38. Demonstration. Probable and Sophistical Reasonings. -- Syllogistic reasoning is the basis of demonstration (apodeixis) with which Aristotle deals in the Posterior Analytics. He calls demonstration" the syllogism which produces science". Demonstration must stop at some indemonstrable first principles which the mind enunciates on account of their immediate evidence as soon as it abstracts them from the data of sense. Aristotle also sets limits to definition (horismos) and to division, for it is impossible to define everything and to divide things ad infinitum.

Demonstration, which begets certitude, is opposed to probable reasoning and to erroneous reasoning. Aristotle devotes a separate treatise to this latter (the Sophistical Reasonings). To probable arguments he attaches, in the Topics, the theory of the topoi or de locis dialecticis, as also the study of the aporiae (aporiai), i.e., the statement of the reasons for and against, prior to the finding of the middle term of the syllogism.^{1}

{1} "Rhetoric is the application of dialectics to government or politics, i.e., to certain practical ends." -- BOUTROUX, op. cit., p. 184.