Combining Texts

All the ideas for 'On the Foundations of Logic and Arithmetic', 'The Problem of Possibilia' and 'A Note on the entscheidungsproblem'

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5 ideas

5. Theory of Logic / K. Features of Logics / 7. Decidability
18758 Validity is provable, but invalidity isn't, because the model is infinite [Church, by McGee]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17697 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
17698 Logic already contains some arithmetic, so the two must be developed together [Hilbert]
10. Modality / B. Possibility / 1. Possibility
9212 Possible states of affairs are not propositions; a proposition can't be a state of affairs! [Fine,K]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
9213 The actual world is a possible world, so we can't define possible worlds as 'what might have been' [Fine,K]