We develop some of Williamson’s ideas regarding how propositional calculus aids in comprehending Aristotelian logic. Specifically, we enhance the utilisation of truth tables to examine the structure of opposition diagrams. Using ‘conditioned truth tables’, we establish logical dependency relationships between the truth values of different propositions. This approach proves effective in interpreting various texts of the Organon concerning the doctrine of opposition.

As a first stab, call a property recurrent if it can be possessed by more than one object, and nonrecurrent if it can be possessed by at most one object. The question whether Aristotle holds that there are nonrecurrent properties has spawned a lively and ongoing debate among commentators over the last forty-five years. One source of textual evidence in the Categories, drawn on in this debate, is Aristotle’s claim that certain properties are inseparable from what they are in. Here (...) the point of contention is whether this commits Aristotle to holding that these properties are inseparable from individuals, since it is commonly held that a property is nonrecurrent, if it is inseparable from an individual. I argue that this evidence is neutral on the question whether there are nonrecurrent properties in Aristotle. One of my aims here is to disentangle the question of recurrence from local issues of individuality and universality in the Categories. But another aim is to turn from the textual considerations, which have dominated the debate, to broader methodological considerations. It is a shared assumption among all those who look to textual evidence from the Categories, so to decide whether Aristotle believes there are nonrecurrent properties, that in this work Aristotle is engaged in a project where the question of recurrence is relevant. I argue that Aristotle’s concerns in the Categories are disjoint from the question of recurrence, and so this shared assumption is false. (shrink)

Although he does not have an explicit theory of supposition as is found in the works of Latin medieval philosophers, Avicenna has two doctrines giving something equivalent: the threefold distinction of quiddity, corresponding to a division of simple, personal and material supposition, and his analyses of truth conditions for categorical propositions, where sentential context determines in part the reference of their terms. While he does address which individuals are being referred to by the universal terms used there, Avicenna concentrates more (...) on the varied temporal durations of the predications being made. In Western terms, he has incorporated ampliation and restriction into the theory of supposition itself. (shrink)

This book investigates Aristotle’s views on abstraction and explores how he uses it. In this work, the author follows Aristotle in focusing on the scientific detail first and then approaches the metaphysical claims, and so creates a reconstructed theory that explains many puzzles of Aristotle’s thought. Understanding the details of his theory of relations and abstraction further illuminates his theory of universals. Some of the features of Aristotle’s theory of abstraction developed in this book include: abstraction is a relation; perception (...) and knowledge are types of abstraction; the objects generated by abstractions are relata which can serve as subjects in their own right, whereupon they can appear as items in other categories. The author goes on to look at how Aristotle distinguishes the concrete from the abstract paronym, how induction is a type of abstraction which typically moves from the perceived individuals to universals and how Aristotle’s metaphysical vocabulary is "relational.’ Beyond those features, this work also looks at how of universals, accidents, forms, causes and potentialities have being only as abstract aspects of individual substances. An individual substance is identical to its essence; the essence has universal features but is the singularity making the individual substance what it is. These theories are expounded within this book. One main attraction in working out the details of Aristotle’s views on abstraction lies in understanding his metaphysics of universals as abstract objects. This work reclaims past ground as the main philosophical tradition of abstraction has been ignored in recent times. It gives a modern version of the medieval doctrine of the threefold distinction of essence, made famous by the Islamic philosopher, Avicenna. (shrink)

ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 Forerunners (...) of Modus Ponens and Modus Tollens 3.4 Wholly Hypothetical Syllogisms 4. Diodorus Cronus and Philo the Logician 5. The Stoics 5.1 Logical Achievements Besides Propositional Logic 5.2 Syntax and Semantics of Complex Propositions 5.3 Arguments 5.4 Stoic Syllogistic 5.5 Logical Paradoxes 6. Epicurus and the Epicureans 7. Later Antiquity. (shrink)

There is a debate about whether particular properties are for Aristotle non-recurrent and trope-like individuals or recurrent universals. I argue that Physics I.7 provides evidence that he took non-substantial particulars to be neither; they are instead non-recurrent modes. Physics I.7 also helps show why this matters. Particular properties must be individual modes in order for Aristotle to preserve three key philosophical commitments: that objects of ordinary experience are primary substances, that primary substances undergo genuine change, and that primary substances are (...) ontologically fundamental. (shrink)

Although there are a very few occasions on which Aristotle speaks of words, on the one hand, or mental concepts, on the other, as universals, he was no nominalist and no conceptualist. This negative thesis I have argued sufficiently, at least to my own satisfaction, in an earlier paper. He was, rather, a realist, but of a very tenuous sort. As I said in the earlier paper, he viewed universals as real entities but lacking numerical oneness; each is numerically many, (...) and yet each is also one in some sense. The specific identity of numerically distinct particulars creates something like a class, and this is the universal.This interpretation was not, in the earlier paper, defended against those who would attribute to Aristotle a much more robust form of realism, and it is that defense which this paper will undertake to provide. The evidence which can be marshalled for the more robust realism is impressive – more so, I would say, than that which can be brought forth for either the nominalist or the conceptualist interpretations. It rests on numerous passages which either explicitly or implicitly seem to tie together as identical, forms, substances, universals, and intelligible objects. (shrink)

According to the Categories, predicates can be ‘said of’ their subjects or they can be ‘present in’ their subjects. The said-of relation has received relatively little scholarly attention, and scholars disagree on the answers to four foundational questions about the relation. (i) What is it? (ii) Is it an essential relation? (iii) How is it related to predication? (iv) Is it primitive? I argue that A is said-of B just in case A is a formal part of B. On this (...) account, said-of is an essential relation and it is definable, but it is not defined in terms of predication. (shrink)

Nexuses such as exemplification are the fundamental ties that structure reality as a whole. They are “formal” in the sense of constituting the form, not the matter of reality and they are “transcendental” inasmuch as they transcend the categorial distinctions between the denizens of reality, including that between existents and non-existents. I shall advocate a moderately particularist view about (external) nexuses and argue that it provides not only the best solution to Bradley’s regress, but also an elegant account of symmetrical (...) relations (both formal and material), as well as of temporal and modal change. These advantages are illustrated by the reconstruction of an Aristotelian ontology of exemplification involving substances, kinds and material attributes. (shrink)

Does Aristotle's terminology provide some guidance when we inquire into the origins of the notion of thing? Naturally, one might think of Aristotle's notion of being, which is meant to capture everything that is. However, ‘being’ in Aristotle seems to be significantly broader than what we take to be a ‘thing’. I will take up a thesis introduced and defended by Rainer-Wolfgang Mann, namely that Aristotle is actually the inventor of the notion of thing in that his Categories conceptualized the (...) distinction between properties on the one hand and their bearers, individual substances, on the other. It will be argued though that Aristotle, when conceptualizing things as bearers of properties, depicts a notion that is actually stronger than what we usually mean by ‘thing’. (shrink)

Aristotle holds that individual substances are ontologically independent from nonsubstances and universal substances but that non-substances and universal substances are ontologically dependent on substances. There is then an asymmetry between individual substances and other kinds of beings with respect to ontological dependence. Under what could plausibly be called the standard interpretation, the ontological independence ascribed to individual substances and denied of non-substances and universal substances is a capacity for independent existence. There is, however, a tension between this interpretation and the (...) asymmetry between individual substances and the other kinds of entities with respect to ontological independence. I will propose an alternative interpretation: to weaken the relevant notion of ontological independence from a capacity for independent existence to the independent possession of a certain ontological status. (shrink)

