ABSTRACT
This chapter describes the operation of uniform substitution of wffs for propositional variables. This operation preserves validity in the sense that if the substitutions are made in a valid wff, the resulting wff is also valid. Another important validity-preserving operation is that of detachment. Like adjunction this is an operation on two formulae, viz. an implication and its antecedent, to obtain a third, viz. the consequent of the implication, which is thus ‘detached’ from its antecedent. A first order inferential schema is valid if and only if no set of uniform and appropriate substitutions for its variables yields an inference with true premisses and a false conclusion. Analogously, a second order inferential schema is valid if and only if no set of uniform and appropriate substitutions for its variables yields a first order inferential schema with valid premisses and an invalid conclusion.
