DEMONSTRATION. — From de-monstrare, mon-
strare, to make visible, with a sense of derivation. In a broad sense, it is the demonstration of any argument by which a proposition or pre-established thesis is proven and made manifest. Demonstration therefore presupposes that the truth to be demonstrated is already known, albeit only as a problematic position, not in its certainty. Insofar as it aims to achieve this goal—namely, to establish certainty and evidence—demonstration is affirmed as a positive logical process in the acquisition of knowledge, and its meaning approaches that of deduction.
In Aristotle, demonstration (ἀπόδεξις) is, in the proper sense, the syllogism that proceeds from necessary, certain, and immediate premises; an argument that is truly scientific, a “syllogismus faciens scire” (Posterior Analytics, I, 22, 71 b 20 ff.; cf. Topics, I, 100 a 27 ff., and Summa Theologiae, I, q. 54, a. 2, ad 2). As such, demonstration cannot extend to first and immediate propositions, which instead serve as the principles and fixed points to which every demonstrative process refers (Posterior Analytics, I, 3, 72 b 18). This in no way diminishes, as a modern relativistic conception might suggest, the apodictic value of science, since the first principles of metaphysical order are posited as absolute certainties grounded in the evident objective necessity of fundamental ontological relations of being. As for the ontological principle of demonstration, Aristotle locates it in essence: πάσης γὰρ ἀποδεξίσεως ἀρχὴ τό εἰ σέχει (De Anima, I, 1, 402 b 25). Demonstration is the process that, starting from principles, shows the necessity of the conclusion; now, whatever does not belong to the essence is an accident (συμβεβηκός) and as such is neither necessary nor capable of serving as a principle of demonstration.
Understood in the broadest sense as a method of proof, demonstration can take various forms. In logic, a distinction is made between direct demonstration, which is based on reasons intrinsic to the terms of the proposition, and indirect demonstration, which proves a proposition rather externally, with more or less relevant reasons—such as when the truth of a doctrine is proven by general consensus or its falsity by the false consequences that follow from II. Further species of direct demonstration, based on the greater or lesser degree of ontological priority and causal immediacy of the premises in relation to the conclusion, are a priori demonstration (from cause to effect, generally from a principle or reason ontologically prior to its consequences), a posteriori demonstration (from effect to cause), propter quid demonstration (from intrinsic and immediate causes and first principles), and quia demonstration (from effects or extrinsic causes).