Here then are four separate rules laid down, one for each variety of

propositions. The rules for the second and third variety are proved

by the rule for the first (the Universal Negative), which is thus the

basis of all. But how does Aristotle prove the rule for the Universal

Negative itself? He proceeds as follows: "If A cannot be predicated

of any one among the B's, neither can B be predicated of any one

among the A's. For if it could be predicated of any one among them

(say C), the proposition that A cannot be predicated of any B would

not be true; since C is one among the B's."[13] Here we have a proof

given which is no proof at all. If I disbelieved or doubted the

proposition to be proved, I should equally disbelieve or doubt the

proposition given to prove it. The proof only becomes valid, when you

add a farther assumption which Aristotle has not distinctly

enunciated, viz.: That if some A (_e.g._ C) is B, then some B must

also be A; which would be contrary to the fundamental supposition.

But this farther assumption cannot be granted here, because it would

imply that we already know the rule respecting the convertibility of

Particular Affirmatives, viz., that they admit of being converted

simply. Now the rule about Particular Affirmatives is afterwards

itself proved by help of the preceding demonstration respecting the

Universal Negative. As the proof stands, therefore, Aristotle

demonstrates each of these by means of the other; which is not

admissible.[14]

[Footnote 13: Ibid. p. 25, a. 15: [Greek: ei) ou)=n mêdeni\ tô=n B

to\ A u(pa/rchei, ou)de\ tô=n A ou)deni\ u(pa/rxei to\ B. ei) ga\r

tini, oi(=on tô=| G, ou)k a)lêthe\s e)/stai to\ mêdeni\ tô=n B to\ A

u(pa/rchein; to\ ga\r G tô=n B ti/ e)stin.]

Julius Pacius (p. 129) proves the Universal Negative to be

convertible _simpliciter_, by a _Reductio ad Absurdum_ cast into a

syllogism in the First figure. But it is surely unphilosophical to

employ the rules of Syllogism as a means of proving the legitimacy of

Conversion, seeing that we are forced to assume conversion in our

process for distinguishing valid from invalid syllogisms. Moreover

the _Reductio ad Absurdum_ assumes the two fundamental Maxims of

Contradiction and Excluded Middle, though these are less obvious, and

stand more in need of proof than the simple conversion of the

Universal Negative, the point that they are brought to establish.]

[Footnote 14: Waitz, in his note (p. 374), endeavours, but I think

without success, to show that Aristotle's proof is not open to the

criticism here advanced. He admits that it is obscurely indicated,

but the amplification of it given by himself still remains exposed to

the same objection.]

Even the friends and companions of Aristotle were not satisfied with

his manner of establishing this fundamental rule as to the conversion

of propositions. Eudêmus is said to have given a different proof; and

Theophrastus assumed as self-evident, without any proof, that the

Universal Negative might always be converted simply.[15] It appears

to me that no other or better evidence of it can be offered, than the

trial upon particular cases, that is to say, Induction.[16] Nothing

is gained by dividing (as Aristotle does) the whole A into parts, one

of which is C; nor can I agree with Theophrastus in thinking that

every learner would assent to it at first hearing, especially at a

time when no universal maxims respecting the logical value of

propositions had ever been proclaimed. Still less would a Megaric

dialectician, if he had never heard the maxim before, be satisfied to

stand upon an alleged _à priori_ necessity without asking for

evidence. Now there is no other evidence except by exemplifying the

formula, No A is B, in separate propositions already known to the

learner as true or false, and by challenging him to produce any one

case, in which, when it is true to say No A is B, it is not equally

true to say, No B is A; the universality of the maxim being liable to

be overthrown by any one contradictory instance.[17] If this proof

does not convince him, no better can be produced. In a short time,

doubtless, he will acquiesce in the general formula at first hearing,

and he may even come to regard it as self-evident. It will recall to

his memory an aggregate of separate cases each individually

forgotten, summing up their united effect under the same aspect, and

thus impressing upon him the general truth as if it were not only

authoritative but self-authorized.

[Footnote 15: See the Scholia of Alexander on this passage, p. 148,

a. 30-45, Brandis; Eudemi Fragm. ci.-cv. pp. 145-149, ed. Spengel.]

[Footnote 16: We find Aristotle declaring in Topica, II. viii. p.

113, b. 15, that in converting a true Universal Affirmative

proposition, the negative of the Subject of the convertend is always

true of the negative of the Predicate of the convertend; _e.g._ If

every man is an animal, every thing which is not an animal is not a

man. This is to be assumed (he says) upon the evidence of

Induction--uncontradicted iteration of particular cases, extended to

all cases universally--[Greek: lamba/nein d' e)x e)pagôgê=s, oi(=on

ei) o( a)/nthrôpos zô=|on, to\ mê\ zô=|on ou)k a)/nthrôpos; o(moi/ôs

de\ kai\ e)pi\ tô=n a)/llôn. . . . . e)pi\ pa/ntôn ou)=n to\

toiou=ton a)xiôte/on.]

The rule for the simple conversion of the Universal Negative rests

upon the same evidence of Induction, never contradicted.]

[Footnote 17: Dr. Wallis, in one of his acute controversial treatises

against Hobbes, remarks upon this as the process pursued by Euclid in

his demonstrations:--"You tell us next that an Induction, without

enumeration of all the particulars, is not sufficient to infer a

conclusion. Yes, Sir, if after the enumeration of some particulars,

there comes a general clause, _and the like in other cases_ (as here

it doth), this may pass for a proofe till there be a possibility of

giving some instance to the contrary, which here you will never be

able to doe. And if such an Induction may not pass for proofe, there

is never a proposition in Euclid demonstrated. For all along he takes

no other course, or at least grounds his Demonstrations on

Propositions no otherwise demonstrated. As, for instance, he

proposeth it in general (i. c. 1.)--_To make an equilateral triangle

on a line given_. And then he shows you how to do it upon the line A

B, which he there shows you, and leaves you to supply: _And the same,

by the like means, may be done upon any other strait line_; and then

infers his general conclusion. Yet I have not heard any man object

that the Induction was not sufficient, because he did not actually

performe it in all lines possible."--(Wallis, Due Correction to Mr.

Hobbes, Oxon. 1656, sect. v. p. 42.) This is induction by _parity of

reasoning_.

So also Aristot. Analyt. Poster. I. iv. p. 73, b. 32: [Greek: to\

katho/lou de\ u(pa/rchei to/te, o(/tan e)pi\ tou= tucho/ntos kai\

prô/tou deiknu/êtai.]]

Aristotle passes next to Affirmatives, both Universal and Particular.

First, if A can be predicated of all B, then B can be predicated of

_some_ A; for if B cannot be predicated of any A, then (by the rule

for the Universal Negative) neither can A be predicated of any B.

Again, if A can be predicated of some B, in this case also, and for

the same reason, B can be predicated of some A.[18] Here the rule for

the Universal Negative, supposed already established, is applied

legitimately to prove the rules for Affirmatives. But in the first

case, that of the Universal, it fails to prove _some_ in the sense of

_not-all_ or _some-at-most_, which is required; whereas, the rules

for both cases can be proved by Induction, like the formula about the

Universal Negative. When we come to the Particular Negative,

Aristotle lays down the position, that it does not admit of being

necessarily converted in any way. He gives no proof of this, beyond

one single exemplification: If some animal is not a man, you are not

thereby warranted in asserting the converse, that some man is not an

animal.[19] It is plain that such an exemplification is only an

appeal to Induction: you produce one particular example, which is

entering on the track of Induction; and one example alone is

sufficient to establish the negative of an universal proposition.[20]

The converse of a Particular Negative is not in all cases true,

though it may be true in many cases.

[Footnote 18: Aristot. Analyt. Prior. I. ii. p. 25, a. 17-22.]

[Footnote 19: Ibid. p. 25, a. 22-26.]

[Footnote 20: Though some may fancy that the rule for converting the

Universal Negative is intuitively known, yet every one must see that

the rule for converting the Universal Affirmative is not thus

self-evident, or derived from natural intuition. In fact, I believe

that every learner at first hears it with great surprise. Some are

apt to fancy that the Universal Affirmative (like the Particular

Affirmative) may be converted _simply_. Indeed this error is not

unfrequently committed in actual reasoning; all the more easily,

because there is a class of cases (with subject and predicate

co-extensive) where the converse of the Universal Affirmative _is_

really true. Also, in the case of the Particular Negative, there are

many true propositions in which the simple converse is true. A novice

might incautiously generalize upon those instances, and conclude that

both were convertible simply. Nor could you convince him of his error

except by producing examples in which, when a true proposition of

this kind is converted simply, the resulting converse is notoriously

false. The appeal to various separate cases is the only basis on

which we can rest for testing the correctness or incorrectness of all

these maxims proclaimed as universal.]

From one proposition taken singly, no new proposition can be

inferred; for purposes of inference, two propositions at least are

required.[21] This brings us to the rules of the Syllogism, where two

propositions as premisses conduct us to a third which necessarily

follows from them; and we are introduced to the well-known three

Figures with their various Modes.[22] To form a valid Syllogism,

there must be three terms and no more; the two, which appear as

Subject and Predicate of the conclusion, are called the _minor_ term

(or minor extreme) and the _major_ term (or major extreme)

respectively; while the third or _middle_ term must appear in each of

the premisses, but not in the conclusion. These terms are called

_extremes_ and _middle_, from the position which they occupy in every

perfect Syllogism--that is in what Aristotle ranks as the First among

the three figures. In _his_ way of enunciating the Syllogism, this

middle position formed a conspicuous feature; whereas the modern

arrangement disguises it, though the denomination _middle_ term is

still retained. Aristotle usually employs letters of the alphabet,

which he was the first to select as abbreviations for exposition;[23]

and he has two ways (conforming to what he had said in the first

chapter of the present treatise) of enunciating the modes of the

First figure. In one way, he begins with the major extreme (Predicate

of the conclusion): A may be predicated of all B, B may be predicated

of all C; therefore, A may be predicated of all C (Universal

Affirmative). Again, A cannot be predicated of any B, B can be

predicated of all C; therefore, A cannot be predicated of any C

(Universal Negative). In the other way, he begins with the minor term

(Subject of the conclusion): C is in the whole B, B is in the whole

A; therefore, C is in the whole A (Universal Affirmative). And, C is

in the whole B, B is not in the whole A; therefore, C is not in the

whole A (Universal Negative). We see thus that in Aristotle's way of

enunciating the First figure, the middle term is really placed

between the two extremes,[24] though this is not so in the Second and

Third figures. In the modern way of enunciating these figures, the

middle term is never placed between the two extremes; yet the

denomination _middle_ still remains.

[Footnote 21: Analyt. Prior. I. xv. p. 34, a. 17; xxiii. p. 40, b.

35; Analyt. Poster. I. iii. p. 73, a. 7.]

[Footnote 22: Aristot. Analyt. Prior. I. iv. p. 25, b. 26, seq.]

[Footnote 23: M. Barthélemy St. Hilaire (Logique d'Aristote, vol. ii.

p. 7, n.), referring to the examples of Conversion in chap. ii.,

observes:--"Voici le prémier usage des lettres représentant des

idées; c'est un procédé tout à fait algébrique, c'est à dire, de

généralisation. Déjà, dans l'Herméneia, ch. 13, § 1 et suiv.,

Aristote a fait usage de tableaux pour représenter sa pensée

relativement à la consécution des modales. Il parle encore

spécialement de figures explicatives, liv. 2. des Derniers

Analytiques, ch. 17, § 7. Vingt passages de l'Histoire des Animaux

attestent qu'il joignait des dessins à ses observations et à ses

théories zoologiques. Les illustrations pittoresques datent donc de

fort loin. L'emploi symbolique des lettres a été appliqué aussi par

Aristote à la Physique. Il l'avait emprunté, sans doute, aux procédés

des mathématiciens."

We may remark, however, that when Aristotle proceeds to specify those

combinations of propositions which _do not_ give a valid conclusion,

he is not satisfied with giving letters of the alphabet; he superadds

special illustrative examples (Analyt. Prior. I. v. p. 27, a. 7, 12,

34, 38).]

[Footnote 24: Aristot. Analyt. Prior. I. iv. p. 25, b. 35: [Greek:

kalô= de\ _me/son_, o(\ kai\ au)to\ e)n a)/llô| kai\ a)/llo e)n

tou/tô| e)sti/n, o(\ kai\ tê=| the/sei gi/netai me/son.]]

The Modes of each figure are distinguished by the different character

and relation of the two premisses, according as these are either

affirmative or negative, either universal or particular. Accordingly,

there are four possible varieties of each, and sixteen possible modes

or varieties of combinations between the two. Aristotle goes through

most of the sixteen modes, and shows that in the first Figure there

are only four among them that are legitimate, carrying with them a

necessary conclusion. He shows, farther, that in all the four there

are two conditions observed, and that both these conditions are

indispensable in the First figure:--(1) The major proposition must be

universal, either affirmative or negative; (2) The minor proposition

must be affirmative, either universal or particular or indefinite.

Such must be the character of the premisses, in the first Figure,

wherever the conclusion is valid and necessary; and _vice versâ_, the

conclusion will be valid and necessary, when such is the character of

the premisses.[25]

[Footnote 25: Aristot. Analyt. Prior. I. iv. p. 26, b. 26, et sup.]

In regard to the four valid modes (_Barbara_, _Celarent_, _Darii_,

_Ferio_, as we read in the scholastic Logic) Aristotle declares at

once in general language that the conclusion follows necessarily;

which he illustrates by setting down in alphabetical letters the

skeleton of a syllogism in _Barbara_. If A is predicated of all B,

and B of all C, A must necessarily be predicated of all C. But he

does not justify it by any real example; he produces no special

syllogism with real terms, and with a conclusion known beforehand to

be true. He seems to think that the general doctrine will be accepted

as evident without any such corroboration. He counts upon the

learner's memory and phantasy for supplying, out of the past

discourse of common life, propositions conforming to the conditions

in which the symbolical letters have been placed, and for not

supplying any contradictory examples. This might suffice for a

treatise; but we may reasonably believe that Aristotle, when teaching

in his school, would superadd illustrative examples; for the doctrine

was then novel, and he is not unmindful of the errors into which

learners often fall spontaneously.[26]

[Footnote 26: Analyt. Poster. I. xxiv. p. 85, b. 21.]

When he deals with the remaining or invalid modes of the First

figure, his manner of showing their invalidity is different, and in

itself somewhat curious. "If (he says) the major term is affirmed of

all the middle, while the middle is denied of all the minor, no

necessary consequence follows from such being the fact, nor will

there be any syllogism of the two extremes; for it is equally

possible, either that the major term may be affirmed of all the

minor, or that it may be denied of all the minor; so that no

conclusion, either universal or particular, is necessary in all

cases."[27] Examples of such double possibility are then exhibited:

first, of three terms arranged in two propositions (A and E), in

which, from the terms specially chosen, the major happens to be truly

affirmable of all the minor; so that the third proposition is an

universal Affirmative:--

Major and }

} Animal is predicable of every Man;

Middle. }

Middle and }

} Man is not predicable of any Horse;

Minor }

Major and }

} Animal is predicable of every Horse.

Minor }

Next, a second example is set out with new terms, in which the major

happens not to be truly predicable of any of the minor; thus

exhibiting as third proposition an universal Negative:--

Major and }

} Animal is predicable of every Man;

Middle. }

Middle and }

} Man is not predicable of any Stone;

Minor }

Major and }

} Animal is not predicable of any Stone.

Minor }

Here we see that the full exposition of a syllogism is indicated with

real terms common and familiar to every one; alphabetical symbols

would not have sufficed, for the learner must himself recognize the

one conclusion as true, the other as false. Hence we are taught that,

after two premisses thus conditioned, if we venture to join together

the major and minor so as to form a pretended conclusion, we may in

some cases obtain a true proposition universally Affirmative, in

other cases a true proposition universally Negative. Therefore

(Aristotle argues) there is no one necessary conclusion, the same in

all cases, derivable from such premisses; in other words, this mode

of syllogism is invalid and proves nothing. He applies the like

reasoning to all the other invalid modes of the first Figure; setting

them aside in the same way, and producing examples wherein double and

opposite conclusions (improperly so called), both true, are obtained

in different cases from the like arrangement of premisses.

[Footnote 27: Analyt. Prior. I. iv. p. 26, a. 2, seq.]

This mode of reasoning plainly depends upon an appeal to prior

experience. The validity or invalidity of each mode of the First

figure is tested by applying it to different particular cases, each

of which is familiar and known to the learner _aliunde_; in one case,

the conjunction of the major and minor terms in the third proposition

makes an universal Affirmative which he knows to be true; in another

case, the like conjunction makes an universal Negative, which he also

knows to be true; so that there is no one _necessary_ (_i.e._ no one

uniform and trustworthy) conclusion derivable from such

premisses.[28] In other words, these modes of the First figure are

not valid or available in form; the negation being sufficiently

proved by one single undisputed example.

[Footnote 28: Though M. Barthélemy St. Hilaire (note, p. 19) declares

Aristotle's exposition to be a model of analysis, it appears to me

that the grounds for disallowing this invalid mode of the First

figure (A--E--A, or A--E--E) are not clearly set forth by Aristotle

himself, while they are rendered still darker by some of his best

commentators. Thus Waitz says (p. 381): "Per exempla allata probat

(Aristoteles) quod demonstrare debebat ex ipsâ ratione quam singuli

termini inter se habeant: est enim proprium artis logicæ, ut

terminorum rationem cognoscat, dum res ignoret. Num de Caio

prædicetur animal nescit, scit de Caio prædicari animal, si animal de

homine et homo de Caio prædicetur."

This comment of Waitz appears to me founded in error. Aristotle had

no means of shewing the invalidity of the mode A E in the First

figure, except by an appeal to particular examples. The invalidity of

the invalid modes, and the validity of the valid modes, rest alike

upon this ultimate reference to examples of propositions known to be

true or false, by prior experience of the learner. The valid modes

are those which will stand this trial and verification; the invalid

modes are those which will not stand it. Not till such verification

has been made, is one warranted in generalizing the result, and

enunciating a formula applicable to unknown particulars (rationem

terminorum cognoscere, dum res ignoret). It was impossible for

Aristotle to do what Waitz requires of him. I take the opposite

ground, and regret that he did not set forth the fundamental test of

appeal to example and experience, in a more emphatic and

unmistakeable manner.

M. Barthélemy St. Hilaire (in the note to his translation, p. 14)

does not lend any additional clearness, when he talks of the

"_conclusion_" from the propositions A and E in the First figure.

Julius Pacius says (p. 134): "Si tamen _conclusio_ dici debet, quæ

non colligitur ex propositionibus," &c. Moreover, M. St. Hilaire (p.

19) slurs over the legitimate foundation, the appeal to experience,

much as Aristotle himself does: "Puis prenant des exemples où la

_conclusion est de toute évidence_, Aristote les applique

successivement à chacune de ces combinaisons; celles qui donnent la

_conclusion fournie d'ailleurs par le bon sens_, sont concluantes ou

syllogistiques, les autres sont asyllogistiques."]

We are now introduced to the Second figure, in which each of the two

premisses has the middle term as Predicate.[29] To give a legitimate

conclusion in this figure, one or other of the premisses must be

negative, and the major premiss must be universal; moreover no

affirmative conclusions can ever be obtained in it--none but negative

conclusions, universal or particular. In this Second figure too,

Aristotle recognizes four valid modes; setting aside the other

possible modes as invalid[30] (in the same way as he had done in the

First figure), because the third proposition or conjunction of the

major term with the minor, might in some cases be a true universal

affirmative, in other cases a true universal negative. As to the

third and fourth of the valid modes, he demonstrates them by assuming

the contradictory of the conclusion, together with the major premiss,

and then showing that these two premisses form a new syllogism, which

leads to a conclusion contradicting the minor premiss. This method,

called _Reductio ad Impossibile_, is here employed for the first

time; and employed without being ushered in or defined, as if it were

familiarly known.[31]

[Footnote 29: Analyt. Prior. I. v. p. 26, b. 34. As Aristotle

enunciates a proposition by putting the predicate before the subject,

he says that in this Second figure the middle term comes [Greek:

prô=ton tê=| the/sei]. In the Third figure, for the same reason, he

calls it [Greek: e)/schaton tê=| the/sei], vi. p. 28, a. 15.]

[Footnote 30: Analyt. Prior. I. v. p. 27, a. 18. In these invalid

modes, Aristotle says there is no _syllogism_; therefore we cannot

properly speak of a _conclusion_, but only of a third proposition,

conjoining the major with the minor.]

[Footnote 31: Ibid. p. 27, a. 15, 26, seq. It is said to involve

[Greek: u(po/thesis], p. 28, a. 7; to be [Greek: e)x u(pothe/seôs]

xxiii. p. 41, a. 25; to be [Greek: tou= e)x u(pothe/seôs], as opposed

to [Greek: deiktiko/s], xxiii. p. 40, b. 25.

M. B. St. Hilaire remarks justly, that Aristotle might be expected to

define or explain what it is, on first mentioning it (note, p. 22).]

Lastly, we have the Third figure, wherein the middle term is the

Subject in both premisses. Here one at least of the premisses must be

universal, either affirmative or negative. But no universal

conclusions can be obtained in this figure; all the conclusions are

particular. Aristotle recognizes six legitimate modes; in all of

which the conclusions are particular, four of them being affirmative,

two negative. The other possible modes he sets aside as in the two

preceding figures.[32]

[Footnote 32: Ibid. I. vi. p. 28, a. 10-p. 29, a. 18.]

But Aristotle assigns to the First figure a marked superiority as

compared with the Second and Third. It is the only one that yields

perfect syllogisms; those furnished by the other two are all

imperfect. The cardinal principle of syllogistic proof, as he

conceives it, is--That whatever can be affirmed or denied of a whole,

can be affirmed or denied of any part thereof.[33] The major

proposition affirms or denies something universally respecting a

certain whole; the minor proposition declares a certain part to be

included in that whole. To this principle the four modes of the First

figure manifestly and unmistakably conform, without any

transformation of their premisses. But in the other figures such

conformity does not obviously appear, and must be demonstrated by

reducing their syllogisms to the First figure; either ostensively by

exposition of a particular case, and conversion of the premisses, or

by _Reductio ad Impossibile_. Aristotle, accordingly, claims

authority for the Second and Third figures only so far as they can be

reduced to the First.[34] We must, however, observe that in this

process of reduction no new evidence is taken in; the matter of

evidence remains unchanged, and the form alone is altered, according

to laws of logical conversion which Aristotle has already laid down

and justified. Another ground of the superiority and perfection which

he claims for the First figure, is, that it is the only one in which

every variety of conclusion can be proved; and especially the only

one in which the Universal Affirmative can be proved--the great aim

of scientific research. Whereas, in the Second figure we can prove

only _negative_ conclusions, universal or particular; and in the

Third figure only _particular_ conclusions, affirmative or

negative.[35]

[Footnote 33: Ibid. I. xli. p. 49, b. 37: [Greek: o(/lôs ga\r o(\ mê/

e)stin ô(s o(/lon pro\s me/ros kai\ a)/llo pro\s tou=to ô(s me/ros

pro\s o(/lon, e)x ou)deno\s tô=n toiou/tôn dei/knusin o( deiknu/ôn,

ô(/ste ou)de\ gi/netai sullogismo/s.]

He had before said this about the relation of the three terms in the

Syllogism, I. iv. p. 25, b. 32: [Greek: o(/tan o(/roi trei=s ou(/tôs

e)/chôsi pro\s a)llê/lous ô(/ste to\n e)/schaton e)n o(/lô| ei)=nai

tô=| me/sô| kai\ to\n me/son e)n o(/lô| tô=| prô/tô| ê)\ ei)=nai ê)\

mê\ ei)=nai, a)na/gkê tô=n a)/krôn ei)=nai sullogismo\n te/leion]

(_Dictum de Omni et Nullo_).]

[Footnote 34: Analyt. Prior. I. vii. p. 29, a. 30-b. 25.]

[Footnote 35: Ibid. I. iv. p. 26, b. 30, p. 27, a. 1, p. 28, a. 9, p.

29, a. 15. An admissible syllogism in the Second or Third figure is

sometimes called [Greek: dunato\s] as opposed to [Greek: te/leios],

p. 41, b. 33. Compare Kampe, Die Erkenntniss-Theorie des Aristoteles,

p. 245, Leipzig, 1870.]

Such are the main principles of syllogistic inference and rules for

syllogistic reasoning, as laid down by Aristotle. During the mediæval

period, they were allowed to ramify into endless subtle

technicalities, and to absorb the attention of teachers and studious

men, long after the time when other useful branches of science and

literature were pressing for attention. Through such prolonged

monopoly--which Aristotle, among the most encyclopedical of all

writers, never thought of claiming for them--they have become so

discredited, that it is difficult to call back attention to them as

they stood in the Aristotelian age. We have to remind the reader,

again, that though language was then used with great ability for

rhetorical and dialectical purposes, there existed as yet hardly any

systematic or scientific study of it in either of these branches. The

scheme and the terminology of any such science were alike unknown,

and Aristotle was obliged to construct it himself from the

foundation. The rhetorical and dialectical teaching as then given (he

tells us) was mere unscientific routine, prescribing specimens of art

to be committed to memory: respecting syllogism (or the conditions of

legitimate deductive inference) absolutely nothing had been said.[36]

Under these circumstances, his theory of names, notions, and

propositions as employed for purposes of exposition and

ratiocination, is a remarkable example of original inventive power.

He had to work it out by patient and laborious research. No way was

open to him except the diligent comparison and analysis of

propositions. And though all students have now become familiar with

the various classes of terms and propositions, together with their

principal characteristics and relations, yet to frame and designate

such classes for the first time without any precedent to follow, to

determine for each the rules and conditions of logical

convertibility, to put together the constituents of the Syllogism,

with its graduation of Figures and difference of Modes, and with a

selection, justified by reasons given, between the valid and the

invalid modes--all this implies a high order of original

systematizing genius, and must have required the most laborious and

multiplied comparisons between propositions in detail.

[Footnote 36: Aristot. Sophist. Elench. p. 184, a. 1, b. 2: [Greek:

dio/per tachei=a me\n a)/technos d' ê)=n ê( didaskali/a toi=s

mantha/nousi par' au)tô=n; ou) ga\r te/chnên a)lla\ ta\ a)po\ tê=s

te/chnês dido/ntes paideu/ein u(pela/mbanon . . . . _peri\ de\ tou=

sullogi/zesthai pantelô=s ou)de\n ei)/chomen pro/teron a)/llo

le/gein, a)ll' ê)\ tribê=| zêtou=ntes polu\n chro/non e)ponou=men_.]]

The preceding abridgment of Aristotle's exposition of the Syllogism

applies only to propositions simply affirmative or simply negative.

But Aristotle himself, as already remarked, complicates the

exposition by putting the Modal propositions (Possible, Necessary)

upon the same line as the above-mentioned Simple propositions. I have

noticed, in dealing with the treatise De Interpretatione, the

confusion that has arisen from thus elevating the Modals into a line

of classification co-ordinate with propositions simply Assertory. In

the Analytica, this confusion is still more sensibly felt, from the

introduction of syllogisms in which one of the premisses is

necessary, while the other is only possible. We may remark, however,

that, in the Analytica, Aristotle is stricter in defining the

Possible than he has been in the De Interpretatione; for he now

disjoins the Possible altogether from the Necessary, making it

equivalent to the Problematical (not merely _may be_, but _may be or

may not be_).[37] In the middle, too, of his diffuse exposition of

the Modals, he inserts one important remark, respecting universal

propositions generally, which belongs quite as much to the preceding

exposition about propositions simply assertory. He observes that

universal propositions have nothing to do with time, present, past,

or future; but are to be understood in a sense absolute and

unqualified.[38]

[Footnote 37: Analyt. Prior. I. viii. p. 29, a. 32; xiii. p. 32, a.

