한국논리학회 회원 여러분께,
안녕하십니까. 한국논리학회 2026년 1학기 두 번째 월례윤독회 일정이 결정되어 다음과 같이 일정에 따라 진행될 예정임을 사전 공지드립니다.
발표자: Byeong-uk Yi (University of Toronto)
주제: Arithmetical Pluralism and Incompleteness Theorems
주제: Arithmetical Pluralism and Incompleteness Theorems
일시: 2026년 4월 29일(수) 오후 7시 (한국 시각)
소개글: Gödel’s incompleteness theorems show that a wide range of formal systems cannot be both consistent and complete. For example, let PA be the first-order Peano arithmetic (PA) and Con(PA) the sentence in the language of PA that encodes the thesis that PA is consistent. Then the second incompleteness theorem implies that Con(PA) is not provable in PA unless PA is inconsistent. Recently, some use the theorem to argue for arithmetical pluralism, the view that there are equally good arithmetical theories that are apparently inconsistent with each other. For example, in this view, adding Con(PA) and its negation to PA yields such theories. Adding one or the other of the two sentences to PA, in the view, gives rise to the change of meaning of, e.g., ‘number’ that assigns a more precise or definite meaning to the expression. I will discuss problems of this view and argue that we have good reason to take PA to be consistent (and thus to take Con(PA) to be true) despite the fact that Con(PA) is not provable in PA.
소개글: Gödel’s incompleteness theorems show that a wide range of formal systems cannot be both consistent and complete. For example, let PA be the first-order Peano arithmetic (PA) and Con(PA) the sentence in the language of PA that encodes the thesis that PA is consistent. Then the second incompleteness theorem implies that Con(PA) is not provable in PA unless PA is inconsistent. Recently, some use the theorem to argue for arithmetical pluralism, the view that there are equally good arithmetical theories that are apparently inconsistent with each other. For example, in this view, adding Con(PA) and its negation to PA yields such theories. Adding one or the other of the two sentences to PA, in the view, gives rise to the change of meaning of, e.g., ‘number’ that assigns a more precise or definite meaning to the expression. I will discuss problems of this view and argue that we have good reason to take PA to be consistent (and thus to take Con(PA) to be true) despite the fact that Con(PA) is not provable in PA.
[References]
Picollo, L. and Waxman, D. 2025. ‘Arithmetical pluralism and the objectivity of syntax.’ Noûs 59: 372–391.
아무쪼록 논리학회 회원님들의 많은 참여와 관심 부탁드리며, 해당 주제에 관심을 가질 만한 분들께 널리 알려주시면 감사하겠습니다.
한국논리학회 학술위원장 드림
한국논리학회 학술위원장 드림