Combining Texts

All the ideas for '', 'Mathematics and Indispensibility' and 'Remarks on the definition and nature of mathematics'

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8 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
17807 To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17806 It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17808 Saying mathematics is logic is merely replacing one undefined term by another [Curry]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
9558 All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]