Combining Texts

All the ideas for 'On Certainty', 'Logic (Port-Royal Art of Thinking)' and 'Mathematics and Philosophy: grand and little'

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15 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
9808 Philosophy aims to reveal the grandeur of mathematics [Badiou]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9812 In mathematics, if a problem can be formulated, it will eventually be solved [Badiou]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
9813 Mathematics shows that thinking is not confined to the finite [Badiou]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
9809 Mathematics inscribes being as such [Badiou]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
9811 It is of the essence of being to appear [Badiou]
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]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
3597 Foundations need not precede other beliefs [Wittgenstein]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
3596 Total doubt can't even get started [Wittgenstein, by Williams,M]
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 / 10. Denial of Meanings
4721 If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein]
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
9814 All great poetry is engaged in rivalry with mathematics [Badiou]