Combining Texts

All the ideas for 'fragments/reports', 'On Second-Order Logic' and 'Making Mind Matter More'

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11 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]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
Either intentionality causes things, or epiphenomenalism is true [Fodor]
17. Mind and Body / D. Property Dualism / 2. Anomalous Monism
Contrary to the 'anomalous monist' view, there may well be intentional causal laws [Fodor]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
Lots of physical properties are multiply realisable, so why shouldn't beliefs be? [Fodor]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]