Combining Texts

All the ideas for 'works', 'Realism in Mathematics' and 'Logic (Port-Royal Art of Thinking)'

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12 ideas

4. Formal Logic / F. Set Theory ST / 7. Natural Sets
8755 Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10718 A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
8756 Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17733 We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
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]
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]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
6610 I believe because it is absurd [Tertullian]