Combining Texts

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

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12 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
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
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
'∀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
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
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
Many concepts can only be expressed by second-order logic [Boolos]
10. Modality / A. Necessity / 8. Transcendental Necessity
Everything happens by reason and necessity [Leucippus]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
We should follow the law in public, and nature in private [Antiphon]
To gain the greatest advantage only treat law as important when other people are present [Antiphon]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
The way you spend your time will form your character [Antiphon]
24. Political Theory / D. Ideologies / 2. Anarchism
Nothing is worse for mankind than anarchy [Antiphon]