Two things become one thing, something having parts, and something becoming something else, are cases of many things being identical with one thing. This apparent contradiction introduces others concerning transitivity of identity, discernibility of identicals, existence, and vague existence. I resolve the contradictions with a theory that identity, number, and existence are relative to standards for counting. What are many on some standard are one and the same on another. The theory gives an account of the discernibility of identicals using (...) phrases like “insofar as”. And it holds that standards for counting remain or shift depending on our purposes. (shrink)

Michael J. Loux here presents a fresh reading of two of the most important books of the Metaphysics, Books Z and H, in which Aristotle presents his mature theory of primary substances. Focusing on the interplay of Aristotle's early and late views, Loux maintans that the later concept of ousia should be understood in terms of a theory of predication that carries interesting implications for contemporary metaphysics. Loux argues that in his first attempt in identifying ousiai in the Categories, Aristotle (...) encountered a set of ontological problems which he wrestled with again in Metaphysics Z and H. In the Categories, where the primary realities are basic subjects of predication construed in essentialist terms as things falling under natural kinds, familiar particulars are the primary ousiai. In subsequent works, Aristotle holds that since familiar particulars come into being and pass away, they must be composites of matter and form; and in Metaphysics Z and H, he explores the implications of this insight for the search for ousia. Maintaining that the substantial forms of familiar particulars are the primary ousiai, the later Aristotle interprets forms as predicable universals rather than as particulars, each uniquely possessed by a single object. (shrink)

Charlotte Witt extracts from this text a coherent and provocative view about sensible substance by focusing on Aristotle's account of form or essence.

Michael Wedin argues against the prevailing notion that Aristotle's views on the nature of reality are fundamentally inconsistent. According to Wedin's new interpretation, the difference between the early theory of the Categories and the later theory of the Metaphysics reflects the fact that Aristotle is engaged in quite different projects in the two works--the earlier focusing on ontology, and the later on explanation.

Baxter (Australas J Philos 79: 449-464, 2001) proposes an ingenious solution to the problem of instantiation based on his theory of cross-count identity. His idea is that where a particular instantiates a universal it shares an aspect with that universal. Both the particular and the universal are numerically identical with the shared aspect in different counts. Although Baxter does not say exactly what a count is, it appears that he takes ways of counting as mysterious primitives against which different numerical (...) identities are defined. In contrast, I defend the idea— suggested, though not quite endorsed, by Baxter himself—that counts are independent dimensions of numerical identity. Different ways of counting are explained by the existence of these different sorts of identity (i.e., counts). For the instantiation of a universal by a particular, I propose one dimension concerned with the individuation of particulars (the p-count) and another dimension concerned with the individuation of universals (the u-count). On that basis, I give a clear definition of cross-count identity that explains its asymmetrical nature (i.e., the fact that particulars instantiate universais, but not vice versa). I extend the theory to a third dimension—that of time, or the t-count—and thereby defend Baxter's ideas on change, and the contingency of instantiation. Baxter (Mind 97(388): 575-582, 1988; Australas J Philos 79: 449-464, 2001) proposes the related idea of composition as (cross-count) identity. Parts are individually cross-count identical with the wholes that they constitute, and they collectively share all aspects across counts with those wholes. I propose an innovation by which totality is shared distinctness across counts. The theory applies to both the totality of particulars that instantiate any given universal, and the totality of parts that constitute any given whole. I argue that this has several advantages over Armstrong's view, which is based on a dubious external totalling relation. I also argue that Armstrong's theory of numbers (or quantities) as internal relations ought to be rejected in favour of an account based on identity and distinctness. The paper concludes with a careful analysis of external relations in Baxter's framework. I argue that we must recognise one further dimension of identity in order to differentiate between, e.g., the aspects of Abelard insofar as he loves Heloise and Abelard insofar as he loves Isobel. Each of these aspects is identical with Abelard and identical with loving-by, yet they must be in some way distinct. I therefore propose the r-count, in which multiple distinct relational properties are the very same relation (-part). The existence of these four independent dimensions explains the fact that particulars, universals, relations, and times are fundamentally different sorts of things in the ontology. Each is individuated with respect to a different dimension of identity. (shrink)

In this paper, I present an Aristotelian solution to the problem of material constitution. The problem of material constitution arises whenever it appears that an object a and an object b share all of the same parts and yet are essentially related to their parts in different ways. (A familiar example: A lump of bronze constitutes a statue of Athena. The lump and the statue share all of the same parts, but it appears that the lump can, whereas the statue (...) cannot, survive radical rearrangements of those parts.) I argue that if we are prepared to follow Aristotle in making a distinction between numerical sameness and identity, we can solve the problem of material constitution without recourse to co-location or contingent identity and without repudiating any of the familiar objects of common sense (such as lumps and statues) or denying that these objects have the essential properties we ordinarily think that they have. (shrink)

The author investigates greek ontologies that apparently rely on a conflation of "binary" (x is f) and "monadic" (x is) uses of 'is'. He uses Aristotelian and other texts to support his proposal that these ontologies are explained by the Greeks using two alternative semantic analyses for 'x is F'. The first views it as asserting a relation between x and F, the second as asserting that a "predicative complex" exists, where a predicative complex is a complex consisting of x (...) and F. The article concludes by indicating some uses for the novel concept of predicative complex in aristotelian interpretation. (shrink)

Michael J. Loux here presents a fresh reading of two of the most important books of the Metaphysics, Books Z and H, in which Aristotle presents his mature ...

