Proof and Demonstration

In the Posterior Analytics, δεικνύναι is often synonymous with ἀποδεικνύναι. This is the case when it means “demonstrate” in the strict sense of a syllogistic deduction. However, in other occurrences, it seems to designate something different, like a “proof” in general or a particular kind of proof. Does this mean that δεικνύναι is an imprecise term, belonging to a weak level of technical terminology and falling outside the semantic core of Aristotle’s theory of science? Conversely, it could be that certain uses of δεικνύναι, despite their relative lack of technicality, reveals something deeper and more significant, regarding Aristotle’s conceptions of proof and demonstration. The purpose of this survey is to evaluate the latter hypothesis. It is argued that Aristotle uses δεικνύναι (and other terms of the same family) so as to preserve ἀποδεικνύναι for the technical sense of “demonstrate” (and preserve ἀπόδειξις for “demonstration”) in the strict meaning of the term, in particular within the expression ἀποδεικνύναι ἁπλῶς.