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. (shrink)

Mugler maintains that interpreters have been mistaken in drawing from the pedagogical plan of Republic VII any general conclusion concerning the relative position which Plato assigned to philosophical speculation and mathematics, that in Plato's own intellectual experience the relation of the two was the reverse of that assigned to them there, mathematics being more often the end of metaphysical reflection than its point of departure, and that he recommended mathematical study to his pupils not merely as a propaedeutic for dialectic (...) but primarily because from his own experience he believed that subsequent philosophical meditation upon the fund of knowledge thus acquired would often lead to mathematical discoveries. Mugler does not say how this thesis is to be reconciled with the fact that at the end of the Laws dialectic is still declared to be the supreme science and that in such a late passage as Philebus 57 D ff. as well as in an early one like Euthydemus 290 C, neither of which is "pedagogical," the supremacy of dialectic and its priority to mathematics are affirmed as emphatically as in Republic VII; he simply says that a close interpretation of the "metaphysical" dialogues and the Timaeus will substantiate his contention, and it is therefore necessary to examine his interpretation in detail. (shrink)

This paper examines socrates' method for determining whether virtue is taught, And discusses some of the opposing interpretations that have been offered (e.G., By robinson and hackforth). Some major conclusions are: that hypotheses that have been deduced from other hypotheses can still be called hypotheses; that it is false that there can be only one hypothesis per argument; and that the several hypotheses in a given argument need not all be hypothesized with the same degree of confidence.

I desire to invite the attention of students of Plato and of Greek mathematics to a solution of a passage which has long been a field of controversy for critics. For brevity's sake I shall take for granted an acquaintance with the two solutions which at present dispute the field, and further adopt certain positions which previous enquirers have established beyond reasonable doubt.