Brouwer's Conception of Language, Mind and Mathematics

概要

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It has been the main stream of research into intuitionsim for some decades to try to interpret intuitionist criticism of classical mathematics from a constructive semantic point of view. In such attempts, however, it is impossible to include all intuitionistic tenets, especially Brouwer's criticism of language and communication, in such a semantic framework. Some parts of Brouwer's thoughts thoroughly resist any kind of semantic interpretation. This is similar to Wittgenstein's later philosophy which also does not fit any kind of semantic interpretation, or to interpretations that his philosophy is constructed to exclude any semantic readings. By this comparison I hope to suggest that we have something to learn from Brouwer's philosophy, especially his criticism of language and linguistic communication that resists any semantic readings. In fact, Brouwer exerted influence on peoples such as Hilbert and Weyl for almost two dacades before the beginning of semantic research, that is, before the formulation of intuitionistic logic by Heyting. So, we can raise a legitimate question about what influence Brouwer exerted. Roughly speaking, I think it was his prior insights into the relation between language and mathematics. In the following, I would like to consider what those insights are, what kind of view on language they are based on and how they influence the foundational debates.
科学基礎論学会の論文
2002-11-25