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Ideas for 'Thinking About Mathematics', 'Psychology from an empirical standpoint' and 'The Possibility of Metaphysics'

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7 ideas

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

8764	Categories are the best foundation for mathematics [Shapiro]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers

8297	Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle

8266	Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe]

8302	Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers

8762	Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

8760	Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]

8761	A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]