Although he briefly considers the notion of contingency (or two-way possibility) in chapter 3, Aristotle does not formulate his “official” definition of this modality until chapter 13: “I mean, by being contingent, and by that which is contingent, whatever is not necessary but, being assumed to obtain, entails no impossible consequences” (32a18–20). “Impossible” in the definiens must refer here to “one-way” possibility, defined as “not necessarily not,” with contingency (two-way possibility) defined in terms of necessity and/or one-way possibility.

We shall consider, however, Wieland's claim that two-way possibility is a modality sui generis. And from a larger perspective, one is confronted with difficult issues concerning the relation of contingency to “belonging by nature,” or “applying always or for the most part,” and, in turn, of the importance of Aristotle's logic of two-way possibility (developed in chapters 14–22 of Pr. An. A) for Aristotelian science. Aristotle touches on this last problem without resolving it in A.3 (25b14–31) and again in A.13 (32b4–22), where he asserts that there are scientific demonstrations concerning things associated “by nature or for the most part,” but not concerning chance associations.

Prominent among the more specific issues are, once again, those having to do with conversion. Here we encounter the usual questions about conversion of terms within A, E, I, and O propositions, only now in a way that requires resolution of a related issue about the “quality” (affirmative or negative) of two-way possibility propositions.

In chapters 14–22, Aristotle methodically considers all the various combinations of premise pairs involving at least one two-way possibility (“problematic” or “contingent”) premise. Chapters 14–16 take up firstfigure moods having, respectively, two problematic premises, one problematic and one assertoric premise, and one problematic and one necessity premise. Chapters 17–19 take up the same combinations, now in the second figure, and 20–22 carry the plan through the third figure. (For a chart of the ground plan of chapters 8–11 and 14–22, see the first page of Chapter 3 herein.) As with the necessity syllogisms of 8–11 and the assertoric ones of 4–6, Aristotle singles out the “complete” or “perfect” (teleios) moods, those whose validity is obvious on the basis of the premises precisely as given, and then validates other moods by reducing them to perfect moods by use of term or qualitative conversion or reductio ad impossibile, or by validating them through ekthesis. Some portions of these chapters are fairly routine and so will be presented here in summary fashion. This will leave us free to focus on a number of logical curiosities and on some significant philosophical issues, including that of the relation of these syllogisms to Aristotelian science.

TWO PROBLEMATIC PREMISES: FIRST FIGURE

All the perfect moods with this combination of premises fall into the first figure and correspond exactly to the four perfect plain moods of Pr. An. A.4. Thus, chapter 14 consists in a discussion of Barbara, Celarent, Darii, and Ferio pp, pp/pp, and of several invalid moods.

BACKGROUND TO THE PRINCIPAL ISSUES

The chapters of the Prior Analytics devoted to modal arguments are notoriously difficult, controversial, and, according to numerous weighty authorities, deeply confused. Accordingly, one major aim of this study will be to examine in detail the internal workings of Aristotle's modal logic – his logic not just of statements simply asserting the application of a predicate to a subject but also of those asserting a necessary or possible or contingent relation between subject and predicate – in order to understand and assess its strengths and its weaknesses. A second aim will be to establish a fundamental connection between Aristotle's metaphysical essentialism (along with his theory of scientific demonstration) on the one hand and his modal logic on the other. These two goals are closely connected, or so it will be argued here, in that the logical system itself must be understood from the start in the light of basic points of syntax and semantics deriving from Aristotle's views on what there is and on the various ways in which we can speak and reason about what there is.

There has always been healthy interest in Aristotle's metaphysical essentialism – interest heightened recently by work on essentialism as such, and especially by work deriving, like Aristotelian essentialism, from intuitions about the natures or essences of things. Such developments have contributed at least indirectly to the study of Aristotle by provoking careful thought about how essentialism might be formulated and how different objects (individual living things, the “natural kinds” of chemistry or physics or biology, sets, numbers) might involve very different sorts of essential properties, discoverable only through a variety of approaches.

Aristotle's syllogistic encompasses several groups of syllogisms— the assertoric ones and six or so modal groups (the exact number would be a matter of contention and is not important here). Almost without exception each type (e.g., those with necessary premises and conclusion) contains its own subset of “perfect” or “complete” (teleios) syllogisms, perfect because they are not only valid, but obviously so just as they stand, and another set of imperfect ones whose validity must be demonstrated “by something additional,” usually by reduction to one or another perfect syllogism. Aristotle says relatively little about this perfection, and for the most part the commentators follow him in this. Everyone agrees that he has in mind, at least in part, the psychological feature of obviousness of validity; but some would maintain – and here controversy begins to set in – that for the assertoric case, at least, he also has in mind a single logical principle that is itself obviously valid and that directly entails the perfect syllogisms Barbara, Celarent, Darii, and Ferio. The principle in question is the dictum de omni et nullo: Everything predicated (or not predicated) of all of some group is predicated (not predicated) of everything contained in that group. If Aristotle does have such a principle in mind, the question arises whether he meant it to apply also to perfect modal syllogisms and hence whether he had a single underlying principle that could ground the perfection of all his perfect syllogisms, plain or modal.

