DEMONSTRATION. — From de-monstrare, to show, to make visible, with a sense of derivation. In the broad sense, every argument by which a proposition or previously established thesis is proved and made manifest is a d. The d. therefore presupposes that the truth one intends to demonstrate is known, but only as a problematic position, not in its value as certainty. Insofar as it tends to attain this end, that is, to establish certainty and evidence, the d. asserts itself as a positive logical pro-
cess in the acquisition of knowledge, and its meaning approaches that of the more universal concept of deduction.
In Aristotle, d. (ἀπόδειξις) in the proper sense is the syllogism that proceeds from necessary, certain, and immediate premises; hence, truly scientific argumentation, « syllogismus faciens scire » (Anal. post., I, 22, 71 b 20 ff.; cf. Top., I, 1, 100 a 37 ff., and Sum. Theol., 1°-2°, q. 54, a. 2, ad 2). As such, the d. cannot extend to the first and immediate propositions, which are instead the principle and fixed point on which every demonstrative process depends (Anal. post., I, 3, 72 b 18). This in no way undermines, as a modern relativistic conception would have it, the apodictic value of science, since the first principles of the metaphysical order are absolute certainties founded on the evident objective necessity of the fundamental ontological relations of being. As for the ontological principle of the d., according to Aristotle it must be sought in essence: πάσης γὰρ ἀποδείξεως ἀρῆν τὸ τί ἐστιν (De Anima, I, 1, 402 b 25). The d. is in fact the process which, starting from principles, shows the necessity of the consequence; now everything that does not belong to essence is an accident (συμβεβηκός) and, as such, is not necessary, and therefore cannot serve as a principle of d.
Understood in the broader sense of a method of proof, the d. may be of various kinds. In logic, a distinction is made between direct d., which is based on reasons intrinsic to the terms of the proposition, and indirect d., which instead demonstrates a proposition rather from outside, by reasons more or less closely connected with it, as, for example, when the truth of a doctrine is proved from general consent, or its falsity from the false consequences that derive from II. Further kinds of direct d., founded on the higher or lower degree of ontological priority and causal immediacy of the premises with respect to the conclusion, are the d. a priori (from cause to effect, generally 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 extrinsic causes).