ga\r e)/sti kai\ mê\ a)podeiknu/nta sullogi/sthai, e)x a)nagkai/ôn d'
ou)k e)/stin a)ll' ê)\ a)podeiknu/nta; tou=to ga\r ê)/dê
a)podei/xeô/s e)stin.] Compare Analyt. Prior. I. ii. p. 53, b. 7-25.]
[Footnote 22: Aristot. Analyt. Post. I. vi. p. 74, b. 18: [Greek:
sêmei=on d' o(/ti ê( a)po/deixis e)x a)nagkai/ôn, o(/ti kai\ ta\s
e)nsta/seis ou(/tô phe/romen pro\s tou\s oi)ome/nous a)podeiknu/nai,
o(/ti ou)k a)na/gkê], &c.]
[Footnote 23: Ibid. vi. p. 74, b. 21-26: [Greek: dê=lon d' e)k
tou/tôn kai\ o(/ti eu)ê/theis oi( lamba/nein oi)o/menoi kalô=s ta\s
a)rcha/s, e)a\n e)/ndoxos ê)=| ê( pro/tasis kai\ a)lêthê/s, oi(=on
oi( sophistai\ o(/ti to\ e)pi/stasthai to\ e)pistê/mên e)/chein;],
&c.]
[Footnote 24: Aristot. Analyt. Post. I. vi. p. 74, b. 26-p. 75, a.
17.]
[Footnote 25: Ibid. vi. p. 75, a. 8-37.
On the point last mentioned, M. Barthélemy St. Hilaire observes in
his note, p. 41: "Dans les questions de dialectique, la conclusion
est nécessaire en ce sens, qu'elle suit nécessairement des prémisses;
elle n'est pas du tout nécessaire en ce sens, que la chose qu'elle
exprime soit nécessaire. Ainsi il faut distinguer la nécessité de la
forme et la nécessité de la matière: ou comme disent les
scholastiques, _necessitas illationis et necessitas materiæ_. La
dialectique se contente de la première, mais la demonstration a
essentiellement besoin des deux."]
In every demonstration three things may be distinguished: (1) The
demonstrated conclusion, or Attribute essential to a certain genus;
(2) The Genus, of which the attributes _per se_ are the matter of
demonstration; (3) The Axioms, out of which, or through which, the
demonstration is obtained. These Axioms may be and are common to
several genera: but the demonstration cannot be transferred from one
genus to another; both the extremes as well as the middle term must
belong to the same genus. An arithmetical demonstration cannot be
transferred to magnitudes and their properties, except in so far as
magnitudes are numbers, which is partially true of some among them.
The demonstrations in arithmetic may indeed be transferred to
harmonics, because harmonics is subordinate to arithmetic; and, for
the like reason, demonstrations in geometry may be transferred to
mechanics and optics. But we cannot introduce into geometry any
property of lines, which does not belong to them _quâ_ lines; such,
for example, as that a straight line is the most beautiful of all
lines, or is the contrary of a circular line; for these predicates
belong to it, not _quâ_ line, but _quâ_ member of a different or more
extensive genus.[26] There can be no complete demonstration about
perishable things, or about any individual line, except in regard to
its attributes as member of the genus line. Where the conclusion is
not eternally true, but true at one time and not true at another,
this can only be because one of its premisses is not universal or
essential. Where both premisses are universal and essential, the
conclusion must be eternal or eternally true. As there is no
demonstration, so also there can be no definition, of perishable
attributes.[27]
[Footnote 26: Ibid. vii. p. 75, a. 38-b. 20. Mr. Poste, in his
translation, here cites (p. 50) a good illustrative passage from Dr.
Whewell's Philosophy of the Inductive Sciences, Book II. ii.:--"But,
in order that we may make any real advance in the discovery of truth,
our ideas must not only be clear; they must also be _appropriate_.
Each science has for its basis a different class of ideas; and the
steps which constitute the progress of one science can never be made
by employing the ideas of another kind of science. No genuine advance
could ever be obtained in Mechanics by applying to the subject the
ideas of space and time merely; no advance in Chemistry by the use of
mere mechanical conceptions; no discovery in Physiology by referring
facts to mere chemical and mechanical principles." &c.]
[Footnote 27: Aristot. Analyt. Post. I. viii. p. 75, b. 21-36.
