著者
水野 浩二
出版者
北海道大学哲学会
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.38, pp.1-17, 2002-07-21
著者
野本 和幸
出版者
北海道大学哲学会
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.40, pp.1-28, 2004-07-18

Firstly I sketch Frege's personal history, his academic career and his publications briefly, and secondly I try to give a general outline of the structural and methodological characteristics of his investigations as a whole. One can divide Frege's logico-philosophical investigations into the three parts as follows: (A) The invention of contemporary logic, its axiomatic systematization and the development of the logicist philosophy of arithmetic. (B) Philosophy of logic. (C) Controversies with his contemporary distinguished scholars concerning psychologism, empiricism, physicalism, formalism, etc., though I do not take them up this time. Concerning (A), firstly I try to explain why Frege must constitute the higher order logic through formulating his formal language (Begriffsschrift) for the accomplishment of his logicist project. Secondly I take note of his theory of judgment/ assertion and inference, and point out its two distinctive features, i.e., (1) his priority thesis of judgment, and (2) his epistemological characterization of judgment and inference. For Frege, a judgment is the recognition of the truth (als wahr anerkennen) of the thought-content and assertion is the manifestation of a judgment with assertoric force,while an inference is the justification (Berechtigung) of the correctness of the conclusion based on its true premises. Thirdly, Frege's claim of the primacy of the sentence or the context principle, and the composition principle are Frege's methodological guiding principles of his syntactic and semantic considerations as a whole. Concerning (B): his philosophy of logic, (1) Frege will neither approve the justifiability of primitive logical laws nor definability of primitive logical terms within his Begriffsschrift. (2) In fact, Frege does not introduce distinctive model theoretic ideas such as variant domains or quantification along with domain fixing. However, Frege explicitly provides lots of semantical 'explanations (Erklärung/Darlegung)' in his ‘explanatory language (Darlegungssprache)' as metalanguage distinguished from his object language (Begriffsschrift as ‘Hilfssprache'). For example, in his main work: GGA, Frege tries to give the proofs of the meaningfulness of his primitive logical symbols, truthfulness of axioms, and the truth-preserving nature of inference-rules. (3) Frege gives further metalinguistic explanations as propedeutic concerning the basic ‘logical forms' such as‘fall-under (subsumption)' and his logical categories: objects versus concepts/functions, and his semantic distinction of sense (Sinn) and Meaning (Bedeutung). In such explanations there might be a certain anticipation of Wittgensteinian idea of ‘saying' and ‘showing'. Furthermore Frege provides meta-meta-linguistic elucidations or suggestions resorting to vivid metaphors concerning his fundamental categories of proper names versus function-signs/concept-words,o r objects versus functions/concepts, the distinction of Begriffsschrft from ordinary language, and the relationship of representation, sense and Meaning, etc. Really Frege is not only the most revolutionary logician since Aristotle, but also a distinguished man of metaphor.
著者
水野 浩二
出版者
北海道大学哲学会
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.39, pp.81-87, 2003-07-20
著者
深山 洋平
出版者
北海道大学哲学会
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.42, pp.1-14, 2006-07-18

F.W. Lawvere described a certain interesting feature on G. Cantor's theory of cardinal numbers, using adjoint functors from the category theory. This paper provides a brief overview of the method he took, and then consider its significance. As a consequence, it is shown that he argues Cantor's theory of cardinal numbers in relationship to structured sets (specifically with topological structures,) and from the method we can get a hint to approach the nature of sets.
著者
田村 圭一
出版者
北海道大学哲学会
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.39, pp.1-18, 2003-07-20
著者
長谷川 吉昌
出版者
北海道大学哲学会
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.36, pp.1-18, 2000-07-23
著者
田村 圭一
出版者
北海道大学哲学会
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
no.39, pp.1-18, 2003
著者
斉藤 健
出版者
北海道大学哲学会
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.37, pp.21-38, 2001-07-15
著者
中澤 務
出版者
北海道大学哲学会
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.37, pp.39-55, 2001-07-15