Combining Philosophers

All the ideas for Phil Dowe, Luitzen E.J. Brouwer and Charlotte Witt

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19 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 / 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For intuitionists excluded middle is an outdated historical convention [Brouwer]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]
9. Objects / D. Essence of Objects / 2. Types of Essence
Aristotelian and Kripkean essentialism are very different theories [Witt]
9. Objects / D. Essence of Objects / 4. Essence as Definition
An Aristotelian essence is a nonlinguistic correlate of the definition [Witt]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
If unity is a matter of degree, then essence may also be a matter of degree [Witt]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Essences mainly explain the existence of unified substance [Witt]
9. Objects / E. Objects over Time / 12. Origin as Essential
Essential properties of origin are too radically individual for an Aristotelian essence [Witt]
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]
26. Natural Theory / C. Causation / 4. Naturalised causation
Causation interaction is an exchange of conserved quantities, such as mass, energy or charge [Dowe, by Psillos]
Physical causation consists in transference of conserved quantities [Dowe, by Mumford/Anjum]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Reality is directional [Witt]
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
Dowe commends the Conserved Quantity theory as it avoids mention of counterfactuals [Dowe, by Psillos]