Compare Metaphys. Z. p. 1040, a. 1: [Greek: dê=lon o(/ti ou)k a)\n
ei)/ê au)tô=n (tô=n phthartô=n) ou)/th' o(rismo\s ou)/t'
a)po/deixis]. Also Biese, Die Philosophie des Aristoteles, ch. iv. p.
249.]
For complete demonstration, it is not sufficient that the premisses
be true, immediate, and undemonstrable; they must, furthermore, be
essential and appropriate to the class in hand. Unless they be such,
you cannot be said to know the conclusion _absolutely_; you know it
only by accident. You can only know a conclusion when demonstrated
from its own appropriate premisses; and you know it best when it is
demonstrated from its highest premisses. It is sometimes difficult to
determine whether we really know or not; for we fancy that we know,
when we demonstrate from true and universal _principia_, without
being aware whether they are, or are not, the _principia_ appropriate
to the case.[28] But these _principia_ must always be assumed without
demonstration--the class whose essential constituent properties are
in question, the universal Axioms, and the Definition or meaning of
the attributes to be demonstrated. If these definitions and axioms
are not always formally enunciated, it is because we tacitly presume
them to be already known and admitted by the learner.[29] He may
indeed always refuse to grant them in express words, but they are
such that he cannot help granting them by internal assent in his
mind, to which every syllogism must address itself. When you assume a
premiss without demonstrating it, though it be really demonstrable,
this, if the learner is favourable and willing to grant it, is an
assumption or Hypothesis, valid relatively to him alone, but not
valid absolutely: if he is reluctant or adverse, it is a Postulate,
which you claim whether he is satisfied or not.[30] The Definition by
itself is not an hypothesis; for it neither affirms nor denies the
existence of anything. The pupil must indeed understand the terms of
it; but this alone is not an hypothesis, unless you call the fact
that the pupil comes to learn, an hypothesis.[31] The Hypothesis or
assumption is contained in the premisses, being that by which the
reason of the conclusion comes to be true. Some object that the
geometer makes a false hypothesis or assumption, when he declares a
given line drawn to be straight, or to be a foot long, though it is
neither one nor the other. But this objection has no pertinence,
since the geometer does not derive his conclusions from what is true
of the visible lines drawn before his eyes, but from what is true of
the lines conceived in his own mind, and signified or illustrated by
the visible diagrams.[32]
[Footnote 28: Ibid. ix. p. 75, b. 37-p. 76, a. 30.]
[Footnote 29: Ibid. x. p. 76, a. 31-b. 22.]
[Footnote 30: Aristot. Analyt. Post. I. x. p. 76, b. 29-34: [Greek:
e)a\n me\n dokou=nta lamba/nê| tô=| mantha/nonti, u(poti/thetai, kai\
e)/stin ou)/ch a(plô=s u(po/thesis, a)lla\ pro\s e)kei=non mo/non,
a)\n de\ ê)\ mêdemi/a=s e)nou/sês do/xês ê)\ kai\ e)nanti/as
e)nou/sês lamba/nê| to\ au)to/, ai)tei=tai. kai\ tou/tô| diaphe/rei
_u(po/thesis_ kai\ _ai)/têma_], &c. Themistius, Paraphras. p. 37,
Spengel.]
[Footnote 31: Ibid. p. 76, b. 36: [Greek: tou=to d' ou)ch
u(po/thesis, ei) mê\ kai\ _to\ a)kou/ein_ u(po/thesi/n tis ei)=nai
phê/sei]. For the meaning of [Greek: _to\ a)kou/ein_], compare
[Greek: o( a)kou/ôn], infra, Analyt. Post. I. xxiv. p. 85, b. 22.]
[Footnote 32: Ibid. p. 77, a. 1: [Greek: o( de\ geôme/três ou)de\n
sumperai/netai tô=| tê/nde ei)=nai tê\n grammê\n ê(\n au)to\s
e)/phthegktai, a)lla\ ta\ dia\ tou/tôn dêlou/mena.]
Themistius, Paraphr. p. 37: [Greek: ô(/sper ou)d' oi( geôme/trai
ke/chrêntai tai=s grammai=s u(pe\r ô(=n diale/gontai kai\
deiknu/ousin, a)ll' a(\s e)/chousin e)n tê=| psuchê=|, ô(=n ei)si\
su/mbola ai( grapho/menai.]
