Combining Texts

All the ideas for 'Thinking About Mathematics', 'Paper of December 1676' and 'Mirror Mirror - Is That All?'

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24 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
9327 Organisms understand their worlds better if they understand themselves [Gulick]
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]
11. Knowledge Aims / A. Knowledge / 2. Understanding
9325 In contrast with knowledge, the notion of understanding emphasizes practical engagement [Gulick]
11. Knowledge Aims / A. Knowledge / 6. Knowing How
9326 Knowing-that is a much richer kind of knowing-how [Gulick]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
9319 Is consciousness a type of self-awareness, or is being self-aware a way of being conscious? [Gulick]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / f. Higher-order thought
9320 Higher-order theories divide over whether the higher level involves thought or perception [Gulick]
9321 Higher-order models reduce the problem of consciousness to intentionality [Gulick]
9322 Maybe qualia only exist at the lower level, and a higher-level is needed for what-it-is-like [Gulick]
17. Mind and Body / A. Mind-Body Dualism / 7. Zombies
12727 It's impossible, but imagine a body carrying on normally, but with no mind [Leibniz]
27. Natural Reality / G. Biology / 2. Life
9324 From the teleopragmatic perspective, life is largely an informational process [Gulick]