Combining Texts

All the ideas for 'Philosophical Letters from England', 'Logic (Port-Royal Art of Thinking)' and 'Mathematics without Numbers'

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10 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
8698 Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
9557 Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
10263 Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
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]
23. Ethics / B. Contract Ethics / 2. Golden Rule
7844 The Golden Rule is accepted everywhere, and gives a fixed target for morality [Voltaire]