Combining Texts

All the ideas for 'On Second-Order Logic', 'Artistic Value and Opportunistic Moralism' and 'Does Ontology Rest on a Mistake?'

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14 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]
7. Existence / D. Theories of Reality / 7. Fictionalism
For me, fictions are internally true, without a significant internal or external truth-value [Yablo]
Make-believe can help us to reason about facts and scientific procedures [Yablo]
'The clouds are angry' can only mean '...if one were attributing emotions to clouds' [Yablo]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
A work can be morally and artistically excellent, despite rejecting moral truth [John,E]
The works we value most are in sympathy with our own moral views [John,E]
We should understand what is morally important in a story, without having to endorse it [John,E]
We value morality in art because that is what we care about - but it is a contingent fact [John,E]