Combining Texts

All the ideas for 'works', 'A World of Propensities' and 'On Second-Order Logic'

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10 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

14249

Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]

10830

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

10829

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

10832

'∀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

10834

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

13841

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

10833

Many concepts can only be expressed by second-order logic [Boolos]

8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers

11946

Propensities are part of a situation, not part of the objects [Popper]

29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy

16713

Philosophers are the forefathers of heretics [Tertullian]

29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism

6610	I believe because it is absurd [Tertullian]