Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, Arend Heyting and Julia Annas

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23 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
12036 Xenophanes began the concern with knowledge [Annas]
1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / c. Classical philosophy
12046 Plato was the first philosopher who was concerned to systematize his ideas [Annas]
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15941 For intuitionists excluded middle is an outdated historical convention [Brouwer]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 / 6. Logicism / d. Logicism critique
8754 Logic is dependent on mathematics, not the other way round [Heyting, by Shapiro]
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]
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]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
3546 'Phronesis' should translate as 'practical intelligence', not as prudence [Annas]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
12037 Euripides's Medea is a key case of reason versus the passions [Annas]
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
3547 Epicureans achieve pleasure through character development [Annas]
23. Ethics / A. Egoism / 3. Cyrenaic School
3543 Cyrenaics pursue pleasure, but don't equate it with happiness [Annas]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
12040 Virtue is a kind of understanding of moral value [Annas]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
3541 Ancient ethics uses attractive notions, not imperatives [Annas]
23. Ethics / D. Deontological Ethics / 1. Deontology
3550 Principles cover life as a whole, where rules just cover actions [Annas]
23. Ethics / D. Deontological Ethics / 2. Duty
3551 Virtue theory tries to explain our duties in terms of our character [Annas]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
3552 If excessively good actions are admirable but not required, then duty isn't basic [Annas]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
3542 We should do good when necessary, not maximise it [Annas]