Combining Texts

All the ideas for 'fragments/reports', 'Logic (Port-Royal Art of Thinking)' and 'On the Foundations of Logic and Arithmetic'

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12 ideas

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logic already contains some arithmetic, so the two must be developed together [Hilbert]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P]
12. Knowledge Sources / B. Perception / 3. Representation
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
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
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
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
No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P]
19. Language / F. Communication / 3. Denial
Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus]
28. God / C. Attitudes to God / 5. Atheism
The gods are just personified human benefits [Prodicus]
He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus]