Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Luitzen E.J. Brouwer and J Hoffman/G Rosenkrantz

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15 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
8964 Entities can be multiplied either by excessive categories, or excessive entities within a category [Hoffman/Rosenkrantz]
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 / D. Assumptions for Logic / 2. Excluded Middle
15941 For intuitionists excluded middle is an outdated historical convention [Brouwer]
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 / 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
18118 Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
12451 Scientific laws largely rest on the results of counting and measuring [Brouwer]
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]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
8962 'There are shapes which are never exemplified' is the toughest example for nominalists [Hoffman/Rosenkrantz]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
8961 Nominalists are motivated by Ockham's Razor and a distrust of unobservables [Hoffman/Rosenkrantz]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
8963 Four theories of possible worlds: conceptualist, combinatorial, abstract, or concrete [Hoffman/Rosenkrantz]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
20653 Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
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]