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Single Idea 13525

[filed under theme 5. Theory of Logic / K. Features of Logics / 10. Monotonicity ]

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.


The 6 ideas with the same theme [if something is proved, nothing new can unprove it]:

Valid deduction is monotonic - that is, it remains valid if further premises are added [Psillos]
Explanations fail to be monotonic [Rosen]
Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS]
In classical logic the relation |= has Monotony built into its definition [Antonelli]
Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved [Antonelli]
Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt]