Godel's Theory Of Parallel Mathematical Philosophy

This paper discusses Godel’s philosophy of mathematics, taking his parallelism as the main thread. It tries to identify some difficulties in the theory and point out a possible way to modify it to avoid them. To start with, I analyze the parallelism contained in Godel’s philosophy of mathematics concretely, examining its ontological aspect and epistemological aspect in details. Specifically, I want to ascertain two things:firstly, what is the difference between the parallelism argument and the indispensability argument for ontological realism; secondly, under epistemological parallelism, what consequences can the new nature of mathematical intuition and the introduction of induction method into mathematical research bring onto the apriority of mathematical knowledge. After all this, I come up with two criticisms to the parallelism, corresponding to the two central notions in Godel’s philosophy, i.e. the notion of concepts existing independently of mind and that of mathematical intuition, respectively. The problem of the former lies in that concepts play a central role in Godel’s epistemology while they are ontologically rootless, which means here Godel’s parallelism argument for ontological realism doesn’t apply to concepts directly. As for mathematical intuition, my criticism then focuses on its actuality. In the end, I attempt to characterize the general features and potentiality of a possible way to modify Godel’s philosophy.