Historical and Logical Investigation into Hilbert Program as a philosophy of mathematics

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In this research project, we aimed at the explication of the following two points; how is the rela-tion between the so-called Hilbert program and Godel's second incompleteness theorem and how did Brouwer's criticism against Hilbert exert an influence on the historical development of Hilbert program. As a result, first of all we could show that the official view which said that Hilbert pro-gram faild because of Godel's second incompleteness theorem would not critically demonstrated. This result is based on Michael Detlefsen's prior research. But what we should derive from this result is not simply the revival of Hilbert program but the insight that Godel's second incom-pleteness theorem would be concerned with the problem of intensionality, that is, the fundamental problem of discripancy between linguistic (or formal) expressions and what we mean by them. Sec-ondly, we could show that Brouwer's criticism against Hilbertian formalism, especially Brouwer's criticism of the linguistic methods in mathematics, was fundamentally important in the process of sophistication of Hilbert's finitism. It should be noted that many strategies of Hilbert program are interpretable as responces to Brouwer's criticism.