Aristotle is said to have held that any kind of actual infinity is impossible. I argue that he was a finitist (or "potentialist") about _magnitude_, but not about _plurality_. He did not deny that there are, or can be, infinitely many things in actuality. If this is right, then it has implications for Aristotle's views about the metaphysics of parts and points.

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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

We present an algorithm that can anticipate tax evasion by modeling the co-evolution of tax schemes with auditing policies. Malicious tax non-compliance, or evasion, accounts for billions of lost revenue each year. Unfortunately when tax administrators change the tax laws or auditing procedures to eliminate known fraudulent schemes another potentially more profitable scheme takes it place. Modeling both the tax schemes and auditing policies within a single framework can therefore provide major advantages. In particular we can explore the likely forms (...) of tax schemes in response to changes in audit policies. This can serve as an early warning system to help focus enforcement efforts. In addition, the audit policies can be fine tuned to help improve tax scheme detection. We demonstrate our approach using the iBOB tax scheme and show it can capture the co-evolution between tax evasion and audit policy. Our experiments shows the expected oscillatory behavior of a biological co-evolving system. (shrink)

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. (shrink)