Ideas of Luitzen E.J. Brouwer, by Theme

[Dutch, 1881 - 1966, Born at Overschie. Professor at the University of Amsterdam. Died at Blaricum.]

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4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
Our dislike of contradiction in logic is a matter of psychology, not mathematics
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
For intuitionists excluded middle is an outdated historical convention
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics is a mental activity which does not use language
6. Mathematics / A. Nature of Mathematics / 3. Numbers / h. Reals from Cauchy
Brouwer saw reals as potential, not actual, and produced by a rule, or a choice
6. Mathematics / A. Nature of Mathematics / 7. Application of Mathematics
Scientific laws largely rest on the results of counting and measuring
Brouwer regards the application of mathematics to the world as somehow 'wicked'
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionist mathematics deduces by introspective construction, and rejects unknown truths
Intuitionists only accept denumerable sets
Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness
19. Language / B. Meaning / 3. Meaning as Verification
Intuitonists in mathematics worried about unjustified assertion, as well as contradiction