Combining Texts

All the ideas for 'On Second-Order Logic', 'A Priori Knowledge Revisited' and 'Consistency and realism (with 1972 note)'

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12 ideas

5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
12430 Classical logic is our preconditions for assessing empirical evidence [Kitcher]
12431 I believe classical logic because I was taught it and use it, but it could be undermined [Kitcher]
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 / D. Knowledge of Modality / 1. A Priori Necessary
12428 Many necessities are inexpressible, and unknowable a priori [Kitcher]
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
12429 Knowing our own existence is a priori, but not necessary [Kitcher]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / f. Ethical non-cognitivism
22454 We tolerate inconsistency in ethics but not in other beliefs (which reflect an independent order) [Williams,B, by Foot]