논리연구 (Korean Journal of Logic)

한국논리학회 (Korean Association for Logic)
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프레게의 Grundgesetze 와 그 이후의 시스템에서의 귀납법 고찰

On Induction Principles in Frege's Grundgesetze and in Systems Thereafter

  • 이계식 (한경대학교 컴퓨터웹정보공학과)
  • Lee, Gyesik (Department of Computer & Web Information Engineering, Hankyong National University)
  • 투고 : 2015.11.06
  • 심사 : 2016.02.12
  • 발행 : 2016.02.28
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초록

프레게의 Grundgesetze에 소개된 시스템과 그 이후에 집합론 및 유형론에서 중요한 역할을 한 시스템들에서 사용된 귀납법에 대해 살펴본다. 먼저 프레게의 자연수 귀납법에 대한 이해를 살펴 본 후에 현대 집합론과 유형론에서 귀납법이 어떻게 정의 및 활용되는가를 살펴본다. 또한 프레게의 접근방식과 기타 접근방식의 차이점을 predicativity와 impredicativity 차원에서 조명한다.

We compare the approaches to natural numbers and the induction principles in Frege's Grundgesetze and in systems thereafter. We start with an illustration of Frege's approach and then explain the use of induction principles in Zermelo-Fraenkel set theory and in modern type theories such as Calculus of Inductive Constructions. A comparison among the different approaches to induction principles is also given by analyzing them in respect of predicativity and impredicativity.

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과제정보

연구 과제 주관 기관 : National Research Foundation of Korea[NRF]

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