Abstract

Issues sometimes arise in deductive practice concerning whether an inference in an argument is really valid. They are usually resolved and the argument enriched with these simpler inferences is accepted as valid when the inference can be broken down into simpler inferences where it is obvious (or trivial, as mathematicians say) that the premisses of the inferences conclusively support the conclusions.

Nevertheless a philosophical issue concerning valid inferences remains, namely to explicate the very concept of conclusive support. Clearly it is not sufficient for the inference to be valid that what the conclusion asserts is entailed by or is a logical consequence of what the premisses assert, although this has often been proposed in philosophy. We need to clarify a narrower concept than entailment. It seems to correspond to what Aristotle called perfect syllogism. Principles will be proposed that together explicate at least partially concepts of valid inference and valid argument.