20-36: [Greek: to\ ga\r a)nagkai=on o(mônu/môs e)nde/chesthai

le/gomen]. In xiv. p. 33, b. 22, he excludes this equivocal meaning

of [Greek: to\ e)ndecho/menon--dei= de\ to\ e)nde/chestha lamba/nein

mê\ e)n toi=s a)nagkai/ois, a)lla\ kata\ to\n ei)rême/non

diorismo/n.] See xiii. p. 32, a. 33, where [Greek: to\ e)nde/chesthai

u(pa/rchein] is asserted to be equivalent to or convertible with

[Greek: to\ e)nde/chesthai mê\ u(pa/rchein]; and xix. p. 38, a. 35:

[Greek: to\ e)x a)na/gkês ou)k ê)=n _e)ndecho/menon_]. Theophrastus

and Eudemus differed from Aristotle about his theory of the Modals in

several points (Scholia ad Analyt. Priora, pp. 161, b. 30; 162, b.

23; 166, a. 12, b. 15, Brand.). Respecting the want of clearness in

Aristotle about [Greek: to\ e)ndecho/menon], see Waitz's note **ad p.

32, b. 16. Moreover, he sometimes uses [Greek: u(pa/rchon] in the

widest sense, including [Greek: e)ndecho/menon] and [Greek:

a)nagkai=on], xxiii. p. 40, b. 24.]

[Footnote 38: Analyt. Prior. I. xv. p. 34, b. 7.]

Having finished with the Modals, Aristotle proceeds to lay it down,

that all demonstration must fall under one or other of the three

figures just described; and therefore that all may be reduced

ultimately to the two first modes of the First figure. You cannot

proceed a step with two terms only and one proposition only. You must

have two propositions including three terms; the middle term

occupying the place assigned to it in one or other of the three

figures.[39] This is obviously true when you demonstrate by direct or

ostensive syllogism; and it is no less true when you proceed by

_Reductio ad Impossibile_. This last is one mode of syllogizing from

an hypothesis or assumption:[40] your conclusion being disputed, you

prove it indirectly, by assuming its contradictory to be true, and

constructing a new syllogism by means of that contradictory together

with a second premiss admitted to be true; the conclusion of this new

syllogism being a proposition obviously false or known beforehand to

be false. Your demonstration must be conducted by a regular

syllogism, as it is when you proceed directly and ostensively. The

difference is, that the conclusion which you obtain is not that which

you wish ultimately to arrive at, but something notoriously false.

But as this false conclusion arises from your assumption or

hypothesis that the contradictory of the conclusion originally

disputed was true, you have indirectly made out your case that this

contradictory must have been false, and therefore that the conclusion

originally disputed was true. All this, however, has been

demonstration by regular syllogism, but starting from an hypothesis

assumed and admitted as one of the premisses.[41]

[Footnote 39: Ibid. xxiii. p. 40, b. 20, p. 41, a. 4-20.]

[Footnote 40: Ibid. p. 40, b. 25: [Greek: e)/ti ê)\ deiktikô=s ê)\

e)x u(pothe/seôs; tou= d' _e)x u(pothe/seôs_ me/ros to\ dia\ tou=

a)duna/tou.]]

[Footnote 41: Ibid. p. 41, b. 23: [Greek: pa/ntes ga\r oi( dia\ tou=

a)duna/tou perai/nontes to\ me\n pseu=dos sullogi/zontai, to\ d' e)x

a)rchê=s _e)x u(pothe/seôs_ deiknu/ousin, o(/tan a)du/nato/n ti

sumbai/nê| tê=s a)ntipha/seôs tethei/sês.]

It deserves to be remarked that Aristotle uses the phrase [Greek:

sullogismo\s _e)x u(pothe/seôs_], not [Greek: sullogismo\s

u(pothetiko/s]. This bears upon the question as to his views upon

what subsequently received the title of _hypothetical syllogisms_;

a subject to which I shall advert in a future note.]

Aristotle here again enforces what he had before urged--that in every

valid syllogism, one premiss at least must be affirmative, and one

premiss at least must be universal. If the conclusion be universal,

both premisses must be so likewise; if it be particular, one of the

premisses may not be universal. But without one universal premiss at

least, there can be no syllogistic proof. If you have a thesis to

support, you cannot assume (or ask to be conceded to you) that very

thesis, without committing _petitio principii,_ (_i.e._ _quæsiti_ or

_probandi_); you must assume (or ask to have conceded to you) some

universal proposition containing it and more besides; under which

universal you may bring the subject of your thesis as a minor, and

thus the premisses necessary for supporting it will be completed.

Aristotle illustrates this by giving a demonstration that the angles

at the base of an isosceles triangle are equal; justifying every step

in the reasoning by an appeal to some universal proposition.[42]

[Footnote 42: Analyt. Prior. I. xxiv. p. 41, b. 6-31. The

demonstration given (b. 13-22) is different from that which we read

in Euclid, and is not easy to follow. It is more clearly explained by

Waitz (p. 434) than either by Julius Pacius or by M. Barth. St.

Hilaire (p. 108).]

Again, every demonstration is effected by two propositions (an _even_

number) and by three terms (an _odd_ number); though the same

proposition may perhaps be demonstrable by more than one pair of

premisses, or through more than one middle term;[43] that is, by two

or more distinct syllogisms. If there be more than three terms and

two propositions, either the syllogism will no longer be one but

several; or there must be particulars introduced for the purpose of

obtaining an universal by induction; or something will be included,

superfluous and not essential to the demonstration, perhaps for the

purpose of concealing from the respondent the real inference

meant.[44] In the case (afterwards called _Sorites_) where the

ultimate conclusion is obtained through several mean terms in

continuous series, the number of terms will always exceed by one the

number of propositions; but the numbers may be odd or even, according

to circumstances. As terms are added, the total of intermediate

conclusions, if drawn out in form, will come to be far greater than

that of the terms or propositions, multiplying as it will do in an

increasing ratio to them.[45]

[Footnote 43: Ibid. I. xxv. p. 41, b. 36, seq.]

[Footnote 44: Ibid. xxv. p. 42, a. 23: [Greek: ma/tên e)/stai

ei)lêmme/na, ei) mê\ e)pagôgê=s ê)\ kru/pseôs ê)/ tinos a)/llou tô=n

toiou/tôn cha/rin.] Ib. a. 38: [Greek: ou(=tos o( lo/gos ê)\ ou)

sullelo/gistai ê)\ plei/ô tô=n a)nagkai/ôn ê)rô/têke pro\s tê\n

the/sin.]]

[Footnote 45: Ibid. p. 42, b. 5-26.]

It will be seen clearly from the foregoing remarks that there is a

great difference between one thesis and another as to facility of

attack or defence in Dialectic. If the thesis be an Universal

Affirmative proposition, it can be demonstrated only in the First

figure, and only by one combination of premisses; while, on the other

hand, it can be impugned either by an universal negative, which can

be demonstrated both in the First and Second figures, or by a

particular negative, which can be demonstrated in all the three

figures. Hence an Universal Affirmative thesis is at once the hardest

to defend and the easiest to oppugn: more so than either a Particular

Affirmative, which can be proved both in the First and Third figures;

or a Universal Negative, which can be proved either in First or

Second.[46] To the opponent, an universal thesis affords an easier

victory than a particular thesis; in fact, speaking generally, his

task is easier than that of the defendant.

[Footnote 46: Analyt. Prior. I. xxvi. p. 42, b. 27, p. 43, a. 15.]

In the Analytica Priora, Aristotle proceeds to tell us that he

contemplates not only theory, but also practice and art. The reader

must be taught, not merely to understand the principles of Syllogism,

but likewise where he can find the matter for constructing syllogisms

readily, and how he can obtain the principles of demonstration

pertinent to each thesis propounded.[47]

[Footnote 47: Ibid. I. xxvii. p. 43, a. 20: [Greek: pô=s d'

eu)porê/somen au)toi\ pro\s to\ tithe/menon a)ei\ sullogismô=n, kai\

dia\ poi/as o(dou= lêpso/metha ta\s peri\ e(/kaston a)rcha/s, nu=n

ê)/dê lekte/on; ou) ga\r mo/non i)/sôs dei= tê\n ge/nesin theôrei=n

tô=n sullogismô=n, a)lla\ kai\ tê\n du/namin e)/chein tou= poiei=n.]

The second section of Book I. here begins.]

A thesis being propounded in appropriate terms, with subject and

predicate, how are you the propounder to seek out arguments for its

defence? In the first place, Aristotle reverts to the distinction

already laid down at the beginning of the Categoriæ.[48] Individual

things or persons are subjects only, never appearing as

predicates--this is the lowest extremity of the logical scale: at

the opposite extremity of the scale, there are the highest

generalities, predicates only, and not subjects of any predication,

though sometimes supposed to be such, as matters of dialectic

discussion.[49] Between the lowest and highest we have intermediate

or graduate generalities, appearing sometimes as subjects, sometimes

as predicates; and it is among these that the materials both of

problems for debate, and of premisses for proof, are usually

found.[50]

[Footnote 48: Ibid. I. xxvii. p. 43, a. 25, seq.]

[Footnote 49: Ibid. p. 43, a. 39: [Greek: plê\n ei) mê\ kata\

do/xan]. Cf. Schol. of Alexander, p. 175, a. 44, Br.: [Greek:

e)ndo/xôs kai\ dialektikô=s, ô(/sper ei)=pen e)n toi=s Topikoi=s],

that even the _principia_ of science may be debated; for example, in

book B. of the Metaphysica. Aristotle does not recognize either

[Greek: to\ o)/n] or [Greek: to\ e(/n] as true genera, but only as

predicates.]

[Footnote 50: Ibid. a. 40-43.]

You must begin by putting down, along with the matter in hand itself,

its definition and its _propria_; after that, its other predicates;

next, those predicates which _cannot_ belong to it; lastly, those

other subjects, of which it may itself be predicated. You must

classify its various predicates distinguishing the essential, the

_propria_, and the accidental; also distinguishing the true and

unquestionable, from the problematical and hypothetical.[51] You must

look out for those predicates which belong to it as subject

universally, and not to certain portions of it only; since universal

propositions are indispensable in syllogistic proof, and indefinite

propositions can only be reckoned as particular. When a subject is

included in some larger genus--as, for example, man in animal--you

must not look for the affirmative or negative predicates which belong

to animal universally (since all these will of course belong to man

also) but for those which distinguish man from other animals; nor

must you, in searching for those lower subjects of which man is the

predicate, fix your attention on the higher genus animal; for animal

will of course be predicable of all those of which man is predicable.

You must collect what pertains to man specially, either as predicate

or subject; nor merely that which pertains to him necessarily and

universally, but also usually and in the majority of cases; for most

of the problems debated belong to this latter class, and the worth of

the conclusion will be co-ordinate with that of the premisses.[52]**

Do not select predicates that are predicable[53] both of the

predicate and subject; for no valid affirmative conclusion can be

obtained from them.

[Footnote 51: Analyt. Prior. I. xxvii. p. 43, b. 8: [Greek: kai\

tou/tôn poi=a doxastikô=s kai\ poi=a kat' a)lê/theian.]]

[Footnote 52: Ibid. I. xxvii. p. 43, b. 10-35.]

[Footnote 53: Ibid. b. 36: [Greek: e)/ti ta\ pa=sin e(po/mena ou)k

e)klekte/on; ou) ga\r e)/stai sullogismo\s e)x au)tô=n.] The phrase

[Greek: ta\ pa=sin e(po/mena], as denoting predicates applicable both

to the predicate and to the subject, is curious. We should hardly

understand it, if it were not explained a little further on, p. 44,

b. 21. Both the Scholiast and the modern commentators understand

[Greek: ta\ pa=sin e(po/mena] in this sense; and I do not venture to

depart from them. At the same time, when I read six lines afterwards

(p. 44, b. 26) the words [Greek: oi(=on ei) ta\ e(po/mena e(kate/rô|

tau)ta/ e)stin]--in which the same meaning as that which the

commentators ascribe to [Greek: ta\ pa=sin e(po/mena] is given in its

own special and appropriate terms, and thus the same supposition

unnecessarily repeated--I cannot help suspecting that Aristotle

intends [Greek: ta\ pa=sin e(po/mena] to mean something different; to

mean such wide and universal predicates as [Greek: to\ e(\n] and

[Greek: to\ o)/n] which soar above the Categories and apply to every

thing, but denote no real _genera_.]

Thus, when the thesis to be maintained is an universal affirmative

(_e.g._ A is predicable of all E), you will survey all the subjects

to which A will apply as predicate, and all the predicates applying

to E as subject. If these two lists coincide in any point, a middle

term will be found for the construction of a good syllogism in the

First figure. Let B represent the list of predicates belonging

universally to A; D, the list of predicates which cannot belong to

it; C, the list of subjects to which A pertains universally as

predicate. Likewise, let F represent the list of predicates belonging

universally to E; H, the list of predicates that cannot belong to E;

G, the list of subjects to which E is applicable as predicate. If,

under these suppositions, there is any coincidence between the list C

and the list F, you can construct a syllogism (in _Barbara_, Fig. 1),

demonstrating that A belongs to _all_ E; since the predicate in F

belongs to all E, and A universally to the subject in C. If the list

C coincides in any point with the list G, you can prove that A

belongs to _some_ E, by a syllogism (in _Darapti_, Fig. 3). If, on

the other hand, the list F coincides in any point with the list D,

you can prove that A cannot belong to any E: for the predicate in D

cannot belong to any A, and therefore (by converting simply the

universal negative) A cannot belong as predicate to any D; but D

coincides with F, and F belongs to all E; accordingly, a syllogism

(in _Celarent_, Fig. 1) may be constructed, shewing that A cannot

belong to any E. So also, if B coincides in any point with H, the

same conclusion can be proved; for the predicate in B belongs to all

A, but B coincides with H, which belongs to no E; whence you obtain a

syllogism (in _Camestres_, Fig. 2), shewing that no A belongs to

E.[54] In collecting the predicates and subjects both of A and of E,

the highest and most universal expression of them is to be preferred,

as affording the largest grasp for the purpose of obtaining a

suitable middle term.[55] It will be seen (as has been declared

already) that every syllogism obtained will have three terms and two

propositions; and that it will be in one or other of the three

figures above described.[56]

[Footnote 54: Analyt. Prior. I. xxviii. p. 43, b. 39-p. 44, a. 35.]