A similar doctrine is asserted, Analyt. Prior. I. xli. p. 49, b. 35,
and still more clearly in De Memoria et Reminiscentia, p. 450,
a. 2-12.]
The process of Demonstration neither requires, nor countenances, the
Platonic theory of Ideas--universal substances beyond and apart from
particulars. But it does require that we should admit universal
predications; that is, one and the same predicate truly applicable in
the same sense to many different particulars. Unless this be so,
there can be no universal major premiss, nor appropriate middle term,
nor valid demonstrative syllogism.[33]
[Footnote 33: Aristot. Analyt. Post. I. xi. p. 77, a. 5-9.]
The Maxim or Axiom of Contradiction, in its most general enunciation,
is never formally enunciated by any special science; but each of them
assumes the Maxim so far as applicable to its own purpose, whenever
the _Reductio ad Absurdum_ is introduced.[34] It is in this and the
other common principles or Axioms that all the sciences find their
point of contact and communion; and that Dialectic also comes into
communion with all of them, as also the science (First Philosophy)
that scrutinizes the validity or demonstrability of the Axioms.[35]
The dialectician is not confined to any one science, or to any
definite subject-matter. His liberty of interrogation is unlimited;
but his procedure is essentially interrogatory, and he is bound to
accept the answer of the respondent--whatever it be, affirmative or
negative--as premiss for any syllogism that he may construct. In this
way he can never be sure of demonstrating any thing; for the
affirmative and the negative will not be equally serviceable for that
purpose. There is indeed also, in discussions on the separate
sciences, a legitimate practice of scientific interrogation. Here the
questions proper to be put are limited in number, and the answers
proper to be made are determined beforehand by the truths of the
science--say Geometry; still, an answer thus correctly made will
serve to the interrogator as premiss for syllogistic
demonstration.[36] The respondent must submit to have such answer
tested by appeal to geometrical _principia_ and to other geometrical
propositions already proved as legitimate conclusions from the
_principia_; if he finds himself involved in contradictions, he is
confuted _quâ_ geometer, and must correct or modify his answer. But
he is not bound, _quâ_ geometer, to undergo scrutiny as to the
geometrical _principia_ themselves; this would carry the dialogue out
of the province of Geometry into that of First Philosophy and
Dialectic. Care, indeed, must be taken to keep both questions and
answers within the limits of the science. Now there can be no
security for this restriction, except in the scientific competence of
the auditors. Refrain, accordingly, from all geometrical discussions
among men ignorant of geometry and confine yourself to geometrical
auditors, who alone can distinguish what questions and answers are
really appropriate. And what is here said about geometry, is equally
true about the other special sciences.[37] Answers may be improper
either as foreign to the science under debate, or as appertaining to
the science, yet false as to the matter, or as equivocal in middle
term; though this last is less likely to occur in Geometry, since the
demonstrations are accompanied by diagrams, which help to render
conspicuous any such ambiguity.[38] To an inductive proposition,
bringing forward a single case as contributory to an ultimate
generalization, no general objection should be offered; the objection
should be reserved until the generalization itself is tendered.[39]
Sometimes the mistake is made of drawing an affirmative conclusion
from premisses in the Second figure; this is formally wrong, but the
conclusion may in some cases be true, if the major premiss happens to
be a reciprocating proposition, having its predicate co-extensive
with its subject. This, however, cannot be presumed; nor can a
conclusion be made to yield up its principles by necessary
reciprocation; for we have already observed that, though the truth of
the premisses certifies the truth of the conclusion, we cannot say
_vice versâ_ that the truth of the conclusion certifies the truth of
the premisses. Yet propositions are more frequently found to
reciprocate in scientific discussion than in Dialectic; because, in
the former, we take no account of accidental properties, but only of
definitions and what follows from them.[40]
[Footnote 34: Ibid. a. 10, seq.]
[Footnote 35: Ibid. a. 26-30: [Greek: kai\ ei)/ tis katho/lou
peirô=|to deiknu/nai ta\ koina/, oi(=on o(/ti a(/pan pha/nai ê)\
a)popha/nai, ê)\ o(/ti i)/sa a)po\ i)/sôn, ê)\ tô=n toiou/tôn
a)/tta.] Compare Metaph. K. p. 1061**, b. 18.]
