Michael White

In Meta. Λ 8, Aristotle argues that the heaven (οὐρανός)–and, thus, the cosmos – is numerically unique on the grounds that its first unmoved mover is numerically unique. The latter is numerically unique because it is ‘essence’ (τὸ δὲ τί ἦν εἶναι) and does not have matter. “But whatever is many in number has matter.” I refer to this inference as Aristotle’s metaphysical argument for the uniqueness of the cosmos. A problem arises: (A) If the subsidiary unmoved movers of the planetary spheres are, like the prime unmoved mover, immaterial substances and belong to the same species of unmoved mover (qua “thinkers thinking themselves”), it seems that they could not be numerically distinct from that first unmoved mover – while Aristotle maintains that they are, in fact, numerically distinct. That is, as immaterial substance(s), it/they could not be individuated by matter. However, (B) if they do, as souls or soul-like forms, inform matter (namely, that of the celestial spheres which they move), it seems that there is no reason why the first unmoved mover, which moves the sphere of fixed stars or outermost, celestial sphere, should not similarly inform the matter of that celestial sphere. In the latter case, Aristotle’s argument for the uniqueness of the heaven and cosmos would be vitiated. The first unmoved mover would be the form of the outermost celestial sphere; and there would evidently be no metaphysical reason why that form could not be materially instantiated by other outermost celestial spheres, each enclosing its own cosmos distinct from our own. I argue that neither of the two salient options for resolving this problem with Aristotle’s metaphysical argument for the uniqueness of the cosmos is satisfactory. The result, so I maintain, is Aristotle’s diremption of divinity into two essentially unrelated aspects: divinity as autonomous, ‘hermetic’ cognition and divinity as ultimate cause(s) of cosmic motion and change.

A Master-like argument, in the usage of the present paper, is an argument that employs a reductio ad impossibile principle to transmit the necessity of what are or become past truths to the remainder of time by means of necessary conditionals of some sort. The conclusion of such an argument is some no-unactualized-possibilities principle. This paper argues that the formulation of a Master-like argument by A. N. Prior in a mixed modal temporal propositional logic introduces certain artifacts into the logical analysis of the argument. One of these, a principle of temporal discreteness, is not essential to a Master-like argument. Another, a principle of forwards temporal linearity, is technically essential; but it is usually tacitly presupposed by the necessary temporal conditionals employed to 'tie together' past and future time in less formal accounts of Master-like arguments

THIS PAPER PRESENTS THE SEMANTIC THEORY FOR A TEMPORAL-MODAL LOGIC WITH RIGIDLY REFERENTIAL TEMPORAL OPERATORS ('dtomorrow' AND 'dnow') IN WHICH THE 'TRADITIONAL' INDETERMINIST INTERPRETATION OF ARISTOTLE'S _DE INTERPRETATIONE 9 CAN BE MODELED. THIS LOGIC HAS, I BELIEVE, SOME INTRINSIC PHILOSOPHICAL INTEREST AND PLAUSIBILITY. HOWEVER, THE PRESENT PAPER IS PRINCIPALLY DEVOTED TO AN INITIAL EXAMINATION OF THE RELATION BETWEEN THE LOGIC AND SUCH TOPICS IN THE ANCIENT PHILOSOPHY OF THE TIME AND OF THE MODALITIES AS THE NECESSITY OF THE PAST, ABSOLUTE VERSUS TEMPORALLY RELATIVE ALETHIC MODALITIES, THE 'PLENITUDE' PRINCIPLE AND UNACTUALIZED POSSIBILITIES, AND THE CYCLICAL NATURE OF TIME

The Megarians, as well as their Stoic heirs, are known to have been fatalists or logical determinists in the following, very broad sense of these terms: with respect to at least certain classes or kinds of nontautologous propositions, they held that the mere truth of a proposition entails its necessity. This paper explores, in a very tentative fashion, the relation between several versions of logical determinism and two passages in the Aristotelian corpus, one of which is specifically directed against Megarian doctrine and the other of which is an argument purporting to establish a thesis concerning the necessity of future events which Aristotle wished to reject but which the Megarian logician Diodorus Cronus apparently accepted.

This paper begins by pointing out that the Aristotelian conception of continuity (synecheia) and the contemporary topological account share the same intuitive, proto-topological basis: the conception of a ?natural whole? or unity without joints or seams. An argument of Aristotle to the effect that what is continuous cannot be constituted of ?indivisibles? (e.g., points) is examined from a topological perspective. From that perspective, the argument fails because Aristotle does not recognize a collective as well as a distributive concept of a multiplicity of points. It is the former concept that allows contemporary topology to identify some point sets with spatial regions (in the proto-topological sense of this term). This identification, in turn, allows contemporary topology to do what Aristotle was unwilling to do: to conceive the property of continuity, as well as the properties of having measure greater than zero and having n- dimension, as emergent properties. Thus, a point set can be continuous (connected) although none of its subsets of sufficiently smaller cardinality can be. Finally, the paper discusses the manner in which a topological principle, viz., the principle that none of the singletons of points of a continuum can be open sets of that continuum, captures certain aspects of the Aristotelian proto-topological conception of the relation between points and continua. E.g., for both Aristotle and contemporary topology, points in a continuum exist simple as limits of the remainder of the continuum: their singletons have empty ?interiors? and, hence, they are not ?chunks? (topologically, regular closed set) of the continuum

