Combining Texts

All the ideas for 'fragments/reports', 'On Second-Order Logic' and 'Essence and Accident'

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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]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / b. Dispositions and powers
The real essence of a thing is its powers, or 'dispositional properties' [Copi]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Essential properties are the 'deepest' ones which explain the others [Copi, by Rami]
9. Objects / D. Essence of Objects / 13. Nominal Essence
In modern science, nominal essence is intended to be real essence [Copi]
9. Objects / E. Objects over Time / 11. End of an Object
Within the four types of change, essential attributes are those whose loss means destruction [Copi]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Modern science seeks essences, and is getting closer to them [Copi]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
Real essences are scientifically knowable, but so are non-essential properties [Copi]