Combining Texts

All the ideas for 'The Philosophy of Philosophy', 'Cardinality, Counting and Equinumerosity' and 'Mathematical Intuition'

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25 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
9593 Progress in philosophy is incremental, not an immature seeking after drama [Williamson]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
9594 Correspondence to the facts is a bad account of analytic truth [Williamson]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
17453 The meaning of a number isn't just the numerals leading up to it [Heck]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
17457 A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17448 In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
17456 Counting is the assignment of successively larger cardinal numbers to collections [Heck]
17455 Is counting basically mindless, and independent of the cardinality involved? [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
17450 Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
17451 We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17459 Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17454 Children can use numbers, without a concept of them as countable objects [Heck]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
18201 General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17458 Equinumerosity is not the same concept as one-one correspondence [Heck]
17449 We can understand cardinality without the idea of one-one correspondence [Heck]
7. Existence / D. Theories of Reality / 4. Anti-realism
9601 The realist/anti-realist debate is notoriously obscure and fruitless [Williamson]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
9599 There cannot be vague objects, so there may be no such thing as a mountain [Williamson]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9602 Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
9598 Modal thinking isn't a special intuition; it is part of ordinary counterfactual thinking [Williamson]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
16536 Williamson can't base metaphysical necessity on the psychology of causal counterfactuals [Lowe on Williamson]
9596 We scorn imagination as a test of possibility, forgetting its role in counterfactuals [Williamson]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
9597 There are 'armchair' truths which are not a priori, because experience was involved [Williamson]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
9592 Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson]
20181 When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson]
19. Language / A. Nature of Meaning / 6. Meaning as Use
9595 You might know that the word 'gob' meant 'mouth', but not be competent to use it [Williamson]
24. Political Theory / B. Nature of a State / 5. Culture
9600 If languages are intertranslatable, and cognition is innate, then cultures are all similar [Williamson]