Combining Texts

All the ideas for 'General Draft', 'Testability and Meaning' and 'On Second-Order Logic'

expand these ideas     |    start again     |     specify just one area for these texts

---

10 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly

22026

Philosophy is homesickness - the urge to be at home everywhere [Novalis]

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]

10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals

14305

In the truth-functional account a burnt-up match was soluble because it never entered water [Carnap]

15. Nature of Minds / C. Capacities of Minds / 6. Idealisation

19591

Desire for perfection is an illness, if it turns against what is imperfect [Novalis]