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Full Idea
In classical logic, Monotony follows immediately from the nature of the relation |=, for Γ |= φ holds precisely when φ is true on every interpretation on which all sentences in Γ are true.
Gist of Idea
In classical logic the relation |= has Monotony built into its definition
Source
G. Aldo Antonelli (Non-Monotonic Logic [2014], 1)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.2
A Reaction
That is, semantic consequence (|=) is defined in terms of a sentence (φ) always being true if some other bunch of sentences (Γ) are true. Hence the addition of further sentences to Γ will make no difference - which is Monotony.
| 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] |