Combining Philosophers

All the ideas for Oswald Veblen, William Lyons and Luitzen E.J. Brouwer

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17 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 / A. Overview of Logic / 2. History of Logic
We have no adequate logic at the moment, so mathematicians must create one [Veblen]
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For intuitionists excluded middle is an outdated historical convention [Brouwer]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]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
Belief is the most important propositional attitude [Lyons]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
Consciousness no longer seems essential to intentionality [Lyons]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
Perceptions could give us information without symbolic representation [Lyons]
18. Thought / A. Modes of Thought / 2. Propositional Attitudes
Propositional attitudes require representation [Lyons]
18. Thought / A. Modes of Thought / 4. Folk Psychology
Folk psychology works badly for alien cultures [Lyons]
18. Thought / C. Content / 1. Content
All thinking has content [Lyons]
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]