[Footnote 55: Ibid. p. 44, a. 39. Alexander and Philoponus (Scholia,

p. 177, a. 19, 39, Brandis) point out an inconsistency between what

Aristotle says here and what he had said in one of the preceding

paragraphs, dissuading the inquirer from attending to the highest

generalities, and recommending him to look only at both subject and

predicate in their special place on the logical scale. Alexander's

way of removing the inconsistency is not successful: I doubt if there

be an inconsistency. I understand Aristotle _here_ to mean only that

the universal expression KZ ([Greek: to\ katho/lou Z]) is to be

preferred to the indefinite or indeterminate (simply Z, [Greek:

a)dio/riston]), also K[Greek: G] ([Greek: to\ katho/lou G]) to simple

[Greek: G (a)dio/riston)]. This appears to me not inconsistent with

the recommendation which Aristotle had given before.]

[Footnote 56: Ibid. p. 44, b. 6-20.]

The way just pointed out is the only way towards obtaining a suitable

middle term. If, for example, you find some predicate applicable both

to A and E, this will not conduct you to a valid syllogism; you will

only obtain a syllogism in the Second figure with two affirmative

premisses, which will not warrant any conclusion. Or if you find some

predicate which cannot belong either to A or to E, this again will

only give you a syllogism in the Second figure with two negative

premisses, which leads to nothing. So also, if you have a term of

which A can be predicated, but which cannot be predicated of E, you

derive from it only a syllogism in the First figure, with its minor

negative; and this, too, is invalid. Lastly, if you have a subject,

of which neither A nor E can be predicated, your syllogism

constructed from these conditions will have both its premisses

negative, and will therefore be worthless.[57]

[Footnote 57: Analyt. Prior. I. xxviii. p. 44, b. 25-37.]

In the survey prescribed, nothing is gained by looking out for

predicates (of A and E) which are different or opposite: we must

collect such as are identical, since our purpose is to obtain from

them a suitable middle term, which must be the same in both

premisses. It is true that if the list B (containing the predicates

universally belonging to A) and the list F (containing the predicates

universally belonging to E) are incompatible or contrary to each

other, you will arrive at a syllogism proving that no A can belong to

E. But this syllogism will proceed, not so much from the fact that B

and F are incompatible, as from the other fact, distinct though

correlative, that B will to a certain extent coincide with H (the

list of predicates which cannot belong to E). The middle term and the

syllogism constituted thereby, is derived from the coincidence

between B and H, not from the opposition between B and F. Those who

derive it from the latter, overlook or disregard the real source, and

adopt a point of view merely incidental and irrelevant.[58]

[Footnote 58: Ibid. p. 44, b. 38-p. 45, a. 22. [Greek: sumbai/nei dê\

toi=s ou(/tôs e)piskopou=si prosepible/pein a)/llên o(do\n tê=s

a)nagkai/as, dia\ to\ lantha/nein tê\n tau)to/têta tô=n B kai\ tô=n

Th.]]

The precept here delivered--That in order to obtain middle terms and

good syllogisms, you must study and collect both the predicates and

the subjects of the two terms of your thesis--Aristotle declares to

be equally applicable to all demonstration, whether direct or by way

of _Reductio ad Impossibile_. In both the process of demonstration is

the same--involving two premisses, three terms, and one of the three

a suitable middle term. The only difference is, that in the direct

demonstration, both premisses are propounded as true, while in the

_Reductio ad Impossibile_, one of the premisses is assumed as true

though known to be false, and the conclusion also.[59] In the other

cases of hypothetical syllogism your attention must be directed, not

to the original _quæsitum_, but to the condition annexed thereto; yet

the search for predicates, subjects, and a middle term, must be

conducted in the same manner.[60] Sometimes, by the help of a

condition extraneous to the premisses, you may demonstrate an

universal from a particular: _e.g._, Suppose C (the list of subjects

to which A belongs as predicate) and G (the list of subjects to which

E belongs as predicate) to be identical; and suppose farther that the

subjects in G are the _only_ ones to which E belongs as predicate

(this seems to be the _extraneous_ or _extra-syllogistic_ condition

assumed, on which Aristotle's argument turns); then, A will be

applicable to all E. Or if D (the list of predicates which cannot

belong to A) and G (the list of subjects to which E belongs as

predicate) are identical; then, assuming the like extraneous

condition, A will not be applicable to any E.[61] In both these

cases, the conclusion is more universal than the premisses; but it is

because we take in an hypothetical assumption, in addition to the

premisses.

[Footnote 59: Ibid. I. xxix. p. 45, a. 25-b. 15.]

[Footnote 60: Ibid. I. xxix. p. 45, b. 15-20. This paragraph is very

obscure. Neither Alexander, nor Waitz, nor St. Hilaire clears it up

**completely. See Schol. pp. 178, b., 179, a. Brandis.

Aristotle concludes by saying that syllogisms from an hypothesis

ought to be reviewed and classified into varieties--[Greek:

e)piske/psasthai de\ dei= kai\ dielei=n posachô=s oi( e)x

u(pothe/seôs] (b. 20). But it is doubtful whether he himself ever

executed this classification. It was done in the Analytica of his

successor Theophrastus (Schol. p. 179, a. 6, 24). Compare the note of

M. Barthélemy St. Hilaire, p. 140.]

[Footnote 61: Analyt. Prior. I. xxix. p. 45, b. 21-30.]

Aristotle has now shown a method of procedure common to all

investigations and proper for the solution of all problems, wherever

soluble. He has shown, first, all the conditions and varieties of

probative Syllogism, two premisses and three terms, with the place

required for the middle term in each of the three figures; next, the

quarter in which we are to look for all the materials necessary or

suitable for constructing valid syllogisms. Having the two terms of

the thesis given, we must study the predicates and subjects belonging

to both, and must provide a large list of them; out of which list we

must make selection according to the purpose of the moment. Our

selection will be different, according as we wish to prove or to

refute, and according as the conclusion that we wish to prove is an

universal or a particular. The lesson here given will be most useful

in teaching the reasoner to confine his attention to the sort of

materials really promising, so that he may avoid wasting his time

upon such as are irrelevant.[62]

[Footnote 62: Ibid. b. 36-xxx. p. 46, a. 10.]

This method of procedure is alike applicable to demonstration in

Philosophy or in any of the special sciences,[63] and to debate in

Dialectic. In both, the premisses or _principia_ of syllogisms must

be put together in the same manner, in order to make the syllogism

valid. In both, too, the range of topics falling under examination is

large and varied; each topic will have its own separate premisses or

_principia_, which must be searched out and selected in the way above

described. Experience alone can furnish these _principia_, in each

separate branch or department. Astronomical experience--the observed

facts and phenomena of astronomy--have furnished the data for the

scientific and demonstrative treatment of astronomy. The like with

every other branch of science or art.[64] When the facts in each

branch are brought together, it will be the province of the logician

or analytical philosopher to set out the demonstrations in a manner

clear and fit for use. For if nothing in the way of true matter of

fact has been omitted from our observation, we shall be able to

discover and unfold the demonstration, on every point where

demonstration is possible; and, wherever it is not possible, to make

the impossibility manifest.[65]

[Footnote 63: Ibid. p. 46, a. 8**: [Greek: kata\ me\n a)lê/theian e)k

tô=n kat' a)lê/theian _diagegramme/nôn_ u(pa/rchein, ei)s de\ tou\s

dialektikou\s sullogismou\s e)k tô=n kata\ do/xan prota/seôn.]

Julius Pacius (p. 257) remarks upon the word [Greek: diagegramme/nôn]

as indicating that Aristotle, while alluding to special sciences

distinguishable from philosophy on one side, and from dialectic on

the other, had in view geometrical demonstrations.]

[Footnote 64: Analyt. Prior. I. xxx. p. 46, a. 10-20**: [Greek: ai(

d' a)rchai\ tô=n sullogismô=n katho/lou me\n ei)/rêntai--i)/diai de\

kath' e(ka/stên ai( plei=stai. dio\ ta\s me\n a)rcha\s ta\s peri\

e(/kaston e)mpeiri/as e)/sti paradou=nai. le/gô d' oi(=on tê\n

a)strologikê\n me\n e)mpeiri/an tê=s a)strologikê=s e)pistê/mês;

lêphthe/ntôn ga\r i(kanô=s tô=n phainome/nôn ou(/tôs eu(re/thêsan ai(

a)strologikai\ a)podei/xeis. o(moi/ôs de\ kai\ peri\ a)/llên

o(poianou=n e)/chei te/chnên te kai\ e)pistê/mên.]

What Aristotle says here--of astronomical observation and experience

as furnishing the basis for astronomical science--stands in marked

contrast with Plato, who rejects this basis, and puts aside, with a

sort of contempt, astronomical observation (Republic, vii. pp.

530-531); treating acoustics also in a similar way. Compare Aristot.

Metaphys. [Greek: L]. p. 1073, a. 6, seq., with the commentary of

Bonitz, p. 506.]

[Footnote 65: Analyt. Prior. I. xxx. p. 46, a. 22-27**: [Greek:

ô(/ste a)\n lêphthê=| ta\ u(pa/rchonta peri\ e(/kaston, ê(me/teron

ê)/dê ta\s a)podei/xeis e(toi/môs e)mphani/zein. ei) ga\r mêde\n

_kata\ tê\n i(stori/an_ paraleiphthei/ê tô=n a)lêthô=s u(parcho/ntôn

toi=s pra/gmasin, e(/xomen peri\ a(/pantos ou(= me\n e)/stin

a)po/deixis, tau/tên eu(rei=n kai\ a)podeiknu/nai, ou(= de\ mê\

pe/phuken a)po/deixis, tou=to poiei=n phanero/n.]

Respecting the word [Greek: i(stori/a]--investigation and record of

matters of fact--the first sentence of Herodotus may be compared with

Aristotle, Histor. Animal. p. 491, a. 12; also p. 757, b. 35;

Rhetoric. p. 1359, b. 32.]

For the fuller development of these important principles, the reader

is referred to the treatise on Dialectic, entitled Topica, which we

shall come to in a future chapter. There is nothing in all

Aristotle's writings more remarkable than the testimony here

afforded, how completely he considered all the generalities of

demonstrative science and deductive reasoning to rest altogether on

experience and inductive observation.

We are next introduced to a comparison between the syllogistic

method, as above described and systematized, and the process called

logical Division into _genera_ and _species_; a process much relied

upon by other philosophers, and especially by Plato. This logical

Division, according to Aristotle, is a mere fragment of the

syllogistic procedure; nothing better than a feeble syllogism.[66]

Those who employed it were ignorant both of Syllogism and of its

conditions. They tried to demonstrate--what never can be

demonstrated--the essential constitution of the subject.[67] Instead

of selecting a middle term, as the Syllogism requires, more universal

than the subject but less universal (or not more so) than the

predicate, they inverted the proper order, and took for their middle

term the highest universal. What really requires to be demonstrated,

they never demonstrated but assume.[68]

[Footnote 66: Analyt. Prior. I. xxxi. p. 46, a. 33. Alexander, in

Scholia, p. 180, a. 14. The Platonic method of [Greek: diai/resis] is

exemplified in the dialogues called Sophistês and Politicus; compare

also Philêbus, c. v., p. 15.]

[Footnote 67: Ibid. p. 46, a. 34: [Greek: prô=ton d' au)to\ tou=to

e)lelê/thei tou\s chrôme/nous au)tê=| pa/ntas, kai\ pei/thein

e)pechei/roun ô(s o)/ntos dunatou= peri\ ou)si/as a)po/deixin

gi/nesthai kai\ tou= ti/ e)stin.]]

[Footnote 68: Ibid. p. 46, b. 1-12.]

Thus, they take the subject man, and propose to prove that man is

mortal. They begin by laying down that man is an animal, and that

every animal is either mortal or immortal. Here, the most universal

term, animal, is selected as middle or as medium of proof; while

after all, the conclusion demonstrated is, not that man is mortal,

but that man is either mortal or immortal. The position that man is

mortal, is assumed but not proved.[69] Moreover, by this method of

logical division, all the steps are affirmative and none negative;

there cannot be any refutation of error. Nor can any proof be given

thus respecting _genus_, or _proprium_, or _accidens_; the _genus_ is

assumed, and the method proceeds from thence to _species_ and

_differentia_. No doubtful matter can be settled, and no unknown

point elucidated by this method; nothing can be done except to

arrange in a certain order what is already ascertained and

unquestionable. To many investigations, accordingly, the method is

altogether inapplicable; while even where it is applicable, it leads

to no useful conclusion.[70]

[Footnote 69: Ibid. p. 46, b. 1-12.]

[Footnote 70: Ibid. b. 26-37. Alexander in Schol. p. 180, b. 1.]

We now come to that which Aristotle indicates as the third section of

this First Book of the Analytica Priora. In the first section he

explained the construction and constituents of Syllogism, the

varieties of figure and mode, and the conditions indispensable to a

valid conclusion. In the second section he tells us where we are to

look for the premisses of syllogisms, and how we may obtain a stock

of materials, apt and ready for use when required. There remains one

more task to complete his plan--that he should teach the manner of

reducing argumentation as it actually occurs (often invalid, and even

when valid, often elliptical and disorderly), to the figures of

syllogism as above set forth, for the purpose of testing its

validity.[71] In performing this third part (Aristotle says) we shall

at the same time confirm and illustrate the two preceding parts; for

truth ought in every way to be consistent with itself.[72]

[Footnote 71: Analyt. Prior. I. xxxii. p. 47, a. 2: [Greek: loipo\n

ga\r e)/ti tou=to tê=s ske/pseôs; ei) ga\r tê/n te ge/nesin tô=n

sullogismô=n theôroi=men kai\ tou= eu(ri/skein e)/choimen du/namin,

e)/ti de\ tou\s gegenême/nous a)nalu/oimen ei)s ta\ proeirême/na

schê/mata, te/los a)\n e)/choi ê( e)x a)rchê=s pro/thesis.]]

[Footnote 72: Ibid. a. 8.]

When a piece of reasoning is before us, we must first try to

disengage the two syllogistic premisses (which are more easily

disengaged than the three terms), and note which of them is universal

or particular. The reasoner, however, may not have set out both of

them clearly: sometimes he will leave out the major, sometimes the

minor, and sometimes, even when enunciating both of them, he will

join with them irrelevant matter. In either of these cases we must

ourselves supply what is wanting and strike out the irrelevant.

Without this aid, reduction to regular syllogism is impracticable;

but it is not always easy to see what the exact deficiency is.

Sometimes indeed the conclusion may follow necessarily from what is

implied in the premisses, while yet the premisses themselves do not

form a correct syllogism; for though every such syllogism carries

with it necessity, there may be necessity without a syllogism. In the

process of reduction, we must first disengage and set down the two

premisses, then the three terms; out of which three, that one which

appears twice will be the middle term. If we do not find one term

twice repeated, we have got no middle and no real syllogism. Whether

the syllogism when obtained will be in the first, second, or third

figure, will depend upon the place of the middle term in the two

premisses. We know by the nature of the conclusion which of the three

figures to look for, since we have already seen what conclusions can

be demonstrated in each.[73]

[Footnote 73: Ibid. a. 10-b. 14.]

Sometimes we may get premisses which look like those of a true

syllogism, but are not so in reality; the major proposition ought to

be an universal, but it may happen to be only indefinite, and the

syllogism will not in all cases be valid; yet the distinction between

the two often passes unnoticed.[74] Another source of fallacy is,

that we may set out the terms incorrectly; by putting (in modern

phrase) the abstract instead of the concrete, or abstract in one

premiss and concrete in the other.[75] To guard against this, we

ought to use the concrete term in preference to the abstract. For

example, let the major proposition be, Health cannot belong to any

disease; and the minor. Disease can belong to any man; _Ergo_, Health

cannot belong to any man. This conclusion seems valid, but is not

really so. We ought to substitute concrete terms to this effect:--It

is impossible that the sick can be well; Any man may be sick; _Ergo_,

It is impossible that any man can be well. To the syllogism, now, as

stated in these concrete terms, we may object, that the major is not

true. A person who is at the present moment sick may at a future time

become well. There is therefore no valid syllogism.[76] When we take

the concrete man, we may say with truth that the two contraries,

health-sickness, knowledge-ignorance, _may_ both alike belong to him;

though not to the same individual at the same time.

[Footnote 74: Ibid. I. xxxiii. p. 47, b. 16-40: [Greek: au(/tê me\n

ou)=n ê( a)pa/tê gi/netai e)n tô=| para\ mikro/n; ôs ga\r ou)de\n

diaphe/ron ei)pei=n _to/de tô=|de u(pa/rchein, ê)\ to/de tô=|de

panti\ u(pa/rchein_, sugchôrou=men.]

M. B. St. Hilaire observes in his note (p. 155): "L'erreur vient

uniquement de ce qu'on confond l'universel et l'indeterminé séparés

par une nuance très faible d'expression, qu'on ne doit pas cependant

negliger." Julius Pacius (p. 264) gives the same explanation at

greater length; but the example chosen by Aristotle ([Greek: o(

A)ristome/nês e)sti\ dianoêto\s A)ristome/nês]) appears open to other

objections besides.]

[Footnote 75: Analyt. Prior. I. xxxiv. p. 48, a. 1-28.]

[Footnote 76: Ibid. a. 2-23. See the Scholion of Alexander, p. 181,

b. 16-27, Brandis.]

Again, we must not suppose that we can always find one distinct and

separate name belonging to each term. Sometimes one or all of the

three terms can only be expressed by an entire phrase or proposition.

In such cases it is very difficult to reduce the reasoning into

regular syllogism. We may even be deceived into fancying that there

are syllogisms without any middle term at all, because there is no

single word to express it. For example, let A represent equal to two

right angles; B, triangle; C, isosceles. Then we have a regular

syllogism, with an explicit and single-worded middle term; A belongs

first to B, and then to C through B as middle term (triangle). But

how do we know that A belongs to B? We know it by demonstration; for

it is a demonstrable truth that every triangle has its three angles

equal to two right angles. Yet there is no other more general truth

about triangles from which it is a deduction; it belongs to the

triangle _per se_, and follows from the fundamental properties of the

figure.[77] There is, however, a middle term in the demonstration,

though it is not single-worded and explicit; it is a declaratory

proposition or a fact. We must not suppose that there can be any

demonstration without a middle term, either single-worded or

many-worded.

[Footnote 77: Ibid. I. xxxv. p. 48, a. 30-39: [Greek: phanero\n o(/ti

to\ me/son ou)ch ou(/tôs a)ei\ lêpte/on ô(s to/de ti, a)ll' e)ni/ote

lo/gon, o(/per sumbai/nei ka)pi\ tou= lechthe/ntos.] A good Scholion

of Philoponus is given, p. 181, b. 28-45, Brand.]

When we are reducing any reasoning to a syllogistic form, and tracing

out the three terms of which it is composed, we must expose or set

out these terms in the nominative case; but when we actually

construct the syllogism or put the terms into propositions, we shall

find that one or other of the oblique cases, genitive, dative, &c.,

is required.[78] Moreover, when we say, 'this belongs to that,' or

'this may be truly predicated of that,' we must recollect that there

are many distinct varieties in the relation of predicate to subject.

Each of the Categories has its own distinct relation to the subject;

predication _secundum quid_ is distinguished from predication

_simpliciter_, simple from combined or compound, &c. This applies to

negatives as well as affirmatives.[79] There will be a material

difference in setting out the terms of the syllogism, according as

the predication is qualified (_secundum quid_) or absolute

(_simpliciter_). If it be qualified, the qualification attaches to

the predicate, not to the subject: when the major proposition is a

qualified predication, we must consider the qualification as

belonging, not to the middle term, but to the major term, and as

destined to re-appear in the conclusion. If the qualification be

attached to the middle term, it cannot appear in the conclusion, and

any conclusion that embraces it will not be proved. Suppose the

conclusion to be proved is. The wholesome is knowledge _quatenus

bonum_ or _quod bonum est_; the three terms of the syllogism must

stand thus:--

_Major_--_Bonum_ is knowable, _quatenus bonum_ or _quod bonum est_.

_Minor_--The wholesome is _bonum_.

_Ergo_--The wholesome is knowable, _quatenus bonum_, &c.

For every syllogism in which the conclusion is qualified, the terms

must be set out accordingly.[80]

[Footnote 78: Analyt. Prior. I. xxxvi. p. 48, a. 40-p. 49, a. 5.

[Greek: a(plô=s le/gomen ga\r tou=to kata\ pa/ntôn, o(/ti tou\s me\n

o(/rous a)/ei thete/on kata\ ta\s klê/seis tô=n o)noma/tôn--ta\s de\

prota/seis lêpte/on kata\ ta\s e(ka/stou ptô/seis.] Several examples

are given of this precept.]

[Footnote 79: Ibid. I. xxxvii. p. 49, a. 6-10. Alexander remarks in

the Scholia (p. 183, a. 2) that the distinction between simple and

compound predication has already been adverted to by Aristotle in De

Interpretatione (see p. 20, b. 35); and that it was largely treated

by Theophrastus in his work, [Greek: Peri\ Katapha/seôs], not

preserved.]

[Footnote 80: Ibid. I. xxxviii. p. 49, a. 11-b. 2. [Greek: phanero\n

ou)=n o(/ti e)n toi=s e)n me/rei sullogismoi=s ou(/tô lêpte/on tou\s

o(/rous.] Alexander explains [Greek: oi( e)n me/rei sullogismoi/]

(Schol. p. 183, b. 32, Br.) to be those in which the predicate has a

qualifying adjunct tacked to it.]

We are permitted, and it is often convenient, to exchange one phrase

or term for another of equivalent signification, and also one word

against any equivalent phrase. By doing this, we often **facilitate

the setting out of the terms. We must carefully note the different

meanings of the same substantive noun, according as the definite

article is or is not prefixed. We must not reckon it the same term,

if it appears in one premiss with the definite article, and in the

other without the definite article.[81] Nor is it the same

proposition to say B is predicable of C (indefinite), and B is

predicable of _all_ C (universal). In setting out the syllogism, it

is not sufficient that the major premiss should be indefinite; the

major premiss must be universal; and the minor premiss also, if the

conclusion is to be universal. If the major premiss be universal,

while the minor premiss is only affirmative indefinite, the

conclusion cannot be universal, but will be no more than indefinite,

that is, counting as particular.[82]

[Footnote 81: Analyt. Prior. I. xxxix.-xl. p. 49, b. 3-13. [Greek:

ou) tau)to\n e)sti to\ ei)=nai tê\n ê(donê\n a)gatho\n kai\ to\

ei)=nai tê\n ê(donê\n to\ a)gatho/n], &c.]

[Footnote 82: Ibid. I. xli. p. 49, b. 14-32. The Scholion of

Alexander (Schol. p. 184, a. 22-40) alludes to the peculiar mode,

called by Theophrastus [Greek: kata\ pro/slêpsin], of stating the

premisses of the syllogism: two terms only, the major and the middle,

being enunciated, while the third or minor was included potentially,

but not enunciated. Theophrastus, however, did not recognize the

distinction of meaning to which Aristotle alludes in this chapter. He

construed as an universal minor, what Aristotle treats as only an

indefinite minor. The liability to mistake the Indefinite for an

Universal is here again adverted to.]

There is no fear of our being misled by setting out a particular case

for the purpose of the general demonstration; for we never make

reference to the specialties of the particular case, but deal with it

as the geometer deals with the diagram that he draws. He calls the

line A B, straight, a foot long, and without breadth, but he does not

draw any conclusion from these assumptions. All that syllogistic

demonstration either requires or employs, is, terms that are related

to each other either as whole to part or as part to whole. Without

this, no demonstration can be made: the exposition of the particular

case is intended as an appeal to the senses, for facilitating the

march of the student, but is not essential to demonstration.[83]

[Footnote 83: Ibid. I. xli. p. 50, a. 1: [Greek: tô=| d'

e)kti/thesthai ou(/tô chrô/metha ô(/sper kai\ tô=| ai)stha/nesthai

to\n mantha/nonta le/gontes; ou) ga\r ou(/tôs ô(s a)/neu tou/tôn

ou)ch oi(=o/n t' a)podeichthê=nai, ô(/sper e)x ô(=n o(

sullogismo/s.]

This chapter is a very remarkable statement of the Nominalistic

doctrine; perceiving or conceiving all the real specialties of a

particular case, but attending to, or reasoning upon, only a portion

of them.

Plato treats it as a mark of the inferior scientific value of

Geometry, as compared with true and pure Dialectic, that the geometer

cannot demonstrate through Ideas and Universals alone, but is

compelled to help himself by visible particular diagrams or

illustrations. (Plato, Repub. vi. pp. 510-511, vii. p. 533, C.)]

Aristotle reminds us once more of what he had before said, that in

the Second and Third figures, not all varieties of conclusion are

possible, but only some varieties; accordingly, when we are reducing

a piece of reasoning to the syllogistic form, the nature of the

conclusion will inform us which of the three figures we must look

for. In the case where the question debated relates to a definition,

and the reasoning which we are trying to reduce turns upon one part

only of that definition, we must take care to look for our three

terms only in regard to that particular part, and not in regard to

the whole definition.[84] All the modes of the Second and Third

figures can be reduced to the First, by conversion of one or other of

the premisses; except the fourth mode (_Baroco_) of the Second, and

the fifth mode (_Bocardo_) of the Third, which can be proved only by

_Reductio ad Absurdum_.[85]

[Footnote 84: Analyt. Prior. I. xlii., xliii. p. 50, a. 5-15. I

follow here the explanation given by Philoponus and Julius Pacius,

which M. Barthélemy St. Hilaire adopts. But the illustrative example

given by Aristotle himself (the definition of _water_) does not

convey much instruction.]

[Footnote 85: Ibid. xlv. p. 50, b. 5-p. 51, b. 2.]

No syllogisms from an Hypothesis, however, are reducible to any of

the three figures; for they are not proved by syllogism alone: they

require besides an extra-syllogistic assumption granted or understood

between speaker and hearer. Suppose an hypothetical proposition

given, with antecedent and consequent: you may perhaps prove or

refute by syllogism either the antecedent separately, or the

consequent separately, or both of them separately; but you cannot

directly either prove or refute by syllogism the conjunction of the

two asserted in the hypothetical. The speaker must ascertain

beforehand that this will be granted to him; otherwise he cannot

proceed.[86] The same is true about the procedure by _Reductio ad

Absurdum_, which involves an hypothesis over and above the syllogism.

In employing such _Reductio ad Absurdum_, you prove syllogistically a

certain conclusion from certain premisses; but the conclusion is

manifestly false; therefore, one at least of the premisses from which

it follows must be false also. But if this reasoning is to have

force, the hearer must know _aliunde_ that the conclusion is false;

your syllogism has not shown it to be false, but has shown it to be

hypothetically true; and unless the hearer is prepared to grant the

conclusion to be false, your purpose is not attained. Sometimes he

will grant it without being expressly asked, when the falsity is

glaring: _e.g._ you prove that the diagonal of a square is

incommensurable with the side, because if it were taken as

commensurable, an odd number might be shown to be equal to an even

number. Few disputants will hesitate to grant that this conclusion is

false, and therefore that its contradictory is true; yet this last

(viz. that the contradictory is true) has not been proved

syllogistically; you must assume it by hypothesis, or depend upon the

hearer to grant it.[87]

[Footnote 86: Ibid. xliv. p. 50, a. 16-28.]

[Footnote 87: Analyt. Prior. I. xliv. p. 50, a. 29-38. See above,

xxiii. p. 40, a. 25.

M. Barthélemy St. Hilaire remarks in the note to his translation of

the Analytica Priora (p. 178): "Ce chapitre suffit à prouver

qu'Aristote a distingué très-nettement les syllogismes par l'absurde,

des syllogismes hypothétiques. Cette dernière dénomination est tout à

fait pour lui ce qu'elle est pour nous." Of these two statements, I

think the _latter_ is more than we can venture to affirm, considering

that the general survey of hypothetical syllogisms, which Aristotle

intended to draw up, either never was really completed, or at least

has perished: the _former_ appears to me incorrect. Aristotle

decidedly reckons the _Reductio ad Impossibile_ among hypothetical

proofs. But he understands by _Reductio ad Impossibile_ something

rather wider than what the moderns understand by it. It now means

only, that you take the contradictory of the conclusion together with

one of the premisses, and by means of these two demonstrate a

conclusion contradictory or contrary to the other premiss. But

Aristotle understood by it this, and something more besides, namely,

whenever, by taking the contradictory of the conclusion, together

with some other incontestable premiss, you demonstrate, by means of

the two, some new conclusion notoriously false. What I here say, is

illustrated by the very example which he gives in this chapter. The

incommensurability of the diagonal (with the side of the square) is

demonstrated by _Reductio ad Impossibile_; because if it be supposed

commensurable, you may demonstrate that an odd number is equal to an

even number; a conclusion which every one will declare to be

inadmissible, but which is not the contradictory of either of the

premisses whereby the true proposition was demonstrated.]

Here Aristotle expressly reserves for separate treatment the general

subject of Syllogisms from Hypothesis.[88]

[Footnote 88: The expressions of Aristotle here are remarkable,

Analyt. Prior. I. xliv. p. 50, a. 39-b. 3: [Greek: polloi\ de\ kai\

e(/teroi perai/nontai e)x u(pothe/seôs, ou(\s e)piske/psasthai dei=

kai\ diasêmê=nai katharô=s. ti/nes me\n ou)=n ai( diaphorai\ tou/tôn,

kai\ posachô=s gi/netai to\ e)x u(pothe/seôs, u(/steron e)rou=men;

nu=n de\ tosou=nton ê(mi=n e)/stô phanero/n, o(/ti ou)k e)/stin

a)nalu/ein ei)s ta\ schê/mata tou\s toiou/tous sullogismou/s. kai\

di' ê(\n ai)ti/an, ei)rê/kamen.]

Syllogisms from Hypothesis were many and various, and Aristotle

intended to treat them in a future treatise; but all that concerns

the present treatise, in his opinion, is, to show that none of them

can be reduced to the three Figures. Among the Syllogisms from

Hypothesis, two varieties recognized by Aristotle (besides [Greek:

oi) dia\ tou= a)duna/tou]) were [Greek: oi( kata\ meta/lêpsin] and

[Greek: oi( kata\ poio/têta]. The same proposition which Aristotle

entitles [Greek: kata\ meta/lêpsin], was afterwards designated by the

Stoics [Greek: kata\ pro/slêpsin] (Alexander ap. Schol. p. 178,

b. 6-24).

It seems that Aristotle never realized this intended future treatise

on Hypothetical Syllogisms; at least Alexander did not know it. The

subject was handled more at large by Theophrastus and Eudêmus after

Aristotle (Schol. p. 184, b. 45. Br.; Boethius, De Syllog.

Hypothetico, pp. 606-607); and was still farther expanded by

Chrysippus and the Stoics.

Compare Prantl, Geschichte der Logik, I. pp. 295, 377, seq. He treats

the Hypothetical Syllogism as having no logical value, and commends

Aristotle for declining to develop or formulate it; while Ritter

(Gesch. Phil. iii. p. 93), and, to a certain extent, Ueberweg (System

der Logik, sect. 121, p. 326), consider this to be a defect in

Aristotle.]

In the last chapter of the first book of the Analytica Priora,

Aristotle returns to the point which we have already considered in

the treatise De Interpretatione, viz. what is really a _negative_

proposition; and how the adverb of negation must be placed in order

to constitute one. We must place this adverb immediately before the

copula and in conjunction with the copula: we must not place it after

the copula and in conjunction with the predicate; for, if we do so,

the proposition resulting will not be negative but affirmative

([Greek: e)k metathe/seôs], by transposition, according to the

technical term introduced afterwards by Theophrastus). Thus of the

four propositions:

1. Est bonum. 2. Non est bonum.

4. Non est non bonum. 3. Est non bonum.

No. 1 is affirmative; No. 3 is affirmative ([Greek: e)k

metathe/seôs]); Nos. 2 and 4 are negative. Wherever No. 1 is

predicable, No. 4 will be predicable also; wherever No. 3 is

predicable, No. 2 will be predicable also--but in neither case _vice

versâ_.[89] Mistakes often flow from incorrectly setting out the two

contradictories.

[Footnote 89: Analyt. Prior. I. xlvi. p. 51, b. 5, ad finem. See

above, Chap. IV. p. 118, seq.]

CHAPTER VI.

ANALYTICA PRIORA II.

The Second Book of the Analytica Priora seems conceived with a view

mainly to Dialectic and Sophistic, as the First Book bore more upon

Demonstration.[1] Aristotle begins the Second Book by shortly

recapitulating what he had stated in the First; and then proceeds to

touch upon some other properties of the Syllogism. Universal

syllogisms (those in which the conclusion is universal) he says, have

always more conclusions than one; particular syllogisms sometimes,

but not always, have more conclusions than one. If the conclusion be

universal, it may always be converted--_simply_, when it is negative,

or _per accidens_, when it is affirmative; and its converse thus

obtained will be proved by the same premisses. If the conclusion be

particular, it will be convertible simply when affirmative, and its

converse thus obtained will be proved by the same premisses; but it

will not be convertible at all when negative, so that the conclusion

proved will be only itself singly.[2] Moreover, in the universal

syllogisms of the First figure (_Barbara_, _Celarent_), any of the

particulars comprehended under the minor term may be substituted in

place of the minor term as subject of the conclusion, and the proof

will hold good in regard to them. So, again, all or any of the

particulars comprehended in the middle term may be introduced as

subject of the conclusion in place of the minor term; and the

conclusion will still remain true. In the Second figure, the change

is admissible only in regard to those particulars comprehended under

the subject of the conclusion or minor term, and not (at least upon

the strength of the syllogism) in regard to those comprehended under

the middle term. Finally, wherever the conclusion is particular, the

change is admissible, though not by reason of the syllogism in regard

to particulars comprehended under the middle term; it is not

admissible as regards the minor term, which is itself particular.[3]

[Footnote 1: This is the remark of the ancient Scholiasts. See Schol.

p. 188, a. 44, b. 11.]

[Footnote 2: Analyt. Prior. II. i. p. 53, a. 3-14.]

[Footnote 3: Analyt. Prior. II. i. p. 53, a. 14-35. M. Barthélemy St.

Hilaire, following Pacius, justly remarks (note, p. 203 of his

translation) that the rule as to particulars breaks down in the cases

of _Baroco_, _Disamis_, and _Bocardo_.

On the chapter in general he remarks (note, p. 204):--"Cette théorie

des conclusions diverses, soit patentes soit cachées, d'un même

syllogisme, est surtout utile en dialectique, dans la discussion; où

il faut faire la plus grande attention à ce qu'on accorde à

l'adversaire, soit explicitement, soit implicitement." This

illustrates the observation cited in the preceding note from the

Scholiasts.]

Aristotle has hitherto regarded the Syllogism with a view to its

_formal_ characteristics: he now makes an important observation which

bears upon its _matter_. Formally speaking, **the two premisses are

always assumed to be true; but in any real case of syllogism (form

and matter combined) it is possible that either one or both may be

false. Now, Aristotle remarks that if both the premisses are true

(the syllogism being correct in form), the conclusion must of

necessity be true; but that if either or both the premisses are

false, the conclusion need not necessarily be false likewise. The

premisses being false, the conclusion may nevertheless be true; but

it will not be true because of or by reason of the premisses.[4]

[Footnote 4: Analyt. Prior. II. ii. p. 53, b. 5-10: [Greek: e)x

a)lêthô=n me\n ou)=n ou)k e)/sti pseu=dos sullogi/sasthai, e)k

pseudô=n d' e)/stin a)lêthe/s, plê\n ou) dio/ti a)ll' o(/ti; tou=

ga\r dio/ti ou)k e)/stin e)k pseudô=n sullogismo/s; di' ê(\n d'

ai)ti/an, e)n toi=s e(pome/nois lechthê/setai.]

The true conclusion is not true by reason of these false premisses,

but by reason of certain other premisses which are true, and which

may be produced to demonstrate it. Compare Analyt. Poster. I. ii. p.

71, b. 19.]

First, he would prove that if the premisses be true, the conclusion

must be true also; but the proof that he gives does not seem more

evident than the _probandum_ itself. Assume that if A exists, B must

exist also: it follows from hence (he argues) that if B does not

exist, neither can A exist; which he announces as a _reductio ad

absurdum_, seeing that it contradicts the fundamental supposition of

the existence of A.[5] Here the _probans_ is indeed equally evident

with the _probandum_, but not at all more evident; one who disputes

the latter, will dispute the former also. Nothing is gained in the

way of proof by making either of them dependent on the other. Both of

them are alike self-evident; that is, if a man hesitates to admit

either of them, you have no means of removing his scruples except by

inviting him to try the general maxim upon as many particular cases

as he chooses, and to see whether it does not hold good without a

single exception.

[Footnote 5: Ibid. II. ii. p. 53, b. 11-16.]

In regard to the case here put forward as illustration, Aristotle has

an observation which shows his anxiety to maintain the characteristic

principles of the Syllogism; one of which principles he had declared

to be--That nothing less than three terms and two propositions, could

warrant the inferential step from premisses to conclusion. In the

present case he assumed, If A exists, then B must exist; giving only

one premiss as ground for the inference. This (he adds) does not

contravene what has been laid down before; for A in the case before

us represents two propositions conceived in conjunction.[6] Here he

has given the type of hypothetical reasoning; not recognizing it as a

variety _per se_, nor following it out into its different forms (as

his successors did after him), but resolving it into the categorical

syllogism.[7] He however conveys very clearly the cardinal principle

of all hypothetical inference--That if the antecedent be true, the

consequent must be true also, but not _vice versâ_; if the consequent

be false, the antecedent must be false also, but not _vice versâ_.

[Footnote 6: Analyt. Prior. II. ii. p. 53, b. 16-25. [Greek: to\

ou)=n A ô(/sper e(\n kei=tai, du/o prota/seis sullêphthei=sai.]]

[Footnote 7: Aristotle, it should be remarked, uses the word [Greek:

katêgoriko/s], not in the sense which it subsequently acquired, as

the antithesis of [Greek: u(pothetiko/s] in application to the

proposition and syllogism, but in the sense of affirmative as opposed

to [Greek: sterêtiko/s].]

Having laid down the principle, that the conclusion may be true,

though one or both the premisses are false, Aristotle proceeds, at

great length, to illustrate it in its application to each of the

three syllogistic figures.[8] No portion of the Analytica is traced

out more perspicuously than the exposition of this most important

logical doctrine.

[Footnote 8: Analyt. Prior. II. ii.-iv. p. 53, b. 26-p. 57, b. 17. At

the close (p. 57, a. 36-b. 17), the general doctrine is summed up.]

It is possible (he then continues, again at considerable length) to

invert the syllogism and to demonstrate _in a circle_. That is, you

may take the conclusion as premiss for a new syllogism, together with

one of the old premisses, transposing its terms; and thus you may

demonstrate the other premiss. You may do this successively, first

with the major, to demonstrate the minor; next, with the minor, to

demonstrate the major. Each of the premisses will thus in turn be

made a demonstrated conclusion; and the circle will be complete. But

this can be done perfectly only in _Barbara_, and when, besides, all

the three terms of the syllogism reciprocate with each other, or are

co-extensive in import; so that each of the two premisses admits of

being simply converted. In all other cases, the process of circular

demonstration, where possible at all, is more or less imperfect.[9]

[Footnote 9: Ibid. II. v.-viii. p. 57, b. 18-p. 59, a. 35.]

Having thus shown under what conditions the conclusion can be

employed for the demonstration of the premisses, Aristotle proceeds

to state by what transformation it can be employed for the refutation

of them. This he calls _converting_ the syllogism; a most

inconvenient use of the term _convert_ ([Greek: a)ntistre/phein]),

since he had already assigned to that same term more than one other

meaning, distinct and different, in logical procedure.[10] What it

here means is _reversing_ the conclusion, so as to exchange it either

for its contrary, or for its contradictory; then employing this

reversed proposition as a new premiss, along with one of the previous

premisses, so as to disprove the other of the previous

premisses--_i.e._ to prove its contrary or contradictory. The result

will here be different, according to the manner in which the

conclusion is reversed; according as you exchange it for its contrary

or its contradictory. Suppose that the syllogism demonstrated is: A

belongs to all B, B belongs to all C; _Ergo_, A belongs to all C

(_Barbara_). Now, if we reverse this conclusion by taking its

_contrary_, A belongs to no C, and if we combine this as a new premiss

with the major of the former syllogism, A belongs to all B, we shall

obtain as a conclusion B belongs to no C; which is the _contrary_ of

the minor, in the form _Camestres_. If, on the other hand, we reverse

the conclusion by taking its _contradictory_, A does not belong to all

C, and combine this with the same major, we shall have as conclusion,

B does not belong to all C; which is the _contradictory_ of the minor,

and in the form _Baroco_: though in the one case as in the other the

minor is disproved. The major is _contradictorily_ disproved, whether

it be the contrary or the contradictory of the conclusion that is

taken along with the minor to form the new syllogism; but still the

form varies from _Felapton_ to _Bocardo_. Aristotle shows farther how

the same process applies to the other modes of the First, and to the

modes of the Second and Third figures.[11] The new syllogism,

obtained by this process of reversal, is always in a different figure

from the syllogism reversed. Thus syllogisms in the First figure are

reversed by the Second and Third; those in the second, by the First

and Third; those in the Third, by the First and Second.[12]

[Footnote 10: Schol. (ad Analyt. Prior. p. 59, b. 1), p. 190, b. 20,

Brandis. Compare the notes of M. Barthélemy St. Hilaire, pp. 55,

242.]

[Footnote 11: Analyt. Prior. II. viii.-x. p. 59, b. 1-p. 61, a. 4.]

[Footnote 12: Ibid. x. p. 61, a. 7-15.]

Of this reversing process, one variety is what is called the

_Reductio ad Absurdum_; in which the conclusion is reversed by taking

its contradictory (never its contrary), and then joining this last

with one of the premisses, in order to prove the contradictory or

contrary of the other premiss.[13] The _Reductio ad Absurdum_ is

distinguished from the other modes of reversal by these

characteristics: (1) That it takes the contradictory, and not the

contrary, of the conclusion; (2) That it is destined to meet the case

where an opponent declines to admit the conclusion; whereas the other

cases of reversion are only intended as confirmatory evidence towards

a person who already admits the conclusion; (3) That it does not

appeal to or require any concession on the part of the opponent; for

if he declines to admit the conclusion, you presume, as a matter of

course, that he must adhere to the contradictory of the conclusion;

and you therefore take this contradictory for granted (without asking

his concurrence) as one of the bases of a new syllogism; (4) That it

presumes as follows:--When, by the contradictory of the conclusion

joined with one of the premisses, you have demonstrated the opposite

of the other premiss, the original conclusion itself is shown to be

beyond all impeachment on the score of form, _i.e._ beyond

impeachment by any one who admits the premisses. You assume to be

true, for the occasion, the very proposition which you mean finally

to prove false; your purpose in the new syllogism is, not to

demonstrate the original conclusion, but to prove it to be true by

demonstrating its contradictory to be false.[14]**

[Footnote 13: Analyt. Prior. II. xi. p. 61, a. 18, seq.]

[Footnote 14: Ibid. p. 62, a. 11: [Greek: phanero\n ou)=n o(/ti ou)

to\ e)nanti/on, a)lla\ to\ a)ntikei/menon, u(pothete/on e)n a(/pasi

toi=s sullogismoi=s. ou(/tô ga\r to\ a)nagkai=on e)/stai kai\ to\

a)xi/ôma e)/ndoxon. ei) ga\r kata\ panto\s ê)\ kata/phasis ê)\

a)po/phasis, deichthe/ntos o(/ti ou)ch ê( a)po/phasis, a)na/gkê tê\n

kata/phasin a)lêtheu/esthai.] See Scholia, p. 190, b. 40, seq.,

Brand.]

By the _Reductio ad Absurdum_ you can in all the three figures

demonstrate all the four varieties of conclusion, universal and

particular, affirmative and negative; with the single exception, that

you cannot by this method demonstrate in the First figure the

Universal Affirmative.[15] With this exception, every true conclusion

admits of being demonstrated by either of the two ways, either

directly and ostensively, or by reduction to the impossible.[16]

[Footnote 15: Ibid. p. 61, a. 35-p. 62, b. 10; xii. p. 62, a. 21.

Alexander, ap. Schol. p. 191, a. 17-36, Brand.]

[Footnote 16: Ibid. xiv. p. 63, b. 12-21.]

In the Second and Third figures, though not in the First, it is

possible to obtain conclusions even from two premisses which are

contradictory or contrary to each other; but the conclusion will, as

a matter of course, be a self-contradictory one. Thus if in the

Second figure you have the two premisses--All Science is good; No

Science is good--you get the conclusion (in _Camestres_), No Science

is Science. In opposed propositions, the same predicate must be

affirmed and denied of the same subject in one of the three different

forms--All and None, All and Not All, Some and None. This shows why

such conclusions cannot be obtained in the First figure; for it is

the characteristic of that figure that the middle term must be

predicate in one premiss, and subject in the other.[17] In dialectic

discussion it will hardly be possible to get contrary or

contradictory premisses conceded by the adversary immediately after

each other, because he will be sure to perceive the contradiction:

you must mask your purpose by asking the two questions not in

immediate succession, but by introducing other questions between the

two, or by other indirect means as suggested in the Topica.[18]

[Footnote 17: Analyt. Prior. II. xv. p. 63, b. 22-p. 64, a. 32.

Aristotle here declares _Subcontraries_ (as they were later

called),--Some men are wise, Some men are not wise,--to be opposed

only in expression or verbally ([Greek: kata\ tê\n le/xin mo/non]).]

[Footnote 18: Ibid. II. xv. p. 64, a. 33-37. See Topica, VIII. i. p.

155, a. 26; Julius Pacius, p. 372, note. In the Topica, Aristotle

suggests modes of concealing the purpose of the questioner and

driving the adversary to contradict himself: [Greek: e)n de\ tô=s

Topikoi=s paradi/dôsi metho/dous tô=n kru/pseôn di' a(\s tou=to

dothê/setai] (Schol. p. 192, a. 18, Br.). Compare also Analyt. Prior.

II. xix. p. 66, a. 33.]

Aristotle now passes to certain general heads of Fallacy, or general

liabilities to Error, with which the syllogizing process is beset.

What the reasoner undertakes is, to demonstrate the conclusion before

him, and to demonstrate it in the natural and appropriate way; that

is, from premisses both more evident in themselves and logically

prior to the conclusion. Whenever he fails thus to demonstrate, there

is error of some kind; but he may err in several ways: (1) He may

produce a defective or informal syllogism; (2) His premisses may be

more unknowable than his conclusion, or equally unknowable; (3) His

premisses, instead of being logically prior to the conclusion, may be

logically posterior to it.[19]

[Footnote 19: Ibid. II. xvi. p. 64, b. 30-35: [Greek: kai\ ga\r ei)

o(/lôs mê\ sullogi/zetai, kai\ ei) di' a)gnôstote/rôn ê)\ o(moi/ôs

a)gnô/stôn, kai\ ei) dia\ tô=n u(ste/rôn to\ pro/teron; ê( ga\r

a)po/deixis e)k pistote/rôn te kai\ prote/rôn e)stin.... ta\ _me\n

di' au(tô=n pe/phuke gnôri/zesthai, ta\ de\ di' a)/llôn_.]]

Distinct from all these three, however, Aristotle singles out and

dwells upon another mode of error, which he calls _Petitio

Principii_. Some truths, the _principia_, are by nature knowable

through or in themselves, others are knowable only through other

things. If you confound this distinction, and ask or assume something

of the latter class as if it belonged to the former, you commit a

_Petitio Principii_. You may commit it either by assuming at once

that which ought to be demonstrated, or by assuming, as if it were a

_principium_, something else among those matters which in natural

propriety would be demonstrated by means of a _principium_. Thus,

there is (let us suppose) a natural propriety that C shall be

demonstrated through A; but you, overlooking this, demonstrate B

through C, and A through B. By thus inverting the legitimate order,

you do what is tantamount to demonstrating A through itself; for your

demonstration will not hold unless you assume A at the beginning, in

order to arrive at C. This is a mistake made not unfrequently, and

especially by some who define parallel lines; for they give a

definition which cannot be understood unless parallel lines be

presupposed.[20]

[Footnote 20: Analyt. Prior. II. xvi. p. 64, b. 33-p. 65, a. 9.

_Petere principium_ is, in the phrase of Aristotle, not [Greek: tê\n

a)rchê\n ai)tei=sthai], but [Greek: to\ e)n a)rchê=| ai)tei=sthai] or

[Greek: to\ e)x a)rchê=s ai)tei=sthai] (xvi. p. 64, b. 28, 34).]

When the problem is such, that it is uncertain whether A can be

predicated either of C or of B, if you then assume that A is

predicable of B, you may perhaps not commit _Petitio Principii_, but

you certainly fail in demonstrating the problem; for no demonstration

will hold where the premiss is equally uncertain with the conclusion.

But if, besides, the case be such, that B is identical with C, that

is, either co-extensive and reciprocally convertible with C, or

related to C as genus or species,--in either of these cases you

commit _Petitio Principii_ by assuming that A may be predicated of

B.[21] For seeing that B reciprocates with C, you might just as well

demonstrate that A is predicable of B, because it is predicable of C;

that is, you might demonstrate the major premiss by means of the

minor and the conclusion, as well as you can demonstrate the

conclusion by means of the major and the minor premiss. If you cannot

so demonstrate the major premiss, this is not because the structure

of the syllogism forbids it, but because the predicate of the major

premiss is more extensive than the subject thereof. If it be

co-extensive and convertible with the subject, we shall have a

circular proof of three propositions in which each may be alternately

premiss and conclusion. The like will be the case, if the _Petitio

Principii_ is in the minor premiss and not in the major. In the First

syllogistic figure it may be in either of the premisses; in the

Second figure it can only be in the minor premiss, and that only in

one mode (_Camestres_) of the figure.[22] The essence of _Petitio

Principii_ consists in this, that you exhibit as true _per se_ that

which is not really true _per se_.[23] You may commit this fault

either in Demonstration, when you assume for true what is not really

true, or in Dialectic, when you assume as probable and conformable to

authoritative opinion what is not really so.[24]**

[Footnote 21: Ibid. p. 65, a. 1-10.]

[Footnote 22: Ibid. p. 65, a. 10: [Greek: ei) ou)=n tis, a)dê/lou

o)/ntos o(/ti to\ A u(pa/rchei tô=| G, o(moi/ôs de\ kai\ o(/ti tô=|

B, ai)toi=to tô=| B u(pa/rchein to\ A, ou(/pô dê=lon ei) to\ e)n

a)rchê=| ai)tei=tai, a)ll' o(/ti ou)k a)podei/knusi, dê=lon; ou) ga\r

a)rchê\ a)podei/xeôs to\ o(moi/ôs a)/dêlon. ei) me/ntoi to\ B pro\s

to\ G ou(/tôs e)/chei ô(/ste tau)to\n ei)=nai, ê)\ dê=lon o(/ti

a)ntistre/phousin, ê)\ u(pa/rchei tha/teron thate/rô|, to\ e)n

a)rchê=| ai)tei=tai. kai\ ga\r a)/n, o(/ti tô=| B to\ A u(pa/rchei,

di' e)kei/nôn deiknu/oi, ei) a)ntistre/phoi. nu=n de\ tou=to kôlu/ei,

a)ll' ou)ch o( tro/pos. ei) de\ tou=to poioi=, to\ ei)rême/non a)\n

poioi= kai\ a)ntistre/phoi ô(s dia\ triô=n.]

This chapter, in which Aristotle declares the nature of Petitio

Principii, is obscure and difficult to follow. It has been explained

at some length, first by Philoponus in the Scholia (p. 192, a. 35, b.

24), afterwards by Julius Pacius (p. 376, whose explanation is

followed by M. B. St. Hilaire, p. 288), and by Waitz, (I. p. 514).

But the translation and comment given by Mr. Poste appear to me the

best: "Assuming the conclusion to be affirmative, let us examine a

syllogism in Barbara:--

All B is A.

. All C is B.

. . All C is A.

And let us first suppose that the major premiss is a Petitio

Principii; _i.e._ that the proposition _All B is A_ is identical with

the proposition _All C is A_. This can only be because the terms B

and C are identical. Next, let us suppose that the minor premiss is a

Petitio Principii: _i.e._ that the proposition _All C is B_ is

identical with the proposition _All C is A_. This can only be because

B and A are identical. The identity of the terms is, their

convertibility or their sequence ([Greek: u(pa/rchei, e(/petai]).

This however requires some limitation; for as the major is always

predicated ([Greek: u(pa/rchei, e(/petai]) of the middle, and the

middle of the minor, if this were enough to constitute Petitio

Principii, every syllogism with a problematical premiss would be a

Petitio Principii." (See the Appendix A, pp. 178-183, attached to Mr.

Poste's edition of Aristotle's Sophistici Elenchi.)

Compare, about Petitio Principii, Aristot. Topic. VIII. xiii. p. 162,

b. 34, in which passage Aristotle gives to the fallacy called Petitio

Principii a still larger sweep than what he assigns to it in the

Analytica Priora. Mr. Poste's remark is perfectly just, that

according to the above passage in the Analytica, every syllogism with

a problematical (_i.e._ real as opposed to verbal) premiss would be a

Petitio Principii; that is, all real deductive reasoning, in the

syllogistic form, would be a Petitio Principii. To this we may add,

that, from the passage above referred to in the Topica, all inductive

reasoning also (reasoning from parts to whole) would involve Petitio

Principii.

Mr. Poste's explanation of this difficult passage brings into view

the original and valuable exposition made by Mr. John Stuart Mill of

the Functions and Logical Value of the Syllogism.--System of Logic,

Book II. ch. iii. sect 2:--"It must be granted, that in every

syllogism, considered as an argument to prove the conclusion, there

is a Petitio Principii," &c.

Petitio Principii, if ranked among the Fallacies, can hardly be

extended beyond the first of the five distinct varieties enumerated

in the Topica, VIII. xiii.]

[Footnote 23: Analyt. Prior. II. xvi. p. 65, a. 23-27: [Greek: to\

ga\r e)x a)rchê=s ti/ du/natai, ei)/rêtai ê(mi=n, o(/ti to\ di'

au(tou= deiknu/nai to\ mê\ di' au(tou= dê=lon.--tou=to d' e)/sti, to\

mê\ deiknu/nai.]

The meaning of some lines in this chapter (p. 65, a. 17-18) is to me

very obscure, after all the explanations of commentators.]

[Footnote 24: Ibid. p. 65, a. 35; Topic. VIII. xiii. p. 162, b. 31.]

We must be careful to note, that when Aristotle speaks of a

_principium_ as knowable in itself, or true in itself, he does not

mean that it is innate, or that it starts up in the mind ready made

without any gradual building up or preparation. What he means is,

that it is not demonstrable deductively from anything else prior or

more knowable by nature than itself. He declares (as we shall see)

that _principia_ are acquired, and mainly by Induction.

Next to _Petitio Principii_, Aristotle indicates another fallacious

or erroneous procedure in dialectic debate; misconception or

misstatement of the real grounds on which a conclusion rests--_Non

per Hoc_. You may impugn the thesis (set up by the respondent)

directly, by proving syllogistically its contrary or contradictory;

or you may also impugn it indirectly by _Reductio ad Absurdum_;

_i.e._ you prove by syllogism some absurd conclusion, which you

contend to be necessarily true, if the thesis is admitted. Suppose

you impugn it in the first method, or directly, by a syllogism

containing only two premisses and a conclusion: _Non per Hoc_ is

inapplicable here, for if either premiss is disallowed, the

conclusion is unproved; the respondent cannot meet you except by

questioning one or both of the premisses of your impugning

syllogism.[25] But if you proceed by the second method or indirectly,

_Non per Hoc_ may become applicable; for there may then be more than

two premisses, and he may, while granting that the absurd conclusion

is correctly made out, contend that the truth or falsehood of his

thesis is noway implicated in it. He declares (in Aristotle's phrase)

that the absurdity or falsehood just made out does not follow as a

consequence from his thesis, but from other premisses independent

thereof; that it would stand equally proved, even though his thesis

were withdrawn.[26] In establishing the falsehood or absurdity you

must take care that it shall be one implicated with or dependent upon

his thesis. It is this last condition that he (the respondent)

affirms to be wanting.[27]

[Footnote 25: Analyt. Prior. II. xvii. p. 65, b. 4: [Greek: o(/tan

a)naire/thê| ti deiktikôs dia\ tô=n A, B, G], &c.; xviii. 66, a. 17:

[Greek: ê)\ ga\r e)k tô=n du/o prota/seôn ê)\ e)k pleio/nôn pa=s

e)sti\ sullogismo/s; ei) me\n ou)=n e)k tô=n du/o, tou/tôn a)na/gkê

tê\n me\n e(te/ran ê)\ kai\ a)mphote/ras ei)=nai pseudei=s;] &c.

Whoever would understand this difficult chapter xvii., will do well

to study it with the notes of Julius Pacius (p. 360), and also the

valuable exposition of Mr. Poste, who has extracted and illustrated

it in Appendix B. (p. 190) of the notes to his edition of the

Sophistici Elenchi. The six illustrative diagrams given by Julius

Pacius afford great help, though the two first of them appear to me

incorrectly printed, as to the brackets connecting the different

propositions.]

[Footnote 26: Ibid. II. xvii. p. 65, b. 38, b. 14, p. 66, a. 2, 7:

[Greek: to\ mê\ _para\ tou=to_ sumbai/nein to\ pseu=dos--tou= mê\

_para\ tê\n the/sin_ ei)=nai to\ pseu=dos--ou) _para\ tê\n the/sin_

sumbai/nei to\ pseu=dos--ou)k a)\n ei)/ê _para\ tê\n the/sin_.]

Instead of the preposition [Greek: para/], Aristotle on two occasions

employs [Greek: dia/--ou(/tô ga\r e)/stai _dia\ tê\n

u(po/thesin_]--p. 65, b. 33, p. 66, a. 3.

The preposition [Greek: para/], with acc. case, means _on account

of_, _owing to_, &c. See Matthiæ and Kühner's Grammars, and the

passage of Thucydides i. 141; [Greek: kai\ e(/kastos _ou) para\ tê\n

e(autou= a)me/leian_ oi)etai bla/psein, me/lein de/ tini kai\ a)/llô|

u(pe\r e(autou= ti proi+dei=n], &c., which I transcribe partly on

account of Dr. Arnold's note, who says about [Greek: para\]

here:--"This is exactly expressed in vulgar English, _all along of_

his own neglect, _i. e._ owing to his own neglect."]

[Footnote 27: Ibid. II. xvii. p. 65, b. 33: [Greek: dei= pro\s tou\s

e)x a)rchê=s o(/rous suna/ptein to\ a)du/naton; ou(/tô ga\r e)/stai

dia\ tê\n u(po/thesin.]]

Aristotle tells us that this was a precaution which the defender of a

thesis was obliged often to employ in dialectic debate, in order to

guard against abuse or misapplication of _Reductio ad Absurdum_ on

the part of opponents, who (it appears) sometimes took credit for

success, when they had introduced and demonstrated some absurd

conclusion that had little or no connection with the thesis.[28] But

even when the absurd conclusion is connected with the thesis

continuously, by a series of propositions each having a common term

with the preceding, in either the ascending or the descending scale,

we have here more than three propositions, and the absurd conclusion

may perhaps be proved by the other premisses, without involving the

thesis. In this case the respondent will meet you with _Non per

Hoc_:[29] he will point out that his thesis is not one of the

premisses requisite for demonstrating your conclusion, and is

therefore not overthrown by the absurdity thereof. Perhaps the thesis

may be false, but you have not shown it to be so, since it is not

among the premisses necessary for proving your _absurdum_. An

_absurdum_ may sometimes admit of being demonstrated by several lines

of premisses,[30] each involving distinct falsehood. Every false

conclusion implies falsity in one or more syllogistic or

prosyllogistic premisses that have preceded it, and is _owing to_ or

occasioned by this first falsehood.[31]

[Footnote 28: Analyt. Prior. II. xvii. p. 65, a. 38: [Greek: o(\

polla/kis e)n toi=s lo/gois ei)ô/thamen le/gein], &c. That the

_Reductio ad Absurdum_ was sometimes made to turn upon matters wholly

irrelevant, we may see from the illustration cited by Aristotle, p.

65, b. 17.]

[Footnote 29: In this chapter of the Analytica, Aristotle designates

the present fallacy by the title, _Non per Hoc_, [Greek: ou) para\

tou=to--ou) para\ tê\n the/sin sumbai/nei to\ pseu=dos]. He makes

express reference to the Topica (_i.e._ to the fifth chapter of

Sophist. Elenchi, which he regards as part of the Topica), where the

same fallacy is designated by a different title, _Non Causa pro

Causâ_, [Greek: to\ a)nai/tion ô(s ai)/tion tithe/nai]. We see

plainly that this chapter of the Anal. Priora was composed later than

the fifth chapter of Soph. El.; whether this is true of the two

treatises as wholes is not so certain. I think it probable that the

change of designation for the same fallacy was deliberately adopted.

It is an improvement to dismiss the vague term Cause.]

[Footnote 30: Ibid. II. xvii. p. 66, a. 11: [Greek: e)pei\ tau)to/ ge

pseu=dos sumbai/nein dia\ pleio/nôn u(pothe/seôn ou)de\n i)/sôs

a)/topon, oi(=on ta\s parallê/lous sumpi/ptein], &c.]

[Footnote 31: Ibid. II. xviii. p. 66, a. 16-24: [Greek: o( de\

pseudê\s lo/gos gi/netai para\ to\ prô=ton pseu=dos], &c.]

In impugning the thesis and in extracting from your opponent the

proper concessions to enable you to do so, you will take care to put

the interrogations in such form and order as will best disguise the

final conclusion which you aim at establishing. If you intend to

arrive at it through preliminary syllogisms (prosyllogisms), you will

ask assent to the necessary premisses in a confused or inverted

order, and will refrain from enunciating at once the conclusion from

any of them. Suppose that you wish to end by showing that A may be

predicated of F, and suppose that there must be intervening steps

through B, C, D, E. You will not put the questions in this regular

order, but will first ask him to grant that A may be predicated of B;

next, that D may be predicated of E; afterwards, that B may be

predicated of C, &c. You will thus try to obtain all the concessions

requisite for your final conclusion, before he perceives your drift.

If you can carry your point by only one syllogism, and have only one

middle term to get conceded, you will do well to put the middle term

first in your questions. This is the best way to conceal your purpose

from the respondent.[32]

[Footnote 32: Analyt. Prior. II. xix. p. 66, a. 33-b. 3: [Greek:

chrê\ d' o(/per phila/ttesthai paragge/llomen a)pokrinome/nous,

au)tou\s e)picheirou=ntas peira=sthai lantha/nein.--ka)\n di' e(no\s

me/sou gi/nêtai o( sullogismo/s, a)po\ tou= me/sou a)/rchesthai;

ma/lista ga\r a)\n ou(/tô la/nthanoi to\n a)pokrino/menon.] See the

explanation of Pacius, p. 385. Since the middle term does not appear

in the conclusion, the respondent is less likely to be prepared for

the conclusion that you want to establish. To put the middle term

first, in enunciating the Syllogism, is regarded by Aristotle as a

perverted and embarrassing order, yet it is the received practice

among modern logicians.]

It will be his business to see that he is not thus tripped up in the

syllogistic process.[33] If you ask the questions in the order above

indicated, without enunciating your preliminary conclusions, he must

take care not to concede the same term twice, either as predicate, or

as subject, or as both; for you can arrive at no conclusion unless he

grants you a middle term; and no term can be employed as middle,

unless it be repeated twice. Knowing the conditions of a conclusion

in each of the three figures, he will avoid making such concessions

as will empower you to conclude in any one of them.[34] If the thesis

which he defends is affirmative, the _elenchus_ by which you impugn

it must be a negative; so that he will be careful not to concede the

premisses for a negative conclusion. If his thesis be negative, your

purpose will require you to meet him by an affirmative; accordingly

he must avoid granting you any sufficient premisses for an

affirmative conclusion. He may thus make it impossible for you to

prove syllogistically the contrary or contradictory of his thesis;

and it is in proving this that the _elenchus_ or refutation consists.

If he will not grant you any affirmative proposition, nor any

universal proposition, you know, by the rules previously laid down,

that no valid syllogism can be constructed; since nothing can be

inferred either from two premisses both negative, or from two

premisses both particular.[35]

[Footnote 33: Analyt Prior. II. xix. p. 66, a. 25-32: [Greek: pro\s

de\ to\ mê\ katasullogi/zesthai paratêrête/on, o(/tan a)/neu tô=n

sumperasma/tôn e)rôta=| to\n lo/gon], &c.

Waitz (p. 520) explains [Greek: katasullogi/zesthai], "disputationum

et interrogationum laqueis aliquem irretire." This is, I think, more

correct than the distinction which M. Barthélemy St. Hilaire seeks to

draw, "entre le Catasyllogisme et la Réfutation," in the valuable

notes to his translation of the Analytica Priora, p. 303.]

[Footnote 34: Ibid. II. xix. p. 66, a. 25-32.]

[Footnote 35: Ibid. xx. p. 66, b. 4-17. The reader will observe how

completely this advice given by Aristotle is shaped for the purpose

of obtaining victory in the argument and how he leaves out of

consideration both the truth of what the opponent asks to be

conceded, and the belief entertained by the defendant. This is

exactly the procedure which he himself makes a ground of contemptuous

reproach against the Sophists.]

We have already seen that error may arise by wrong enunciation or

arrangement of the terms of a syllogism, that is, defects in its

form; but sometimes also, even when the form is correct, error may

arise from wrong belief as to the matters affirmed or denied.[36]

Thus the same predicate may belong, immediately and essentially,

alike to several distinct subjects; but you may believe (what is the

truth) that it belongs to one of them, and you may at the same time

believe (erroneously) that it does not belong to another. Suppose

that A is predicable essentially both of B and C, and that A, B, and

C, are all predicable essentially of D. You may know that A is

predicable of all B, and that B is predicable of all D; but you may

at the same time believe (erroneously) that A is not predicable of

any C, and that C is predicable of all D. Under this state of

knowledge and belief, you may construct two valid syllogisms; the

first (in _Barbara_, with B for its middle term) proving that A

belongs to _all_ D; the second (in _Celarent_, with C for its middle

term) proving that A belongs to _no_ D. The case will be the same,

even if all the terms taken belong to the same ascending or

descending logical series. Here, then, you _know_ one proposition;

yet you _believe_ the proposition contrary to it.[37] How can such a

mental condition be explained? It would, indeed, be an impossibility,

if the middle term of the two syllogisms were the same, and if the

premisses of the one syllogism thus contradicted directly and in

terms, the premisses of the other: should that happen, you cannot

know one side of the alternative and believe the other. But if the

middle term be different, so that the contradiction between the

premisses of the one syllogism and those of the other, is not direct,

there is no impossibility. Thus, you know that A is predicable of all

B, and B of all D; while you believe at the same time that A is

predicable of _no_ C, and C of _all_ D; the middle term being in one

syllogism B, in the other, C.[38] This last form of error is

analogous to what often occurs in respect to our knowledge of

particulars. You know that A belongs to all B, and B to all C; you

know, therefore, that A belongs to all C. Yet you may perhaps be

ignorant of the existence of C. Suppose A to denote equal to two

right angles; B, to be the triangle generally; C, a particular

visible triangle. You know A B the universal proposition; yet you may

at the same time believe that C does not exist; and thus it may

happen that you know, and do not know, the same thing at the same

time. For, in truth, the knowledge, that every triangle has its three

angles equal to two right angles, is not (as a mental fact) simple

and absolute, but has two distinct aspects; one as concerns the

universal, the other as concerns the several particulars. Now,

assuming the case above imagined, you possess the knowledge in the

first of these two aspects, but not in the second; so that the

apparent contrariety between knowledge and no knowledge is not

real.[39] And in this sense the doctrine of Plato in the Menon is

partially true--that learning is reminiscence. We can never know

beforehand particular cases _per se_; but in proportion as we extend

our induction to each case **successively, we, as it were, recognize

that, which we knew beforehand as a general truth, to be realized in

each. Thus when we ascertain the given figure before us to be a

triangle, we know immediately that its three angles are equal to two

right angles.[40]

[Footnote 36: Analyt. Prior. II. xxi. p. 66, b. 18: [Greek:

sumbai/nei d' e)ni/ote, katha/per e)n tê=| the/sei tô=n o(/rôn

a)patô/metha, kai\ kata\ tê\n u(po/lêpsin gi/nesthai tê\n a)pa/tên.]

The vague and general way in which Aristotle uses the term [Greek:

u(po/lêpsis], seems to be best rendered by our word _belief_. See

Trendelenburg ad Aristot. De Animâ, p. 469; Biese, Philos. des

Aristot. i. p. 211.]

[Footnote 37: Ibid. II. xxi. p. 66, b. 33: [Greek: ô(/ste o(/ pôs

e)pi/statai, tou=to o(/lôs a)xioi= mê\ u(polamba/nein; o(/per

a)du/naton.]]

[Footnote 38: Ibid. II. xxi. p. 67, a. 5-8.]