Combining Texts

All the ideas for 'Particulars in Particular Clothing', 'On Second-Order Logic' and 'Introspection'

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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]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards]
12. Knowledge Sources / B. Perception / 8. Adverbial Theory
The adverbial account of sensation says not 'see a red image' but be 'appeared to redly' [Shoemaker]
16. Persons / C. Self-Awareness / 1. Introspection
For true introspection, must we be aware that we are aware of our mental events? [Shoemaker]
Empirical foundationalism says basic knowledge is self-intimating, and incorrigible or infallible [Shoemaker]