more from Herbert B. Enderton

Single Idea 9721

[catalogued under 5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth]

Full Idea

A is a logical truth (tautology) (|= A) iff it is a semantic consequence of the empty set of premises (φ |= A), that is, every interpretation makes A true.

Gist of Idea

A logical truth or tautology is a logical consequence of the empty set


Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.3.4)

Book Reference

Enderton,Herbert B.: 'A Mathematical Introduction to Logic' [Academic Press 2001], p.4

A Reaction

So the final column of every line of the truth table will be T.