Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, Stephen Houlgate and Paul Audi

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23 ideas

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15941 For intuitionists excluded middle is an outdated historical convention [Brouwer]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]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
17292 Avoid 'in virtue of' for grounding, since it might imply a reflexive relation such as identity [Audi,P]
17295 Ground relations depend on the properties [Audi,P]
17297 A ball's being spherical non-causally determines its power to roll [Audi,P]
17302 Ground is irreflexive, asymmetric, transitive, non-monotonic etc. [Audi,P]
17303 The best critique of grounding says it is actually either identity or elimination [Audi,P]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
17294 Grounding is a singular relation between worldly facts [Audi,P]
17300 If grounding relates facts, properties must be included, as well as objects [Audi,P]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
17296 We must accept grounding, for our important explanations [Audi,P]
7. Existence / C. Structure of Existence / 1. Grounding / d. Grounding and reduction
17301 Reduction is just identity, so the two things are the same fact, so reduction isn't grounding [Audi,P]
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
17293 Worldly facts are obtaining states of affairs, with constituents; conceptual facts also depend on concepts [Audi,P]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
17298 Two things being identical (like water and H2O) is not an explanation [Audi,P]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
17299 There are plenty of examples of non-causal explanation [Audi,P]
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]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
21788 The moral will is self-determining, but the ethical will is met in society [Houlgate]