[Footnote 36: Aristot. Analyt. Post. I. xii, p. 77, a. 36-40;
Themistius, p. 40.
The text is here very obscure. He proceeds to distinguish Geometry
especially (also other sciences, though less emphatically) from
[Greek: ta\ e)n toi=s dialo/gois] (I. xii. p. 78, a. 12).
Julius Pacius, ad Analyt. Post. I. viii. (he divides the chapters
differently), p. 417, says:--"Differentia interrogationis dialecticæ
et demonstrativæ hæc est. Dialecticus ita interrogat, ut optionem det
adversario, utrum malit affirmare an negare. Demonstrator vero
interrogat ut rem evidentiorem faciat; id est, ut doceat ex
principiis auditori notis."]
[Footnote 37: Ibid. I. xii. p. 77, b. 1-15; Themistius, p. 41:
[Greek: ou) ga\r ô(/sper tô=n e)ndo/xôn oi( polloi\ kritai/, ou(/tô
kai\ tô=n kat' e)pistê/mên oi( a)nepistê/mones].]
[Footnote 38: Analyt. Post. I. xii. p. 77, b. 16-33. Propositions
within the limits of the science, but false as to matter, are styled
by Aristotle [Greek: pseudographê/mata]. See Aristot. Sophist.
Elench. xi. p. 171, b. 14; p. 172, a. 1.
"L'interrogation syllogistique se confondant avec la proposition, il
s'ensuit que l'interrogation doit être, comme la proposition, propre
à la science dont il s'agit." (Barthélemy St Hilaire, note, p. 70).
Interrogation here has a different meaning from that which it bears
in Dialectic.]
[Footnote 39: Ibid. I. xii. p. 77**, b. 34 seq. This passage is to
me hardly intelligible. It is differently understood by commentators
and translators. John Philoponus in the Scholia (p. 217, b. 17-32,
Brandis), cites the explanation of it given by Ammonius, but rejects
that explanation, and waits for others to supply him with a better.
Zabarella (Comm. in Analyt. Post. pp. 426, 456, ed. Venet 1617)
admits that as it stands, and where it stands, it is unintelligible,
but transposes it to another part of the book (to the end of cap.
xvii., immediately before the words [Greek: phanero\n de\ kai\
o(/ti], &c., of c. xviii.), and gives an explanation of it in this
altered position. But I do not think he has succeeded in clearing it
up.]
[Footnote 40: Ibid. I. xii. p. 77, b. 40-p. 78, a. 13.]
Knowledge of Fact and knowledge of the Cause must be distinguished,
and even within the same Science.[41] In some syllogisms the
conclusion only brings out [Greek: to\ o(/ti]--the reality of certain
facts; in others, it ends in [Greek: to\ dio/ti]--the affirmation of
a cause, or of the _Why_. The syllogism of the _Why_ is, where the
middle term is not merely the cause, but the proximate cause, of the
conclusion. Often, however, the effect is more notorious, so that we
employ it as middle term, and conclude from it to its reciprocating
cause; in which case our syllogism is only of the [Greek: o(/ti]; and
so it is also when we employ as middle term a cause not proximate but
remote, concluding from that to the effect.[42] Sometimes the
syllogisms of the [Greek: o(/ti] may fall under one science, those of
the [Greek: dio/ti] under another, namely, in the case where one
science is subordinate to another, as optics to geometry, and
harmonics to arithmetic; the facts of optics and harmonics belonging
to sense and observation, the causes thereof to mathematical
reasoning. It may happen, then, that a man knows [Greek: to\ dio/ti]
well, but is comparatively ignorant [Greek: tou= o(/ti]: the geometer
may have paid little attention to optical facts.[43] Cognition of the
[Greek: dio/ti] is the maximum, the perfection, of all cognition; and
this, comprising arithmetical and geometrical theorems, is almost
always attained by syllogisms in the First figure. This figure is the
most truly scientific of the three; the other two figures depend upon
it for expansion and condensation. It is, besides, the only one in
which universal affirmative conclusions can be obtained; for in the
Second figure we get only negative conclusions; in the Third, only
particular. Accordingly, propositions declaring Essence or
Definition, obtained only through universal affirmative conclusions,
are yielded in none but the First figure.[44]
[Footnote 41: Ibid. I. xiii. p. 77, a. 22 seq.]
[Footnote 42: Themistius, p. 45: [Greek: polla/kis sumbai/nei kai\
a)ntistre/phein a)llê/lois to\ ai)tion kai\ to\ sêmei=on kai\ a)/mphô
dei/knusthai di' a)llê/lôn, dia\ tou= sêmei/ou me\n ô(s to\ o(/ti,
dia\ thate/rou de\ ô(s to\ dio/ti.]
"Cum enim vera demonstratio, id est [Greek: tou= dio/ti], fiat per
causam proximam, consequens est, ut demonstratio vel per effectum
proximum, vel per causam remotam, sit demonstratio [Greek: tou=
o(/ti]" (Julius Pacius, Comm. p. 422).
M. Barthélemy St. Hilaire observes (Note, p. 82):--"La cause éloignée
non immédiate, donne un syllogisme dans la seconde figure.--Il est
vrai qu'Aristote n'appelle cause que la cause immédiate; et que la
cause éloignée n'est pas pour lui une véritable cause."
See in Schol. p. 188, a. 19, the explanation given by Alexander of
the syllogism [Greek: tou= dio/ti].]
[Footnote 43: Analyt. Post. I. xiii. p. 79, a. 2, seq.: [Greek:
e)ntau=tha ga\r to\ me\n o(/ti tô=n ai)sthêtikô=n ei)de/nai, to\ de\
dio/ti tô=n mathêmatikô=n], &c. Compare Analyt. Prior. II. xxi. p.
67, a. 11; and Metaphys. A. p. 981, a. 15.]
[Footnote 44: Analyt. Post. I. xiv. p. 79, a. 17-32.]
As there are some affirmative propositions that are indivisible,
_i.e._, having affirmative predicates which belong to a subject at
once, directly, immediately, indivisibly,--so there are also some
indivisible negative propositions, _i.e._, with predicates that
belong negatively to a subject at once, directly, &c. In all such
there is no intermediate step to justify either the affirmation of
the predicate, or the negation of the predicate, respecting the given
subject. This will be the case where neither the predicate nor the
subject is contained in any higher genus.[45]
[Footnote 45: Ibid. I. xv. p. 79, a. 33-b. 22. The point which
Aristotle here especially insists upon is, that there may be and are
immediate, undemonstrable, _negative_ (as well as affirmative)
predicates: [Greek: phanero\n ou)=n o(/ti e)nde/chetai/ te a)/llo
a)/llô| _mê\ u(pa/rchein_ a)to/môs]. (Themistius, Paraphr. p. 48,
Spengel: [Greek: a)/mesoi de\ prota/seis ou) katapha/seis mo/non
ei)si/n, a)lla\ kai\ a)popha/seis o(moi/ôs ai(\ mê\ du/nantai dia\
sullogismou= deichthê=nai, au(=tai d' ei)si\n e)ph' ô(=n ou)dete/rou
tô=n o(/rôn a)/llos tis o(/lou katêgorei=tai.]) It had been already
shown, in an earlier chapter of this treatise (p. 72, b. 19), that
there were _affirmative_ predicates immediate and undemonstrable.
This may be compared with that which Plato declares in the Sophistes
(pp. 253-254, seq.) about the intercommunion [Greek: tô=n genô=n kai\
tô=n ei)dô=n] with each other. Some of them admit such
intercommunion, others repudiate it.]
In regard both to these propositions immediate and indivisible, and
to propositions mediate and deducible, there are two varieties of
error.[46] You may err simply, from ignorance, not knowing better,
and not supposing yourself to know at all; or your error may be a
false conclusion, deduced by syllogism through a middle term, and
accompanied by a belief on your part that you do know. This may
happen in different ways. Suppose the negative proposition, No B is
A, to be true immediately or indivisibly. Then, if you conclude the
contrary of this[47] (All B is A) to be true, by syllogism through
the middle term C, your syllogism must be in the First figure; it
must have the minor premiss false (since B is brought under C, when
it is not contained in any higher genus), and it may have both
premisses false. Again, suppose the affirmative proposition, All B is
A, to be true immediately or indivisibly. Then if you conclude the
contrary of this (No B is A) to be true, by syllogism through the
middle term C, your syllogism may be in the First figure, but it may
also be in the Second figure, your false conclusion being negative.
