Combining Texts

All the ideas for 'The Basing Relation', 'Thinking About Mathematics' and 'Maxims'

expand these ideas     |    start again     |     specify just one area for these texts

25 ideas

1. Philosophy / A. Wisdom / 2. Wise People
7914 To try to be wise all on one's own is folly [Rochefoucauld]
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 / 4. Belief / a. Beliefs
19696 There are reasons 'for which' a belief is held, reasons 'why' it is believed, and reasons 'to' believe it [Neta]
19697 The basing relation of a reason to a belief should both support and explain the belief [Neta]
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 / 2. Unconscious Mind
7118 La Rochefoucauld's idea of disguised self-love implies an unconscious mind [Rochefoucauld, by Sartre]
22. Metaethics / B. Value / 2. Values / g. Love
7912 Judging by effects, love looks more like hatred than friendship [Rochefoucauld]
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
7915 Supreme cleverness is knowledge of the real value of things [Rochefoucauld]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
7917 Realising our future misery is a kind of happiness [Rochefoucauld]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
7913 Virtue doesn't go far without the support of vanity [Rochefoucauld]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
7916 True friendship is even rarer than true love [Rochefoucauld]
23. Ethics / F. Existentialism / 4. Boredom
9299 We are bored by people to whom we ourselves are boring [Rochefoucauld]