Combining Texts

All the ideas for 'On Second-Order Logic', 'On a supposed right to lie' and 'Metaphysics as a Guide to Morals'

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10 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]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
We know perfection when we see what is imperfect [Murdoch]
23. Ethics / B. Contract Ethics / 3. Promise Keeping
If lies were ever acceptable, with would undermine all duties based on contract [Kant]
23. Ethics / D. Deontological Ethics / 2. Duty
The law will protect you if you tell a truth which results in murder [Kant]