This paper concerns Aristotle's kind‐crossing prohibition. My aim is twofold. I argue that the traditional accounts of the prohibition are subject to serious internal difficulties and should be questioned. According to these accounts, Aristotle's prohibition is based on the individuation of scientific disciplines and the general kind that a discipline is about, and it says that scientific demonstrations must not cross from one discipline, and corresponding kind, to another. I propose a very different account of the prohibition. The prohibition is (...) based on Aristotle's scientific and metaphysical essentialism, according to which a scientific demonstration must take as its starting point a set of per se properties of a subject, if these make up a single, unitary definition. The subject of demonstration here is a kind, although not the general kind associated with a discipline, but rather the particular kind that the particular demonstration is about. (shrink)

I argue against a formidable interpretation of Plato’s Divided Line image according to which dianoetic correctly applies the same method as dialectic. The difference between the dianoetic and dialectic sections of the Line is not methodological, but ontological. I maintain that while this interpretation correctly identifies the mathematical method with dialectic, ( i.e. , the method of philosophy), it incorrectly identifies the mathematical method with dianoetic. Rather, Plato takes dianoetic to be a misapplication of the mathematical method by a subset (...) of practicing mathematicians. Thus, Plato’s critique of dianoetic is a not a critique of mathematics, as such, but of mathematicians. (shrink)

Plato's Republic critiques Athenian democracy as practised during the Peloponnesian War years. The diseased city Socrates attempts to purge mirrors Athens in crucial particulars, and his proposals should be evaluated as counter-weights to existing institutions and practices, not as absolutes to be instantiated. Plato's assessment of the Athenian polity incorporates two strategies -- one rhetorical, the other argumentative -- both of which I address. Failure to consider Athens a catalyst for Socrates' arguments has led to the misconception that Plato was (...) dogmatically committed to a single political doctrine for all and for all time. (shrink)