Combining Texts

All the ideas for 'Thinking About Mathematics', 'Letter to Clerk Maxwell' and 'Miscellaneous Observations'

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24 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
19574 If man sacrifices truth he sacrifices himself, by acting against his own convictions [Novalis]
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
19571 Delusion and truth differ in their life functions [Novalis]
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]
9. Objects / D. Essence of Objects / 3. Individual Essences
19575 Refinement of senses increasingly distinguishes individuals [Novalis]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
19572 Experiences tests reason, and reason tests experience [Novalis]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
19573 The seat of the soul is where our inner and outer worlds interpenetrate [Novalis]
18. Thought / E. Abstraction / 2. Abstracta by Selection
19577 Everything is a chaotic unity, then we abstract, then we reunify the world into a free alliance [Novalis]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
19578 Only self-illuminated perfect individuals are beautiful [Novalis]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
15313 By 'force' I mean the sources of all actions - sometimes called 'powers' by their outcomes [Breheny]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
19576 Religion needs an intermediary, because none of us can connect directly to a godhead [Novalis]