Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, Arthur N. Prior and William Crathorn

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17 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15941 For intuitionists excluded middle is an outdated historical convention [Brouwer]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
17896 We need to know the meaning of 'and', prior to its role in reasoning [Prior,AN, by Belnap]
17898 Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B [Belnap on Prior,AN]
11021 Prior rejected accounts of logical connectives by inference pattern, with 'tonk' his absurd example [Prior,AN, by Read]
13836 Maybe introducing or defining logical connectives by rules of inference leads to absurdity [Prior,AN, by Hacking]
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
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 / 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 / D. Theories of Reality / 8. Facts / b. Types of fact
15201 That Queen Anne is dead is a 'general fact', not a fact about Queen Anne [Prior,AN]
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]
27. Natural Reality / D. Time / 1. Nature of Time / e. Eventless time
16697 Time is independent of motion, because God could stop everything for a short or long time [Crathorn, by Pasnau]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
22899 'Thank goodness that's over' is not like 'thank goodness that happened on Friday' [Prior,AN]