more from G. Aldo Antonelli

Single Idea 19110

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

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


G. Aldo Antonelli (Non-Monotonic Logic [2014], 1)

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [], 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.