more from Peter Smith

### Single Idea 10602

#### [catalogued under 5. Theory of Logic / H. Proof Systems / 4. Natural Deduction]

Full Idea

A 'natural deduction system' will have no logical axioms but may rules of inference.

Gist of Idea

A 'natural deduction system' has no axioms but many rules

Source

Peter Smith (Intro to Gödel's Theorems [2007], 09.1)

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.59

A Reaction

He contrasts this with 'Hilbert-style systems', which have many axioms but few rules. Natural deduction uses many assumptions which are then discharged, and so tree-systems are good for representing it.