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Ideas for 'Parmenides', 'A Tour through Mathematical Logic' and 'The Basing Relation'

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

13538	If a theory is complete, only a more powerful language can strengthen it [Wolf,RS]
	Full Idea: It is valuable to know that a theory is complete, because then we know it cannot be strengthened without passing to a more powerful language.
	From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.5)

5. Theory of Logic / K. Features of Logics / 10. Monotonicity

13525	Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS]
	Full Idea: Deductive logic, including first-order logic and other types of logic used in mathematics, is 'monotonic'. This means that we never retract a theorem on the basis of new givens. If T|-φ and T⊆SW, then S|-φ. Ordinary reasoning is nonmonotonic.
	From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 1.7)
	A reaction: The classic example of nonmonotonic reasoning is the induction that 'all birds can fly', which is retracted when the bird turns out to be a penguin. He says nonmonotonic logic is a rich field in computer science.