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All the ideas for 'Thinking About Mathematics', 'fragments/reports' and 'The soul's dependence on the body'

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23 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
23269 Philosophy must start from clearly observed facts [Galen]
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]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
23266 The spirit in the soul wants freedom, power and honour [Galen]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
5880 Xenocrates held that the soul had no form or substance, but was number [Xenocrates, by Cicero]
15. Nature of Minds / A. Nature of Mind / 8. Brain
23219 Stopping the heart doesn't terminate activity; pressing the brain does that [Galen, by Cobb]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
23264 Philosophers think faculties are in substances, and invent a faculty for every activity [Galen]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
23220 The brain contains memory and reason, and is the source of sensation and decision [Galen]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
23265 The rational part of the soul is the desire for truth, understanding and recollection [Galen]
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
23268 We execute irredeemable people, to protect ourselves, as a deterrent, and ending a bad life [Galen]