논리학, 존재론, 그리고 양상 = Logic, Ontology, and Modality

국문 초록 (Abstract)

논리학이 존재론과 무관하다는 생각이 널리 받아들여져 왔음에도 불구하고, 오늘날의 메타논리학은 집합 개념들을 통해서 논리적 개념들을 정의하고 논리학을 기술함으로써 논리학에 집합 존재론을 부가하게 된다. 유명론자들의 관점에서와 같이 논리학의 외적 측면에서 보더라도 집합과 같은 수학적 존재자는 형이상학적으로 받아들이기 힘든 존재자이지만, 논리학의 존재론적 보수성을 위반하기 때문에 집합론적 메타논리학은 논리학의 내적 측면에서조차 올바른 메타논리학으로 간주될 수 없다. 본 논문은 먼저 메타논리학이 논리학의 의미론을 제시하는 바로 그 측면에서 논리학에 특유한 존재론적 문제를 제기한다는 점을 지적함으로써, 그 동안 논리학이 존재론적과 무관하다는 생각과 집합론적 메타논리학을 동시에 받아들이는 견해를 비판한다. 나아가 논리학이 타당성과 같은 양상적 속성들을 지니기 때문에, 메타논리학은 이러한 논리학의 양상성을 만족스럽게 설명해야 하며, 무엇보다 양상성 일반과 관련하여 통합적인 방식으로 다루어야 한다. 메타논리학에서 논리학을 성공적으로 그리고 통합적인 방식으로 다루기 위해서는 가능세계 개념이 요구되는데, 가능세계에 대한 기존의 이론들은 논리학의 존재론적 보수성을 위반하게 된다. 마지막으로 양상성과 관련하여 존재론적 부담이 없지만, 양상성을 만족스럽게 설명하는 이론을 통해서, 메타논리학에서도 논리학이 존재론과 무관하다는 직관을 구제하면서도 양상성을 통합적으로 설명할 수 있는 이론의 가능성을 제시한다.

다국어 초록 (Multilingual Abstract)

Today’s metalogic, so-called mathematical logic describes logic by defining various logical concepts in terms of set-theoretic concepts such as sets, functions, and models. Consequently, set-theoretic metalogic imposes ontological burden of mathematical entities to logic, and this contradicts our intuition that logic is ontology-free. Although there might be some reasons that ontological purity of logic and set-theoretic metalogic are compatible, I cannot see any plausibility in those answers. In order for logic to be ontologically innocent, we are not allowed to bring set-theoretic entities into metalogic because set-theoretic metalogic contravenes ontological conservativeness of logic. In addition, metalogic must give satisfactory and unified explanation of modality of logic such as logical consequence. For this, metalogic needs to appeal to the concept of possible worlds. Unfortunately, however, existing theories of modality, whether realist or antirealist, cannot be in line with ontological conservativeness of logic, so they cannot shed light on the pursuit of philosophically correct metalogic. Nevertheless, there is an adequate approach to modality, Modal Quasi-Realism, according to which, it is possible to present unified theory of modality without ontological commitment to existence of possible worlds. Applying this to metalogic, we can delineate a form of metalogic that can cope with ontological conservativeness and modality of logic in successful way.

목차 (Table of Contents)

• Ⅰ. 논리학과 존재론
• Ⅱ. 논리학과 양상
• Ⅲ. 양상과 존재론
• Ⅳ. 결론
• 참고문헌
• Abstracts

참고문헌 (Reference)

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