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All the ideas for 'Concepts and Counting', 'Universal Arithmetick' and 'Philosophical Studies 1611-19'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17462 A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
17783 A number is not a multitude, but a unified ratio between quantities [Newton]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
17461 Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt]
9. Objects / C. Structure of Objects / 2. Hylomorphism / c. Form as causal
16625 In hylomorphism all the explanation of actions is in the form, and the matter doesn't do anything [Bacon]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
16624 Stripped and passive matter is just a human invention [Bacon]