Late ancient Platonists and Aristotelians describe the method of reasoning to first principles as "analysis." This is a metaphor from geometrical practice. How far back were philosophers taking geometric analysis as a model for philosophy, and what work did they mean this model to do? After giving a logical description of analysis in geometry, and arguing that the standard (not entirely accurate) late ancient logical description of analysis was already familiar in the time of Plato and Aristotle, I argue that Plato, in the second geometrical passage of the Meno (86e4-87b2), is taking analysis as a model for one kind of philosophical reasoning, and I explore the advantages and limits of this model for philosophical discovery, and in particular for how first principles can be discovered, without circularity, by argument.
Simplicius cites Porphyry’s lost greater commentary on the Categories by the name of its addressee: Πρὸς Γεδάλειον. It has been assumed that we know nothing about Gedalius, and even suggested that he may have been a fictional construct. But his name is Jewish, and Porphyry had no reason to make up a Jewish addressee. It was extremely rare for Greek pagan texts to be dedicated to a Jewish addressee. But Porphyry had an unusual degree of involvement with Judaism. I collect the evidence, and make a tentative proposal about the context for Porphyry’s dedicating this work to Gedalius.
Aristotle in Physics I,1 says some strange-sounding things about how we come to know wholes and parts, universals and particulars. In explicating these, Simplicius distinguishes an initial rough cognition of a thing as a whole, an intermediate “cognition according to the definition and through the elements,” and a final cognition of how the thing’s many elements are united: only this last is πιστήμη. Simplicius refers to the Theaetetus for the point about what is needed for πιστήμη and the ways that cognition according to the definition and through the elements falls short. By unpacking this reference I try to reconstruct Simplicius’ reading of “Socrates’ Dream,” its place in the Theaetetus’ larger argument, and its harmony with other Platonic and Aristotelian texts. But this reconstruction depends on undoing some catastrophic emendations in Diels’s text of Simplicius. Diels’s emendations arise from his assumptions about definitions and elements, in Socrates’ Dream and elsewhere, and rethinking the Simplicius passage may help us rethink those assumptions.