Ἀπόδειξις

Demonstration differs from definition.¹ First, we have to investigate definition, whether it is either one method in virtue of which the definitions of all existing things can be offered, or many. And if [it is] one, which one; but if many, how many in number and what kinds. And when by means of a description or a definition we discover so many and such things, another investigation again appears to us: which methods we have to make use of with regard to which objects. And when we discover this, since definition is by genera and differentiae, [we have to establish] which the genus of the object that is set before is and which the differentiae are, in order that we can offer its definition while combining the coherent differentiae by genus. There is another difficulty too. For in whatever something is present primarily, this also belongs to it by itself. And [the expression] "by itself" means "what is according to substance".² But it is not the case that if something is present by itself, this also is present in a primary way. For animal belongs by itself to man, although not in a primary sense. Therefore, even though there is no man, there is animal, so animal belongs to man not in a primary sense. Similarly figure also [belongs] by itself to triangle, although not primarily. But a demonstration in the strict sense arises from what belongs to [something] by itself and in a primary sense. And without qualification,[a demonstration is what] confirms the caused effects out of causes and the particulars out of the universals. And [a demonstration] confirming causes out of caused effects is called "conclusive proof";³ for instance, to show that the moon is spherical from of its illumination. For if it were shown that it is illuminated in this manner because it is spherical, that would be a demonstration in the strict sense. For what is caused would be shown out of a cause. But we have not made use of this mode of proof in this case, because what is caused is clearer to us than the cause. A conclusive demonstration is also to discover and understand that there is fire because there is smoke.⁴ And if what is caused absolutely follows the cause, this is called "conclusive proof"; and a conclusive proof is an irrefutable sign.⁵ But if [what is caused] did not absolutely follow [the cause], it would be called a sign but not a conclusive proof, because [in that case] it is not irrefutable, such as it happens in the case [of a woman] who is pale because she has given birth to a child. For having given birth to a child is not absolutely concomitant with paleness.⁶ A demonstration is a deductive method through deductive arguments,⁷ and it exists when a deductive argument arises from true and primary premises.