Lastly, we have the Third figure, wherein the middle term is the Subject in both premisses. Here one at least of the premisses must be universal, either affirmative or negative. But no universal conclusions can be obtained in this figure; all the conclusions are particular. Aristotle recognizes six legitimate modes; in all of which the conclusions are particular, four of them being affirmative, two negative. The other possible modes he sets aside as in the two preceding figures.[32] [Footnote 32: Ibid. I. vi. p. 28, a. 10-p. 29, a. 18.] But Aristotle assigns to the First figure a marked superiority as compared with the Second and Third. It is the only one that yields perfect syllogisms; those furnished by the other two are all imperfect. The cardinal principle of syllogistic proof, as he conceives it, is--That whatever can be affirmed or denied of a whole, can be affirmed or denied of any part thereof.[33] The major proposition affirms or denies something universally respecting a certain whole; the minor proposition declares a certain part to be included in that whole. To this principle the four modes of the First figure manifestly and unmistakably conform, without any transformation of their premisses. But in the other figures such conformity does not obviously appear, and must be demonstrated by reducing their syllogisms to the First figure; either ostensively by exposition of a particular case, and conversion of the premisses, or by _Reductio ad Impossibile_. Aristotle, accordingly, claims authority for the Second and Third figures only so far as they can be reduced to the First.[34] We must, however, observe that in this process of reduction no new evidence is taken in; the matter of evidence remains unchanged, and the form alone is altered, according to laws of logical conversion which Aristotle has already laid down and justified. Another ground of the superiority and perfection which he claims for the First figure, is, that it is the only one in which every variety of conclusion can be proved; and especially the only one in which the Universal Affirmative can be proved--the great aim of scientific research. Whereas, in the Second figure we can prove only _negative_ conclusions, universal or particular; and in the Third figure only _particular_ conclusions, affirmative or negative.[35] [Footnote 33: Ibid. I. xli. p. 49, b. 37: [Greek: o(/lôs ga\r o(\ mê/ e)stin ô(s o(/lon pro\s me/ros kai\ a)/llo pro\s tou=to ô(s me/ros pro\s o(/lon, e)x ou)deno\s tô=n toiou/tôn dei/knusin o( deiknu/ôn, ô(/ste ou)de\ gi/netai sullogismo/s.] He had before said this about the relation of the three terms in the Syllogism, I. iv. p. 25, b. 32: [Greek: o(/tan o(/roi trei=s ou(/tôs e)/chôsi pro\s a)llê/lous ô(/ste to\n e)/schaton e)n o(/lô| ei)=nai tô=| me/sô| kai\ to\n me/son e)n o(/lô| tô=| prô/tô| ê)\ ei)=nai ê)\ mê\ ei)=nai, a)na/gkê tô=n a)/krôn ei)=nai sullogismo\n te/leion] (_Dictum de Omni et Nullo_).]