[Footnote 39: Analyt. Prior. II. xxi. p. 67, a. 19: [Greek: ou(/tô

me\n ou)=n ô(s tê=| katho/lou ou)=de to G o(/ti du/o o)rthai/, ô(s

de\ tê=| kath' e(/kaston ou)k oi)=den, ô(/st' ou)ch e(/xei ta\s

e)nanti/as] (sc. [Greek: e)pistê/mos]).]

[Footnote 40: Ibid. a. 22: [Greek: ou)damou= ga\r sumbai/nei

proepi/stasthai to\ kath' e(/kaston, a)ll' a(/ma tê=| e)pagôgê=|

lamba/nein tê\n tô=n kata\ me/ros e)pistê/mên _ô(/sper

a)nagnôri/zontas_], &c. Cf. Anal. Post. I. ii. p. 71, b. 9, seq.;

Plato, Menon, pp. 81-82.]

We thus, by help of the universal, acquire a theoretical knowledge of

particulars, but we do not know them by the special observation

properly belonging to each particular case: so that we may err in

respect to them without any positive contrariety between our

cognition and our error; since what we know is the universal, while

what we err in is the particular. We may even know that A is

predicable of all B, and that B is predicable of all C; and yet we

may believe that A is not predicable of C. We may know that every

mule is barren, and that the animal before us is a mule, yet still we

may believe her to be in foal; for perhaps we may never have combined

in our minds the particular case along with the universal

proposition.[41] _A fortiori_, therefore, we may make the like

mistake, if we know the universal only, and do not know the

particular. And this is perfectly possible. For take any one of the

visible particular instances, even one which we have already

inspected, so soon as it is out of sight we do not know it by actual

and present cognition; we only know it, partly from the remembrance

of past special inspection, partly from the universal under which it

falls.[42] We may know in one, or other, or all, of these three

distinct ways: either by the universal; or specially (as remembered):

or by combination of both--actual and present cognition, that is, by

the application of a foreknown generality to a case submitted to our

senses. And as we may know in each of these three ways, so we may

also err or be deceived in each of the same three ways.[43] It is

therefore quite possible that we may know, and that we may err or be

deceived about the same thing, and that, too, without any

contrariety. This is what happens when we know both the two premisses

of the syllogism, but have never reflected on them before, nor

brought them into conjunction in our minds. When we believe that the

mule before us is in foal, we are destitute of the actual knowledge;

yet our erroneous belief is not for that reason contrary to

knowledge; for an erroneous belief, contrary to the universal

proposition, must be represented by a counter-syllogism.[44]

[Footnote 41: Ibid. II. xxi. p. 67, a. 36: [Greek: ou) ga\r

e)pi/statai o(/ti to\ A tô=| G, _mê\ suntheôrô=n_ to\ kath'

e(ka/teron.]]

[Footnote 42: Analyt. Prior. II. xxi. p. 67, a. 39: [Greek: ou)de\n

ga\r tô=n ai)sthêtô=n e)/xô tê=s ai)sthê/seôs geno/menon i)/smen,

ou)/d' a)\n ê)|sthême/noi tugcha/nômen, ei) mê\ ô(s tô=| katho/lou

kai\ tô=| e)/chein tê\n oi)kei/an e)pistê/mên, a)ll' _ou)ch ô(s tô=|

e)nergei=n_.]

Complete cognition ([Greek: to\ e)nergei=n], according to the view

here set forth) consists of one mental act corresponding to the major

premiss; another corresponding to the minor; and a third including

both the two in conscious juxta-position. The third implies both the

first and the second; but the first and the second do not necessarily

imply the third, nor does either of them imply the other; though a

person cognizant of the first is _in a certain way, and to a certain

extent_, cognizant of _all_ the particulars to which the second

applies. Thus the person who knows Ontology (the most universal of

all sciences, [Greek: tou= o)/ntos ê(=| o)/n]), knows _in a certain

way_ all _scibilia_. Metaphys. A., p. 982, a. 21: [Greek: tou/tôn de\

to\ me\n pa/nta e)pi/stasthai tô=| ma/lista e)/chonti tê\n katho/lou

e)pistê/mên a)nagkai=on u(pa/rchein; ou(/tos ga\r _oi)=de/ pôs_

pa/nta ta\ u(pokei/mena.] Ib. a. 8: [Greek: u(polamba/nomen dê\

prô=ton me\n e)pi/stasthai pa/nta to\n sopho\n ô(s _e)nde/chetai, mê\

kath' e(/kaston e)/chonta e)pistê/mên au)tô=n_.] See the Scholia of

Alexander on these passages, pp. 525, 526, Brandis; also Aristot.

Analyt. Post. I. xxiv. p. 86, a. 25; Physica, VII. p. 247, a. 5.

Bonitz observes justly (Comm. **ad Metaphys. p. 41) as to the doctrine

of Aristotle: "Scientia et ars versatur in notionibus universalibus,

solutis ac liberis à conceptu singularum rerum; ideoque, _etsi orta

est à principio et experientiâ_, tradi tamen etiam iis potest qui

careant experientiâ."]

[Footnote 43: Analyt. Prior. II. xxi. p. 67, b. 3: [Greek: to\ ga\r

e)pi/stasthai le/getai trichô=s, ê)\ ô(s tê=| katho/lou, ê)\ ô(s tê=|

oi)kei/a|, ê)\ ô(s tô=| e)nergei=n; ô(/ste kai\ to\ ê)patê=sthai

tosautachô=s.]]

[Footnote 44: Ibid. b. 5: [Greek: ou)de\n ou)=n kôlu/ei kai\

ei)de/nai kai\ ê)patê=sthai peri\ au)to/, plê\n ou)k e)nanti/ôs.

o(/per sumbai/nei kai\ tô=| kath' e(kate/ran ei)do/ti tê\n pro/tasin

kai\ mê\ e)peskemme/nô| pro/teron. u(polamba/nôn ga\r ku/ein tê\n

ê(mi/onon ou)k e)/chei tê\n kata\ to\ e)nergei=n e)pistê/mên, ou)d'

au)= dia\ tê\n u(po/lêpsin e)nanti/an a)pa/tên tê=| e)pistê/mê|;

sullogismo\s ga\r ê( e)nanti/a a)pa/tê tê=| katho/lou.] About

erroneous belief, where a man believes the contrary of a true

conclusion, adopting a counter-syllogism, compare Analyt. Post. I.

xvi. p. 79, b. 23: [Greek: a)/gnoia kata\ dia/thesin].]

It is impossible, however, for a man to believe that one contrary is

predicable of its contrary, or that one contrary is identical with

its contrary, essentially and as an universal proposition; though he

may believe that it is so by accident (_i.e._ in some particular

case, by reason of the peculiarities of that case). In various ways

this last is possible; but this we reserve for fuller

examination.[45]

[Footnote 45: Analyt. Prior. II. xxi. p. 67, b. 23: [Greek: a)ll'

i)/sôs e)kei=no pseu=dos, to\ u(polabei=n tina\ kakô=| ei)=nai to\

a)gathô=| ei)=nai, ei) mê\ kata\ sumbebêko/s; pollachô=s ga\r

e)gchôrei= tou=th' u(polamba/nein. e)piskepte/on de\ tou=to

be/ltion.] This distinction is illustrated by what we read in Plato,

Republic, v. pp. 478-479. The impossibility of believing that one

contrary is identical with its contrary, is maintained by Sokrates in

Plato, Theætetus, p. 190, B-D, as a part of the long discussion

respecting [Greek: pseudê\s do/xa]: either there is no such thing as

[Greek: pseudê\s do/xa], or a man may know, and not know, the same

thing, ibid. p. 196 C. Aristotle has here tried to show in what sense

this last-mentioned case is possible.]

Whenever (Aristotle next goes on to say) the extremes of a syllogism

reciprocate or are co-extensive with each other (_i.e._ when the

conclusion being affirmative is convertible simply), the middle term

must reciprocate or be co-extensive with both.[46] If there be four

terms (A, B, C, D), such that A reciprocates with B, and C with D,

and if either A or C must necessarily be predicable of every subject;

then it follows that either B or D must necessarily also be

predicable of every subject. Again, if either A or B must necessarily

be predicable of every subject, but never both predicable of the same

at once; and if, either C or D must be predicable of every subject,

but never both predicable of the same at once; then, if A and C

reciprocate, B and D will also reciprocate.[47] When A is predicable

of all B and all C, but of no other subject besides, and when B is

predicable of all C, then A and B must reciprocate with each other,

or be co-extensive with each other; that is, B may be predicated of

every subject of which A can be predicated, though B cannot be

predicated of A itself.[48] Again, when A and B are predicable of all

C, and when C reciprocates with B, then A must also be predicable of

all B.[49]

[Footnote 46: Ibid. II. xxii. p. 67, b. 27, seq. In this chapter

Aristotle introduces us to affirmative universal propositions

convertible _simpliciter_; that is, in which the predicate must be

understood to be distributed as well as the subject. Here, then, the

quantity of the predicate is determined in thought. This is (as

Julius Pacius remarks, p. 371) in order to lay down principles for

the resolution of Induction into Syllogism, which is to be explained

in the next chapter. In these peculiar propositions, the reason urged

by Sir W. Hamilton for his favourite precept of verbally indicating

the quantity of the predicate, is well founded as a fact: though _he_

says that in _all_ propositions the quantity of the predicate is

understood in thought, which I hold to be incorrect.

We may remark that this recognition by Aristotle of a class of

universal affirmative propositions in which predicate and subject

reciprocate, contrived in order to force Induction into the

syllogistic framework, is at variance with his general view both of

reciprocating propositions and of Induction. He tells us (Analyt.

Post. I. iii. p. 73, a. 18) that such reciprocating propositions are

very rare, which would not be true if they are taken to represent

every Induction; and he forbids us emphatically to annex the mark of

universality to the predicate; which he has no right to do, if he

calls upon us to reason on the predicate as distributed (Analyt.

Prior. I. xxvii., p. 43, b. 17; De Interpret. p. 17, b. 14).]

[Footnote 47: Ibid. II. xxii. p. 68, a. 2-15.]

[Footnote 48: Ibid. a. 16-21. [Greek: plê\n au)tou= tou= A]. Waitz

explains these words in his note (p. 531): yet I do not clearly make

them out; and Alexander of Aphrodisias declared them to assert what

was erroneous ([Greek: e)spha/lthai le/gei], Schol. p. 194, a. 40,

Brandis).]

[Footnote 49: Ibid. II. xxii. p. 68, a. 21-25.]

Lastly, suppose two pairs of opposites, A and B, C and D; let A be

more eligible than B, and D more eligible than C. Then, if A C is

more eligible than B D, A will also be more eligible than D. For A is

as much worthy of pursuit as B is worthy of avoidance, they being two

opposites; the like also respecting C and D. If then A and D are

equally worthy of pursuit, B and C are equally worthy of avoidance;

for each is equal to each. Accordingly the two together, A C, will be

equal to the two together, B D. But this would be contrary to the

supposition; since we assumed A to be more eligible than B, and D to

be more eligible than C. It will be seen that on this supposition A

is more worthy of pursuit than D, and that C is less worthy of

avoidance than B; the greater good and the lesser evil being more

eligible than the lesser good and the greater evil. Now apply this to

a particular case of a lover, so far forth as lover. Let A represent

his possession of those qualities which inspire reciprocity of love

towards him in the person beloved; B, the absence of those qualities;

D, the attainment of actual sexual enjoyment; C, the non-attainment

thereof. In this state of circumstances, it is evident that A is more

eligible or worthy of preference than D. The being loved is a greater

object of desire to the lover _qua_ lover than sexual gratification;

it is the real end or purpose to which love aspires; and sexual

gratification is either not at all the purpose, or at best only

subordinate and accessory. The like is the case with our other

appetites and pursuits.[50]

[Footnote 50: Analyt. Prior. II. xxii. p. 68, a. 25-b. 17. Aristotle

may be right in the conclusion which he here emphatically asserts;

but I am surprised that he should consider it to be proved by the

reasoning that precedes.

It is probable that Aristotle here understood the object of [Greek:

e)/rôs] (as it is conceived through most part of the Symposion of

Plato) to be a beautiful youth: (see Plato, Sympos. pp. 218-222; also

Xenophon, Sympos. c. viii., Hiero, c. xi. 11, Memorab. I. ii. 29,

30). Yet this we must say--what the two women said when they informed

Simætha of the faithlessness of Delphis (Theokrit. Id. ii.

149)--[Greek: Kê)=|pe/ moi a)/lla te polla/, kai\ ô(s a)/ra De/lphis

e)/ratai;

Kê)/|te min au)=te gunaiko\s e)/chei po/thos, ei)/te kai\ a)ndro/s,

Ou)k e)/phat' a)treke\s i)/dmen.]]

Such is the relation of the terms of a syllogism in regard to

reciprocation and antithesis. Let it next be understood that the

canons hitherto laid down belong not merely to demonstrative and

dialectic syllogisms, but to rhetorical and other syllogisms also;

all of which must be constructed in one or other of the three

figures. In fact, every case of belief on evidence, whatever be the

method followed, must be tested by these same canons. We believe

everything either through Syllogism or upon Induction.[51]

[Footnote 51: Ibid. II. xxiii. p. 68, b. 13: [Greek: a(/panta ga\r

pisteu/omen ê)\ dia\ sullogismou= ê)\ e)x e)pagôgê=s.]]

Though Aristotle might seem, even here, to have emphatically

contrasted Syllogism with Induction as a ground of belief, he

proceeds forthwith to indicate a peculiar form of Syllogism which may

be constructed out of Induction. Induction, and the Syllogism from or

out of Induction (he says) is a process in which we invert the order

of the terms. Instead of concluding from the major through the middle

to the minor (_i.e._ concluding that the major is predicable of the

minor), we now begin from the minor and conclude from thence through

the middle to the major (_i.e._ we conclude that the major is

predicable of the middle).[52] In Syllogism as hitherto described, we

concluded that A the major was predicable of C the minor, through the

middle B; in the Syllogism from Induction we begin by affirming that

A the major is predicable of C the minor; next, we affirm that B the

middle is also predicable of C the minor. The two premisses, standing

thus, correspond to the Third figure of the Syllogism (as explained

in the preceding pages) and would not therefore by themselves justify

anything more than a _particular_ affirmative conclusion. But we

reinforce them by introducing an extraneous assumption:--That the

minor C is co-extensive with the middle B, and comprises the entire

aggregate of individuals of which B is the universal or class-term.

