[Footnote 43: Analyt. Post. I. xiii. p. 79, a. 2, seq.: [Greek: e)ntau=tha ga\r to\ me\n o(/ti tô=n ai)sthêtikô=n ei)de/nai, to\ de\ dio/ti tô=n mathêmatikô=n], &c. Compare Analyt. Prior. II. xxi. p. 67, a. 11; and Metaphys. A. p. 981, a. 15.] [Footnote 44: Analyt. Post. I. xiv. p. 79, a. 17-32.] As there are some affirmative propositions that are indivisible, _i.e._, having affirmative predicates which belong to a subject at once, directly, immediately, indivisibly,--so there are also some indivisible negative propositions, _i.e._, with predicates that belong negatively to a subject at once, directly, &c. In all such there is no intermediate step to justify either the affirmation of the predicate, or the negation of the predicate, respecting the given subject. This will be the case where neither the predicate nor the subject is contained in any higher genus.[45] [Footnote 45: Ibid. I. xv. p. 79, a. 33-b. 22. The point which Aristotle here especially insists upon is, that there may be and are immediate, undemonstrable, _negative_ (as well as affirmative) predicates: [Greek: phanero\n ou)=n o(/ti e)nde/chetai/ te a)/llo a)/llô| _mê\ u(pa/rchein_ a)to/môs]. (Themistius, Paraphr. p. 48, Spengel: [Greek: a)/mesoi de\ prota/seis ou) katapha/seis mo/non ei)si/n, a)lla\ kai\ a)popha/seis o(moi/ôs ai(\ mê\ du/nantai dia\ sullogismou= deichthê=nai, au(=tai d' ei)si\n e)ph' ô(=n ou)dete/rou tô=n o(/rôn a)/llos tis o(/lou katêgorei=tai.]) It had been already shown, in an earlier chapter of this treatise (p. 72, b. 19), that there were _affirmative_ predicates immediate and undemonstrable. This may be compared with that which Plato declares in the Sophistes (pp. 253-254, seq.) about the intercommunion [Greek: tô=n genô=n kai\ tô=n ei)dô=n] with each other. Some of them admit such intercommunion, others repudiate it.]