This is a survey of Aristotle's development of the concept of substance in the Categories and Book VII (Zeta) of the Metaphysics. We begin with the Categories conception of a primary substance as that which is not "in a subject" -- i.e., not ontologically dependent on anything else -- and also not "said of a subject" -- i.e., not predicated of any item beneath it in its categorial tree. This gives us the idea of primary substances as ontologically basic individuals, (...) the fundamental subjects of predication and of change. We then examine the conception of substance in Metaphysics Zeta, where Aristotle is interested not just in the question of what the primary substances are, but in the question of what makes them substances, or, as he would put it, what the "substance OF something" is. The conception of substance that Aristotle ends up with seems (as has been frequently noted) to be threatened with inconsistency, in that Aristotle seems to want to maintain, simultaneously, that (i) substance is form, (ii) form is universal, and (iii) no universal is a substance. Two main approaches toward resolving this inconsistency are considered, and a sketch is provided of how one of these approaches might be fleshed out. On the line I propose, the substantial form of a material compound is predicated accidentally and universally of the matter of that compound, but it is not the substance of the matter of which it is predicated. Rather, it is the substance of itself; but since it is the cause of the compound's being essentially the kind of thing that it is, the substantial form is, in a derivative way, the substance of the compound as well. (shrink)

I argue via examples that there are cases in which things that are not two distinct things qualitatively differ without contradiction. In other words, there are cases in which something differs from itself. Standard responses to such cases are to divide the thing into distinct parts, or to conceive of the thing under different descriptions, or to appeal to different times, or to deny that the property had is the property lacked. I show these responses to be unsatisfactory. I then (...) gather and systematize available ways of talking about such cases with phrases like ‘insofar as’, ‘qua’, ‘to the extent that’, ‘in some respect’, etc., while paying special attention to the scope of ‘not’ when used with these phrases. This allows me to show how we can speak of self-differing without contradiction. (shrink)

Construing the instantiation of a universal by a particular in terms of my theory of aspects resolves the basic mystery of this "non-relational tie", and gives theoretical unity to the four characteristics of instantiation discerned by Armstrong. Taking aspects as distinct in a way akin to Scotus's formal distinction, I suggest that instantiation is the sharing of an aspect by a universal and a particular--a kind of partial identity. This approach allows me to address Plato's multiple location and One over (...) Many problems, Bradley's problem concerning the instantiation of relations, and the problem of change. (shrink)

One of the advantages of my account in the essay “Instantiation as Partial Identity” was capturing the contingency of instantiation—something David Armstrong gave up in his experiment with a similar view. What made the contingency possible for me was my own non-standard account of identity, complete with the apparatus of counts and aspects. The need remains to lift some obscurity from the account in order to display its virtues to greater advantage. To that end, I propose to respond to those (...) who have grappled with it in print. There are various criticisms by commentators: that it is rendered absurd by the transitivity of identity, that it makes instantiation necessary instead of contingent, that it is unclear what counts are, that aspects are simply tropes, that my view does not capture multiple location, that I make an unclear reference to a theory of composition as identity, that the account suffers from problems with polyadicity, and that it is not a realist account of universals after all. I give responses to these objections. (shrink)

In considering the nature of properties four controversial decisions must be made. (1) Are properties universals or tropes? (2) Are properties attributes of particulars, or are particulars just bundles of properties? (3) Are properties categorical (qualitative) in nature, or are they powers? (4) If a property attaches to a particular, is this predication contingent, or is it necessary? These choices seem to be in a great degree independent of each other. The author indicates his own choices.

This book takes up the central themes of Aristotle's metaphysical theory and the various transformations they undergo prior to their full expression in the Metaphysics. Aristotle's metaphysics is bedevilled by classic puzzles involving such notions as form, predication, universal, and substance, which result from his attempt to adapt the various requirements on primary substance developed in his earlier works so that they fit the very different metaphysical picture in his later work. Professor Lewis argues that Aristotle is himself aware of (...) most if not all of these difficulties and in the Metaphysics works hard to ensure the coherence of his theory. He presents Aristotle's views as a formal theory complete with axioms, definitions, and theorems. (shrink)

This book claims that Aristotle followed an aspect theory of predication.

v. 1. General introduction, the works on logic -- v. 2. The metaphysics, semantics in Aristotle's strategy of argument.

This work presents and discusses the conception of instantiation as ‘partial identity’. The theory has been previously proposed in two different guises by Baxter and Armstrong . Attention will be paid mostly to Baxter’s presentation, which seems the best de veloped, and where instantiation is understood as identity of ‘aspects’ of a universal and a particular. The theory seems to offer a solution to the vexed question of Bradley’s Regress, because instantiation is no longer conceived as a relation between numerically (...) different entities. The proposed solution requires an ontology of ‘aspects’ in order to work. Aspects are presented in the form [ x insofar as j] where x is filled by the entity to which the aspect pertains and j is filled by the respect in which the entity in question is considered. Aspects are numerically identical with the entity to which they pertain and with the other aspects of the same entity. Aspects, nonetheless, are not mere ways in which one can conceive an entity. Aspects are objective. Rejection of the principle of indiscernibility of identicals is crucial to this theory. The attributions of one aspect are not also attributions to the other aspects of the same entity. Hence, aspects offer ways to deal with seemingly incoherent attributions to the same entity. Baxter uses them to solve the problem of the multi-location of universals, temporary intrinsics and trans-world identity, besides the nature of instantiation. Several difficulties are presented, both to the general metaphysics of aspects, and to the conception of instantiation as identity of aspects. In general: it is not clear how to distinguish objective aspects from the mere forms in which we conceive an entity; it is not clear what are the conditions of identity of an aspect; and although the necessity of identity is rejected in general, it reappears as necessity of ‘aspectual’ identity. The necessity of aspectual identity raises concerns about the stability of the view. In respect to the specific conception of instantiation as identity of aspects, it will be pointed out that the theory implies the complete identity of universals and particulars that instantiate them and, further, that it implies the identity of everything with everything. (shrink)