Combining Texts

All the ideas for 'Cardinality, Counting and Equinumerosity', 'On Propositions: What they are, and Meaning' and 'Conceptions of Consequence'

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21 ideas

3. Truth / A. Truth Problems / 5. Truth Bearers
5784 In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell]
3. Truth / B. Truthmakers / 1. For Truthmakers
5777 The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
5783 Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell]
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]
17455 Is counting basically mindless, and independent of the cardinality involved? [Heck]
17456 Counting is the assignment of successively larger cardinal numbers to collections [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 / 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]
11. Knowledge Aims / A. Knowledge / 2. Understanding
18810 Aristotle's proofs give understanding, so it can't be otherwise, so consequence is necessary [Smiley, by Rumfitt]
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
5780 The three questions about belief are its contents, its success, and its character [Russell]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
5778 If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
5779 There are distinct sets of psychological and physical causal laws [Russell]
19. Language / D. Propositions / 1. Propositions
5781 Our important beliefs all, if put into words, take the form of propositions [Russell]
5782 A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell]
5776 A proposition is what we believe when we believe truly or falsely [Russell]