Demonstration

DEMONSTRATION. - From de-monstrare, to show, to make seen, with a sense of derivation. In a broad sense, a demonstration is any argument by which a pre-established proposition or thesis is proved and made manifest. The demonstration therefore presupposes that the truth which one intends to demonstrate is known, though only as a problematic position, not in its character of certainty. Insofar as it tends to attain this end, that is, to establish certainty and evidence, the demonstration asserts itself as a positive logical process in the conquest of knowledge, and its meaning approaches the more universal one of deduction.

In Aristotle, demonstration (ἀπόδειξις) is in the proper sense the syllogism that starts from necessary, certain and immediate premises; an argument therefore that is truly scientific, "syllogismus faciens scire" (Anal. post., I, 22, 71 b 20 ff.; cf. Top., I, 1, 100 a 37 ff., and Sum. Theol., 1a-2ae, q. 54, a. 2, ad 2). As such, demonstration cannot extend to the first and immediate propositions, which are instead the principle and fixed point to which every demonstrative process refers (Anal. post., I, 3, 72 b 18). By this the apodictic value of science is in no way weakened, as a modern relativistic conception would have it, since the first principles of the metaphysical order stand as absolute certainties founded on the evident objective necessity of the fundamental ontological relations of being. As for the ontological principle of demonstration, it must be sought, according to Aristotle, in the essence: πάσης γὰρ ἀποδείξεως ἀρχὴν τὸ τί ἐστιν (De Anima, I, 1, 402 b 25). Demonstration is in fact the process which, starting from the principles, shows the necessity of the consequence; now everything that does not belong to the essence is accident (συμβεβηκός) and as such is not necessary, nor therefore can it serve as a principle of demonstration.

Understood in the broader sense of a method of proof, demonstration can be of various kinds. In logic, a distinction is made between direct demonstration, which is founded on reasons intrinsic to the terms of the proposition, and indirect demonstration, which instead proves a proposition rather from the outside, with reasons more or less closely connected, as, for example, when one proves the truth of a doctrine from general consent, or its falsity from the false consequences that follow from it. Further kinds of direct demonstration, founded on the more or less high degree of ontological priority and causal immediacy of the premises with regard to the conclusion, are demonstration a priori (from cause to effect, in general from a principle or reason ontologically prior to its consequences), a posteriori (from effect to cause), propter quid (from intrinsic and immediate causes and principles), quia (from effects or from extrinsic causes).

Ugo Viglino