Combining Texts

Ideas for 'The Bhagavad Gita', 'Plato on Parts and Wholes' and 'First-order Logic, 2nd-order, Completeness'

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2 ideas

5. Theory of Logic / K. Features of Logics / 4. Completeness

10761	Completeness can always be achieved by cunning model-design [Rossberg]
	Full Idea: All that should be required to get a semantics relative to which a given deductive system is complete is a sufficiently cunning model-theorist.
	From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §5)

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

10755	A deductive system is only incomplete with respect to a formal semantics [Rossberg]
	Full Idea: No deductive system is semantically incomplete in and of itself; rather a deductive system is incomplete with respect to a specified formal semantics.
	From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3)
	A reaction: This important point indicates that a system might be complete with one semantics and incomplete with another. E.g. second-order logic can be made complete by employing a 'Henkin semantics'.