On Brouwer’s criticism of classical logic and mathematics

Tomasz Placek

DOI: http://dx.doi.org/10.12775/LLP.1997.002

Abstract


The aim of this paper is to reconstruct Brouwer’s justification for the intuitionistic revision of logic and mathematics. It is attempted to show that pivotal premisses of his argument are supplied by his philosophy. To this end, the basic tenets of his philosophical doctrine are discussed: the concepts of mind, causal attention, intuition of two-ity and his repudiation of realism.The restriction of intuitionistically allowable objects to spreads and species is traced back to Brouwer’s concept of intuition that is a defining feature of his notion of mind. On the other hand, it is argued that his objections to some laws of classical logic result from the rejection of the rule of double negation elimination, which in turn follows from both, the claim that rules of logic should preserve evidence for assertions rather than truth, and too restrictive a concept of evidence.

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References


Brouwer, L. E. J. CW Collected Works, vol. 1, ed. by A. Heyting, North Holland, 1975.

Brouwer, L. E. J. 1907 “On the foundation of mathematics”, in CW, p. 11–101.

Brouwer, L. E. J. 1919 “Signifische Sprachforschung”, in CW, p. 222–229.

Brouwer, L. E. J. 1929 “Mathematik, Wissenschaft und Sprache”, in CW, p. 417–428.

Brouwer, L. E. J. 1933 “Volition, knowledge, language”, in CW, p. 443–446.

Brouwer, L. E. J. 1937 “Signific dialogues’, in CW, p. 447–542.

Brouwer, L. E. J. 1948 “Consciousness, philosophy and mathematics”, in CW, p. 480–494.

Brouwer, L. E. J. 1952 “Historical background, principles and methods of intuitionism”, in CW, p. 508–515.

Brouwer, L. E. J. 1954 “Points and spaces”, in CW, p. 522–538.

Brouwer, L. E. J. 1981 Brouwer’s Cambridge Lectures on Intuitionism, ed. by D. van Dalen, Cambridge University Press, Cambridge.

Heyting, A. 1956 Intuitionism. An Introduction, North Holland, Amsterdam.

Łukasiewicz, J. 1954 “On determinism”, in his Selected Works, North Holland, Amsterdam, 1970.

van Stigt, W. P. 1979 “The rejected parts of Brouwer’s dissertation on the foundations of mathematics”, Historia Mathematica 6 (1979), p. 385–404.

van Stigt, 1990 Brouwer’s Intuitionism, North Holland, Amsterdam.

Wittgenstein, L. 1958 Philosophical Investigation, Basil Blackwell, Oxford.








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