Combining Texts

All the ideas for '', 'The Theory of Transfinite Numbers' and 'works'

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8 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

9616	A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]

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 / D. Assumptions for Logic / 2. Excluded Middle

15941

For intuitionists excluded middle is an outdated historical convention [Brouwer]

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]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy

18247

Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities

15896

Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]

19. Language / F. Communication / 3. Denial

11214

We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]