By reason of this assumption the minor proposition becomes

convertible simply, and we are enabled to infer (according to the

last preceding chapter) an universal affirmative conclusion, that the

major term A is predicable of the middle term B. Thus, let A (the

major term) mean the class-term, long-lived; let B (the middle term)

mean the class-term, bile-less, or the having no bile; let C (the

minor term) mean the individual animals--man, horse, mule, &c.,

coming under the class-term B, bile-less.[53] We are supposed to

know, or to have ascertained, that A may be predicated of all C;

(_i.e._ that all men, horses, mules, &c., are long-lived); we farther

know that B is predicable of all C (_i.e._ that men, horses, mules,

&c., belong to the class bile-less). Here, then, we have two

premisses in the Third syllogistic figure, which in themselves would

warrant us in drawing the particular affirmative conclusion, that A

is predicable of _some_ B, but no more. Accordingly, Aristotle

directs us to supplement these premisses[54] by the extraneous

assumption or postulate, that C the minor comprises all the

individual animals that are bile-less, or all those that correspond

to the class-term B; in other words, the assumption, that B the

middle does not denote any more individuals than those which are

covered by C the minor--that B the middle does not stretch beyond or

overpass C the minor.[55] Having the two premisses, and this

postulate besides, we acquire the right to conclude that A is

predicable of _all_ B. But we could not draw that conclusion from the

premisses alone, or without the postulate which declares B and C to

be co-extensive. The conclusion, then, becomes a particular

exemplification of the general doctrine laid down in the last

chapter, respecting the reciprocation of extremes and the

consequences thereof. We thus see that this very peculiar Syllogism

from Induction is (as indeed Aristotle himself remarks) the opposite

or antithesis of a genuine Syllogism. It has no proper middle term;

the conclusion in which it results is the first or major proposition,

the characteristic feature of which it is to be _immediate_, or not

to be demonstrated through a middle term. Aristotle adds that the

genuine Syllogism, which demonstrates through a middle term, is by

nature prior and more effective as to cognition; but that the

Syllogism from Induction is _to us_ plainer and clearer.[56]

[Footnote 52: Analyt. Prior. II. xxiii. p. 68, b. 15: [Greek:

e)pagôgê\ me\n ou)=n e)sti\ kai\ o( e)x e)pagôgê=s sullogismo\s to\

dia\ tou= e(te/rou tha/teron a)/kron tô=| me/sô| sullogi/sasthai;

oi(=on ei) tô=n AG me/son to\ B, dia\ tou= G dei=xai to\ A tô=| B

u(pa/rchon; ou(/tô ga\r poiou/metha ta\s e)pagôga/s.]

Waitz in his note (p. 532) says: "Fit Inductio, cum per minorem

terminum demonstratur _medium prædicari de majore_." This is an

erroneous explanation. It should have been: "demonstratur _majorem

prædicari de medio_." Analyt. Prior. II. xxiii. 68, b. 32: [Greek:

kai\ tro/pon tina\ a)ntikei=tai ê( e)pagôgê\ tô=| sullogismô=|; o(

me\n ga\r dia\ tou= me/sou to\ a)/kron tô=| tri/tô| dei/knusin, ê(

de\ dia\ tou= tri/tou to\ a)/kron tô=| me/sô|.]]

[Footnote 53: Ibid. II. xxiii. p. 68, b. 18: [Greek: oi(=on e)/stô

to\ A makro/bion, to\ d' e)ph' ô(=| B, to\ cholê\n mê\ e)/chon, e)ph'

ô(=| de\ G, to\ kath' e(/kaston _makro/bion_, oi(=on a)/nthrôpos kai\

i(/ppos kai\ ê(mi/onos. tô=| dê\ G o(/lô| u(pa/rchei to\ A; pa=n ga\r

to\ a)/cholon makro/bion; a)lla\ kai\ to\ B, to\ mê\ e)/chein

cholê/n, panti\ u(pa/rchei tô=| G. ei) ou)=n a)ntistre/phei to\ G

tô=| B kai\ mê\ u(pertei/nei to\ me/son, a)na/gkê to\ A tô=| B

u(pa/rchein.]

I have transcribed this Greek text as it stands in the editions of

Buhle, Bekker, Waitz, and F. Didot. Yet, notwithstanding these high

authorities, I venture to contend that it is not wholly correct; that

the word [Greek: _makro/bion_], which I have emphasized, is neither

consistent with the context, nor suitable for the point which

Aristotle is illustrating. Instead of [Greek: _makro/bion_], we ought

in that place to read [Greek: a)/cholon]; and I have given the sense

of the passage in my English text as if it did stand [Greek:

a)/cholon] in that place.

I proceed to justify this change. If we turn back to the edition by

Julius Pacius (1584, p. 377), we find the text given as follows after

the word [Greek: ê(mi/onos] (down to that word the text is the same):

[Greek: tô=| dê\ G o(/lô| u(pa/rchei to\ A; pa=n ga\r to\ G

makro/bion; a)lla\ kai\ to\ B, to\ mê\ e)/chon cholê/n, panti\

u(pa/rchei tô=| G. ei) ou)=n a)ntistre/phei to\ G tô=| B, kai\ mê\

u(pertei/nei to\ me/son, a)na/gkê to\ A tô=| B u(pa/rchein.] Earlier

than Pacius, the edition of Erasmus (Basil. 1550) has the same text

in this chapter.

Here it will be seen that in place of the words given in Waitz's

text, [Greek: pa=n ga\r to\ _a)/cholon_ makro/bion], Pacius gives

[Greek: pa=n ga\r _to\ G_ makro/bion]: annexing however to the letter

[Greek: G] an asterisk referring to the margin, where we find the

word [Greek: a)/cholon] inserted in small letters, seemingly as a

various reading not approved by Pacius. And M. Barthélemy St. Hilaire

has accommodated his French translation (p. 328) to the text of

Pacius: "Donc A est à C tout entier, car tout C est longève."

Boethius in his Latin translation (p. 519) recognizes as his original

[Greek: pa=n ga\r to\ a)/cholon makro/bion], but he alters the text

in the words immediately preceding:--"Ergo _toti B_ (instead of _toti

C_) inest A, omne enim quod sine cholera est, longævum," &c. (p.

519). The edition of Aldus (Venet. 1495) has the text conformable to

the Latin of Boethius: [Greek: tô=| dê\ B o(/lô| u(pa/rchei to\ A;

pa=n ga\r to\ a)/cholon makro/bion]. Three distinct Latin

translations of the 16th century are adapted to the same text, viz.,

that of Vives and Valentinus (Basil. 1542); that published by the

Junta (Venet. 1552); and that of Cyriacus (Basil. 1563). Lastly, the

two Greek editions of Sylburg (1587) and Casaubon (Lugduni 1590),

have the same text also: [Greek: tô=| dê\ B o(/lô| u(pa/rchei to\ A;

pa=n ga\r [to\ G] to\ a)/cholon makro/bion]. Casaubon prints in

brackets the words [Greek: [to\ G]] before [Greek: to\ a)/cholon].

Now it appears to me that the text of Bekker and Waitz (though Waitz

gives it without any comment or explanation) is erroneous; neither

consisting with itself, nor conforming to the general view enunciated

by Aristotle of the Syllogism from Induction. I have cited two

distinct versions, each different from this text, as given by the

earliest editors; in both the confusion appears to have been felt,

and an attempt made to avoid it, though not successfully.

Aristotle's view of the Syllogism from Induction is very clearly

explained by M. Barthélemy St. Hilaire in the instructive notes of

his translation, pp. 326-328; also in his Preface, p.

lvii.:--"L'induction n'est au fond qu'un syllogisme dont le mineur et

le moyen sont d'extension égale. Du reste, il n'est qu'une seule

manière dont le moyen et le mineur puissent être d'égale extension;

c'est que le mineur se compose de toutes les parties dont le moyen

représente la totalité. D'une part, tous les individus: de l'autre,

l'espèce totale qu'ils forment. L'intelligence fait aussitôt

équation entre les deux termes égaux."

According to the Aristotelian text, as given both by Pacius and the

others, A, the major term, represents _longævum_ (long-lived, the

class-term or total); B, the middle term, represents _vacans bile_

(bile-less, the class-term or total); C, the minor term, represents

the aggregate individuals of the class _longævum_, man, horse, mule,

&c.

Julius Pacius draws out the Inductive Syllogism, thus:--

1. Omnis homo, equus, asinus, &c., est longævus.

2. Omnis homo, equus, asinus, &c., vacat bile.

Ergo:

3. Quicquid vacat bile, est longævum.

Convertible into a Syllogism in Barbara:--

1. Omnis homo, equus, asinus, &c., est longævus.

2. Quicquid vacat bile, est homo, equus, asinus, &c.

Ergo:

3. Quicquid vacat bile, est longævum.

Here the force of the proof (or the possibility, in this exceptional

case, of converting a syllogism in the Third figure into another in

_Barbara_ of the First figure) depends upon the equation or

co-extensiveness (not enunciated in the premisses, but assumed in

addition to the premisses) of the minor term C with the middle term

B. But I contend that this is _not_ the condition peremptorily

required, or sufficient for proof, if we suppose C the minor term to

represent _omne longævum_. We must understand C the minor term to

represent _omne vacans bile_, or _quicquid vacat bile_: and unless we

understand this, the proof fails. In other words, _homo, equus,

asinus, &c._ (the aggregate of individuals), must be co-extensive

with the class-term bile-less or _vacans bile_: but they need not be

co-extensive with the class-term long-lived or _longævum_. In the

final conclusion, the subject _vacans bile_ is distributed; but the

predicate _longævum_ is not distributed; this latter may include,

besides all bile-less animals, any number of other animals, without

impeachment of the syllogistic proof.

Such being the case, I think that there is a mistake in the text as

given by all the editors, from Pacius down to Bekker and Waitz. What

they give, in setting out the terms of the Aristotelian Syllogism

from Induction, is: [Greek: e)/stô to\ A makro/bion, to\ d' e)ph'

ô(=| B, to\ cholên mê\ e)/chon, e)ph' ô(=| de\ G, _to\ kath'

e(/kaston makro/bion_, oi(=on a)/nthrôpos kai\ i(/ppos kai\

ê(mi/onos.] Instead of which the text ought to run, [Greek: e)ph'

ô(=| de\ G, _to\ kath' e(/kaston a)/cholon_, oi(=on a)/nthr. k. i(/p.

k. ê(mi/]. That these last words were the original text, is seen by

the words immediately following: [Greek: tô=| dê\ G o(/lô| u(pa/rchei

to\ A. _pa=n ga\r to\ a)/cholon makro/bion_]. For the reason thus

assigned (in the particle [Greek: ga/r]) is irrelevant and unmeaning

if [Greek: G] designates [Greek: to\ kath' e(/kaston _makro/bion_ ],

while it is pertinent and even indispensable if [Greek: G] designates

[Greek: to\ kath' e(/kaston _a)/cholon_]. Pacius (or those whose

guidance he followed in his text) appears to have perceived the

incongruity of the reason conveyed in the words [Greek: pa=n ga\r to\

a)/cholon makro/bion]; for he gives, instead of these words, [Greek:

pa=n ga\r _to\ G_ makro/bion]. In this version the reason is indeed

no longer incongruous, but simply useless and unnecessary; for when

we are told that A designates the class _longævum_, and that [Greek:

G] designates the individual _longæva_, we surely require no reason

from without to satisfy us that A is predicable of all [Greek: G].

The text, as translated by Boethius and others, escapes that

particular incongruity, though in another way, but it introduces a

version inadmissible on other grounds. Instead of [Greek: tô=| _dê\

G_ o(/lô| u(pa/rchei to\ A, pa=n ga\r to\ a)/cholon makro/bion],

Boethius has [Greek: tô=| _dê\ B_ o(/lô| u(pa/rchei to\ A, pa=n ga\r

to\ a)/cholon makro/bion]. This cannot be accepted, because it

enunciates the conclusion of the syllogism as if it were one of the

premisses. We must remember that the conclusion of the Aristotelian

Syllogism from Induction is, that A is predicable of B, one of the

premisses to prove it being that A is predicable of the minor term C.

But obviously we cannot admit as one of the premisses the proposition

that A may be predicated of B, since this proposition would then be

used as premiss to prove itself as conclusion.

If we examine the Aristotelian Inductive Syllogism which is intended

to conduct us to the final _probandum_, we shall see that the terms

of it are incorrectly set out by Bekker and Waitz, when they give the

minor term [Greek: G] as designating [Greek: to\ kath' e(/kaston

makro/bion]. This last is not one of the three terms, nor has it any

place in the syllogism. The three terms are:

1. A--major--the class-term or class [Greek: makro/bion]--_longævum_.

2. B--middle--the class term or class [Greek: a)/cholon]--bile-less.

3. C--minor--the individual bile-less animals, man, horse, &c.

There is no term in the syllogism corresponding to the individual

_longæva_ or long-lived animals; this last (I repeat) has no place in

the reasoning. We are noway concerned with the totality of long-lived

animals; all that the syllogism undertakes to prove is, that in and

among that totality all bile-less animals are included; whether there

are or are not other long-lived animals besides the bile-less, the

syllogism does not pretend to determine. The equation or

co-extensiveness required (as described by M. Barthélemy St. Hilaire

in his note) is not between the individual long-lived animals and the

class, bile-less animals (middle term), but between the aggregate of

individual animals known to be bile-less and the class, bile-less

animals. The real minor term, therefore, is (not the individual

_long-lived_ animals, but) the individual _bile-less_ animals. The

two premisses of the Inductive Syllogism will stand thus:--

Men, Horses, Mules, &c., are long-lived (major).

Men, Horses, Mules, &c., are bile-less (minor).

And, inasmuch as the subject of the minor proposition is co-extensive

with the predicate (which, if quantified according to Hamilton's

phraseology, would be, _All_ bile-less animals), so that the

proposition admits of being converted simply,--the middle term will

become the subject of the conclusion, All bileless animals are

long-lived.]

[Footnote 54: Analyt. Prior. II. xxiii. p. 68, b. 27: [Greek: dei=

de\ noei=n to\ G to\ e)x a(pa/ntôn tô=n kath' e(/kaston sugkei/menon;

ê( ga\r e)pagôgê\ dia\ pa/ntôn.]]

[Footnote 55: Analyt. Prior. II. **xxiii. p. 68, p. 23: [Greek: ei)

ou)=n a)ntistre/phei to\ G tô=| B, kai\ mê\ u(pertei/nei to\ me/son,

a)na/gkê to\ A tô=| B u(pa/rchein.]

Julius Pacius translates this: "Si igitur convertatur [Greek: to\ G]

cum B, nec medium excedat, necesse est [Greek: to\ A tô=| B] inesse."

These Latin words include the same grammatical ambiguity as is found

in the Greek original: _medium_, like [Greek: to\ me/son], may be

either an accusative case governed by _excedat_, or a nominative case

preceding _excedat_. The same may be said of the other Latin

translations, from Boethius downwards.

But M. Barthélemy St. Hilaire in his French translation, and Sir W.

Hamilton in his English translation (Lectures on Logic, Vol. II. iv.

p. 358, Appendix), steer clear of this ambiguity. The former says:

"Si donc C est réciproque à B, et qu'il ne dépasse pas le moyen, il

est nécessaire alors que A soit à B:" to the same purpose, Hamilton,

_l. c._ These words are quite plain and unequivocal. Yet I do not

think that they convey the meaning of Aristotle. In my judgment,

Aristotle meant to say: "If then C reciprocates with B, and if the

middle term (B) does not stretch beyond (the minor C), it is

necessary that A should be predicable of B." To show that this must

be the meaning, we have only to reflect on what C and B respectively

designate. It is assumed that C designates the sum of individual

bile-less animals; and that B designates the class or class-term

bile-less, that is, the totality thereof. Now the sum of individuals

included in the minor (C) cannot upon any supposition overpass the

totality: but it may very possibly fall short of totality; or (to

state the same thing in other words) the totality may possibly

surpass the sum of individuals under survey, but it cannot possibly

fall short thereof. B is here the limit, and may possibly stretch

beyond C; but cannot stretch beyond B. Hence I contend that the

translations, both by M. Barthélemy St. Hilaire and Sir W. Hamilton,

take the wrong side in the grammatical alternative admissible under

the words [Greek: kai\ mê\ u(pertei/nei to\ me/son]. The only doubt

that could possibly arise in the case was, whether the aggregate of

individuals designated by the minor did, or did not, reach up to the

totality designated by the middle term; or (changing the phrase)

whether the totality designated by the middle term did, or did not,

stretch beyond the aggregate of individuals designated by the minor.

Aristotle terminates this doubt by the words: "And if the middle term

does _not_ stretch beyond (the minor)." Of course the middle term

does not stretch beyond, when the terms reciprocate; but when they do

not reciprocate, the middle term must be the _more_ extensive of the

two; it can _never_ be the _less_ extensive of the two, since the

aggregate of individuals cannot possibly exceed totality, though it

may fall short thereof.

I have given in the text what I think the true meaning of Aristotle,

departing from the translations of M. Barthélemy St. Hilaire and

Sir** W. Hamilton.]

[Footnote 56: Analyt. Prior. II. xxiii. p. 68, b. 30-38: [Greek:

e)/sti d' o( toiou=tos sullogismo\s tê=s prô/tês kai\ a)me/sou

prota/seôs; ô(=n me\n ga/r e)sti me/son, dia\ tou= me/sou o(

sullogismo/s, ô(=n de\ mê/ e)sti, di' e)pagôgê=s.--phu/sei me\n ou)=n

pro/teros kai\ gnôrimô/teros o( dia\ tou= me/sou sullogismo/s, ê(mi=n

d' e)narge/steros o( dia\ tê=s e)pagôgê=s.]]

From Induction he proceeds to Example. You here take in (besides the

three terms, major, middle, and minor, of the Syllogism) a fourth

term; that is, a new particular case analogous to the minor. Your

purpose here is to show--not, as in the ordinary Syllogism, that the

major term is predicable of the minor, but, as in the Inductive

Syllogism--that the major term is predicable of the middle term; and

you prove this conclusion, not (as in the Inductive Syllogism)

through the minor term, but through the new case or fourth term

analogous to the minor.[57] Let A represent evil or mischievous; B,

war against neighbours, generally; C, war of Athens against Thebes,

an event to come and under deliberation; D, war of Thebes against

Phokis, a past event of which the issue is known to have been

signally mischievous. You assume as known, first, that A is

predicable of D, _i.e._ that the war of Thebes against Phokis has

been disastrous; next, that B is predicable both of C and of D,

_i.e._ that each of the two wars, of Athens against Thebes, and of

Thebes against Phokis, is a war of neighbours against neighbours, or

a conterminous war. Now from the premiss that A is predicable of D,

along with the premiss that B is predicable of D, you infer that A is

predicable of the class B, or of conterminous wars generally; and

hence you draw the farther inference, that A is also predicable of C,

another particular case under the same class B. The inference here

is, in the first instance, from part to whole; and finally, through

that whole, from the one part to another part of the same whole.

_Induction_ includes in its major premiss all the particulars,

declaring all of them to be severally subjects of the major as

predicate; hence it infers as conclusion, that the major is also

predicable of the middle or class-term comprising all these

particulars, but comprising no others. _Example_ includes not all,

but only one or a few particulars; inferring from it or them, first,

to the entire class, next, to some new analogous particular belonging

to the class.[58]

[Footnote 57: Ibid. II. xxiv. p. 68, b. 38: [Greek: paradei=gma d'

e)sti\n o(/tan tô=| me/sô| to\ a)/kron u(pa/rchon deichthê=| dia\

tou= o(moi/ou tô=| tri/tô|.]]

[Footnote 58: Analyt. Prior. II. xxiv. p. 69, a. 1-19**.

Julius Pacius (p. 400) notes the unauthorized character of

this so-called Paradeigmatic Syllogism, contradicting the rules of

the figures laid down by Aristotle, and also the confused manner in

which the scope of it is described: first, to infer from a single

example to the universal; next, to infer from a single example

_through_ the universal to another parallel case. To which we may add

the confused description in p. 69, a. 17, 18, where [Greek: to\

a)/kron] in the first of the two lines signifies the _major_

extreme--in the second of the two the _minor_ extreme. See Waitz's

note, p. 533.

If we turn to ch. xxvii. p. 70, a. 30-34, we shall find Aristotle on

a different occasion disallowing altogether this so-called Syllogism

from Example.]

These chapters respecting Induction and Example are among the most

obscure and perplexing in the Aristotelian Analytica. The attempt to

throw both Induction and Example into the syllogistic form is alike

complicated and unfortunate; moreover, the unsatisfactory reading and

diversities in the text, among commentators and translators, show

that the reasoning of Aristotle has hitherto been imperfectly

apprehended.[59] From some of his phrases, we see that he was aware

of the essential antithesis between Induction and Syllogism; yet the

syllogistic forms appear to have exercised such fascination over his

mind, that he could not be satisfied without trying to find some

abnormal form of Syllogism to represent and give validity to

Induction. In explaining generally what the Syllogism is, and what

Induction is, he informs us that the Syllogism presupposes and rests

upon the process of Induction as its postulate. For there can be no

valid Syllogism without an universal proposition in one (at least) of

the premisses; and he declares, unequivocally, that universal

propositions are obtained only through Induction. How Induction

operates through the particular facts of sense, remembered, compared,

and coalescing into clusters held together by associating similarity,

he has also told us; it is thus that Experience, with its universal

notions and conjunctions, is obtained. But this important process is

radically distinct from that of syllogizing, though it furnishes the

basis upon which all syllogizing is built.

[Footnote 59: Sir W. Hamilton (Lectures on Logic, vol. i. p. 319)

says justly, that Aristotle has been very brief and unexplicit in his

treatment of Induction. Yet the objections that Hamilton makes to

Aristotle are very different from those which I should make. In the

learned and valuable Appendix to his Lectures (vol. iv. pp. 358-369),

he collects various interesting criticisms of logicians respecting

Induction as handled by Aristotle. Ramus (in his Scholæ Dialecticæ,

VIII. xi.) says very truly:--"Quid vero sit Inductio, perobscure ab

Aristotele declaratur; nec ab interpretibus intelligitur, quo modo

_syllogismus_ per medium concludat majus extremum de minore;

_inductio_, majus de medio per minus."

The Inductive Syllogism, as constructed by Aristotle, requires a

reciprocating minor premiss. It may, indeed, be cited (as I have

already remarked) in support of Hamilton's favourite precept of

quantifying the predicate. The predicate of this minor must be

assumed as _quantified in thought_, the subject being taken as

co-extensive therewith. Therefore Hamilton's demand that it shall be

_quantified in speech_ has really in this case that foundation which

he erroneously claims for it in all cases. He complains that Lambert

and some other logicians dispense with the necessity of quantifying

the predicate of the minor by making it disjunctive; and adds the

remarkable statement that "the recent German logicians, Herbart,

Twesten, Drobisch, &c., following Lambert, make the Inductive

Syllogism a byeword" (p. 366). I agree with them in thinking the

attempted transformation of Induction into Syllogism very

unfortunate, though my reasons are probably not the same as theirs.

Trendelenburg agrees with those who said that Aristotle's doctrine

about the Inductive Syllogism required that the minor should be

disjunctively enunciated (Logische Untersuchungen, xiv. p. 175, xvi.

pp. 262, 263; also Erläuterungen zu den Elementen der Aristotelischen

Logik, ss. 34-36, p. 71). Ueberweg takes a similar view (System der

**Logik, sect. 128, p. 367, 3rd ed.). If the Inductive Inference

is to be twisted into Syllogism, it seems more naturally to fall into

an _hypothetical_ syllogism, _e. g._:--

If this, that, and the other magnet attract iron, all magnets attract

iron;

But this, that, and the other magnet do attract iron: _Ergo_,

&c.]

The central idea of the Syllogism, as defined by Aristotle, is that

of a conclusion following from given premisses by _necessary_

sequence;[60] meaning by the term _necessary_ thus much and no

more--that you cannot grant the premisses, and deny the conclusion,

without being inconsistent with yourself, or falling into

contradiction. In all the various combinations of propositions, set

forth by Aristotle as the different figures and modes of Syllogism,

this property of necessary sequence is found. But it is a property

which no Induction can ever possess.[61] When Aristotle professes to

point out a particular mode of Syllogism to which Induction conforms,

he can only do so by falsifying the process of Induction, and by not

accurately distinguishing between what is observed and what is

inferred. In the case which he takes to illustrate the Inductive

Syllogism--the inference from all particular bile-less animals to the

whole class bile-less--he assumes that we have ascertained the

attribute to belong to _all_ the particulars, and that the inductive

inference consists in passing from all of them to the class-term; the

passage from premisses to conclusion being here necessary, and thus

falling under the definition of Syllogism; since, to grant the

premisses, and yet to deny the conclusion, involves a contradiction.

But this doctrine misconceives what the inductive inference really is.

We never can observe _all_ the particulars of a class, which is

indefinite as to number of particulars, and definite only in respect

of the attributes connoted by the class-term. We can only observe

_some_ of the particulars, a greater or smaller proportion. Now it is

in the transition from these _to_ the totality of particulars, that

the real inductive inference consists; not in the transition _from_

the totality to the class-term which denotes that totality and

connotes its determining common attribute. In fact, the distinction

between the totality of particulars and the meaning of the

class-term, is one not commonly attended to; though it is worthy of

note in an analysis of the intellectual process, and is therefore

brought to view by Aristotle. But he employs it incorrectly as an

intermediate step to slur over the radical distinction between

Induction and Syllogism. He subjoins:[62]--"You must conceive the

minor term C (in the Inductive Syllogism) as composed of all the

particulars; for Induction is through all of them." You may say that

Induction is _through_ all the particulars, if you distinguish this

totality from the class-term, and if you treat the class-term as the

ultimate _terminus ad quem_. But the Induction must first travel _to_

all the particulars; being forced to take start from a part only, and

then to jump onward far enough to cover the indefinite unobserved

remainder. This jump is the real Induction; and this can never be

brought under the definition of Syllogism; for in the best and most

certain Induction the sequence is never a necessary one: you may

grant the premisses and deny the conclusion without contradicting

yourself.

[Footnote 60: Alexander intimates that Aristotle enunciated

"necessary sequence" as a part of his definition of Syllogism, for

the express purpose of distinguishing it from Induction, which is a

sequence _not necessary_ (Schol. ad Top. p. 253, a. 19, Br.): [Greek:

to\ d' _e)x a)na/gkês_ proskei/menon e)n tô=| o(/rô|, tê=s

**e)pagôgê=s chôri/zei to\n sullogismo/n; **e)/sti me\n ga\r kai\

e)pagôgê\ lo/gos e)n ô(=| tethe/ntôn tinô=n e(/tero/n ti tô=n

keime/nôn sumbai/nei, a)ll' _ou)k_ e)x a)na/gkês.]]

[Footnote 61: Alexander (in his Scholia on the Metaphysica, E. i. p.

406**, ed. Bonitz) observes truly: [Greek: a)ll' ei) e)k tê=s

ai)sthê/seôs kai\ tê=s e)pagôgê=s pi/stis, ou)k e)/stin a)po/deixis,

pro\s pa=san ga\r e)pagôgê\n du/natai/ tis e)ni/stasthai kai\ mê\

e)a=|n to\ katho/lou sumperai/nein.]]

[Footnote 62: Analyt. Prior. II. xxiii. p. 68, b. 27: [Greek: dei=

de\ noei=n to\ G to\ e)x a(pa/ntôn tô=n kath' e(/kaston sugkei/menon;

ê( ga\r e)pagôgê\ dia\ pa/ntôn.] See Professor Bain's 'Inductive

Logic,' chap. i. s. 2, where this process is properly criticised.]

Aristotle states very clearly:--"We believe everything either through

Syllogism, or from Induction."[63] Here, as well as in several other

passages, he notes the two processes as essentially distinct. The

Syllogism requires in its premisses at least one general proposition;

nor does Aristotle conceive the "generalities as the original

data:"[64] he derives them from antecedent Induction. The two

processes are (as he says) opposite in a certain way; that is, they

are complementary halves of the same whole; Induction being the

establishment of those universals which are essential for the

deductive march of the Syllogism; while the two together make up the

entire process of scientific reasoning. But he forgets or

relinquishes this antithesis, when he presents to us the Inductive

process as a given variety of Syllogism. And the objection to such a

doctrine becomes the more manifest, since in constructing his

Inductive Syllogism, he is compelled to admit either that there is no

middle term, or that the middle term is subject of the conclusion, in

violation of the syllogistic canons.[65]

[Footnote 63: Ibid. II. xxiii. p. 68, b. 13: [Greek: a(/panta ga\r

pisteu/omen ê)\ dia\ sullogismou= ê)\ e)x e)pagôgê=s]. Here Induction

includes Example, though in the next stage he puts the two apart.

Compare Anal. Poster. I. i. p. 71, a. 9.]

[Footnote 64: See Mr. John Stuart Mill's System of Logic, Bk. II. ch.

iii. a. 4, p. 219, 5th ed.]

[Footnote 65: Aldrich (Artis Log. Rudim. ch. iii. 9, 2, p. 175) and

Archbishop Whately (Elem. of Logic, ch. i. p. 209) agree in treating

the argument of Induction as a defective or informal Syllogism: see

also to the same purpose Sir.** W. Hamilton, Lectures on Logic, vol.

i. p. 322. Aldrich treats it as a Syllogism in _Barbara_, with the

minor suppressed; but Whately rejects this, because the minor

necessary to be supplied is false. He maintains that the premiss

suppressed is the major, not the minor. I dissent from both. It

appears to me that the opinion which Whately pronounces to be a

fallacy is the real truth: "Induction is a distinct kind of argument

from the Syllogism" (p. 208). It is the essential property of the

Syllogism, as defined by Aristotle and by every one after him, that

the truth of the conclusion follows _necessarily_ from the truth of

its premisses: that you cannot admit the premisses and reject the

conclusion without contradicting yourself. Now this is what the best

Induction never attains; and I contend that the presence or absence

of this important characteristic is quite enough to constitute "two

_distinct kinds_ of argument." Whately objects to Aldrich (whom

Hamilton defends) for supplying a suppressed _minor_, because it is

"manifestly false" (p. 209). I object to Whately's supplied _major_,

because it is uncertified, and therefore cannot be used to prove any

conclusion. By clothing arguments from Induction in syllogistic form,

we invest them with a character of necessity which does not really

belong to them. The establishment of general propositions, and the

interpretation of them when established (to use the phraseology of

Mr. Mill), must always be distinct mental processes; and the forms

appropriate to the latter, involving necessary sequence, ought not to

be employed to disguise the want of necessity--the varying and

graduated probability, inherent in the former. Mr. Mill says (Syst.

Log. Bk. III. ch. iii. s. 1, p. 343, 5th ed.:)--"As Whately remarks,

every induction is a syllogism with the major premiss suppressed; or

(as I prefer expressing it) every induction may be thrown into the

form of a syllogism, by supplying a major premiss." Even in this

modified phraseology, I cannot admit the propriety of throwing

Induction into syllogistic forms of argument. By doing this we efface

the special character of Induction, as the jump from particular

cases, more or fewer, to an universal proposition comprising them and

an indefinite number of others besides. To state this in forms which

imply that it is a necessary step, involving nothing more than the

interpretation of a higher universal proposition, appears to me

unphilosophical. Mr. Mill says with truth (in his admirable chapter

explaining the real function of the major premiss in a Syllogism, p.

211), that the individual cases are all the evidence which we

possess; the step from them to universal propositions ought not to be

expressed in forms which suppose universal propositions to be already

attained.

I will here add that, though Aldrich himself (as I stated at the

beginning of this note) treats the argument from Induction as a

defective or informal Syllogism, his anonymous Oxonian editor and

commentator takes a sounder view. He says (pp. 176, 177, 184, ed.

1823. Oxon.):--

"The principles acquired by human powers may be considered as

twofold. Some are _intuitive_, and are commonly called Axioms; the

other class of general principles are those acquired by Induction.

But it may be doubted whether this distinction is correct. It is

highly probable, if not certain, that those primary Axioms generally

esteemed _intuitive_, are in fact acquired by an inductive process;

although that process is less discernible, because it takes place

long before we think of tracing the actings of our own minds. It is

often found necessary to facilitate the understanding of those

Axioms, when they are first proposed to the judgment, by

illustrations drawn from individual cases. But whether it is, as is

generally supposed, the mere _enunciation_ of the principle, or the

_principle itself_, which requires the illustration, may admit of a

doubt. It seems probable, however that, such illustrations are

nothing more than a recurrence to the original method by which the

knowledge of those principles was acquired. Thus, the repeated trial

or observation of the necessary connection between mathematical

coincidence and equality, first authorizes the general position or

Axiom relative to that subject. If this conjecture is founded in

fact, it follows that both _primary_ and _ultimate_ principles have

the same nature and are alike acquired by the exercise of the

inductive faculty." "Those who acquiesce in the preceding

observations will feel a regret to find _Induction_ classed among

defective or informal Syllogisms. It is in fact prior in its order to

Syllogism; nor can syllogistic reasoning he carried on to any extent

without previous Induction" (p. 184).]

We must presume Syllogisms without a middle term, when we read:--"The

Syllogism through a middle term is _by nature_ prior, and of greater

cognitive efficacy; but _to us_ the Syllogism through Induction is

plainer and clearer."[66] Nor, indeed, is the saying, when literally

taken, at all well-founded; for the pretended Syllogisms from

Induction and Example, far from being clear and plain, are more

involved and difficult to follow than _Barbara_ and _Celarent_. Yet

the substance of Aristotle's thought is true and important, when

considered as declaring the antithesis (not between varieties of

Syllogisms, but) between Induction and Example on the one part, and

Syllogism (Deduction) on the other. It is thus that he sets out the

same antithesis elsewhere, both in the Analytica Posteriora and the

Topica.[67] Prior and more cognizable _by nature_ or _absolutely_,

prior and more cognizable _to us_ or _in relation to us_--these two

are not merely distinct, but the one is the correlate and antithesis

of the other.

[Footnote 66: Analyt. Prior. II. xxiii. p. 68, b. 35: [Greek: phu/sei

me\n ou)=n pro/teros kai\ gnôrimô/teros o( dia\ tou= me/sou

sullogismo/s, ê(mi=n d' e)narge/steros o( dia\ tê=s e)pagôgê=s.]]

[Footnote 67: Analyt. Post. I. ii. p. 72, a. 2, b. 29; Ethic. Nik.

VI. iii**. p. 1139, b. 28: [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.] Compare Topica, I. xii. p. 105, a.

11; VI. iv. pp. 141, 142**; Physica, I. i. p. 184, a. 16; Metaphysic.

E. iv. p. 1029, b**. 4-12. Compare also Trendelenburg's explanation

of this doctrine, Erläuterungen zu den Elementen der Aristotelischen

Logik, sects. 18, 19, 20, p. 33, seq.]

_To us_ the particulars of sense stand first, and are the earliest

objects of knowledge. _To us_, means to the large variety of

individual minds, which grow up imperceptibly from the simple

capacities of infancy to the mature accomplishments of adult years;

each acquiring its own stock of sensible impressions, remembered,

compared, associated; and each learning a language, which both

embodies in general terms and propositions the received

classification of objects, and communicates the current emotional

beliefs. We all begin by being learners; and we ascend by different

paths to those universal notions and beliefs which constitute the

common fund of the advanced intellect; developed in some minds into

_principia_ of philosophy with their consequences. _By nature_, or

_absolutely_, these _principia_ are considered as prior, and as

forming the point of departure: the advanced position is regarded as

gained, and the march taken is not that of the novice, but that of

the trained adult, who having already learnt much, is doubly equipped

either for learning more or for teaching others; who thus stands on a

summit from whence he surveys nature as a classified and coherent

whole, manifesting herself in details which he can interpret and

sometimes predict. The path of knowledge, seen _relatively to us_, is

one through particulars, by way of example to fresh particulars, or

by way of induction to universals. The path of knowledge, _by nature_

or _absolutely_, is from universals by way of deduction either to new

universals or to new particulars. By the cognitive _nature_ of man,

Aristotle means the full equipment, of and for cognition, which our

mature age exhibits; _notiora naturâ_ are the acquisitions, points of

view, and processes, familiar in greater or less perfection to such

mature individuals and societies. _Notiora nobis_ are the facts and

processes with which all of us begin, and which belong to the

intellect in its highest as well as its lowest stage; though, in the

higher stages, they are employed, directed, and modified, by an

acquired intellectual capital, and by the permanent machinery of

universal significant terms in which that capital is invested.

Such is the antithesis between _notiora naturâ_ (or _simpliciter_)

and _notiora nobis_ (or _quoad nos_), which Aristotle recognizes as a

capital point in his philosophy, and insists upon in many of his

writings. The antithesis is represented by Example and Induction, in

the point of view--_quoad nos_--last mentioned; by Syllogism or

Deduction, in the other point of view--_naturâ_. Induction (he

says),[68] or the rising from particulars to universals, is plainer,

more persuasive, more within the cognizance of sensible perception,

more within the apprehension of mankind generally, than Syllogism;

but Syllogism is more cogent and of greater efficacy against

controversial opponents. What he affirms here about Induction is

equally true about the inference from Example, that is, the inference

from one or some particulars, to other analogous particulars; the

rudimentary intellectual process, common to all human and to many

animal minds, of which Induction is an improvement and an exaltation.

While Induction will be more impressive, and will carry assent more

easily with an ordinary uncultivated mind, an acute disputant may

always deny the ultimate inference, for the denial involves no

contradiction. But the rightly constructed Syllogism constrains

assent;[69] the disputant cannot grant the premisses and deny the

conclusion without contradicting himself. The constraining force,

however, does not come into accurate and regulated working until the

principles and conditions of deductive reasoning have been set

forth--until the Syllogism has been analysed, and the characteristics

of its validity, as distinguished from its invalidity, have been

marked out. This is what Aristotle teaches in the Analytica and

Topica. It admits of being set out in regular figure and mode--forms

of premisses with the conclusion appropriate to each; and the lesson

must be learnt before we can know how far the force of deductive

reasoning, which begins with the _notiora naturâ_, is legitimately

binding and trustworthy.

[Footnote 68: Aristot. Topica, I. xii. p. 105, a. 13-19: [Greek:

e)pagôgê\ de\ ê( a)po\ tô=n kath' e(/kaston e)pi\ ta\ katho/lou

e)/phodos; oi(=on ei) e)/sti kubernê/tês o( e)pista/menos kra/tistos

kai\ ê(ni/ochos, kai\ o(/lôs e)sti\n o( e)pista/menos peri\ e(/kaston

a)/ristos. e)/sti d' ê( me\n e)pagôgê\ pithanô/teron kai\

saphe/steron kai\ kata\ tê\n ai)/sthêsin gnôrimô/teron, _kai\ toi=s

polloi=s koino/n_; o( de\ sullogismo\s biastikô/teron kai\ pro\s

tou\s a)ntilogikou\s e)nerge/steron.] Also the same treatise. VI. iv.

p. 141, b. 17.

The inductive interrogations of Sokrates relating to matters of

common life, and the way in which they convinced ordinary hearers,

are strikingly illustrated in the Memorabilia of Xenophon, especially

IV. vi.: [Greek: polu\ ma/lista ô(=n e)gô\ oi)=da, o(/te le/goi,

tou\s a)kou/ontas o(mologou=ntas parei=chen] (15). The same can

hardly be said of the Platonic dialogues.]

[Footnote 69: Bacon, Novum Organ. I. Aphor. 13:--"Syllogismus

assensum constringit, non res."]

Both the two main points of Aristotle's doctrine--the antithesis

between Induction and Deduction, and the dependence of the latter

process upon premisses furnished by the former, so that the two

together form the two halves of complete ratiocination and

authoritative proof--both these two are confused and darkened by his

attempt to present the Inductive inference and the Analogical or

Paradeigmatic inference as two special forms of Syllogistic

deduction.[70] But when we put aside this attempt, and adhere to

Aristotle's main doctrine--of Induction as a process antithetical to

and separate from Deduction, yet as an essential preliminary

thereto,--we see that it forms the basis of that complete and

comprehensive System of Logic, recently elaborated in the work of Mr.

John Stuart Mill. The inference from Example (_i.e._ from some

particulars to other similar particulars) is distinguished by

Aristotle from Induction, and is recognized by him as the primitive

intellectual energy, common to all men, through which Induction is

reached; its results he calls Experience ([Greek: e)mpeiri/a]), and

he describes it as the real guide, more essential than philosophical

generalities, to exactness of performance in detail.[71] Mr. John

Mill has been the first to assign to Experience, thus understood, its

full value and true position in the theory of Ratiocination; and to

show that the Paradeigmatic process exhibits the prime and ultimate

reality of all Inference, the real premisses and the real conclusion

which Inference connects together. Between these two is interposed

the double process of which Induction forms the first half and

Deduction the second; neither the one nor the other being

indispensable to Inference, but both of them being required as

securities for Scientific inference, if we desire to have its

correctness tested and its sufficiency certified; the real evidence,

whereby the conclusion of a Syllogism is proved, being the minor

premiss, together with (not the major premiss itself, but) the

assemblage of particular facts from which by Induction the major

premiss is drawn. Now Aristotle had present to his mind the

conception of Inference as an entire process, enabling us from some

particular truths to discover and prove other particular truths: he

considers it as an unscientific process, of which to a limited extent

other animals besides man are capable, and which, as operative under

the title of Experience in mature practical men, is a safer guide

than Science amidst the doubts and difficulties of action. Upon this

foundation he erects the superstructure of Science; the universal

propositions acquired through Induction, and applied again to

particulars or to lower generalities, through the rules of the

deductive Syllogism. He signalizes, with just emphasis, the

universalizing point of view called Science or Theory; but he regards

it as emerging from particular facts, and as travelling again

downwards towards particular facts. The misfortune is, that he

contents himself with barely recognizing, though he distinctly

proclaims the necessity of, the inductive part of this complex

operation; while he bestows elaborate care upon the analysis of the

deductive part, and of the rules for conducting it. From this

disproportionate treatment, one half of Logic is made to look like

the whole; Science is disjoined from Experience, and is presented as

consisting in Deduction alone; every thing which is not Deduction, is

degraded into unscientific Experience; the major premiss of the

Syllogism being considered as part of the proof of the conclusion,

and the conclusion being necessarily connected therewith, we appear

to have acquired a _locus standi_ and a binding cogency such as

Experience could never supply; lastly, when Aristotle resolves

Induction into a peculiar variety of the Syllogism, he appears

finally to abolish all its separate dignity and jurisdiction. This

one-sided view of Logic has been embraced and perpetuated by the

Aristotelian expositors, who have carefully illustrated, and to a

certain extent even amplified, the part which was already in

comparative excess, while they have added nothing to the part that

was in defect, and have scarcely even preserved Aristotle's

recognition of it as being not merely legitimate but essential. The

vast body of Inductive Science, accumulated during the last three

centuries, has thus, until recently, been allowed to grow up, as if

its proofs and processes had nothing to do with Logic.

[Footnote 70: Heyder (in his learned treatise, Darstellung der

Aristotelischen und Hegelschen Dialektik, p. 226), after having

considered the unsatisfactory process whereby Aristotle attempts to

resolve Induction into a variety of Syllogism, concludes by a remark

which I think just:--"Aus alle dem erhellt zur Genüge, dass sich

Aristoteles bei dem Versuch die Induction auf eine Schlussform

zurückzuführen, selbst sich nicht recht befriedigt fühlte, und

derselbe wohl nur aus seinem durchgängigen Bestreben zu erklären ist,

alles wissenschaftliche Verfahren in die Form des Schlusses zu

bringen; dass dagegen, seiner eigentlichen Meinung und der strengen

Consequenz seiner Lehre zu Folge, die Induction zum syllogistischen

und beweisenden Verfahren einen in dem Begriff der beiden

Verfahrungsweisen liegenden Gegensatz bildete, was sich ihm dann auch

auf das Verhältniss der Induction zur Begriffsbestimmung ausdehnen

musste."]

[Footnote 71: Aristot. Analyt. Prior. II. xxiii. p. 68, b. 12; xxvi.

p. 69, a. 17. Analyt. Post. II. xix. p. 99, b. 30, seq**.; xiii. p.

97, b. 7. Topica, VIII. i. p. 155, b. 35; p. 156, b. 10; p. 157, a.

14-23; p. 160, a. 36. Metaphys. A. i. p. 980, b. 25-p. 981, a. 30.

This first chapter of the Metaphysica is one of the most remarkable

passages of Aristotle, respecting the analytical philosophy of mind.]

But though this restricted conception of Logic or the theory of

Reasoning has arisen naturally from Aristotle's treatment, I maintain

that it does not adequately represent his view of that theory. In his

numerous treatises on other subjects, scarcely any allusion is made

to the Syllogism; nor is appeal made to the rules for it laid down in

the Analytica. His conviction that the formalities of Deduction were

only one part of the process of general reasoning, and that the value

of the final conclusion depended not merely upon their being

correctly performed, but also upon the correctness of that initial

part whereby they are supplied with matter for premisses--is

manifested as well by his industry (unrivalled among his

contemporaries) in collecting multifarious facts, as by his specific

declarations respecting Induction. Indeed, a recent most erudite

logician, Sir William Hamilton, who insists upon the construction of

Logic in its strictest sense as purely formal, blames Aristotle[72]

for having transgressed this boundary, and for introducing other

considerations bearing on diversities of matter and of material

evidence. The charge so made, to whatever extent it is well-founded,

does rather partake of the nature of praise; inasmuch as it evinces

Aristotle's larger views of the theory of Inference, and confirms his

own statement that the Deductive process was only the last half of

it, presupposing a prior Induction. It is only this last half that

Aristotle has here analysed, setting forth its formal conditions with

precepts founded thereupon; while he claims to have accomplished the

work by long and patient investigation, having found not the smallest

foundation laid by others, and bespeaks indulgence[73] as for a first

attempt requiring to be brought to completion by others. He made this

first step for himself; and if any one would make a second step, so

as to apply the same analysis to the other half, and to bring out in

like manner the formal conditions and principles of Induction, we may

fairly believe that Aristotle would have welcomed the act, as filling

up what he himself recognized to be a gap in the entire compass of

Reasoning. As to his own achievement, it is certain that he could not

have composed the Analytica and Topica, if he had not had before him

many specimens of the deductive process to study and compare. Neither

could the inductive process have been analysed, until after the

examples of successful advance in inductive science which recent

years have furnished. Upon these examples, mainly, has been based the

profound System of Mr. John Stuart Mill, analysing and discriminating

the formalities of Induction in the same way as those of Deduction

had before been handled by Aristotle; also fusing the two together as

co-operative towards one comprehensive scheme of Logic--the Logic of

Evidence generally, or of Truth as discoverable and proveable. In

this scheme the Syllogistic Theory, or Logic of Consistency between

one proposition and others, is recognized as an essential part, but

is no longer tolerated as an independent whole.[74]

[Footnote 72: See his Discussions on Philosophy, p. 139, seq.;

Lectures on Logic, vol. i. p. 27.]

[Footnote 73: See the remarkable paragraph at the close of the

Sophistici Elenchi, already quoted (supra, p. 140, note).]

[Footnote 74: Mr. John Stuart Mill says (Bk. II. ch. i. sect. 3):

**"Induction is inferring a proposition from premisses _less general_

than itself, and Ratiocination is inferring a proposition from

premisses _equally or more general_." Again in another passage: "We

have found that all Inference, consequently all Proof, and all

discovery of truths not self-evident, consists of inductions, and the

interpretation of inductions; that all our knowledge, not intuitive,

comes to us exclusively from that source. What Induction is,

therefore, and what conditions render it legitimate, cannot but be

deemed the main question of logic--the question which includes all

others. It is however one which professed writers on logic have

almost entirely passed over. The generalities of the subject, indeed,

have not been altogether neglected by metaphysicians; but, for want

of sufficient acquaintance with the processes by which science has

actually succeeded in establishing general truths, their analysis of

the inductive operation, even when unexceptionable as to correctness,

has not been specific enough to be made the foundation of practical

rules, which might be for Induction itself what the rules of the

Syllogism are for interpretation of Induction" (Bk. III. ch. i. s. 1.

p. 313.)--"The business of Inductive Logic is to provide rules and

models (such as the Syllogism and its rules are for ratiocination) to

which if inductive arguments conform, those arguments are conclusive,

and not otherwise. This is what the Four Methods profess to be, and

what I believe they are universally considered to be by experimental

philosophers, who had practised all of them long before any one

sought to reduce the practice to theory" (Bk. III. ch. ix. s. 5, p.

471, 5th ed.)--See also the same point of view more copiously set

forth, in Mr. Mill's later work, 'Examination of Sir W. Hamilton's

Philosophy' (ch. xx. pp. 454-462, 3rd ed.): "It is only as a means to

material truth that the formal (or to speak more clearly, the

conditional) validity of an operation of thought is of any value; and

even that value is only negative: we have not made the smallest

positive advance towards right thinking, by merely keeping ourselves

consistent in what is perhaps systematic error. This by no means

implies that Formal Logic, even in its narrowest sense, is not of

very great, though purely negative value."--"Not only however is it

indispensable that the larger Logic, which embraces all the general

conditions of the ascertainment of truth, should be studied in

addition to the smaller Logic, which only concerns itself with the

conditions of consistency; but the smaller Logic ought to be (at

least, finally) studied as part of the greater--as a portion of the

means to the same end; and its relation to the other parts--to the

other means--should be distinctly displayed."]

After adverting to another variety of ratiocinative procedure, which

he calls _Apagoge_ or Abduction (where the minor is hardly more

evident than the conclusion, and might sometimes conveniently become

a conclusion first to be proved),[75] Aristotle goes on to treat of

Objection generally--the function of the dialectical respondent. The

_Enstasis_ or Objection is a proposition opposed not to a conclusion,

but to the proposition set up by the defendant. When the proposition

set up by him is universal, as it must be if he seeks to establish an

universal conclusion, your objection may be either universal or

particular: you may deny either the whole of his proposition, or only

one portion of the particulars contained under it; the denial of one

single particular, when substantiated, being enough to overthrow his

universal. Accordingly, your objection, being thus variously opposed

to the proposition, will lie in the syllogistic figures which admit

opposite conclusions; that is, either in the First or Third; for the

Second figure admits only negative conclusions not opposed to each

other. If the defendant has set up an Universal Affirmative, you may

deny the whole and establish a contrary negative, in the First

figure; or you may deny a part only, and establish a contradictory

negative, in the Third figure. The like, if he has set up an

Universal Negative: you may impugn it either by an universal contrary

affirmative, in the First figure; or by a particular contradictory

affirmative, in the Third figure.[76]

[Footnote 75: Analyt. Prior. II. xxv. p. 69, a. 20-36.]

[Footnote 76: Ibid. II. xxvi. p. 69, a. 37-b. 37.

In objecting to A _universally_, you take a term comprehending the

original subject; in objecting _particularly_, a term comprehended by

it. Of the new term in each case you deny the original predicate, and

have thus, as a major premiss, E. For a minor premiss, you affirm, in

the first case, the new term as predicate of the original subject

(less comprehensive); in the second case, the original subject (more

comprehensive) as predicate of the new term. This gives you, in the

first case, a conclusion in _Celarent_ (Fig. I.), and, in the second,

a conclusion in _Felapton_ (Fig. III.); opposed, the one universally

or contrarily, the other particularly or contradictorily, to the

original proposition.]

The Enthymeme is a syllogism from Probabilities or Signs;[77] the two

being not exactly the same. _Probabilities_ are propositions commonly

accepted, and true in the greater number of cases; such as, Envious

men hate those whom they envy, Persons who are beloved look with

affection on those who love them. We call it a _Sign_, when one fact

is the antecedent or consequent of another, and therefore serves as

mark or evidence thereof. The conjunction may be either constant, or

frequent, or merely occasional: if constant, we obtain for the major

premiss of our syllogism a proposition approaching that which is

universally or necessarily true; if not constant but only frequent or

occasional, the major premiss of our syllogism will at best only be

probable. The constant conjunction will furnish us with a Syllogism

or Enthymeme in the First figure; the significant mark being here a

genuine middle term--subject in the major premiss, and predicate in

the minor. We can then get a conclusion both affirmative and

universally true. In other cases, we cannot obtain premisses for a

syllogism in the First figure, but only for a syllogism in the Second

or Third. In the Third figure, since we get by right no universal

conclusions at all, but only particular conclusions, the conclusion

of the Enthymeme, though it may happen to be true, is open to

refutation. Where by the laws of Syllogism no affirmative conclusion

whatever is possible, as in the Second figure, the conclusion

obtained by Enthymeme is altogether suspicious. In contrast with the

Sign in these figures, that which enters as an effective middle term

into the First figure, should be distinguished under the name of

_Proof_ ([Greek: tekmê/rion].)[78]

[Footnote 77: Ibid. II. xxvii. p. 70, a. 10: [Greek: e)nthu/mêma me\n

ou)=n e)sti\ sullogismo\s e)x ei)ko/tôn ê)\ sêmei/ôn; lamba/netai de\

to\ sêmei=on trichô=s, o(sachô=s kai\ to\ me/son e)n toi=s

schê/masi.]]

[Footnote 78: Analyt. Prior. II. xxvii. p. 70, a. 31-b. 6.

Aristotle throws in the remark (a. 24), that, when one premiss only

of the Enthymeme is enunciated, it is a Sign; when the other is

added, it becomes a Syllogism. In the examples given to illustrate

the description of the Enthymeme, that which belongs to the First

figure has its three terms and two propositions specified like a

complete and regular Syllogism; but when we come to the Third and

Second figures, Aristotle gives two alternate ways of stating each:

one way in full, with both premisses enunciated, constituting a

normal, though invalid, Syllogism; the other way, with only one of

the premisses enunciated, the other being suppressed as well-known

and familiar.

Among logicians posterior to Aristotle, the definition given of the

Enthymeme, and supposed to be derived from Aristotle was, that it was

a Syllogism with one of the premisses suppressed--[Greek:

monolê/mmatos]. Sir W. Hamilton has impugned this doctrine, and has

declared the definition to be both absurd in itself, and not

countenanced by Aristotle. (Lectures on Logic, Vol. I. Lect. xx. p.

386, seq.) I think Hamilton is mistaken on this point. (See Mr.

Cope's Introd. to Arist. Rhetoric, p. 103, seq.) Even in the present

chapter Aristotle distinctly alludes to the monolemmatic enunciation

of the Enthymeme as one mode of distinguishing it from a full

Syllogism; and in the Rhetorica he brings out this characteristic

still more forcibly. The distinction is one which belongs to Rhetoric

more than to Logic; the rhetor, in enunciating his premisses, must be

careful not to weary his auditors; he must glance at or omit reasons

that are familiar to them; logical fulness and accuracy would be

inconsistent with his purpose. The writers subsequent to Aristotle,

who think much of the rhetorical and little of the logical point of

view, bring out the distinction yet more forcibly. But the rhetorical

mode of stating premisses is often not so much an omission either of

major or minor, as a confused blending or packing up of both into

one.]

Aristotle concludes his Analytica Priora by applying this doctrine of

Signs to determine the limits within which Physiognomy as a science

is practicable. The basis upon which it rests is this general fact or

postulate: That in all natural affections of the animal, bodily

changes and mental changes accompany each other. The former,

therefore, may become signs or proofs of the latter,[79] if, in each

class of animals, we can discriminate the one specific bodily

phenomenon which attaches to each mental phenomenon. Thus, the lion

is a courageous animal. What is the bodily sign accompanying a

courageous disposition? It is (we assume here) the having extremities

of great size. This belongs to all lions, as a _proprium_; in the

sense that, though it may or does belong also to some individuals of

other races (as men), it does not belong to any other entire race.

Physiognomy as a science will, then, be possible, if we can find

races of animals which have only one characteristic mental attribute,

and if we can discover what is the physical attribute correlating

with it.[80] But the difficulties are greater when the same race has

two characteristic mental attributes (_e.g._ lions are both

courageous and generous), each with its correlative physical

attribute; for how can we tell which belongs to which? We have then

to study individuals of other races possessing one of these

attributes without the other; thus, if we find that courageous men,

who are not generous, agree in having large extremities, we may infer

that this last circumstance is, in the lion, the correlative mark of

his courage and not of his generosity. The physiognomonic inference

will be expressed by a syllogism in the First figure, in which the

major term (A) reciprocates and is convertible with the middle term

(B), while B stretches beyond (or is more extensive than) the minor

(C); this relation of the terms being necessary, if there is to be a

single mark for a particular attribute.[81]

[Footnote 79: Analyt. Prior. II. xxvii. p. 70, b. 7-16: [Greek: ei)/

tis di/dôsin a(/ma metaba/llein to\ sô=ma kai\ tê\n psuchê/n, o(/sa

phusika/ e)sti pathê/mata;--sumpa/schein ga\r a)llê/lois

u(pokei=tai.] See the Aristotelian treatise entitled [Greek:

Phusiognômonika/], pp. 808-809, Bekk.]

[Footnote 80: Ibid. II. xxvii. p. 70, b. 22. About the

characteristics of the lion see Aristot. Physiognom. p. 809, b.

14-36: [Greek: ta\ peri\ tê\n psuchê\n dotiko\n kai\ e)leu/theron,

megalo/psuchon kai\ philo/nikon, kai\ prau+\ kai\ di/kaion kai\

philo/storgon pro\s a(\ a)\n o(milê/sê|.]]

[Footnote 81: Ibid. II. xxvii. p. 70, b. 31-36.]

Here the treatise ends; but the reader will remember that, in

describing the canons laid down by Aristotle for the Syllogism with

its three Figures and the Modes contained therein, I confined myself

to the simple Assertory syllogism, postponing for the moment the long

expositions added by him about Modal syllogisms, involving the

Possible and the Necessary. What is proper to be said about this

complicated and useless portion of the Analytica Priora, may well

come in here; for, in truth, the doctrines just laid down about

Probabilities, Signs, and Proofs, bring us back to the Modals under a

different set of phrases. The Possible or Problematical is that, of

the occurrence or reality of which we doubt, neither believing nor

disbelieving it, not being prepared to assert either that it is, or

that it is not; _that which may be or may not be_. It is our manner

of speaking, when we have only signs or probabilities to guide us,

and not certain proofs. The feeling of doubt is, as a psychological

phenomenon, essentially distinct from the feeling of belief which, in

its objective aspect, correlates with certainty or matter of fact; as

well as from the feeling of disbelief, the correlate of which can

only be described negatively. Every man knows these feelings by his

own mental experience. But in describing the feeling of doubt, as to

its matter or in its objective aspect, we must take care to use

phrases which declare plainly both sides of its disjunctive or

alternative character. The Possible is, _That which either may be or

may not be_. As _That which may be_, it stands opposed to the

Impossible; as _That which may not be_, it stands opposed to the

Necessary. It thus carries with it negation both of impossibility and

of necessity; but, in common parlance, the first half of this meaning

stands out prominently, and is mistaken for the whole. Aristotle, as

we saw previously, speaks equivocally on this point, recognizing a

double signification of the term: he sometimes uses it in the sense

opposed only to impossible, maintaining that what is necessary must

also be possible; sometimes in the truer sense, opposed both to

necessity and to impossibility.[82]

[Footnote 82: Aristot. De Interpret. xiii. p. 22. Analyt. Prior. I.

xiii. p. 32, a. 21, 29, 36, xiv. p. 33, b. 22; xix. p. 38, a. 35.]

The Possible or Problematical, however, in this latter complete

sense--_What may or may not be_--exhibits various modifications or

gradations. 1. The chances on either side may be conceived as

perfectly equal, so that there is no probability, and we have no more

reason for expecting one side of the alternative than the other; the

sequence or conjunction is indeterminate. Aristotle construes this

indeterminateness in many cases (not as _subjective_, or as depending

upon our want of complete knowledge and calculating power, but) as

_objective_, insuperable, and inherent in many phenomenal agencies;

characterizing it, under the names of Spontaneity and Chance, as the

essentially unpredictable. 2. The chances on both sides may be

conceived as unequal and the ratio between them as varying

infinitely: the usual and ordinary tendency of phenomena--what

Aristotle calls Nature--prevails in the majority of cases, but not in

all; being liable to occasional counteraction from Chance and other

forces. Thus, between Necessity and perfect constancy at one extreme

(such as the rotation of the sidereal sphere), and Chance at the

other, there may be every shade of gradation; from natural agency

next below the constant, down to the lowest degree of

probability.[83]

[Footnote 83: Analyt. Prior. I. xiii. p. 32, b. 5-19. [Greek: to\ d'

a)o/riston tô=| mêde\n ma=llon ou(/tôs ê)\ e)kei/nôs]. Compare

Metaphys. K. p. 1064, b. 32.]

Now, within the range of these limits lie what Aristotle describes as

Signs and Probabilities; in fact, all the marks which we shall

presently come to as distinguishing the _dialectical_ syllogism from

the _demonstrative_. But here is involved rather the matter of the

Syllogism than its form. The form indeed is so far implicated, that

(as Aristotle justly remarks at the end of the Analytica Priora[84]),

the First figure is the only one that will prove both conjunctions

and disjunctions, as well constant as occasional; the Third figure

proves only occasional conjunctions and occasional disjunctions, not

constant; the Second figure will prove no conjunctions at all, but

only disjunctions, constant as well as occasional. Here a difference

of form is properly pointed out as coupled with and founded on a

difference of matter. But the special rules given by Aristotle, early

in the present treatise, for the conversion of Modal Propositions,

and the distinctions that he draws as to the modal character of the

conclusion according as one or other of the premisses belongs to one

or other of the different modes,--are both prolix and of little

practical value.[85]

[Footnote 84: Analyt. Prior. II. xxvii. p. 70, a. 2-38. Compare what

is said here about [Greek: ei)ko/s, sêmei=on, tekmê/rion], with the

first chapter of the Topica, and the dialectic syllogism as there

described: [Greek: o( e)x e)ndo/xôn sullogizo/menos].]

[Footnote 85: Ibid. I. viii.-xxii. p. 29, b. 29-p. 40, b. 16.]

What he calls the Necessary might indeed, from the point of view now

reached, cease to be recognized as a separate mode at all. The

Certain and the Problematical are real modes of the Proposition;

objective correlates to the subjective phases called Belief and

Doubt. But no proposition can be more than certain: the word

_necessary_, in strictness, implies only a peculiarity of the

evidence on which our belief is grounded. Granting certain given

premisses to be true, a given conclusion must be true also, if we

would avoid inconsistency and contradiction.

CHAPTER VII.

ANALYTICA POSTERIORA I.

In the two books of Analytica Priora, Aristotle has carried us

through the full doctrine of the functions and varieties of the

Syllogism; with an intimation that it might be applied to two

purposes--Demonstration and Dialectic. We are now introduced to these

two distinct applications of the Syllogism: first, in the Analytica

Posteriora, to Demonstration; next, in the Topica, to Dialectic. We

are indeed distinctly told that, as far as the forms and rules of

Syllogism go, these are alike applicable to both;[1] but the

difference of matter and purpose in the two cases is so considerable

as to require a distinct theory and precepts for the one and for the

other.

[Footnote 1: Analyt. Prior. I. xxx. p. 46, a. 4-10; Analyt. Post. I.

ii. p. 71, a. 23.]

The contrast between Dialectic (along with Rhetoric) on the one hand

and Science on the other is one deeply present to the mind of

Aristotle. He seems to have proceeded upon the same fundamental

antithesis as that which appears in the Platonic dialogues; but to

have modified it both in meaning and in terminology, dismissing at

the same time various hypotheses with which Plato had connected it.

The antithesis that both thinkers have in view is Opinion or Common

Sense _versus_ Science or Special Teaching and Learning; those

aptitudes, acquirements, sentiments, antipathies, &c., which a man

imbibes and appropriates insensibly, partly by his own doing and

suffering, partly by living amidst the drill and example of a given

society--as distinguished from those accomplishments which he derives

from a teacher already known to possess them, and in which both the

time of his apprenticeship and the steps of his progress are alike

assignable.

Common Sense is the region of Opinion, in which there is diversity of

authorities and contradiction of arguments without any settled truth;

all affirmations being particular and relative, true at one time and

place, false at another. Science, on the contrary, deals with

imperishable Forms and universal truths, which Plato regards, in

their subjective aspect, as the innate, though buried, furniture of

the soul, inherited from an external pre-existence, and revived in it

out of the misleading data of sense by a process first of the

cross-examining _Elenchus_, next of scientific Demonstration. Plato

depreciates altogether the untaught, unexamined, stock of

acquirements which passes under the name of Common Sense, as a mere

worthless semblance of knowledge without reality; as requiring to be

broken up by the scrutinizing _Elenchus_, in order to impress a

painful but healthy consciousness of ignorance, and to prepare the

mind for that process of teaching whereby alone Science or Cognition

can be imparted.[2] He admits that Opinion may be right as well as

wrong. Yet even when right, it is essentially different from Science,

and is essentially transitory; a safe guide to action while it lasts,

but not to be trusted for stability or permanence.[3] By Plato,

Rhetoric is treated as belonging to the province of Opinion,

Dialectic to that of Science. The rhetor addresses multitudes in

continuous speech, appeals to received common places, and persuades:

the dialectician, conversing only with one or a few, receives and

imparts the stimulus of short question and answer; thus awakening the

dormant capacities of the soul to the reminiscence of those universal

Forms or Ideas which are the only true Knowable.

[Footnote 2: Plato, Sophistes, pp. 228-229; Symposion, pp. 203-204;

Theætetus, pp. 148, 149, 150. Compare also 'Plato and the Other

Companions of Sokrates,' Vol. I. chs. vi.-vii. pp. 245-288; II. ch.

xxvi. p. 376, seq.]

[Footnote 3: Plato, Republic, v. pp. 477-478; Menon, pp. 97-98.]

Like Plato, Aristotle distinguishes the region of Common Sense or

Opinion from that of Science, and regards Universals as the objects

of Science. But his Universals are very different from those of

Plato: they are not self-existent realities, known by the mind from a

long period of pre-existence, and called up by reminiscence out of

the chaos of sensible impressions. To operate such revival is the

great function that Plato assigns to Dialectic. But in the philosophy

of Aristotle Dialectic is something very different. It is placed

alongside of Rhetoric in the region of Opinion. Both the rhetor and

the dialectician deal with all subjects, recognizing no limit; they

attack or defend any or all conclusions, employing the process of

ratiocination which Aristotle has treated under the name of

Syllogism; they take up as premisses any one of the various opinions

in circulation, for which some plausible authority may be cited; they

follow out the consequences of one opinion in its bearing upon

others, favourable or unfavourable, and thus become well furnished

with arguments for and against all. The ultimate foundation here

supposed is some sort of recognized presumption or authoritative

sanction[4]--law, custom, or creed, established among this or that

portion of mankind, some maxim enunciated by an eminent poet, some

doctrine of the Pythagoreans or other philosophers, current proverb,

answer from the Delphian oracle, &c. Any one of these may serve as a

dialectical authority. But these authorities, far from being

harmonious with each other, are recognized as independent,

discordant, and often contradictory. Though not all of equal

value,[5] each is sufficient to warrant the setting up of a thesis

for debate. In Dialectic, one of the disputants undertakes to do

this, and to answer all questions that may be put to him respecting

the thesis, without implicating himself in inconsistencies or

contradiction. The questioner or assailant, on the other hand, shapes

his questions with a view to refute the thesis, by eliciting answers

which may furnish him with premisses for some syllogism in

contradiction thereof. But he is tied down by the laws of debate to

syllogize only from such premisses as the respondent has expressly

granted; and to put questions in such manner that the respondent is

required only to give or withhold assent, according as he thinks

right.

[Footnote 4: Aristot. Topica, I. x. p. 104, a. 8, xi. p. 104, b. 19.

Compare Metaphysica, A. p. 995, a. 1-10.]

[Footnote 5: Analyt. Post. I. xix. p. 81, b. 18: [Greek: kata\ me\n

ou)=n do/xan sullogizome/nois kai\ mo/non dialektikô=s dê=lon o(/ti

tou=to mo/non skepte/on, ei) e)x ô(=n e)nde/chetai e)ndoxota/tôn

gi/netai o( sullogismo/s, ô(/st' ei) kai\ e)/sti ti tê=| a)lêthei/a|

tô=n AB me/son, dokei= de\ mê/, o( dia\ tou/tou sullogizo/menos

sullelo/gistai dialektikô=s, pro\s d' a)lê/theian e)k tô=n

u(parcho/ntôn dei= skopei=n.] Compare Topica, VIII. xii. p. 162, b.

27.]

We shall see more fully how Aristotle deals with Dialectic, when we

come to the Topica: here I put it forward briefly, in order that the

reader may better understand, by contrast, its extreme antithesis,

viz., Demonstrative Science and Necessary Truth as conceived by

Aristotle. First, instead of two debaters, one of whom sets up a

thesis which he professes to understand and undertakes to maintain,

while the other puts questions upon it,--Demonstrative Science

assumes a teacher who knows, and a learner conscious of ignorance but

wishing to know. The teacher lays down premisses which the learner is

bound to receive; or if they are put in the form of questions, the

learner must answer them as the teacher expects, not according to his

own knowledge. Secondly, instead of the unbounded miscellany of

subjects treated in Dialectic, Demonstrative Science is confined to a

few special subjects, in which alone appropriate premisses can be

obtained, and definitions framed. Thirdly, instead of the several

heterogeneous authorities recognized in Dialectic, Demonstrative

Science has _principia_ of its own, serving as points of departure;

some _principia_ common to all its varieties, others special or

confined to one alone. Fourthly, there is no conflict of authorities

in Demonstrative Science; its propositions are essential, universal,

and true _per se_, from the commencement to the conclusion; while

Dialectic takes in accidental premisses as well as essential.

Fifthly, the _principia_ of Demonstrative Science are obtained from

Induction only; originating in particulars which are all that the

ordinary growing mind can at first apprehend (_notiora nobis_), but

culminating in universals which correspond to the perfection of our

cognitive comprehension (_notiora naturâ_.)[6]

[Footnote 6: Aristot. Topica, VI. iv. p. 141, b. 3-14. [Greek: oi(

polloi\ ga\r ta\ toiau=ta prognôri/zousin; ta\ me\n ga\r tê=s

tuchou/sês, ta\ d' a)kribou=s kai\ perittê=s dianoi/as katamathei=n

e)sti/n.] Compare in Analyt. Post. I. xii. pp. 77-78, the contrast

between [Greek: ta\ mathê/mata] and [Greek: oi( dia/logoi].]

Amidst all these diversities, Dialectic and Demonstrative Science

have in common the process of Syllogism, including such assumptions

as the rules of syllogizing postulate. In both, the conclusions are

hypothetically true (_i.e._ granting the premisses to be so). But, in

demonstrative syllogism, the conclusions are true universally,

absolutely, and necessarily; deriving this character from their

premisses, which Aristotle holds up as the cause, reason, or

condition of the conclusion. What he means by Demonstrative Science,

we may best conceive, by taking it as a small [Greek: te/menos] or

specially cultivated enclosure, subdivided into still smaller

separate compartments--the extreme antithesis to the vast common land

of Dialectic. Between the two lies a large region, neither

essentially determinate like the one, nor essentially indeterminate

like the other; an intermediate region in which are comprehended the

subjects of the treatises forming the very miscellaneous Encyclopædia

of Aristotle. These subjects do not admit of being handled with equal

exactness; accordingly, he admonishes us that it is important to know

how much exactness is attainable in each, and not to aspire to

more.[7]

[Footnote 7: Aristot. Ethic. Nikom. I. p. 1094, b. 12-25; p. 1098, a.

26-b. 8; Metaphys. A. p. 995, a. 15; Ethic. Eudem. I. p. 1216, b.

30-p. 1217, a. 17; Politic. VII. p. 1328, a. 19; Meteorolog. I. p. 338,

a. 35. Compare Analyt. Post. I. xiii. p. 78, b. 32 (with Waitz's

note, II. p. 335); and I. xxvii. p. 87, a. 31.

The passages above named in the Nikomachean Ethica are remarkable:

[Greek: le/goito d' a)\n i(kanô=s, ei) kata\ tê\n u(pokeime/nên

u(/lên diasaphêthei/ê; to\ ga\r a)kribe\s ou)ch o(moi/ôs e)n a(/pasi

toi=s lo/gois e)pizêtête/on, ô(/sper ou)d' e)n toi=s

dêmiourgoume/nois. tê\n a)kri/beian mê\ o(moi/ôs e)n a(/pasin

e)pizêtei=n (chrê/), a)ll' e)n e(ka/stois kata\ tê\n u(pokeime/nên

u(/lên, kai\ e)pi\ tosou=ton e)ph' o(/son oi)kei=on tê=| methodô=|.]

Compare Metaphys. E. p. 1025, b. 13: [Greek: a)podeiknu/ousin ê)\

a)nagkai/oteron ê)\ malakô/teron.]

The different degrees of exactness attainable in different

departments of science, and the reasons upon which such difference

depends are well explained in the sixth book of Mr. John Stuart

Mill's System of Logic, vol. II. chap. iii. pp. 422-425, 5th ed.

Aristotle says that there can be no scientific theory or cognition

about [Greek: to\ sumbebêko/s] which he defines to be that which

belongs to a subject neither necessarily, nor constantly, nor

usually, but only on occasion (Metaphys. E. p. 1026, b. 3, 26, 33; K.

p. 1065, a. 1, meaning [Greek: to\ sumbebêko\s mê\ kath'

au(to/],--Analyt. Post. I. 6, 75, a. 18; for he uses the term in two

different senses--Metaph. [Greek: D]. p. 1025, a. 31). In his view,

there can be no science except about constant conjunctions; and we

find the same doctrine in the following passage of Mr. Mill:--"Any

facts are fitted, in themselves, to be a subject of science, which

follow one another according to constant laws; although those laws

may not have been discovered, nor even be discoverable by our

existing resources. Take, for instance, the most familiar class of

meteorological phenomena, those of rain and sunshine. Scientific

inquiry has not yet succeeded in ascertaining the order of antecedence

and consequence among these phenomena, so as to be able, at least in

our regions of the earth, to predict them with certainty, or even with

any high degree of probability. Yet no one doubts that the phenomena

depend on laws. . . . . Meteorology not only has in itself every

requisite for being, but actually is, a science; though from the

difficulty of observing the facts upon which the phenomena depend (a

difficulty inherent in the peculiar nature of those phenomena), the

science is extremely imperfect; and were it perfect, might probably be

of little avail in practice, since the data requisite for applying its

principles to particular instances would rarely be procurable.

"A case may be conceived of an intermediate character between the

perfection of science, and this its extreme imperfection. It may

happen that the greater causes, those on which the principal part of

the phenomena depends, are within the reach of observation and

measurement; so that, if no other causes intervened, a complete

explanation could be given, not only of the phenomenon in general,

but of all the variations and modifications which it admits of. But

inasmuch as other, perhaps many other, causes, separately

insignificant in their effects, co-operate or conflict in many or in

all cases with those greater causes, the effect, accordingly,

presents more or less of aberration from what would be produced by

the greater causes alone. Now if these minor causes are not so

constantly accessible, or not accessible at all, to accurate

observation, the principal mass of the effect may still, as before,

be accounted for, and even predicted; but there will be variations

and modifications which we shall not be competent to explain

thoroughly, and our predictions will not be fulfilled accurately, but

only approximately.

"It is thus, for example, with the theory of the Tides. . . . . And

this is what is or ought to be meant by those who speak of sciences

which are not exact sciences. Astronomy was once a science, without

being an exact science. It could not become exact until not only the

general course of the planetary motions, but the perturbations also,

were accounted for and referred to their causes. It has become an

exact science because its phenomena have been brought under laws

comprehending the whole of the causes by which the phenomena are

influenced, whether in a great or only in a trifling degree, whether

in all or only in some cases, and assigning to each of those causes

the share of effect that really belongs to it. . . . . The science of

human nature falls far short of the standard of exactness now

realized in Astronomy; but there is no reason that it should not be

as much a science as Tidology is, or as Astronomy was when its

calculations had only mastered the main phenomena, but not the

perturbations."]

In setting out the process of Demonstration, Aristotle begins from

the idea of teaching and learning. In every variety thereof some

_præcognita_ must be assumed, which the learner must know before he

comes to be taught, and upon which the teacher must found his

instruction.[8] This is equally true, whether we proceed (as in

Syllogism) from the more general to the less general, or (as in

Induction) from the particular to the general. He who comes to learn

Geometry must know beforehand the figures called circle and triangle,

and must have a triangular figure drawn to contemplate; he must know

what is a unit or monad, and must have, besides, exposed before him

what is chosen as the unit for the reasoning on which he is about to

enter. These are the _præcognita_ required for Geometry and

Arithmetic. Some _præcognita_ are also required preparatory to any

and all reasoning: _e.g._, the maxim of Identity (fixed meaning of

terms and propositions), and the maxims of Contradiction and of

Excluded Middle (impossibility that a proposition and its

contradictory can either be both true or both false.)[9] The learner

must thus know beforehand certain Definitions and Axioms, as

conditions without which the teacher cannot instruct him in any

demonstrative science.

[Footnote 8: Analyt. Post. I. i. pp. 71-72; Metaphys. A. IX. p. 992,

b. 30.]

[Footnote 9: Aristot. Analyt. Post. I, i. p. 71, a. 11-17. [Greek:

a(/pan ê)\ phê=sai ê)\ a)pophê=sai a)lêthe/s].]

Aristotle, here at the beginning, seeks to clear up a difficulty

which had been raised in the time of Plato as between knowledge and

learning. How is it possible to _learn_ at all? is a question started

in the Menon.[10] You either know a thing already, and, on this

supposition, you do not want to learn it; or you do not know it, and

in this case you cannot learn it, because, even when you have learnt,

you cannot tell whether the matter learnt is what you were in search

of. To this difficulty, the reply made in the Menon is, that you

never _do_ learn any thing really new. What you are said to learn, is

nothing more than reminiscence of what had once been known in an

anterior life, and forgotten at birth into the present life; what is

supposed to be learnt is only the recall of that which you once knew,

but had forgotten. Such is the Platonic doctrine of Reminiscence.

Aristotle will not accept that doctrine as a solution; but he

acknowledges the difficulty, and intimates that others had already

tried to solve it without success. His own solution is that there are

two grades of cognition: (1) the full, complete, absolute; (2) the

partial, incomplete, qualified. What you already know by the first of

these grades, you cannot be said to learn; but you may learn that

which you know only by the second grade, and by such learning you

bring your incomplete cognition up to completeness.

[Footnote 10: Plato, Menon. p. 80.]

Thus, you have learnt, and you know, the universal truth, that every

triangle has its three angles equal to two right angles; but you do

not yet know that A B C, D E F, G H I, &c., have their two angles

equal to two right angles; for you have not yet seen any of these

figures, and you do not know that they _are_ triangles. The moment

that you see A B C, or hear what figure it is, you learn at one and

the same time two facts: first, that it is a triangle; next, by

virtue of your previous cognition, that it possesses the

above-mentioned property. You knew this _in a certain way_ or

incompletely before, by having followed the demonstration of the

universal truth, and by thus knowing that _every_ triangle had its

three angles equal to two right angles; but you did not know it

absolutely, being ignorant that A B C was a triangle.[11]

[Footnote 11: Aristot. Analyt. Post. I. i. p. 71, a. 17-b. 8: [Greek:

e)/sti de\ gnôri/zein ta\ me\n pro/teron gnôri/zonta, tô=n de\ kai\

a)/ma lamba/nonta tê\n gnô=sin, oi(=on o(/sa tugcha/nei o)/nta u(po\

to\ katho/lou, ô(=n e)/chei tê\n gnô=sin. o(/ti me\n ga\r pa=n

tri/gônon e)/chei dusi\n o)rthai=s i)/sas, proê/|dei; o(/ti de\ to/de

to\ e)n tô=| ê(mikukli/ô| tri/gôno/n e)stin, a(/ma e)pago/menos

e)gnô/risen.--pri\n d' e)pachthê=nai ê)\ labei=n sullogismo/n,

tro/pon me/n tina i)/sôs phate/on e)pi/stasthai, tro/pon d' a)/llon

ou)/. o(\ ga\r mê\ ê)/|dei ei) e)/stin a(plô=s, tou=to pô=s ê)/|dei

o(/ti du/o o)rtha\s e)/chei a(plô=s? a)lla\ dê=lon ô(s _ô(di\ me\n

e)pi/statai, o(/ti katho/lou e)pi/statai, a(plô=s d' ou)k

e)pi/statai_.--ou)de\n (oi)=mai) kôlu/ei, o(\ mantha/nei, e)/stin ô(s

e)pi/stasthai, e)/sti d' ô(s a)gnoei=n; a)/topon ga\r ou)k ei)

oi)=de/ pôs o(\ mantha/nei, a)ll' ei) ô(di/, oi(=on ê(=| mantha/nei

kai\ ô(/s.] Compare also Anal. Post. I. xxiv. p. 86, a. 23, and

Metaph. A. ii. p. 982, a. 8; Anal. Prior. II. xxi. p. 67, a. 5-b.

10.)

Aristotle reports the solution given by others, but from which he

himself dissented, of the Platonic puzzle. The respondent was asked,

Do you know that every Dyad is even?--Yes. Some Dyad was then

produced, which the respondent did not know to be a Dyad; accordingly

he did not know it to be even. Now the critics alluded to by

Aristotle said that the respondent made a wrong answer; instead of

saying I know every Dyad is even, he ought to have said. Every Dyad

_which I know to be a Dyad_ is even. Aristotle pronounces that this

criticism is incorrect. The respondent knows the conclusion which had

previously been demonstrated to him; and that conclusion was, Every

triangle has its three angles equal to two right angles; it was not,

Every thing _which I know_ to be a triangle has its three angles

equal to two right angles. This last proposition had never been

demonstrated, nor even stated: [Greek: ou)demi/a ga\r pro/tasis

lamba/netai toiau/tê, o(/ti _o(\n su\ oi)=das_ a)rithmo/n, _ê)\ o(\

su\ oi)=das_ eu)thu/grammon, a)lla\ _kata\ panto/s_] (b. 3-5).

This discussion, in the commencement of the Analytica Posteriora

(combined with Analyt. Priora, II. xxi.), is interesting, because it

shows that even then the difficulties were felt, about the major

proposition of the Syllogism, which Mr. John Stuart Mill has so ably

cleared up, for the first time, in his System of Logic. See Book II.

ch. iii. of that work, especially as it stands in the sixth edition,

with the note there added, pp. 232-233. You affirm, in the major

proposition of the Syllogism, that every triangle has its three

angles equal to two right angles; does not this include the triangle

A, B, C, and is it not therefore a _petitio principii_? Or, if it be

not so, does it not assert more than you know? The Sophists (upon

whom both Plato and Aristotle are always severe, but who were

valuable contributors to the theory of Logic by fastening upon the

weak points) attacked it on this ground, and raised against it the

puzzle described by Aristotle (in this chapter), afterwards known as

the Sophism entitled [Greek: o( e)gkekalumme/nos] (see Themistius

Paraphras. I. i.; also 'Plato and the Other Companions of Sokrates,'

Vol. III. ch. xxxviii. p. 489). The critics whom Aristotle here cites

and disapproves, virtually admitted the pertinence of this puzzle by

modifying their assertion, and by cutting it down to "Everything

_which we know to be a triangle_ has its three angles equal to two

right angles." Aristotle finds fault with this modification, which,

however, is one way of abating the excess of absolute and peremptory

pretension contained in the major, and of intimating the want of a

minor to be added for interpreting and supplementing the major; while

Aristotle himself arrives at the same result by admitting that the

knowledge corresponding to the major proposition is not yet absolute,

but incomplete and qualified; and that it is only made absolute when

supplemented by a minor.

The very same point, substantially, is raised in the discussion

between Mr. John Stuart Mill and an opponent, in the note above

referred to. "A writer in the 'British Quarterly Review' endeavours

to show that there is no _petitio principii_ in the Syllogism, by

denying that the proposition All men are mortal, asserts or assumes

that Socrates is mortal. In support of this denial, he argues that we

may, and in fact do, admit the general proposition without having

particularly examined the case of Socrates, and even without knowing

whether the individual so named is a man or something else. But this

of course was never denied. That we can and do draw inferences

concerning cases specifically unknown to us, is the datum from which

all who discuss this subject must set out. The question is, in what

terms the evidence or ground on which we draw these conclusions may

best be designated--whether it is most correct to say that the

unknown case is proved by known cases, or that it is proved by a

general proposition including both sets of cases, the known and the

unknown? I contend for the former mode of expression. I hold it an

abuse of language to say, that the proof that Socrates is mortal, is

that all men are mortal. Turn it in what way we will, this seems to

me asserting that a thing is the proof of itself. Whoever pronounces

the words, All men are mortal, has affirmed that Socrates is mortal,

though he may never have heard of Socrates; for since Socrates,

whether known to be a man or not, really is a man, he is included in

the words, All men, and in every assertion of which they are the

subject. . . . . The reviewer acknowledges that the maxim (Dictum de

Omni et Nullo) as commonly expressed--'Whatever is true of a class is

true of everything included in the class,' is a mere identical

proposition, since the class _is_ nothing but the things included in

it. But he thinks this defect would be cured by wording the maxim

thus: 'Whatever is true of a class is true of everything which can be

shown to be a member of the class:' as if a thing could be shown to

be a member of the class without being one."

The qualified manner in which the maxim is here enunciated by the

reviewer (what _can be shown_ to be a member of the class)

corresponds with the qualification introduced by those critics whom

Aristotle impugns ([Greek: lu/ousi ga\r ou) pha/skontes ei)de/nai

pa=san dua/da a)rti/an ou)=san, a)ll' _ê(\n i)/sasin o(/ti dua/s_]);

and the reply of Mr. Mill would have suited for these critics as well

as for the reviewer. The puzzle started in the Platonic Menon is, at

bottom, founded on the same view as that of Mr. Mill, when he states

that the major proposition of the Syllogism includes beforehand the

conclusion. "The general principle, (says Mr. Mill, p. 205), instead

of being given as evidence of the particular case, cannot itself be

taken for true without exception, until every shadow of doubt which

could affect any case comprised in it is dispelled by evidence

_aliunde_; and then what remains for the syllogism to prove? From a

general principle we cannot infer any particulars but those which the

principle itself assumes as known."

To enunciate this in the language of the Platonic Menon, we learn

nothing by or through the evidence of the Syllogism, except a part of

what we have already professed ourselves to know by asserting the

major premiss.]

Aristotle proceeds to tell us what is meant by knowing a thing

_absolutely_ or completely ([Greek: a(plô=s]). It is when we believe

ourselves to know the cause or reason through which the matter known

exists, so that it cannot but be as it is. That is what

Demonstration, or Scientific Syllogism, teaches us;[12] a Syllogism

derived from premisses true, immediate, prior to, and more knowable

than the conclusion--causes of the conclusion, and specially

appropriate thereto. These premisses must be known beforehand without

being demonstrated (_i.e._ known not through a middle term); and must

be known not merely in the sense of understanding the signification

of the terms, but also in that of being able to affirm the truth of

the proposition. _Prior_ or _more knowable_ is understood here as

prior or more knowable _by nature_ (not _relatively to us_, according

to the antithesis formerly explained); first, most universal,

undemonstrable _principia_ are meant. Some of these are Axioms, which

the learner must "bring with him from home," or know before the

teacher can instruct him in any special science; some are Definitions

of the name and its essential meaning; others, again, are Hypotheses

or affirmations of the existence of the thing defined, which the

learner must accept upon the authority of the teacher.[13] As these

are the _principia_ of Demonstration, so it is necessary that the

learner should know them, not merely as well as the conclusions

demonstrated, but even better; and that among matters contradictory

to the _principia_ there should be none that he knows better or

trusts more.[14]

[Footnote 12: Aristot. Analyt. Post I. ii. p. 71, b. 9-17. Julius

Pacius says in a note, ad c. ii. p. 394: "Propositio demonstrativa

est prima, immediata, et indemonstrabilis. His tribus verbis

significatur una et eadem conditio; nam propositio prima est, quæ,

quod medio caret, demonstrari nequit."

So also Zabarella (In lib. I. Post. Anal. Comm., p. 340, Op. ed.

Venet. 1617): "Duæ illæ dictiones (_primis_ et _immediatis_) unam

tantum significant conditionem ordine secundam, non duas; idem namque

est, principia esse medio carentia, ac esse prima."]

[Footnote 13: Aristot. Analyt. Post. I. ii. p. 72, a. 1-24;

Themistius, Paraphr. I. ii. p. 10, ed. Spengel; Schol. p. 199, b. 44.

Themistius quotes the definition of an Axiom as given by

Theophrastus: [Greek: A)xi/ôma/ e)sti _do/xa_ tis], &c. This shows

the difficulty of adhering precisely to a scientific terminology.

Theophrastus explains an axiom to be a sort of [Greek: do/xa], thus

lapsing into the common loose use of the word. Yet still both he and

Aristotle declare [Greek: do/xa] to be of inferior intellectual worth

as compared with [Greek: e)pistê/mê] (Anal. Post. I. xxiii.), while

at the same time they declare the Axiom to be the very maximum of

scientific truth. Theophrastus gave, as examples of Axioms, the

**maxim of Contradiction, universally applicable, and, "If

equals be taken from equals the remainders will be equal," applicable

to homogeneous quantities. Even Aristotle himself sometimes falls

into the same vague employment of [Greek: do/xa], as including the

Axioms. See Metaphys. B. ii. p. 996, b. 28; [Greek: G]. iii. p. 1005,

b. 33.]

[Footnote 14: Aristot. Anal. Post. I. ii. p. 72, a. 25, b. 4. I

translate these words in conformity with Themistius, pp. 12-13, and

with Mr. Poste's translation, p. 43. Julius Pacius and M. Barthélemy

St. Hilaire render them somewhat differently. They also read [Greek:

a)meta/ptôtos], while Waitz and Firmin Didot read [Greek:

a)meta/peistos], which last seems preferable.]

In Aristotle's time two doctrines had been advanced, in opposition to

the preceding theory: (1) Some denied the necessity of any

indemonstrable _principia_, and affirmed the possibility of,

demonstrating backwards _ad infinitum_; (2) Others agreed in denying

the necessity of any indemonstrable _principia_, but contended that

demonstration in a circle is valid and legitimate--_e.g._ that A may

be demonstrated by means of B, and B by means of A. Against both

these doctrines Aristotle enters his protest. The first of them--the

supposition of an interminable regress--he pronounces to be obviously

absurd: the second he declares tantamount to proving a thing by

itself; the circular demonstration, besides, having been shown to be

impossible, except in the First figure, with propositions in which

the predicate reciprocates or is co-extensive with the subject--a

very small proportion among propositions generally used in

demonstrating.[15]

[Footnote 15: Aristot. Analyt. Post. I. iii. p. 72, b. 5-p. 73, a.

20: [Greek: ô(/st' e)peidê\ _o)li/ga toiau=ta_ e)n tai=s

a)podei/xesin], &c.]

Demonstrative Science is attained only by syllogizing from necessary

premisses, such as cannot possibly be other than they are. The

predicate must be (1) _de omni_, (2) _per se_, (3) _quatenus ipsum_,

so that it is a _Primum Universale_; this third characteristic not

being realized without the preceding two. First, the predicate must

belong, and belong at all times, to everything called by the name of

the subject. Next, it must belong thereunto _per se_, or essentially;

that is, either the predicate must be stated in the definition

declaring the essence of the subject, or the subject must be stated

in the definition declaring the essence of the predicate. The

predicate must not be extra-essential to the subject, nor attached to

it as an adjunct from without, simply concomitant or accidental. The

like distinction holds in regard to events: some are accidentally

concomitant sequences which may or may not be realized (_e.g._, a

flash of lightning occurring when a man is on his journey); in

others, the conjunction is necessary or causal (as when an animal

dies under the sacrificial knife).[16] Both these two characteristics

(_de omni_ and _per se_) are presupposed in the third (_quatenus

ipsum_); but this last implies farther, that the predicate is

attached to the subject in the highest universality consistent with

truth; _i.e._, that it is a First Universal, a primary predicate and

not a derivative predicate. Thus, the predicate of having its three

angles equal to two right angles, is a characteristic not merely _de

omni_ and _per se_, but also a First Universal, applied to a

triangle. It is applied to a triangle, _quatenus_ triangle, as a

primary predicate. If applied to a subject of higher universality

(_e.g._, to every geometrical figure), it would not be always true.

If applied to a subject of lower universality (_e.g._, to a

right-angled triangle or an isosceles triangle), it would be

universally true and would be true _per se_, but it would be a

derivative predicate and not a First Universal; it would not be

applied to the isosceles _quatenus_ isosceles, for there is a still

higher Universal of which it is predicable, being true respecting

any triangle you please. Thus, the properties with which

Demonstration, or full and absolute Science, is conversant, are _de

omni_, _per se_, and _quatenus ipsum_, or _Universalia Prima_;[17]

all of them necessary, such as cannot but be true.]

[Footnote 16: Aristot. Analyt. Post. I. iv. p. 73, a. 21, b. 16.

[Greek: Ta\ a)/ra lego/mena e)pi\ tô=n a(plô=s e)pistêtô=n kath'

au(ta\ ou(/tôs ô(s e)nupa/rchein toi=s katêgoroume/nois ê)\

e)nupa/rchesthai di' au(ta/ te/ e)sti kai\ e)x a)na/gkês] (b. 16,

seq.). _Line_ must be included in the definition of the opposites

_straight_ or _curve_. Also it is essential to every line that it is

either straight or curve. _Number_ must be included in the definition

of the opposites _odd_ or _even_; and to be either odd or even is

essentially predicable of every number. You cannot understand what is

meant by _straight_ or _curve_ unless you have the notion of a

_line_.

The example given by Aristotle of _causal_ conjunction (the death of

an animal under the sacrificial knife) shows that he had in his mind

the perfection of Inductive Observation, including full application

of the Method of Difference.]

[Footnote 17: Aristot. Analyt. Post. I. iv. p. 73, b. 25-p. 74, a. 3.

[Greek: o(\ toi/nun _to\ tucho\n prô=ton_ dei/knutai du/o o)rtha\s

e)/chon ê)\ o(tiou=n a)/llo, tou/tô| prô/tô| u(pa/rchei katho/lou,

kai\ ê( _a)po/deixis kath' au(to\_ tou/tou katho/lou e)sti\, tô=n d'

a)/llôn tro/pon tina\ ou) kath' au(to/; ou)de\ tou= i)soske/lous ou)k

e)/sti katho/lou a)ll' e)pi\ ple/on.]

About the precise signification of [Greek: katho/lou] in Aristotle,

see a valuable note of Bonitz (ad Metaphys. Z. iii.) p. 299; also

Waitz (ad Aristot. De Interpr. c. vii.) I. p. 334. Aristotle gives it

here, b. 26: [Greek: katho/lou de\ le/gô o(\ a)\n kata\ panto/s te

u(pa/rchê| kai\ kath' au(to\ kai\ ê(=| au)to/.] Compare Themistius,

Paraphr. p. 19, Spengel. [Greek: To\ kath' au(to/] is described by

Aristotle confusedly. [Greek: To\ katho/lou], is that which is

predicable of the subject as a whole or _summum genus_: [Greek: to\

kata\ panto/s], that which is predicable of every individual, either

of the _summum genus_ or of any inferior species contained therein.

Cf. Analyt. Post. 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]--the subject is

itself the cause or _fundamentum_ of the properties _per se_. See the

explanation and references in Kampe, Die Erkenntniss-theorie des

Aristoteles, ch. v. pp. 160-165.]

Aristotle remarks that there is great liability to error about these

_Universalia Prima_. We sometimes demonstrate a predicate to be true,

universally and _per se_, of a lower species, without being aware

that it might also be demonstrated to be true, universally and _per

se_, of the higher genus to which that species belongs; perhaps,

indeed, that higher genus may not yet have obtained a current name.

That proportions hold by permutation, was demonstrated severally for

numbers, lines, solids, and intervals of time; but this belongs to

each of them, not from any separate property of each, but from what

is common to all: that, however, which is common to all had received

no name, so that it was not known that one demonstration might

comprise all the four.[18] In like manner, a man may know that an

equilateral and an isosceles triangle have their three angles equal

to two right angles, and also that a scalene triangle has its three

angles equal to two right angles; yet he may not know (except

sophistically and by accident[19]) that a triangle _in genere_ has

its three angles equal to two right angles, though there be no other

triangles except equilateral, isosceles, and scalene. He does not

know that this may be demonstrated of every triangle _quatenus_

triangle. The only way to obtain a certain recognition of _Primum

Universale_, is, to abstract successively from the several conditions

of a demonstration respecting the concrete and particular, until the

proposition ceases to be true. Thus, you have before you a brazen

isosceles triangle, the three angles whereof are equal to two right

angles. You may eliminate the condition brazen, and the proposition

will still remain true. You may also eliminate the condition

isosceles; still the proposition is true. But you cannot eliminate

the condition triangle, so as to retain only the higher genus,

geometrical figure; for the proposition then ceases to be always

true. Triangle is in this case the _Primum Universale_.[20]

[Footnote 18: Aristot. Analyt. Post I. v. p. 74, a. 4-23. [Greek:

a)lla\ dia\ to\ mê\ ei)=nai ô)nomasme/non ti pa/nta tau=ta e(/n,

a)rithmoi/, mê/kê, chro/nos, sterea/, kai\ ei)/dei diaphe/rein

a)llê/lôn, chôri\s e)lamba/neto.] What these four have in common is

that which he himself expresses by [Greek: Poso/n]--_Quantum_--in the

Categoriæ and elsewhere. (Categor. p. 4, b. 20, seq.; Metaph. [Greek:

D]. p. 1020, a. 7, seq.)]

[Footnote 19: Aristot. Analyt. Post. I. v. p. 74, a. 27: [Greek:

ou)/pô oi)=de to\ tri/gônon o(/ti du/o o)rthai=s, ei) mê\ _to\n

sophistiko\n tro/pon_ ou)de\ katho/lou tri/gônon, ou)/d' ei) mêde/n

e)sti para\ tau=ta tri/gônon e(/teron.] The phrase [Greek: to\n

sophistiko\n tro/pon] is equivalent to [Greek: to\n sophistiko\n

**tro/pon to\n kata\ sumbebêko/s], p. 71, b. 10. I see nothing

in it connected with Aristotle's characteristic of a Sophist (special

professional life purpose--[Greek: tou= bi/ou tê=| proaire/sei],

Metaphys. [Greek: G]. p. 1004, b. 24): the phrase means nothing more

than _unscientific_.]

[Footnote 20: Aristot. Analyt Post I. v. p. 74, a. 32-b. 4.]

In every demonstration the _principia_ or premisses must be not only

true, but necessarily true; the conclusion also will then be

necessarily true, by reason of the premisses, and this constitutes

Demonstration. Wherever the premisses are necessarily true, the

conclusion will be necessarily true; but you cannot say, _vice

versâ_, that wherever the conclusion is necessarily true, the

syllogistic premisses from which it follows must always be

necessarily true. They may be true without being necessarily true, or

they may even be false: if, then, the conclusion be necessarily true,

it is not so by reason of these premisses; and the syllogistic proof

is in this case no demonstration. Your syllogism may have true

premisses and may lead to a conclusion which is true by reason of

them; but still you have not demonstrated, since neither premisses

nor conclusion are _necessarily_ true.[21] When an opponent contests

your demonstration, he succeeds if he can disprove the _necessity_ of

your conclusion; if he can show any single case in which it either is

or may be false.[22] It is not enough to proceed upon a premiss which

is either probable or simply true: it may be true, yet not

appropriate to the case: you must take your departure from the first

or highest universal of the genus about which you attempt to

demonstrate.[23] Again, unless you can state the _why_ of your

conclusion; that is to say, unless the middle term, by reason of

which the conclusion is necessarily true, be itself necessarily

true,--you have not demonstrated it, nor do you know it absolutely.

Your middle term not being necessary may vanish, while the conclusion

to which it was supposed to lead abides: in truth no conclusion was

known through that middle.[24] In the complete demonstrative or

scientific syllogism, the major term must be predicable essentially

or _per se_ of the middle, and the middle term must be predicable

essentially or _per se_ of the minor; thus alone can you be sure that

the conclusion also is _per se_ or necessary. The demonstration

cannot take effect through a middle term which is merely a Sign; the

sign, even though it be a constant concomitant, yet being not, or at

least not known to be, _per se_, will not bring out the _why_ of the

conclusion, nor make the conclusion necessary. Of non-essential

concomitants altogether there is no demonstration; wherefore it might

seem to be useless to put questions about such; yet, though the

questions cannot yield necessary premisses for a demonstrative

conclusion, they may yield premisses from which a conclusion will

necessarily follow.[25]