In his groundbreaking work of 1969, Spinoza's Metaphysics: An Essay in Interpretation, Edwin Curley attacked the traditional understanding of the substance-mode relation in Spinoza, according to which modes inhere in substance. Curley argued that such an interpretation generates insurmountable problems, as had already been claimed by Pierre Bayle in his famous Dictionary entry on Spinoza. Instead of having modes inhere in substance Curley suggested that the modes’ dependence upon substance should be interpreted in terms of (efficient) causation, i.e., as committing (...) Spinoza to nothing over and above the claim that substance is the (efficient) cause of the modes. These bold and fascinating claims generated one of the most important scholarly controversies in Spinoza scholarship of the past thirty-five years. In this paper I argue against Curley’s interpretation and attempt to reestablish the traditional understanding of Spinozistic modes as inhering in God and as predicated of God. I also criticize Curley’s philosophical motivation for suggesting this interpretation. In order to show that, for Spinoza, modes are predicated of - and inhere in - substance, I will proceed in the following manner. First, I will summarize Curley’s arguments against substance-mode inherence and present his alternative interpretation of the substance-mode relation. I will then present what I consider to be the most compelling arguments against Curley’s interpretation. Some of these arguments have already been suggested in the literature of the past thirty years (and by Bayle); however, as far as I know, most of the arguments I will be making are new. In the subsequent section I will respond to objections that Curley and Bayle advance against Spinoza’s view of God as the substratum in which all things inhere. Finally, I will address whether Spinozistic modes are predicated of (and not only inhere in) substance, and whether Spinoza considered modes to be particular properties (or “tropes,” in the jargon of contemporary metaphysics). Since Bayle’s claims will be used both in support of and against Curley’s interpretation, it would be appropriate to say a few introductory words on Bayle’s stance. In his Spinoza entry, Bayle criticizes Spinoza’s claim that all things are modes of God, claiming that it “is the most monstrous hypothesis that could be imagined, the most absurd, and the most diametrically opposed to the most evident notions of our mind.” Bayle, however, has no doubt that when Spinoza claims that all things are modes of God, Spinoza means that all things inhere in God. Curley embraces Bayle’s arguments against Spinoza, but uses them in order to claim that we should not ascribe to Spinoza a view which is allegedly shown by Bayle to be absurd. What we should do, Curley argues, is to reinterpret the substance-mode relation as a relation of causal dependence, which would set Spinoza free from Bayle’s hook. Interestingly, as we shall soon see, Bayle himself discusses and rejects a very similar revisionary interpretation of the substance-mode relation. (shrink)

Much recent work on Aristotle's Categories assumes that there is an ontological theory presented in that work and tries to reconstruct it on the basis of the slender evidence in the book. I claim that this is misguided. Using a distinction made by G.E.L. Owen between theory and the "phaenomena", I argue that the Categories is mainly concerned with setting out the phenomena -- the intuitions that any ontology must explain. This thesis has consequences for the interpretation of Aristotle's ontological (...) writings. I explore some of these. (shrink)

There is a dispute as to what sort of entity non-substantial individuals are in Aristotle's Categories. The traditional interpretation holds that non-substantial individuals are individual qualities, quantities, etc. For example, Socrates' white is an individual quality belonging to him alone, numerically distinct from (though possibly specifically identical with) other individual colors. I will refer to these sorts of entities as 'individual instances.' The new interpretation1 suggests instead that non-substantial individuals are atomic species such as a specific shade of white that (...) is indivisible into more specific shades. On this view, non-substantial individuals are what we would call universals2 which can be present in different individual substances, but are labelled 'individuals' by Aristotle because, like individual substances, there is nothing they are said of.3 In this paper I will defend the traditional account by attempting to show that it is supported by the slender textual evidence that is available. I will begin by stating three serious objections to the traditional interpretation. Next I will show that in works later than the Categories Aristotle accepted individual instances of properties of the sort found in the Categories by the traditional interpretation. Finally, I will set out the evidence that supports the traditional interpretation and answer the three objections. (shrink)

