Among the universal propositions which are not derived from Induction, but which serve as [Greek: a)rchai\] for Deduction and Demonstration, we may reckon the religious, ethical, æsthetical, social, political, &c., beliefs received in each different community, and impressed upon all newcomers born into it by the force of precept, example, authority. Here the major premiss is felt by each individual as carrying an authority of its own, stamped and enforced by the sanction of society, and by the disgrace or other penalties in store for those who disobey it. It is ready to be interpreted and diversified by suitable minor premisses in all inferential applications. But these [Greek: a)rchai\] for deduction, differing widely at different times and places, though generated in the same manner and enforced by the same sanction, would belong more properly to the class which Aristotle terms [Greek: ta\ e)/ndoxa].] We have thus recognized that there exist immediate (ultimate or primary) propositions, wherein the conjunction between predicate and subject is such that no intermediate term can be assigned between them. When A is predicated both of B and C, this may perhaps be in consequence of some common property possessed by B and C, and such common property will form a middle term. For example, equality of angles to two right angles belongs both to an isosceles and to a scalene triangle, and it belongs to them by reason of their common property--triangular figure; which last is thus the middle term. But this need not be always the case.[66] It is possible that the two propositions--A predicated of B, A predicated of C--may both of them be immediate propositions; and that there may be no community of nature between B and C. Whenever a middle term can be found, demonstration is possible; but where no middle term can be found, demonstration is impossible. The proposition, whether affirmative or negative, is then an immediate or indivisible one. Such propositions, and the terms of which they are composed, are the ultimate elements or _principia_ of Demonstration. Predicate and subject are brought constantly into closer and closer conjunction, until at last they become one and indivisible.[67] Here we reach the unit or element of the syllogizing process. In all scientific calculations there is assumed an unit to start from, though in each branch of science it is a different unit; _e.g._ in barology, the pound-weight; in harmonics, the quarter-tone; in other branches of science, other units.[68] Analytical research teaches us that the corresponding unit in Syllogism is the affirmative or negative proposition which is primary, immediate, indivisible. In Demonstration and Science it is the Noûs or Intellect.[69] [Footnote 66: Analyt. Post. I. xxiii. p. 84, b. 3-18. [Greek: tou=to d' ou)k a)ei\ ou(/tôs e)/chei.]]