The hypothetical method in Plato's middle dialogues

The purpose of this dissertation is to offer an interpretation of Plato's hypothetical method in his middle dialogues. The hypothetical method is given in three accounts, one in the Meno, the Phaedo and the Republic. These three accounts of the method besides their affinities, seem to present some differences. The first main problem is to see whether we can speak of one single method, or of three different hypothetical method. Plato, in the Meno (86e) says that his method is similar to one which the geometers use and gives as an elucidation of it, an obscure geometrical problem to which I offer a new solution. The second main problem of this dissertation is to examine whether there is any relation (and if there is, of what kind) between Plato's accounts of the hypothetical method and the various methodologies in Greek geometry at that time. I show In this dissertation that we have one method, in a broad sense, that employs hypotheses and proceeds in two ways: firstly, a way upwards (or backwards) towards the premisses of the argument or towards prior questions and, secondly, a way downwards from the premisses to the desired conclusion. The upward way is a heuristic process, whilst the downward one is deductive. Although we have essentially one method in all three dialogues, it is somewhat differentiated from one dialogue to the next (and in particular between the Phaedo and the Republic). In the three accounts of the hypothetical method, I see three stages of an evolutionary process similar to a corresponding one which took place in the evolution of the method of Indirect proof in geometry. More precisely, I argue that the three accounts of Plato's method reflect three corresponding stages in the evolution of the reductive method of Hippocrates of Chios (apagoge) to the geometrical method of analysis and synthesis. I argue furthermore, as regards the relation between Plato's philosophy and mathematics, that the axiomatization of geometry had an Impact on Plato's conception of knowledge and upon his conception of dialectic. Moreover, I try to show that we have good reasons to suppose that Plato proposed a programme of reducing the principles of mathematics into the fewest possible and his contribution to this programme was decisive. There is another problem regarding Plato's hypothetical method. In his middle dialogues, Plato clearly speaks about a new philosophical method of great importance and he gives extensive theoretical accounts of it. The strange thing is that it seems (and here almost all scholars agree) that nowhere does he apply his method (with the exception of a small-scale application of It In the Meno). However, this does not seem very likely. In chapters V and VI, I shall argue that we have extensive applications of the method in both the Phaedo and the Republic.