Volume 44, Issue 3

I argue that Euclid's highly abstract definitions in Book I of the Elements play a key role, enabling general conclusions from particular diagrams. I argue four points. First, definitions limit focus to the most generalized features of elementary geometrical objects. Second, an explicit reciprocal dependency relation exists between figure and boundary. Third, Euclid's derivation style employs a combination of diagrams in tandem with the highly abstract definitions. Fourth, this combination renders all non-universal features of a particular diagram irrelevant. The result limits the role of diagrams in a way that is reminiscent of Aristotle's characterization of the geometer's use of diagrams.

This paper proposes a new interpretation of Parmenides B 16. After a short review of the status quaestionis (section 1), I will proceed to a detailed examination of the context of quotation in Aristotle (section 2) and Theophrastus, whose report will be shown to disclose some new possibilities for our understanding of the fragment. I shall argue that B 16 is not a theory of sense-perception, but a fragment of a comprehensive theory of cognition (section 3). This theory is consistent with Parmenides' own claims to genuine knowledge of Being (section 4), once we recognize that neither a dualism of ontological domains (“intelligible” vs. “sensible”) nor of cognitive faculties (“reason” vs. “the senses”) can be consistently ascribed to Parmenides. Moreover, our discussion will provide some elements for a reappraisal of Aristotle and Theophrastus as interpreters of their predecessors.

One aim of this paper is to bring to the surface the problems with the traditional, non-literal interpretation of the pre-cosmos in the Timaeus. Contrary to this traditional interpretation, I show that Necessity is an ateleological cause capable of bringing about the events in the pre-cosmos, and that Intelligence is a teleological cause that produces effects only for the sake of maximizing the good. I conclude that there are no grounds for supposing that Intelligence is a causal force operating in the pre-cosmos, and that the account of the pre-cosmos should be taken literally: it is an account of the works of Necessity alone.