Combining Texts

All the ideas for 'Laches', 'Mathematics without Foundations' and 'Nominalism'

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12 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
291 Don't assume that wisdom is the automatic consequence of old age [Plato]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
8956 What is a singleton set, if a set is meant to be a collection of objects? [Szabó]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
9944 We understand some statements about all sets [Putnam]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
9937 I do not believe mathematics either has or needs 'foundations' [Putnam]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
9939 It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
9940 Maybe mathematics is empirical in that we could try to change it [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
9941 Science requires more than consistency of mathematics [Putnam]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
8953 Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things [Szabó]
7. Existence / D. Theories of Reality / 4. Anti-realism
9943 You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
8954 Geometrical circles cannot identify a circular paint patch, presumably because they lack something [Szabó]
18. Thought / E. Abstraction / 5. Abstracta by Negation
8955 Abstractions are imperceptible, non-causal, and non-spatiotemporal (the third explaining the others) [Szabó]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
293 Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]