more from Herbert B. Enderton

### Single Idea 9718

#### [catalogued under 5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence]

Full Idea

The point of logic is to give an account of the notion of validity,..in two standard ways: the semantic way says that a valid inference preserves truth (symbol |=), and the proof-theoretic way is defined in terms of purely formal procedures (symbol |-).

Gist of Idea

Validity is either semantic (what preserves truth), or proof-theoretic (following procedures)

Source

Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.3..)

Book Reference

Enderton,Herbert B.: 'A Mathematical Introduction to Logic' [Academic Press 2001], p.1

A Reaction

This division can be mirrored in mathematics, where it is either to do with counting or theorising about things in the physical world, or following sets of rules from axioms. Language can discuss reality, or play word-games.