chapter  13
4 Pages

Axiomatic Systems

WithG. E. Hughes, D. G. Londey

An inferential schema may be thought of as a claim that given as premisses certain valid propositional schemata, a further propositional schema is also valid. If the inferential schema is valid, then the claim is a good one – the schema is a guarantee of the validity of the conclusion, given the validity of the premisses. We might therefore formulate a rule of inference corresponding to each valid inferential schema. Each such rule of inference is a rule for the employment of some inferential operation, and licenses us to assert as valid a new wff of the prescribed form. It is in this sense that we may say that the rules of inference generate new formulae.