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All the ideas for 'Thinking About Mathematics', 'Sense and Sensibilia' and 'Ideas, Qualities and Corpuscles'

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22 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
8729 Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
8763 The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
18249 Cauchy gave a formal definition of a converging sequence. [Shapiro]
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 / 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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
8744 Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
8749 Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
8750 Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
8752 Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8753 Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
8731 Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8730 'Impredicative' definitions refer to the thing being described [Shapiro]
7. Existence / D. Theories of Reality / 10. Vagueness / a. Problem of vagueness
21598 Austin revealed many meanings for 'vague': rough, ambiguous, general, incomplete... [Austin,JL, by Williamson]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
15959 If the substantial form of brass implies its stability, how can it melt and remain brass? [Alexander,P]
9. Objects / C. Structure of Objects / 2. Hylomorphism / b. Form as principle
15956 The peripatetics treated forms and real qualities as independent of matter, and non-material [Alexander,P]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
15975 Can the qualities of a body be split into two groups, where the smaller explains the larger? [Alexander,P]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
15963 Science has been partly motivated by the belief that the universe is run by God's laws [Alexander,P]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
15951 Alchemists tried to separate out essences, which influenced later chemistry [Alexander,P]
27. Natural Reality / C. Space / 4. Substantival Space
15981 Absolute space either provides locations, or exists but lacks 'marks' for locations [Alexander,P]