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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.
Gist of Idea
Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens
Source
Robert S. Wolf (A Tour through Mathematical Logic [2005], 1.7)
Book Ref
Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.54
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.
4810 | Valid deduction is monotonic - that is, it remains valid if further premises are added [Psillos] |
14096 | Explanations fail to be monotonic [Rosen] |
13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
19110 | In classical logic the relation |= has Monotony built into its definition [Antonelli] |
19112 | Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved [Antonelli] |
18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |