Chapter VIII: Analytica Posteriora II (2)

The question then arises, Can there be more than one cause of the same _causatum_? Is it necessary that the same effect should be produced in all cases by the same cause? In other words, when the same predicate is demonstrated to be true of two distinct minors, may it not be demonstrated in one case by one middle term, and in the other case by a different middle term?[58] Answer: In genuine and proper scientific problems the middle term is the rational account (definition, interpretation) of the major extreme; this middle term therefore, or the cause, must in all cases be one and the same. The demonstration in these cases is derived from the same essence; it is _per se_, not _per accidens_. But there are other problems, not strictly and properly scientific, in which cause and _causatum_ are connected merely _per accidens_; the demonstration being operated by a middle term which is not of the essence of the major, but is only a sign or concomitant.[59] According as the terms of the conclusion are related to each other, so also will the middle term be related to both. If the conclusion be equivocal, the middle term will be equivocal also; if the predicate in the conclusion be in generic relation to the subject, the major also will be in generic relation to the middle. Thus, if you are demonstrating that one triangle is similar to another, and that one colour is similar to another, the word similar in these two cases is not univocal, but equivocal; accordingly, the middle term in the demonstration will also be equivocal. Again, if you are demonstrating that four proportionals will also be proportionals alternately, there will be one cause or middle term, if the subject of the conclusion be lines; another, if the subject be numbers. Yet the middle term or cause in both is the same, in as far as both involve a certain fact of increment.[60]

[Footnote 58: Analyt. Post. II. xvi. p. 98, b. 25.]

[Footnote 59: Ibid. xvii. p. 99, a. 4: [Greek: e)/sti de\ kai\ ou(= ai)/tion kai\ ô(=| skopei=n kata\ sumbebêko/s; ou) mê\n dokei= problê/mata ei)=nai.]

"Veluti si probemus grammaticum esse aptum ad ridendum, quia homo est aptus ad ridendum." (Julius Pacius, p. 514.)]

[Footnote 60: Analyt. Post. II. xvii. p. 99, a. 8-16.]

The major term of the syllogism will in point of extension be larger than any particular minor, but equal or co-extensive with the sum total of the particulars. Thus the predicate deciduous, affirmable of all plants with broad leaves, is greater in extension than the subject vines, also than the subject fig-trees; but it is equal in extension to the sum total of vines and fig-trees (the other particular broad-leaved plant). The middle also, in an universal demonstration, reciprocates with the major, being its definition. Here the true middle or cause of the effect that vines and fig-trees shed their leaves, is not that they are broad-leaved plants, but rather a coagulation of sap or some such fact.[61]

[Footnote 61: Ibid. a. 16 seq.]

The last chapter of the present treatise is announced by Aristotle as the appendix and completion of his entire theory of Demonstrative Science, contained in the Analytica Priora, which treats of Syllogism, and the Analytica Posteriora, which treats of Demonstration. After formally winding up the whole enquiry, he proceeds to ask regarding the _principia_ of Demonstrative Science: What are they? How do they become known? What is the mental habit or condition that is cognizant of them?[62]

[Footnote 62: Analyt. Post. II. xix. p. 99, b. 15-19: [Greek: peri\ me\n ou)=n sullogismou= kai\ a)podei/xeôs, ti/ te e(ka/tero/n e)sti kai\ pô=s gi/netai, phanero/n, a(/ma **de\ kai\ peri\ e)pistê/mês a)podeiktikê=s; tau)to\n ga/r e)stin. peri\ de\ tô=n a)rchô=n, pô=s te gi/nontai gnô/rimoi, kai\ _ti/s ê( gnôri/zousa e(/xis_, e)nteu=the/n e)sti dê=lon proaporê/sasi prô=ton.]

Bekker and Waitz, in their editions, include all these words in ch. xix.: the older editions placed the words preceding [Greek: peri\ de\] in ch. xviii. Zabarella observes the transition to a new subject (Comm. ad Analyt. Post. II. ch. xv. p. 640):--"Postremum hoc caput (beginning at [Greek: peri\ de\]) extra primariam tractationem positum esse manifestum est: quum præcesserit epilogus respondens prooemio quod legitur in initio primi libri Priorum Analyticorum."]

Aristotle has already laid down that there can be no Demonstration without certain _præcognita_ to start from; and that these _præcognita_ must, in the last resort, be _principia_ undemonstrable, immediately known, and known even more accurately than the conclusions deduced from them. Are they then cognitions, or cognizant habits and possessions, born along with us, and complete from the first? This is impossible (Aristotle declares); we cannot have such valuable and accurate cognitions from the first moments of childhood, and yet not be at all aware of them. They must therefore be acquired; yet how is it possible for us to acquire them?[63] The fact is, that, though we do not from the first possess any such complete and accurate cognitions as these, we have from the first an inborn capacity or potentiality of arriving at them. And something of the same kind belongs to all animals.[64] All of them possess an apprehending and discriminating power born with them, called Sensible Perception; but, though all possess such power, there is this difference, that with some the act of perception dwells for a longer or shorter time in the mind; with others it does not. In animals with whom it does not dwell, there can be no knowledge beyond perception, at least as to all those matters wherein perception is evanescent; but with those that both perceive and retain perceptions in their minds, ulterior knowledge grows up.[65] There are many such retentive animals, and they differ among themselves: with some of them reason or rational notions arise out of the perceptions retained; with others, it is not so. First, out of perception arises memory; next, out of memory of the same often repeated, arises experience, since many remembrances numerically distinct are summed up into one experience. Lastly, out of experience, or out of the universal notion, the _unum et idem_ which pervades and characterizes a multitude of particulars, when it has taken rest and root in the mind, there arises the _principium_ of art and science: of science, in respect to objects existent; of art, in respect to things generable.[66] And thus these mental habits or acquirements neither exist in our minds determined from the beginning, nor do they spring from other acquirements of greater cognitive efficacy. They spring from sensible perception; and we may illustrate their growth by what happens in the panic of a terrified host, where first one runaway stops in his flight, then a second, then a third, until at last a number docile to command is collected. One characteristic feature of the mind is to be capable of this process.[67]

[Footnote 63: Analyt. Post. II. xix. p. 99, b. 25-30: [Greek: po/teron ou)k e)nou=sai ai( e(/xeis e)ggi/nontai, ê)\ e)nou=sai lelê/thasin. ei) me\n dê\ e)/chomen au)ta/s, a)/topon; sumbai/nei ga\r a)kribeste/ras e)/chontas gnô/seis a)podei/xeôs lantha/nein; ei) de\ lamba/nomen mê\ e)/chontes pro/teron, pô=s a)\n gnôri/zoimen kai\ mantha/noimen e)k mê\ prou+parchou/sês gnô/seôs?] Compare, supra, Analyt. Post. I. iii. p. 72, b. 20-30; Metaphys. A. ix. p. 993, a. 1, with the Comment. of Alexander, p. 96, Bonitz.]

[Footnote 64: Analyt. Post. II. xix. p. 99, b. 30: [Greek: phanero\n toi/nun ou)/t' e)/chein oi(=o/n te, ou)/t' a)gnoou=si kai\ mêdemi/an e)/chousin e(/xin e)ggi/nesthai; a)na/gkê a)/ra e)/chein me/n tina du/namin, mê\ toiau/tên d' e)/chein ê)\ e)/stai tou/tôn timiôte/ra kat' a)kri/beian. phai/netai de\ tou=to/ ge pa=sin u(pa/rchon toi=s zô/|ois.]]

[Footnote 65: Analyt. Post II. xix. p. 99, b. 37: [Greek: o(/sois me\n ou)=n mê\ e)ggi/netai, ê)\ o(/lôs ê)\ peri\ a(\ mê\ e)ggi/netai, ou)k e)/sti tou/tois gnô=sis e)/xô tou= ai)stha/nesthai; e)n oi(=s d' e)/nestin ai)sthanome/nois e)/chein e)/ti e)n tê=| psuchê=|. pollô=n de\ toiou/tôn ginome/nôn ê)/dê diaphora/ tis gi/netai, ô(/ste toi=s me\n gi/nesthai lo/gon e)k tê=s tô=n toiou/tôn monê=s, toi=s de\ mê/.] Compare Analyt. Poster. I. p. 81, a. 38, seq., where the dependence of Induction on the perceptions of sense is also affirmed. See Themistius, pp. 50-51, ed. Spengel. The first chapter of the Metaphysica (p. 981), contains a striking account of this generation of universal notions from memory and comparison of sensible particulars: [Greek: gi/netai de\ te/chnê, o(/tan e)k pollô=n tê=s e)mpeiri/as e)nnoêma/tôn mi/a katho/lou ge/nêtai peri\ tô=n o(moi/ôn u(po/lêpsis] ("_intellecta similitudo"_). Also in the Physica VII. p. 247, b. 20 (in the Paraphrase of Themistius, as printed in the Berlin edition, at bottom of page): [Greek: e)k ga\r tê=s kata\ me/ros e)mpeiri/as tê\n katho/lou lamba/nomen e)pistê/mên.]]

[Footnote 66: Analyt Post II. xix. p. 100, a. 3-10: [Greek: e)k me\n ou)=n ai)sthê/seôs gi/netai mnê/mê, ô(/sper le/gomen, e)k de\ mnê/mês polla/kis tou= au)tou= ginome/nês e)mpeiri/a; ai( ga\r pollai\ mnê=mai tô=| a)rithmô=| e)mpeiri/a mi/a e)sti/n. e)k d' e)mpeiri/as, ê)\ e)k panto\s ê)remê/santos tou= katho/lou e)n tê=| psuchê=|, tou= e(no\s para\ ta\ polla/, o(\ a)\n e)n a(/pasin e(\n e)nê=| e)kei/nois to\ au)to/, te/chnês a)rchê\ kai\ e)pistê/mês; e)a\n me\n peri\ ge/nesin, te/chnês, e)a\n de\ peri\ to\ o)/n, e)pistê/mês.]

A theory very analogous to this (respecting the gradual generation of scientific universal notions in the mind out of the particulars of sense) is stated in the Phædon of Plato, ch. xlv. p. 96, B., where Sokrates reckons up the unsuccessful tentatives which he had made in philosophy: [Greek: kai\ po/teron to\ ai(=ma/ e)stin ô(=| phronou=men, ê)\ o( a)ê\r, ê)\ to\ pu=r, ê)\ tou/tôn me\n ou)de/n, o( de\ e)gke/phalo/s e)stin o( ta\s ai)sthê/seis pare/chôn tou= a)kou/ein kai\ o(pa=n kai\ o)sphrai/nesthai, e)k _tou/tôn de\ gi/gnoito mnê/mê kai\ do/xa_, e)k _de\ mnê/mês kai\ do/xês, labou/sês to\ ê)remei=n, kata\ tau=ta gi/gnesthai e)pistê/mên_.]

Boethius says, Comm. in Ciceronis Topica, p. 805:--"Plato ideas quasdam esse ponebat, id est, species incorporeas, substantiasque constantes et per se ab aliis naturæ ratione separatas, ut hoc ipsum _homo_, quibus participantes cæteræ res homines vel animalia fierent. At vero Aristoteles nullas putat extra esse substantias; sed _intellectam similitudinem plurimorum inter se differentium substantialem_, genus putat esse vel speciem. Nam cum homo et equus differunt rationabilitate et irrationabilitate, horum _intellecta similitudo_ efficit genus. Ergo communitas quædam et plurimorum inter se differentium similitudo _notio_ est; cujus notionis aliud _genus_ est, aliud _forma_. Sed quoniam _similium intelligentia_ est omnis notio, in rebus vero similibus necessaria est differentiarum discretio, idcirco indiget notio quadam enodatione ac divisione; velut ipse intellectus animalis sibi ipsi non sufficit," &c.

The phrase _intellecta similitudo plurimorum_ embodies both Induction and Intellection in one. A like doctrine appears in the obscure passages of Aristotle, De Animâ, III. viii. p. 429, b. 10; also p. 432, a. 3: [Greek: o( nou=s, ei)=dos ei)dô=n, kai\ ê( ai)/sthêsis, ei)=dos ai)sthêtô=n. e)pei\ de\ ou)de\ pra=gma ou)the/n e)sti para\ ta\ mege/thê, ô(s dokei=, ta\ ai)sthêta\ kechôrisme/non, e)n toi=s ei)/desi toi=s ai)sthêtoi=s ta\ noêta/ e)stin.]]

[Footnote 67: Analyt. Post. II. xix. p. 100, a. 10-14: [Greek: ou)/te dê\ e)nupa/rchousin a)phôrisme/nai ai( e(/xeis, ou)/t' a)p' a)/llôn e(/xeôn gi/nontai gnôrimôte/rôn, a)ll' a)po\ ai)sthê/seôs,--ê( de\ psuchê\ u(pa/rchei toiau/tê ou)=sa oi(/a du/nasthai pa/schein tou=to.]

The varieties of intellectual [Greek: e(/xeis] enumerated by Aristotle in the sixth book of the Nikomachean Ethica, are elucidated by Alexander in his Comment. on the Metaphysica. (A. p. 981) pp. 7, 8, Bonitz. The difference of [Greek: e(/xis] and [Greek: dia/thesis], the durable condition as contrasted with the transient, is noted in Categoriæ, pp. 8, 9. See also Eth. Nikom. II. i. ii. pp 1103, 4.]

Aristotle proceeds to repeat the illustration in clearer terms--at least in terms which he thinks clearer.[68] We perceive the particular individual; yet sensible perception is of the universal in the particular (as, for example, when Kallias is before us, we perceive man, not the man Kallias). Now, when one of a set of particulars dwells some time in the mind, first an universal notion arises; next, more particulars are perceived and detained, and universal notions arise upon them more and more comprehensive, until at last we reach the highest stage--the most universal and simple. From Kallias we rise to man; from such and such an animal, to animal _in genere_; from animal _in genere_, still higher, until we reach the highest or indivisible genus.[69] Hence it is plain that the first and highest _principia_ can become known to us only by Induction; for it is by this process that sensible perception builds up in us the Universal.[70] Now among )those intellective habits or acquirements, whereby we come to apprehend truth, there are some (Science and Noûs) that are uniformly and unerringly true, while others (Opinion and Ratiocination) admit an alternative of falsehood.[71] Comparing Science with Noûs, the latter, and the latter only, is more accurate and unerring than Science. But all Science implies demonstration, and all that we know by Science is conclusions deduced by demonstration. We have already said that the _principia_ of these demonstrations cannot be themselves demonstrated, and therefore cannot be known by Science; we have also said that they must be known more accurately than the conclusions. How then can these _principia_ themselves be known? They can be known only by Noûs, and from particulars. It is from the _principia_ known by Noûs, with the maximum of accuracy, that Science demonstrates her conclusions. Noûs is the great _principium_ of Science.[72]

[Footnote 68: Analyt. Post. II. xix. p. 100, a. 14: [Greek: o(\ d' _e)le/chthê me\n pa/lai_, ou) saphô=s de\ e)le/chthê, pa/lin ei)/pômen.]

Waitz supposes that Aristotle here refers to a passage in the first book of the Analytica Posteriora, c. xxxi. p. 87, b. 30. M. Barthélemy St. Hilaire thinks (p. 290) that reference is intended to an earlier sentence of this same chapter. Neither of these suppositions seems to suit (least of all the last) with the meaning of [Greek: pa/lai]. But whichever he meant, Aristotle has not done much _to clear up_ what was obscure in the antecedent statements.]

[Footnote 69: Analyt. Post. II. xix. p. 100, a. 15: [Greek: sta/ntos ga\r tô=n a)diapho/rôn e(no/s, prô=ton me\n e)n tê=| psuchê=| katho/lou (kai\ ga\r ai)sthêsis tou= katho/lou e)sti/n, oi(=on a)nthrô/pou, a)ll' ou) Kalli/ou a)nthrô/pou) pa/lin d' e)n tou/tois i(/statai, _e(/ôs a)\n ta\ a)merê= stê=| kai\ ta\ katho/lou_, oi(=on toiondi\ zô=|on, e(/ôs zô=|on; kai\ e)n tou/tô| ô(sau/tôs.]

These words are obscure: [Greek: ta\ a)merê=] must mean the highest genera; indivisible, _i.e._ being a _minimum_ in respect of _comprehension_. Instead of [Greek: ta\ katho/lou], we might have expected [Greek: ta\ ma/lista katho/lou], or, perhaps, that [Greek: kai\] should be omitted. Trendelenburg comments at length on this passage, Arist. De Animâ Comment. pp. 170-174.]

[Footnote 70: Analyt. Post. II. xix. p. 100, b. 3: [Greek: dê=lon dê\ o(/ti ê(mi=n ta\ prô=ta e)pagôgê=| gnôri/zein a)nagkai=on; kai\ ga\r kai\ ai)/sthêsis ou(/tô to\ katho/lou e)mpoiei=.] Compare, supra, Analyt. Post. I. xviii. p. 81, b. 1. Some commentators contended that Aristotle did not mean to ascribe an inductive origin to the common Axioms properly so called, but only to the special _principia_ belonging to each science. Zabarella refutes this doctrine, and maintains that the Axioms (Dignitates) are derived from Induction (Comm. in Analyt. Post. II. xix. p. 649, ed. Venet., 1617):--"Quum igitur inductio non sit proprie discursus, nec ratio, jure dicit Aristoteles principiorum notitiam non esse cum ratione, quia non ex aliis innotescunt, sed ex seipsis dum per inductionem innotescunt. Propterea in illa propositione, quæ in initio **primi libri legitur, sub doctrina discursiva cognitio principiorum non comprehenditur, quia non est dianoëtica. Hoc, quod modo diximus, si nonnulli advertissent, fortasse non negassent principia communia, quæ dicuntur Dignitates, inductione cognosci. Dixerunt enim Aristotelem hic de principiis loquentem sola principia propria considerasse, quæ cum non proprio lumine cognoscantur, inductione innotescunt; at Dignitates (inquiunt) proprio lumine ab intellectu nostro cognoscuntur per solam terminorum intelligentiam, ut quod omne totum majus est suâ parte; hoc enim non magis est evidens sensui in particulari, quam intellectui in universali, proinde inductione non eget. Sed hanc sententiam hic Averroes refutat, dicens hæc quoque inductione cognosci, sed non animadverti nobis tempus hujus inductionis; id enim omnino confitendum est, omnem intellectualem doctrinam à sensu originem ducere, et nihil esse in intellectu quod prius in sensu non fuerit, ut ubique asserit Aristoteles."

To the same purpose Zabarella expresses himself in an earlier portion of his Commentary on the Analyt. Post., where he lays it down that the truth of the proposition, Every whole is greater than its part, is known from antecedent knowledge of particulars by way of Induction. Compare the Scholion of Philoponus, ad Analyt. Post. p. 225, a. 32, Brand., where the same is said about the Axiom, Things equal to the same are equal to each other.]

[Footnote 71: Analyt. Post. II. xix. p. 100, b. 5: [Greek: e)pei\ de\ tô=n peri\ tê\n dia/noian e(/xeôn, ai(=s a)lêtheu/omen, ai( me\n a)ei\ a)lêthei=s ei)si/n, ai( de\ e)pide/chontai to\ pseu=dos], &c.]

[Footnote 72: Ibid. fin. p. 100.]

The manner in which Aristotle here describes how the _principia_ of Syllogism become known to the mind deserves particular attention. The march up to _principia_ is not only different from, but the reverse of, the march down from _principia_; like the athlete who runs first to the end of the stadium, and then back.[73] Generalizing or universalizing is an acquired intellectual habit or permanent endowment; growing out of numerous particular acts or judgments of sense, remembered, compared, and coalescing into one mental group through associating resemblance. As the ethical, moral, practical habits, are acquirements growing out of a repetition of particular acts, so also the intellectual, theorizing habits are mental results generated by a multitude of particular judgments of sense, retained and compared, so as to imprint upon the mind a lasting stamp of some identity common to all. The Universal (_notius naturâ_) is thus generated in the mind by a process of Induction out of particulars which are _notiora nobis_; the potentiality of this process, together with sense and memory, is all that is innate or connatural.

[Footnote 73: Aristot. Eth. Nikom. I. iv. p. 1095, b. 1.]

The _principia_, from which the conclusions of Syllogism are deduced, being thus obtained by Induction, are, in Aristotle's view, appreciated by, or correlated with, the infallible and unerring Noûs or Intellect.[74] He conceives repeated and uncontradicted Induction as carrying with it the maximum of certainty and necessity: the syllogistic deductions constituting Science he regards as also certain; but their certainty is only derivative, and the _principia_ from which they flow he ranks still higher, as being still more certain.[75] Both the one and the other he pointedly contrasts with Opinion and Calculation, which he declares to be liable to error.

[Footnote 74: The passages respecting [Greek: a)rchai\] or _principia_, in the Nikomachean Ethica (especially Books I. and VI.), are instructive as to Aristotle's views. The _principia_ are universal notions and propositions, not starting up ready-made nor as original promptings of the intellect, but gradually built up out of the particulars of sense and Induction, and repeated particular acts. They are judged and sanctioned by [Greek: Nou=s] or Intellect, but it requires much care to define them well. They belong to the [Greek: o(/ti], while demonstration belongs to the [Greek: dio/ti]. Eth. Nik. I. vii. p. 1098, a. 33: [Greek: ou)k a)paitête/on d' ou)de\ tê\n ai)ti/an e)n a(/pasin o(moi/ôs, a)ll' i(kano\n e)/n tisi to\ o(/ti deichthê=nai kalô=s, oi(=on kai\ peri\ ta\s a)rcha/s; to\ d' o(/ti prô=ton kai\ a)rchê/. tô=n a)rchô=n d' ai( me\n e)pagôgê=| theôrou=ntai, ai( d' ai)sthê/sei, ai( d' e)thismô=| tini, kai\ a)/llai d' a)llô=s. metie/nai de\ peirate/on e(ka/stas ê(=| pephu/kasin, kai\ spoudaste/on o(/pôs o(risthô=si kalô=s; mega/lên ga\r e)/chousi r(opê\n pro\s ta\ e(po/mena.]

Compare Eth. Nik. VI. iii. p. 1139, b. 25, where the Analytica is cited by name--[Greek: ê( me\n dê\ e)pagôgê\ a)rchê/ e)sti kai\ tou= katho/lou, o( de\ sullogismo\s e)k tô=n katho/lou; ei)si\n a)/ra a)rchai\ e)x ô(=n o( sullogismo/s, ô(=n ou)/k e)sti sullogismo/s; e)pagôgê\ a)/ra.]--ib. p. 1141, a. 7: [Greek: lei/petai nou=n ei)=nai tô=n a)rchô=n.]--p. 1142, a. 25: [Greek: o( me\n ga\r nou=s tô=n o(/rôn, ô(=n ou)/k e)sti lo/gos].--p. 1143, b. 1.]

[Footnote 75: Analyt. Post. I. ii. p. 72, a. 37: [Greek: to\n de\ me/llonta e(/xein tê\n e)pistê/mên tê\n di' a)podei/xeôs ou) mo/non dei= ta\s a)rcha\s gnôri/zein kai\ ma=llon au)tai=s pisteu/ein ê)\ tô=| deiknume/nô|, a)lla\ mêd' a)/llo au)tô=| pisto/teron ei)=nai mêde\ gnôrimô/teron tô=n a)ntikeime/nôn tai=s a)rchai=s, e)x ô(=n e)/stai sullogismo\s o( tê=s e)nanti/as a)pa/tês, ei)/per dei= to\n e)pista/menon a(plô=s a)meta/peiston ei)=nai.]]

Aristotle had inherited from Plato this doctrine of an infallible Noûs or Intellect, enjoying complete immunity from error. But, instead of connecting it (as Plato had done) with reminiscences of an anterior life among the Ideas, he assigned to it a position as terminus and correlate to the process of Induction.[76] The like postulate and pretension passed afterwards to the Stoics, and various other philosophical sects: they could not be satisfied without finding infallibility somewhere. It was against this pretension that the Academics and Sceptics entered their protest; contending, on grounds sometimes sophistical but often very forcible, that it was impossible to escape from the region of fallibility, and that no criterion of truth, at once universal and imperative, could be set up.

[Footnote 76: Ibid. iii. p. 72, b. 20-30. [Greek: kai\ ou) mo/non e)pistê/mên a)lla\ kai\ a)rchê\n e)pistê/mês ei)=nai tina/ phamen, ê(=| tou\s o(/rous gnôri/zomen.]

Themistius, p. 14: [Greek: ô(=n dê\ a)/rchei pa/lin o( nou=s ô(=| tou\s o(/rous thêreu/omen, e)x ô(=n sugkei\tai ta\ a)xiô/mata.]

The Paraphrase of Themistius (pp. 100-104) is clear and instructive, where he amplifies the last chapter, and explains [Greek: Nou=s] as the generalizing or universalizing aptitude of the soul, growing up gradually out of the particulars furnished by Sense and Induction.]

It is to be regretted that Aristotle should have contented himself with proclaiming this Inductive process as an ideal, culminating in the infallible Noûs; and that he should only have superficially noticed those conditions under which it must be conducted in reality, in order to avoid erroneous or uncertified results. This is a deficiency however which has remained unsupplied until the present century.[77]

[Footnote 77: Sir W. Hamilton, Lectures on Logic, Vol. III. Lect. xix. p. 380, says:--"In regard to simple syllogisms, it was an original dogma of the Platonic School, and an early dogma of the Peripatetic, that philosophy (science strictly so-called) was only conversant with, and was exclusively contained in, universals; and the doctrine of Aristotle, which taught that all our general knowledge is only an induction from an observation of particulars, was too easily forgotten or perverted by his followers. It thus obtained almost the force of an acknowledged principle, that everything to be known must be known under some general form or notion. Hence the exaggerated importance attributed to definition and deductions, it not being considered that we only take out of a general notion what we had previously placed therein, and that the amplification of our knowledge is not to be sought for from above but from below,--not from speculation about abstract generalities, but from the observation of concrete particulars. But however erroneous and irrational, the persuasion had its day and influence, and it perhaps determined, as one of its effects, the total neglect of one half, and that not the least important half, of the reasoning process. For while men thought only of looking upward to the more extensive notions, as the only objects and the only media of science, they took little heed of the more comprehensive notions, and absolutely contemned individuals, as objects which could neither be scientifically known in themselves nor supply the conditions of scientifically knowing aught besides. The Logic of Comprehension and of Induction was therefore neglected or ignored,--the Logic of Extension and Deduction exclusively cultivated, as alone affording the rules by which we might evolve higher notions into their subordinate concepts."

(Hamilton, in this passage, considers the Logic of _Induction_ to be the same as the Logic of _Comprehension_.)]