H. P. Grice's Demonstratum

DEMONSTRATUM. demonstration Logic, epistemology [from Latin de, away, from + monstrare, show; its Greek counterpart is apo, away + deixis, show] For Aristotle, demonstration was the inference of new knowledge from certain previously established knowledge or axioms, in contrast to intuition, which directly apprehends first principles. All syllogism is demonstration, although not all demonstration is syllogism. For Descartes and Locke, demonstration was the discovery of the connections of ideas and the comparison of ideas by reason alone. It amounts to rational justification and contrasts with immediate knowledge. Hume proposes that demonstrative knowledge is indubitable knowledge, in contrast to contingent knowledge about matters of fact. In contemporary philosophy, demonstration amounts to proof, that is, the deduction of a conclusion from one or more accepted premises by means of a set of valid rules of inference. “In the nature of the case the essential elements of demonstration are three: the subject, the attributes, and the basic premises.” Aristotle, Posterior Analytics