Combining Texts

All the ideas for 'works (fragments)', 'On the Individuation of Attributes' and 'On Second-Order Logic'

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12 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]
8. Modes of Existence / B. Properties / 12. Denial of Properties
18439 Because things can share attributes, we cannot individuate attributes clearly [Quine]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
18442 You only know an attribute if you know what things have it [Quine]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
18441 No entity without identity (which requires a principle of individuation) [Quine]
9. Objects / F. Identity among Objects / 6. Identity between Objects
18440 Identity of physical objects is just being coextensive [Quine]
28. God / C. Attitudes to God / 3. Deism
1558 Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus]