著者

八杉 滿利子

出版者

科学基礎論学会

雑誌

科学基礎論研究 (ISSN:00227668)

巻号頁・発行日

vol.43, no.1-2, pp.17-30, 2016-03-30 (Released:2017-08-31)

参考文献数

17

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In the early volumes of this journal, there are many articles in which the authors present their viewpoints on formalism, that is, on formal systems of mathematics and their relations to practices of mathematics. Their discussions may be condensed into the philosophical matters of substance and form, epistemology and ontology, for taking the stand of formalism must necessarily admit the substance behind it. I will take up some of the old articles which are concerned with formalism and formal systems and review them from my present standpoint, in order to excavate fresh and honest thoughts of our seniors and to see how the views on formalism and formal systems of mathematics in this journal have changed with the passage of time.

著者

八杉 滿利子

出版者

京都大学哲学論叢刊行会

雑誌

哲学論叢 (ISSN:0914143X)

巻号頁・発行日

vol.39, no.別冊, pp.S24-S35, 2012

著者

八杉 滿利子

出版者

京都大学 (Kyoto University)

巻号頁・発行日

2014-03-24

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新制・課程博士

著者

八杉 滿利子

出版者

科学基礎論学会

雑誌

科学基礎論研究 (ISSN:00227668)

巻号頁・発行日

vol.42, no.2, pp.97-104, 2015-03-30 (Released:2017-08-31)

参考文献数

14

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The halting property as such is not guaranteed for limitimg recursion, since its evaluation process requires infinitely many steps. Nevertheless, as limiting recursive functions are useful in the study of computational aspects of mathematics on the continuum, it is desirable that some extended notion of computation be bestowed upon limiting recursion. We will here present a framework which general recursion and limiting recursion can share in characterizing their functions, and in which the halting property of the former and the identification in the limit of the latter can be expressed in terms of a formula stating a kind of compactness of a sequence of sets. We regard this fact as claiming that limiting recursion is conjunctive to general recursion, and hence can be viewed as a computation in an extended sense.