Lato e diagonale negli Analitici di Aristotele. Un caso di apagogia

Apagogy is the most conclusive of the apodictic demonstrations. Aristotle theorises it, in various senses, in his Analytics: in particular, apagogy is presented as a kind of demonstration “by hypothesis”. More precisely, Aristotle recognises that demonstration by absurdity is a complex structure, in which: (1) a “false” conclusion is obtained by means of a “direct syllogism”; (2) except that, the assumption of the hypothesis from which the false conclusion is drawn does not belong to this direct deduction; nor does the confrontation with the contradictory proposition of the false conclusion, and consequently neither does the confirmation of the thesis whose negation generates contradiction. It can thus be argued that, if apagogy is reducible to syllogism according to figures, it is limited to moment (1) of the previous scansion. As an emblematic case of apagogy, Aristotle points to the demonstration of the incommensurability of the side and diagonal of the square, of which, however, he does not offer the articulate illustration (which is instead offered to us, besides Euclid, by Alexander of Aphrodisia).