Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, F.A. Hayek and Berit Brogaard

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15 ideas

4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
For intuitionists excluded middle is an outdated historical convention [Brouwer]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
Scientific laws largely rest on the results of counting and measuring [Brouwer]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionists only accept denumerable sets [Brouwer]
Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
18. Thought / A. Modes of Thought / 9. Indexical Thought
If two people can have phenomenally identical experiences, they can't involve the self [Brogaard]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman]
24. Political Theory / D. Ideologies / 8. Socialism
Socialist economics needs a very strong central power, virtually leading to slavery [Hayek, by Oksala]
25. Social Practice / A. Freedoms / 4. Free market
Hayek was a liberal, but mainly concerned with market freedom [Hayek, by Dunt]
Impeding the market is likely to lead to extensive state control [Hayek]
25. Social Practice / D. Justice / 1. Basis of justice
'Social justice' is a confused idea, and inequalities need no justification [Hayek, by Swift]