Combining Texts

All the ideas for 'fragments/reports', 'The Logic of Decision' and 'On Second-Order Logic'

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

10 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / b. Worlds as fictions
16285 A possible world can be seen as a complete and consistent novel [Jeffrey]
14. Science / C. Induction / 6. Bayes's Theorem
19155 Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey, by Davidson]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
6004 The cardinal virtues are theoretical (based on knowledge), and others are 'non-theoretical' [Hecato, by Dorandi]