In this paper I shall defend the traditional claim that Aristotle's nonsubstantial particulars discussed in the second chapter of the Categories are unsharable particulars against G. E. L. Owen's claim that they are sharable universals. I shall proceed by presenting first a sketch of the traditional position that makes explicit why it holds that non-substantial particulars are unsharable particulars. Secondly, I shall sketch Owen's position and recount how it differs in certain important respects from the traditional position. Thirdly, I shall (...) present some of my own considerations that I believe support the traditional position at the expense of Owen's position. Finally, I shall offer what I take to be the primary reason Aristotle was committed to the existence of such odd items as non-substantial particulars. (shrink)

I argue there are two ways predication relations can hold according to the Categories: they can hold directly or they can hold mediately. The distinction between direct and mediated predication is a distinction between whether or not a given prediction fact holds in virtue of another predication fact’s holding. We can tell Aristotle endorses this distinction from multiple places in the text where he licenses an inference from one predication fact’s holding to another predication fact’s holding. The best explanation for (...) each such inference is that he takes some predication facts to be mediated by others. Once the distinction between direct and mediated predication has been explained and argued for, I show how it can help solve a persistent problem for the traditional view of non-substantial particulars in the Categories—that is, the view that non-substantial particulars are particular in the sense of being non-recurrent. Along with vindicating the traditional view, the direct/mediated predication distinction gives us a distinctive way of understanding what it is for something to be recurrent (or non-recurrent) as well as a better understanding of Aristotle’s broader commitments in the Categories as a whole. (shrink)

"However that may be, Aristotelian syllogistic concerned itself exclusively with monadic predicates. Hence it could not begin to investigate multiple quantification. And that is why it never got very far. None the less, the underlying grammar of Aristotle's logic did not in itself..

A trope is an abstract particular. Trope theorists maintain that tropes exist and argue that they can solve important philosophical problems, such as explaining the nature of properties. While many contemporary interpreters of Aristotle read him as a trope theorist, few commentators distinguish different versions of trope theory. Which, of any, of these versions did Aristotle hold? Classical trope theorists say that individuals just are bundles of tropes. This essay offers a reading of Categories 2-5 and Metaphysics VII-VIII that aligns (...) Aristotle's view with nonclassical trope theory, according to which objects are more than just bundles of tropes. (shrink)

In the following pages, the reader will find a detailed study of what Aristotle considered the most difficult aporia formulated in Metaphysics III (Beta), which is answered in chapter 2 of Book X (Iota): the Eleventh Aporia. In such aporia, Aristotle rivals: (i) the conception assumed by the ancient Physiologoi, which takes the One to be an underlying nature whose being is not exhausted by being One, and (ii) the Platonic-Pythagorean view, which prefers to conceive the One in itself, according (...) to its own determinations and apart from any connection with some reality outside it. (shrink)

The Eleventh Aporia results from the breakup of the entire Greek philosophy previous to Aristotle in two manners of conceiving and proposing the first principles (archai), specially the One (to hen): (i) the manner by which Physiologoi conceived the One as a principle, namely, assuming an underlying nature, different from the One in itself, not adequately characterized by the simple fact of being one and which is denoted by the concept of One, and (ii) the manner inaugurated by the Pythagoreans (...) and later endorsed by Plato, marked by the abandonment of the appeal to an underlying nature and by conceiving the One in itself (auto to hen) as a principle, depriving it of any connection with some reality not strictly characterized by being one. Aristotle faces this aporia in Metaphysics Iota 2 and, according to the interpretation I propose: (a) refuses the Pythagorean-Platonic manner of conceiving and proposing principles, (b) endorses the course of action of the Physiologoi, and, in doing so, (c) steps back and retakes the “project” of the Physiologoi at the point where it was interrupted, namely, during the search for a principle of motion. From this scenario, I will try to show that the final outcome of the Eleventh Aporia can be the introduction of the Prime Mover as the properly Aristotelian (and cosmological) candidate to the title of One between the principles. (shrink)