데데킨트 - 공리적 방법과 논리주의

국문 초록 (Abstract)

이 글에서 나는 윌프리드 지이크가 더크 슐림 및 레베카 모리스와 함께 제시한 데데킨트의 방법론에 대한 해석을 평가한다. 나의 논의 결과는 다음 세 주장으로 요약된다. (1) 데데킨트가 최종적으로 우리 사고에 의해 자연수들이 창조되었다는 주장을 포기했다는 데 대해 그들이 제시하는 근거는 설득력이 있다. (2) 하지만 데데킨트의 공리적인 개념 형성방법이 로체 식의 추상화에 의존한다는 그들의 주장은 잘못된 것이다. (3) 데데킨트의 공리적 개념 형성절차는 추상화 절차가 아니라 개별 구조에 대한 단칭 진술에서 존재 진술로 나아가는 논리적 추론에서 우리가 수행하는 술어 내용의 인식절차이다. 마지막으로 나는 개념도입에 관한 데데킨트와 프레게의 이론은 깊은 연관성을 갖고 있다고 주장한다.

다국어 초록 (Multilingual Abstract)

In this paper I try to evaluate the interpretation of Dedekind’s methodology which Wilfrid Sieg has recently given with Dirk Schlimm and Rebecca Morris. The results of my investigation are epitomized as the following three theses. (1) The grounds which they provided in order to show that Dedekind gave up eventually the thesis that natural numbers have been created by our thought are very compelling. (2) But their assertion that Dedekind’s axiomatic formation of concepts depends upon a kind of Lotzean abstraction is unfounded. (3) Dedekind’s axiomatic formation of a concept is not any kind of conceptual abstraction, but a kind of recognition of content of a predicate without which we could not infer logically an existential statement from a singular statement about an individual structure. Finally I assert that Dedekind and Frege have deep connections in their theories of formation of new concepts.

목차 (Table of Contents)

• 한글요약
• Ⅰ. 들어가는 말
• Ⅱ. 데데킨트와 공리적 방법
• Ⅲ. 공리적 정의와 추상화
• Ⅳ. 공리적 정의와 메타이론
• Ⅴ. 나오는 말
• 참고문헌
• Abstract

참고문헌 (Reference)

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