Combining Texts

All the ideas for 'A Puzzle about Belief', 'Summa Contra Gentiles' and 'On Second-Order Logic'

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11 ideas

1. Philosophy / A. Wisdom / 2. Wise People
Wise people should contemplate and discuss the truth, and fight against falsehood [Aquinas]
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]
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
Without God's influence every operation would stop, so God causes everything [Aquinas]
18. Thought / B. Mechanics of Thought / 5. Mental Files
Puzzled Pierre has two mental files about the same object [Recanati on Kripke]
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
Eternity coexists with passing time, as the centre of a circle coexists with its circumference [Aquinas]