This paper develops an interpretation of the fourth account of conditionals in Sextus Empiricus's Outlines of Pyrrhonism that conceptually links it with contemporary ?relevance? interpretations of entailment. It is argued that the third account of conditionals, which analyzes the truth of a conditional in terms of the joint impossibility of antecedent and denial of consequent, should not be interpreted in terms of a relative incompatibility of antecedent and denial of consequent because of Stoic acceptance of the truth of some conditionals of the form p ? ?p and its converse. Rather, it is suggested, ancient attempts to avoid the so-called paradoxes of implication involve the fourth account of conditionals. I hypothesize that this account is related to Stoic attempts to define truth conditions for conditionals in terms of a theory of the concludency (validity) of arguments in opposition to the more common procedure (represented by the first three accounts of conditionals) of specifying truth conditions for conditionals ?semantically? and using those truth conditions in the development of a theory of argument validity

There is what might be called a ‘majority position’ in the history of Western philosophy according to which causes are sufficient for or ‘necessitate’ their effects. However, there is also a singificant ‘minority position’ according to which causes are necessary relative to their effects. The second/third century A.D. Peripatetic Alexander of Aphrodisias is an ancient representative of the minority position. He attributes his own view — with some justification, I shall suggest – to Aristotle. This paper has two, somewhat loosely connected purposes. The first is to explore the origin of the conception of ‘causes’ as necessary conditions in Aristotle, particularly in On Generation and Corruption 2.11 and Posterior Analytics 2.12, and the development and use of the conception in Alexander's De fato. The second purpose of the paper is to explore and criticize a sophisticated contemporary version of the conception of causes as ‘necessary in the circumstances,’ that of J.L. Mackie.

The “Aristotelian” conception of human agency and responsibility locates agency and responsibility in the exercise of practical reason in deliberation. A characteristic of such deliberation is that it must pertain to matters that can be decided either one way or the other. Some of Aristotle’s texts suggest an interpretation of deliberation that appears to yield the paradoxical result that agents are most responsible for (or act most freely with respect to) choices that are least determined, to the exclusion of other possible choices, by the practical reasoning issuing in those choices. This essay explores this strand of thought in Aristotle. It then proceeds to examine the response to the “paradox” in a middle-Platonist work, the De fato of Pseudo-Plutarch, and in the thought of the eminenttwentieth-century neo-Thomist, Reginald Garrigou-Lagrange.

DESPITE THE WELL-KNOWN historical significance of Aristotle’s doctrine of the productive or active intellect it is not unusual to find contemporary discussions treating the doctrine as an excrescence on the text of the De anima, a work, it is frequently nowadays supposed, in which an otherwise securely naturalistic epistemology and rational psychology are developed. Although the doctrine of the intellectus agens is found only in one place in Aristotle’s extant texts, the third book of the De anima, I shall nonetheless maintain that an argument can be ferreted out of Aristotle’s discussion that establishes that the doctrine can be seen to follow from principles that are fundamental to Aristotle’s thought. I shall call this an “Aristotelian” argument for nous poiêtikos because of the fact that the argument obviously is not found, as I state it, on the surface of Aristotle’s text. I claim that there is a significant sense in which it is there, but that one must dig for it or, as I just put it, ferret it out. In a schematic form, the Aristotelian argument goes as follows

A well-known epigram by Callimachus on the philosopher Diodorus Cronus reads as follows:The question of the third line, while perhaps recondite from a contemporary perspective, was clear in antiquity. The crows are asking ‘What follows ?’, in allusion to the Hellenistic disputes concerning the truth conditions of conditional propositions , disputes in which the views of Diodorus figured prominently.I agree with Sedley that the question of the last line is ‘much more problematic’. The common interpretation has been to read the αθι as a form of αθις and to interpret it temporally. The result, in Pfeiffer's estimation, is ‘quomodo posthac erimus?’.This interpretation derives from Sextus Empiricus' discussion at M. 1.309–12 of the last two lines of the epigram. After crediting the grammarian with the ability to understand the allusion in the crows' first question , he proceeds to argue that the philosopher has a better chance than the grammarian of understanding the second question. But, to quote Sedley, Sextus ‘makes a ghastly mess of it’ when he attempts his own elucidation. According to an argument of Diodorus, a living thing does not die in the time in which it lives nor in a time in which it does not live. Hence, Sextus concludes, it must be the case that it never dies and, ‘if this is the case, we are always living and, according to him, we shall come to be hereafter ’

This book presents a detailed analysis of three ancient models of spatial magnitude, time, and local motion. The Aristotelian model is presented as an application of the ancient, geometrically orthodox conception of extension to the physical world. The other two models, which represent departures from mathematical orthodoxy, are a "quantum" model of spatial magnitude, and a Stoic model, according to which limit entities such as points, edges, and surfaces do not exist in (physical) reality. The book is unique in its discussion of these ancient models within the context of later philosophical, scientific, and mathematical developments.