Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Letters to Antoine Arnauld' and 'The Evolution of Logic'

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2 ideas

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

17894	We have no argument to show a statement is absolutely undecidable [Koellner]
	Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable.
	From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3)

5. Theory of Logic / K. Features of Logics / 6. Compactness

13496	First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD]
	Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences.
	From: William D. Hart (The Evolution of Logic [2010], 3)