힐버트 형식주의와 이념적 방법 = Hilbert`s Formalism and Ideal Method

국문 초록 (Abstract)

이념적 수학에 관한 힐버트의 사상은 많은 해석가들에 의해 유명론적 도구주의로 간주되어 왔다. 나는 이런 해석가들 대부분 힐버트의 이념적인 것과 현실적인 것 사이의 구분을 내용적인 것과 형식적인 것 사이의 구분으로 잘못 이해했다고 생각한다. 이 글은 이런 해석이 근거가 없다는 것을 보이는 데 목적이 있다. 이를 위해, 나는 힐버트의 1919-1920년의 강연록 『자연과 수학적 인식』에 나타난 이념적 방법, 그리고 「무한에 관하여」(1926)를 비롯해서 후기 힐버트의 저술에 나타난 그 방법의 적용 사례를 살펴본다. 이런 검토를 기반으로 나는 힐버트의 이념적 수학을 유명론적 도구주의로 이해하는 일은 유지되지 힘들다고 결론짓는다.

다국어 초록 (Multilingual Abstract)

Hilbert`s thought on ideal mathematics has been regarded by many interpretators as a nominalistic instrumantalism. I believe that most of them falsely identified Hilbert`s distinction between the ideal and the actual with the distinction between the formal and the contentual. The purpose of this paper is to show that this identification is unfounded. At first, I reconstruct Hilbert`s general view on ideal methods which can be found in his lecture notes of 1919-1920, titled as "Natur und Mathematische Erkennen". Secondly, I consider how he applied such a view to his proof theory in 1920s. On the basis of this, I conclude that such a nominalistic interpretation of Hilbertian ideal mathematics is untenable.

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