Combining Philosophers

All the ideas for Hippolytus, G.A. Cohen and Luitzen E.J. Brouwer

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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For intuitionists excluded middle is an outdated historical convention [Brouwer]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
Scientific laws largely rest on the results of counting and measuring [Brouwer]
Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
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]
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]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
The right-wing conception of freedom is based on the idea of self-ownership [Cohen,GA]
Plenty of people have self-ownership, but still lack autonomy [Cohen,GA]
25. Social Practice / C. Rights / 4. Property rights
It is doubtful whether any private property was originally acquired legitimately [Cohen,GA]
It is plausible that no one has an initial right to own land and natural resources [Cohen,GA]
Every thing which is now private started out as unowned [Cohen,GA]