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
12452

Our dislike of contradiction in logic is a matter of psychology, not mathematics

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
15941

For intuitionists excluded middle is an outdated historical convention

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
18119

Mathematics is a mental activity which does not use language [Bostock]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
18247

Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Shapiro]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
12451

Scientific laws largely rest on the results of counting and measuring

18118

Brouwer regards the application of mathematics to the world as somehow 'wicked' [Bostock]

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
12454

Intuitionists only accept denumerable sets

12453

Neointuitionism abstracts from the reuniting of moments, to intuit bare twooneness

8728

Intuitionist mathematics deduces by introspective construction, and rejects unknown truths

19. Language / A. Nature of Meaning / 5. Meaning as Verification
10117

Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [George/Velleman]
