Combining Texts

All the ideas for 'fragments/reports', 'Logicism and Ontological Commits. of Arithmetic' and 'Cardinality, Counting and Equinumerosity'

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

22 ideas

3. Truth / F. Semantic Truth / 2. Semantic Truth
10017 Truth in a model is more tractable than the general notion of truth [Hodes]
10018 Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10015 Higher-order logic may be unintelligible, but it isn't set theory [Hodes]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10011 Identity is a level one relation with a second-order definition [Hodes]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10016 When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes]
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]
10027 Mathematics is higher-order modal logic [Hodes]
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 / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
10026 Arithmetic must allow for the possibility of only a finite total of objects [Hodes]
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 / a. For mathematical platonism
10021 It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes]
10022 Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes]
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]
7. Existence / D. Theories of Reality / 7. Fictionalism
10023 Talk of mirror images is 'encoded fictions' about real facts [Hodes]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]