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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.
| 19111 | Reasoning may be defeated by new premises, or by finding out more about the given ones [Antonelli] |
| 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] |
| 19113 | Weakest Link Principle: prefer the argument whose weakest link is the stronger [Antonelli] |
| 19114 | Should we accept Floating Conclusions, derived from two arguments in conflict? [Antonelli] |
| 19115 | You can 'rebut' an argument's conclusion, or 'undercut' its premises [Antonelli] |
| 19116 | Non-monotonic core: Reflexivity, Cut, Cautious Monotonicity, Left Logical Equivalence, Right Weakening [Antonelli] |
| 19117 | We can rank a formula by the level of surprise if it were to hold [Antonelli] |
| 19118 | People don't actually use classical logic, but may actually use non-monotonic logic [Antonelli] |
| 19119 | We infer that other objects are like some exceptional object, if they share some of its properties [Antonelli] |