[Footnote 5: Ibid. I. iv. p. 25, b. 30.] As a foundation for the syllogistic theory, propositions are classified according to their quantity (more formally than in the treatise De Interpretatione) into Universal, Particular, and Indefinite or Indeterminate;[6] Aristotle does not recognize the Singular Proposition as a distinct variety. In regard to the Universal Proposition, he introduces a different phraseology according as it is looked at from the side of the Subject, or from that of the Predicate. The Subject is, or is not, in the whole Predicate; the Predicate is affirmed or denied respecting all or every one of the Subject.[7] The minor term of the Syllogism (in the first mode of the first figure) is declared to be in the whole middle term; the major is declared to belong to, or to be predicable of, all and every the middle term. Aristotle says that the two are the same; we ought rather to say that each is the concomitant and correlate of the other, though his phraseology is such as to obscure the correlation. [Footnote 6: Ibid. I. i. p. 24, a. 17. The Particular ([Greek: e)n me/rei]), here for the first time expressly distinguished by Aristotle, is thus defined:--[Greek: e)n me/rei de\ to\ tini\ ê)\ mê\ tini\ ê)\ mê\ panti\ u(pa/rchein.]] [Footnote 7: Ibid. b. 26: [Greek: to\ d' e)n o(/lô| ei)nai e(/teron e(te/rô|, kai\ to\ kata\ panto\s katêgorei=sthai thate/rou tha/teron, tau)to/n e)sti--tau)to\n], _i.e._ [Greek: _a)ntestramme/nôs_], as Waitz remarks in note. Julius Pacius says:--"Idem re, sed ratione differunt ut ascensus et descensus; nam subjectum dicitur esse vel non esse in toto attributo, quia attributum dicitur de omni vel de nullo subjecto" (p. 128).] The definition given of a Syllogism is very clear and remarkable:--"It is a speech in which, some positions having been laid down, something different from these positions follows as a necessary consequence from their being laid down." In a _perfect_ Syllogism nothing additional is required to make the necessity of the consequence obvious as well as complete. But there are also _imperfect_ Syllogisms, in which such necessity, though equally complete, is not so obviously conveyed in the premisses, but requires some change to be effected in the position of the terms in order to render it conspicuous.[8] [Footnote 8: Aristot. Anal. Prior. I. i. p. 24, b. 18-26. The same, with a little difference of wording, at the commencement of Topica, p. 100, a. 25. Compare also Analyt. Poster. I. x. p. 76, b. 38: [Greek: o(/sôn o)/ntôn tô=| e)kei=na ei)=nai gi/netai to\ sumpe/rasma.]]