Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, Otto Neurath and Tyler Burge

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27 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
7081 Philosophy is not separate from or above empirical science [Neurath]
4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
12452 Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
13479 Given that thinking aims at truth, logic gives universal rules for how to do it [Burge]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
15941 For intuitionists excluded middle is an outdated historical convention [Brouwer]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
8132 We now have a much more sophisticated understanding of logical form in language [Burge]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17622 We come to believe mathematical propositions via their grounding in the structure [Burge]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
18119 Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
16901 The equivalent algebra model of geometry loses some essential spatial meaning [Burge]
9159 You can't simply convert geometry into algebra, as some spatial content is lost [Burge]
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 [Brouwer, by 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 [Brouwer]
18118 Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
16902 Peano arithmetic requires grasping 0 as a primitive number [Burge]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
12454 Intuitionists only accept denumerable sets [Brouwer]
12453 Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
8728 Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
16892 Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
10486 If we are rebuilding our ship at sea, we should jettison some cargo [Boolos on Neurath]
8485 We must always rebuild our ship on the open sea; we can't reconstruct it properly in dry-dock [Neurath]
13. Knowledge Criteria / C. External Justification / 1. External Justification
9382 Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge]
15. Nature of Minds / A. Nature of Mind / 6. Anti-Individualism
8126 Anti-individualism says the environment is involved in the individuation of some mental states [Burge]
8127 Broad concepts suggest an extension of the mind into the environment (less computer-like) [Burge]
16. Persons / C. Self-Awareness / 2. Knowing the Self
8129 Anti-individualism may be incompatible with some sorts of self-knowledge [Burge]
17. Mind and Body / C. Functionalism / 1. Functionalism
8131 Some qualities of experience, like blurred vision, have no function at all [Burge]
18. Thought / C. Content / 1. Content
3115 Are meaning and expressed concept the same thing? [Burge, by Segal]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10117 Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
14349 If there are no finks or antidotes at the fundamental level, the laws can't be ceteris paribus [Burge, by Corry]