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All the ideas for 'Thinking About Mathematics', 'On Fate ('De fato')' and 'Essence and Accident'

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24 ideas

5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
21677 How can the not-true fail to be false, or the not-false fail to be true? [Cicero]
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]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / b. Dispositions and powers
12312 The real essence of a thing is its powers, or 'dispositional properties' [Copi]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
10937 Essential properties are the 'deepest' ones which explain the others [Copi, by Rami]
9. Objects / D. Essence of Objects / 13. Nominal Essence
12308 In modern science, nominal essence is intended to be real essence [Copi]
9. Objects / E. Objects over Time / 11. End of an Object
12303 Within the four types of change, essential attributes are those whose loss means destruction [Copi]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
19. Language / F. Communication / 1. Rhetoric
21667 Oratory and philosophy are closely allied; orators borrow from philosophy, and ornament it [Cicero]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
21678 If desire is not in our power then neither are choices, so we should not be praised or punished [Cicero]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
12307 Modern science seeks essences, and is getting closer to them [Copi]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
12310 Real essences are scientifically knowable, but so are non-essential properties [Copi]