Jacob Rosen

This chapter attempts to clarify Aristotle’s claims that a thing’s formal cause is often one with, or the same as, its final cause. This claim has confused scholarly understanding regarding the teleology, essences, and causation in Aristotle’s thought. When Aristotle’s sameness claim is understood in a straightforward way, it is open to obvious counter-example. Furthermore, this sameness claim admits many interpretations, since there is more than one way of being a final cause and there is more than one way of being the same. Yet the sameness claim has had a great influence in the interpretation of Aristotle. Hence this chapter is motivated by the conviction that Aristotle’s concepts of formal cause and of final cause possess great and enduring philosophical interest, and that a certain kind of work will help us recover a clearer understanding of them.

In Prior Analytics 1. 15, Aristotle states the following rule of modal logic, which we may call the possibility rule: given the premiss that A is possible, and given a derivation of B from A, it can be inferred that B is possible. Aristotle is the first philosopher known to state this rule, and it stands among his most significant contributions to philosophical thought about modality. He applies the possibility rule in arguments that are central to his physical and metaphysical views, in works such as the _Physics, De caelo, De generationeetcorruptione_, and the _Metaphysics_. These arguments have proved difficult to understand, largely because the exact nature of the possibility rule and its role in each argument is often unclear. The chapter offers a comprehensive treatment of the arguments throughout Aristotle's works, resulting in a better understanding both of the possibility rule and of the individual arguments in which it appears.

In histories of thought about the infinite, Aristotle is constantly said to have rejected any form of actual infinite, and to have allowed quantities to be at most _potentially_ infinite. Aristotle does reject actual infinites in spatial _magnitude_: nothing is infinitely big or infinitely small. But in the central case of _plurality_, the evidence for potentialism is much weaker. This paper argues that Aristotle had no principled objection to the idea that there are actually infinitely many things. One part of the argument concerns the distinction in Aristotle between plurality ( πλῆθος ) and number ( ἀριθμός ). Another part concerns the meaning of phrases like ‘infinite by division’, arguing that such phrases do not refer to _how many times_ something has been divided, but rather to _how small_ something is. The argument of this paper, if successful, affects how we should think about the metaphysics of parts in Aristotle’s theory of the continuum.

On Zeno Beach there are infinitely many grains of sand, each half the size of the last. Supposing Aristotle denied the possibility of Zeno Beach, did he have a good argument for the denial? Three arguments, each of ancient origin, are examined: the beach would be infinitely large; the beach would be impossible to walk across; the beach would contain a part equal to the whole, whereas parts must be lesser. It is attempted to show that none of these arguments was Aristotle’s. Indeed, perhaps Aristotle’s finitism applied to magnitude only, not plurality.

Malink’s interpretation is designed to validate Aristotle’s claims of validity and invalidity of syllogistic-style arguments, as well as his conversion claims. The remaining sorts of claims in Aristotle's text are allowed to fall out as they may. Thus, not all of Aristotle’s examples turn out correct: on some occasions, Aristotle claims that a given pair of terms yields a true (false) sentence of a given type although, under Malink’s interpretation, the sentence in question is false (true). Similarly, some of Aristotle’s claims of invalidity of nonsyllogistic-style arguments come out false. For example, under Malink’s interpretation, ‘A applies to all B’ and ‘B necessarily applies to all C’ entail ‘A necessarily applies to some B’, contrary to what Aristotle says.

Aristotle offers several arguments in Physics viii.8 for his thesis that, when something moves back and forth, it does not undergo a single motion. These arguments occur against the background of a sophisticated theory, expounded in Physics v—vi, of the basic structure of motions and of other continuous entities such as times and magnitudes. The arguments in Physics viii.8 stand in a complex relation to that theory. On the one hand, Aristotle evidently relies on the theory in a number of crucial steps. Yet in other steps he seems to contradict or misapply the theory. This situation offers the occasion to examine Aristotle’s views about some fundamentals in the metaphysics of motion, while also raising questions about the unity of the text which has come down to us as the Physics.

Abstract This paper illustrates how Aristotle's topological theses about change in Physics 5-6 can help address metaphysical issues. Two distinctions from Physics 5. 1 are discussed: changing per se versus changing per aliud ; motion versus change. Change from white to black is motion and alteration, whereas change from white to not white is neither. But is not every change from white to black identical with a change from white to not white? Theses from Physics 6 refute the identity. Is change from white to black at least accompanied by change from white to not white? Perhaps, but given further theses from Physics 6, this supposition yields unwelcome consequences. Most likely, when something changes from white to black it changes merely per aliud , not per se , from white to not white. Genuine change between white and not white is found elsewhere; its admission has bearing on Aristotle's theory of perception

In Prior Analytics 1.15 Aristotle undertakes to establish certain modal syllogisms of the form XQM. Although these syllogisms are central to his modal system, the proofs he offers for them are problematic. The precise structure of these proofs is disputed, and it is often thought that they are invalid. We propose an interpretation which resolves the main difficulties with them: the proofs are valid given a small number of intrinsically plausible assumptions, although they are in tension with some claims found elsewhere in Aristotle’s modal syllogistic. The proofs make use of a rule of propositional modal logic which we call the possibility rule. We investigate how this rule interacts and coheres with the core elements of the modal syllogistic.