著者
斉藤 健
出版者
北海道大学哲学会 = The Philosophical Society of Hokkaido University
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.42, pp.15-33, 2006-07-18

Structuralism considers structures to be principal. According to in re structuralism, a structure resides in particular systems exemplifying the former. I characterize a schema for any mathematical entity as a pattern framed by its definition including its axioms in mathematics, no matter how described by set theory or category theory. The aim of this paper is to present in re structuralism by schema and to argue for it. In re structuralism commits less abstract entities than ante rem structuralism. From the presented position we can regard all the structures (including variable sets) as schemas framed by definitions in mathematics. Such schemas can be comprehended through mathematicians' communication in metalanguage.
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
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
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.44, pp.右137-右152, 2008-02-29
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
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
著者
柏葉 武秀
出版者
北海道大学哲学会
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.44, pp.47-65, 2008-02-29
著者
日吉 大輔
出版者
北海道大学
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.41, pp.右1-右19, 2005-07-17

In Posterior Analytics B1-10, Aristotle constructs theory of inquiry, which has two crucial theses: (a) "everything which is inquired is the inquiry into a middle term" and (b) "what it is and why it is are the same." These are concerned with definition and demonstration. Then I will show how the relation between (a) and (b) is, while he seems to put them as mutually dependent conceptions in the relevant context. I distinguish B1-10 into three phases: phase 1; practice of inquiry (B1-2), phase 2; traditional framework (B3-7), phase 3; his theory of inquiry (B8-10).These three phases, I think, reflect on the relation between (a) and (b), and provide us backgrounds of the construction of the theory. Especially, phase 2 maintains the balance of definition and demonstration in the beginning of B8 on the basis of a traditional concept; essence.
著者
坂井 昭宏
出版者
北海道大学
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.42, pp.右23-右32, 2006-07-18