The philosophical use of mathematical analysis
Faller, Mark Andrew
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This dissertation defends the thesis that Plato's employs methods of philosophical analysis that are akin to and based upon mathematical analysis. It identifies and describes three kinds of ancient mathematical analysis, rectilinear, dioristic, and poristic. It then shows that there are corresponding philosophical modes of analysis in portions of the Meno and Phaedo. Recognizing Plato's method in these dialogues provides insight into the doctrines Plato advances there and the arguments that support them. It also makes it possible to address three scholarly controversies. First, there is a dispute between F. Cornford and R. Robinson on whether mathematical analysis is a deductive or non-deductive procedure. The dissertation shows that some types are deductive and some are not. Second, there is an issue raised by K. Dorter whether the philosophical method of hypothesis proceeds ultimately to an unconditioned first principle, the good. The dissertation shows how philosophical analysis that is modeled on mathematical poristic could ultimately arrive at an unconditioned principle. Third, there is the question raised by Charles Kahn and others whether the divided line of the Republic delineates methods, each of which is applicable to a different type of being. The dissertation shows that, though some methods are most properly applied to particular types of being, Platoapplies all the different types of philosophical analysis to all the types of being.