Combining Texts

All the ideas for 'On the Foundations of Logic and Arithmetic', 'Philosophy of Language' and 'Realism in Mathematics'

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14 ideas

4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
Singular terms refer, using proper names, definite descriptions, singular personal pronouns, demonstratives, etc. [Lycan]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logic already contains some arithmetic, so the two must be developed together [Hilbert]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
The truth conditions theory sees meaning as representation [Lycan]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Meaning must be known before we can consider verification [Lycan]
19. Language / A. Nature of Meaning / 6. Meaning as Use
Could I successfully use an expression, without actually understanding it? [Lycan]
It is hard to state a rule of use for a proper name [Lycan]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
Truth conditions will come out the same for sentences with 'renate' or 'cordate' [Lycan]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
A sentence's truth conditions is the set of possible worlds in which the sentence is true [Lycan]
Possible worlds explain aspects of meaning neatly - entailment, for example, is the subset relation [Lycan]