ARISTOTLE'S GENERAL INTRODUCTION TO THE MODALITIES

In the terminology of ‘A belonging to or applying to B’ (‘A huparchei + dat. B’), dominant in Pr. An. A.4–22, the three basic readings described earlier go as follows: On a de dicto version, Aristotle employs only one copulative expression, huparchei (‘belongs to’, ‘applies to’), but three sentential operators for possibility, necessity, and two-way possibility, each attaching to a plain proposition to form a new modal dictum asserting that the original statement is necessarily true, possibly true (in the sense of not necessarily false), or contingently true (i.e., neither necessarily true nor necessarily false). A modalized predicate reading also calls for the plain copulative expression huparchei, but now with three term-forming operators on terms: n, let us say, which attaches to a given term A to form the term ‘necessarily A’ or ‘necessary-A’ (nA), and the operators p and pp for ‘possibly A’ (pA) and ‘two-way possibly A’ (ppA). Finally, the copulative reading involves no sentential operators and no term-forming operators on terms, but rather four expressions linking Aristotle's general terms: huparchei, ‘belongs to, applies to’; ex anangkēs huparchei, ‘necessarily belongs to’ (symbolized as ‘A N all B’); endechetai (or dunatai) huparchein, ‘possibly applies to’ (A P some B’) or ‘two-way possibly applies to’ (‘A PP all B’). (Negation and quantification pose other questions and may well be, in Aristotle's view, copula operators. The matter is discussed at the end of this section.)

This is a study of Aristotle's theory of substance, more precisely of his theory of sublunary substance. Although some philosophers, upon reading the Metaphysics, see the influence of Aristotle's biology, others – and I am one of them – see Plato. Indeed (although Aristotle would not have put the point in this way), I would go so far as to say that Aristotle can be seen as attempting to offer a defensible version of Platonism. What I mean when I say “a version of Platonism” is that for Aristotle, as for Plato, there is something which is first in knowledge, definition, and time, and that for Aristotle, as for Plato, whatever is knowable must be eternal and unchanging. In the case of Plato, it is, of course, the Forms which are intended to meet these requirements. But Aristotle finds the Forms problematic on both metaphysical and epistemological grounds, and while Plato himself certainly struggled with some of the difficulties that Aristotle complains of, Aristotle believes that Plato's solutions fail, chiefly on account of separation. Specifically, Aristotle seems to believe that separation creates a gap that recollection cannot fully bridge and that Plato's blurring of the distinction between universality and particularity not only leads to regress but casts doubt upon the very intelligibility of Forms.

Aristotle's account of substance involves yet another case – indeed the most central case – of his use of numerical sameness without identity, and in this chapter I offer an interpretation of Aristotle's views about substance which depends on that distinction. The task of interpreting VII–VIII has, of course, been undertaken many times, and yet nothing approaching a consensus has been reached. My strategy is to argue that Aristotelian substances are specimens of natural kinds, where such specimens are numerically the same as but not identical with sensible objects. I maintain that, if a distinction between numerical sameness and identity is posited, Aristotle's view is consistent, his claim about the separation of substance is intelligible, and his requirement that substances have ontological and epistemological priority is satisfied. This chapter begins with a brief discussion of the Categories and proceeds to consideration of how Aristotle's position in that work is affected by the demand in the Metaphysics for the epistemic priority of substances; separation and ontological priority will be considered in later chapters.

In the Categories, an early work, Aristotle makes a distinction between what is present in a subject, what is said of a subject, what is both, and what is neither (1a20–1b6).

In the interpretation of Aristotle's account of substance I have proposed thus far, I have claimed that Aristotle believes that by denying separation he can uphold the epistemological, and, as I will argue in Chapter VI, ontological priority of substances, where those requirements are understood in very Platonic terms. I have claimed further that my interpretation of the motivations for Aristotle's view of substance makes understandable his account of how we come to have knowledge. Nevertheless, as I said in Chapter I, even as Aristotle criticizes Plato for separating the Forms, he says of substances that they must be separate. In Metaphysics VII 1, for example, Aristotle says:

In this book I have argued that the assumption that Aristotle distinguishes numerical sameness from identity provides a wide-ranging explanation of referential opacity in his works and makes possible an interpretation of substance that sees Aristotle's theory as a response to what he takes to be the flaws in Platonism. I have not attempted to defend distinguishing between numerical sameness and identity on philosophical grounds or even to consider the philosophical implications of such a view; as I said in Chapter II, the logic of a metaphysics that confounds counting has to be, to say the least, problematic. It may be, of course, that Aristotle adopted a position that cannot be made coherent or attractive, although such a conclusion would be disappointing. Although I will not in this final chapter try to offer a philosophical analysis or defense of the distinction, I will nevertheless describe an interesting occurrence of it in the recent philosophical literature. But the primary goal of this chapter is to argue that substances, understood as specimens of natural kinds, can defensibly be said to be ontologically prior to the sensible objects with which they are numerically the same, and for that argument too the example now to be offered will prove useful.