Combining Texts

All the ideas for 'On Second-Order Logic', 'On Mental Entities' and 'Beyond Individualism'

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12 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]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
Sense-data are dubious abstractions, with none of the plausibility of tables [Quine]
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
Empiricism says evidence rests on the senses, but that insight is derived from science [Quine]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
Passion for progress is always short-lived [Sandel]
24. Political Theory / D. Ideologies / 3. Conservatism
Conservatives are either individualistic, or communal [Sandel]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Modern liberalism fails to articulate a vision of the common good [Sandel]