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Single Idea 13841

[filed under theme 5. Theory of Logic / K. Features of Logics / 6. Compactness ]

Full Idea

Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself.

Gist of Idea

Why should compactness be definitive of logic?

Source

report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13

Book Ref

'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.245

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The 7 ideas from 'On Second-Order Logic'

14249

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

13841

Why should compactness be definitive of logic? [Boolos, by Hacking]

10829

A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]

10830

Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]

10832

'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]

10833

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

10834

Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]