., A, 27, 43a27-32) 4. It is only the subject that can be distributed and not the predicate. (PrA., A, 27, 43b16-22; OI, I, 7, 17b12-16) Therefore, we can say e.g. ‘Every man is animal’ but we cannot say ‘Every man is every animal.’ 5. It is the reason of the relation between subjects and predicates, that is the reason of predication, which is the subject of inquiry. (Met., Z, 1041a20-24) In other words, since it is a meaningless inquiry to ask why a thing is itself (Met., Z, 1041a14-15), the only remaining meaningful inquiry is to ask why something is something else, i.e. to ask about the reason of predication. 6. A subject cannot categorize its predicate in the same category in which it is categorized by it. If e.g. A is a quality of B, B cannot be a quality of A. Therefore, there is no reciprocation in the same category. (PsA., A, 22, 83a36-39) 13) Characteristics of series of predications 1. A series of secondary accidental predication cannot go ad infinitum for not even more than two terms can be comnbined. For an accident is not an accident of an accident, unless it be because both are accidents of the same subject. (Met., Γ, 1007b1-4) 2. Infinite series cannot be traversed in thought. (PsA., A, 22, 83b6-7) 3. The predications of genera on each other must be ended and cannot go to infinity because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) Therefore, a series of predication of genera on each other must be limited on both sides. There must be an upward limit in general categories as well as a downward limit in individual because they cannot be predicated of others. Whatever lies between these limits can both be predicated of others and others be predicated of them. (PrA., A, 27, 43a36-43) 4. The order of predicates matters: it makes a difference whether the series be ABC or BAC. (PsA., B, 13, 96b25-32) . (shrink)