But the above doctrine will hold only in cases where there _is_ a distinct or extraneous cause; it will not hold in cases where there is none. It is only in the former (as has been said) that a middle term can be shown; rendering it possible that Quiddity or Essence should be declared by a valid formal syllogism, though it cannot be demonstrated by syllogism. In the latter, where there is no distinct cause, no such middle term can be enunciated: the Quiddity or Essence must be assumed as an immediate or undemonstrable principium, and must be exposed or set out in the best manner practicable as an existent reality, on Induction or on some other authority. The arithmetician makes his first steps by assuming both what a monad is and that there exists such a monad.[22] [Footnote 22: Analyt. Post. II. ix. p. 93, b. 21. [Greek: e)/sti de\ tô=n me\n e(/tero/n ti ai)/tion, tô=n d' ou)k e)/stin. ô(/ste dê=lon o(/ti kai\ tô=n ti/ e)sti ta\ me\n a)/mesa kai\ a)rchai/ ei)sin, a(\ kai\ ei)=nai kai\ ti/ e)stin u(pothe/sthai dei= ê)\ a)/llon tro/pon phanera\ poiê=sai. o(/per o( a)rithmêtiko\s poiei=; kai\ ga\r ti/ e)sti tê\n mona/da u(poti/thetai, kai\ o(/ti e)/stin.] Themistius, p. 80: [Greek: a(\ kai\ ei)=nai kai\ ti/ e)stin u(pothe/sthai dei=, ê)\ a)/llon tro/pon phanera\ poiê=sai e)x e)pagôgê=s ê)\ pi/steôs ê)\ e)mpeiri/as.] Rassow, De Notionis Definitione, pp. 18-22.] We may distinguish three varieties of Definition. 1. Sometimes it is the mere explanation what a word signifies; in this sense, it has nothing to do with essence or existence; it is a nominal definition and nothing more.[23] 2. Sometimes it enunciates the Essence, cause, or reason of the _definitum_; this will happen where the cause is distinct or extraneous, and where there is accordingly an intervening middle term: the definition will then differ from a demonstration only by condensing into one enunciation the two premisses and the conclusion which together constitute the demonstration.[24] 3. Sometimes it is an immediate proposition, an indemonstrable hypothesis, assuming Essence or Quiddity; the essence itself being cause, and no extraneous cause--no intervening middle term--being obtainable.[25] [Footnote 23: Analyt. Post. II. x. p. 93, b. 29-37.] [Footnote 24: Ibid. p. 93, b. 38, seq. [Greek: oi(=on a)po/deixis tou= ti/ e)stin, tê=| the/sei diaphe/rôn tê=s a)podei/xeôs;--sullogismo\s tou= ti/ e)sti, ptô/sei diaphe/rôn tê=s a)podei/xeôs]--differing "situ et positione terminorum" (Julius Pacius, p. 493).] [Footnote 25: Ibid. p. 94, a. 9: [Greek: o( de\ tô=n a)me/sôn o(rismo/s, the/sis e)sti\ tou= ti/ e)stin a)napo/deiktos.] Compare I. xxiv. p. 85, b. 24: [Greek: ô(=| ga\r kath' au(to\ u(pa/rchei ti, tou=to au)to\ au(tô=| ai)/tion.] See Kampe, Die Erkenntniss-theorie des Aristoteles, p. 212, seq.] To know or cognize is, to know the Cause; when we know the Cause, we are satisfied with our cognition. Now there are four Causes, or varieties of Cause:--