Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, Arnauld / Nicole and Blaise Pascal

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31 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
6675 The heart has its reasons of which reason knows nothing [Pascal]
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15941 For intuitionists excluded middle is an outdated historical convention [Brouwer]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 / D. Assumptions for Logic / 3. Contradiction
10121 Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal]
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 / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
10502 We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P]
12. Knowledge Sources / B. Perception / 3. Representation
18258 We can only know the exterior world via our ideas [Arnauld,A/Nicole,P]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
22011 The first principles of truth are not rational, but are known by the heart [Pascal]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
16784 Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
10499 We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
10501 A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
10500 No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,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]
19. Language / F. Communication / 1. Rhetoric
6681 We only want to know things so that we can talk about them [Pascal]
21. Aesthetics / C. Artistic Issues / 3. Artistic Representation
6676 Painting makes us admire things of which we do not admire the originals [Pascal]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
6680 It is a funny sort of justice whose limits are marked by a river [Pascal]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
6677 Imagination creates beauty, justice and happiness, which is the supreme good [Pascal]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
6678 We live for the past or future, and so are never happy in the present [Pascal]
23. Ethics / F. Existentialism / 3. Angst
20732 If man considers himself as lost and imprisoned in the universe, he will be terrified [Pascal]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
6682 Majority opinion is visible and authoritative, although not very clever [Pascal]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
6679 It is not good to be too free [Pascal]
28. God / B. Proving God / 2. Proofs of Reason / d. Pascal's Wager
7455 Pascal knows you can't force belief, but you can make it much more probable [Pascal, by Hacking]
7457 Pascal is right, but relies on the unsupported claim of a half as the chance of God's existence [Hacking on Pascal]
7456 The libertine would lose a life of enjoyable sin if he chose the cloisters [Hacking on Pascal]
6684 If you win the wager on God's existence you win everything, if you lose you lose nothing [Pascal]