Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, Francis de Vitoria and Alistair Mitchell

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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For intuitionists excluded middle is an outdated historical convention [Brouwer]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]
14. Science / C. Induction / 3. Limits of Induction
Maybe induction is only reliable IF reality is stable [Mitchell,A]
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 / E. Policies / 1. War / a. Just wars
Leaders can only attack foreigners who have done wrong (as with their own subjects) [Vitoria]
The only just cause for a war is a wrong received [Vitoria]
25. Social Practice / E. Policies / 1. War / c. Combatants
Princes should not justify a war to their subjects, and doing so would undermine the state [Vitoria]
25. Social Practice / E. Policies / 1. War / d. Non-combatants
Sacking a city is lawful if it motivates the attacking troops [Vitoria]