If it be in the First figure, both its premisses may be false, or one
of them only may be false, either indifferently.[48] If it be in the
Second figure, either premiss singly may be wholly false, or both may
be partly false.[49]
[Footnote 46: Analyt. Post. I. xvi. p. 79, b. 23: [Greek: a)/gnoia
kat' a)po/phasin--a)/gnoia kata\ dia/thesin]. See Themistius, p. 49,
Spengel. In regard to simple and uncombined ideas, ignorance is not
possible as an erroneous combination, but only as a mental blank. You
either have the idea and thus know so much truth, or you have not the
idea and are thus ignorant to that extent; this is the only
alternative. Cf. Aristot. Metaph. [Greek: Th]. p. 1051, a. 34; De
Animâ, III. vi. p. 430, a. 26.]
[Footnote 47: Analyt. Post. I. xvi. p. 79, b. 29. M. Barthélemy St.
Hilaire remarks (p. 95, n.):--"Il faut remarquer qu'Aristote ne
s'occupe que des modes universels dans la première et dans la seconde
figure, parceque, la démonstration étant toujours universelle, les
propositions qui expriment l'erreur opposée doivent l'être comme
elle. Ainsi ce sont les propositions contraires, et non les
contradictoires, dont il sera question ici."
For the like reason the Third figure is not mentioned here, but only
the First and Second: because in the Third figure no universal
conclusion can be proved (Julius Pacius, p. 431).]
[Footnote 48: Analyt. Post. I. xvi. p. 80, a. 6-26.]
[Footnote 49: Ibid. a. 27-b. 14: [Greek: e)n de\ tô=| me/sô|
schê/mati o(/las me\n ei)=nai ta\s prota/seis a)mphote/ras pseudei=s
ou)k e)nde/chetai--e)pi/ ti d' e(kate/ran ou)de\n kôlu/ei pseudê=
ei)=nai.]]
Let us next assume the affirmative proposition, All B is A, to be
true, but mediate and deducible through the middle term C. If you
conclude the contrary of this (No B is A) through the same middle
term C, in the First figure, your error cannot arise from falsity in
the minor premiss, because your minor (by the laws of the figure)
must be affirmative; your error must arise from a false major,
because a negative major is not inconsistent with the laws of the
First figure. On the other hand, if you conclude the contrary in the
First figure through a different middle term, D, either both your
premisses will be false, or your minor premiss will be false.[50] If
you employ the Second figure to conclude your contrary, both your
premisses cannot be false, though either one of them singly may be
false.[51]
[Footnote 50: Analyt. Post. I. xvi. p. 80, b. 17-p. 81, a. 4.]
[Footnote 51: Ibid. p. 81, a. 5-14.]
Such will be the case when the deducible proposition assumed to be
true is affirmative, and when therefore the contrary conclusion which
you profess to have proved is negative. But if the deducible
proposition assumed to be true is negative, and if consequently the
contrary conclusion must be affirmative,--then, if you try to prove
this contrary through the same middle term, your premisses cannot
both be false, but your major premiss must always be false.[52] If,
however, you try to prove the contrary through a different and
inappropriate middle term, you cannot convert the minor premiss to
its contrary (because the minor premiss must continue affirmative, in
order that you may arrive at any conclusion at all), but the major
can be so converted. Should the major premiss thus converted be true,
the minor will be false; should the major premiss thus converted be
false, the minor may be either true or false. Either one of the
premisses, or both the premisses, may thus be false.[53]
[Footnote 52: Ibid. xvii. p. 81, a. 15-20.]
[Footnote 53: Ibid. a. 20-34. Mr. Poste's translation (pp. 65-70) is
very perspicuous and instructive in regard to these two difficult
chapters.]
Errors of simple ignorance (not concluded from false syllogism) may
proceed from defect or failure of sensible perception, in one or
other of its branches. For without sensation there can be no
induction; and it is from induction only that the premisses for
demonstration by syllogism are obtained. We cannot arrive at
universal propositions, even in what are called abstract sciences,
except through induction of particulars; nor can we demonstrate
except from universals. Induction and Demonstration are the only two
ways of learning; and the particulars composing our inductions can
only be known through sense.[54]
[Footnote 54: Analyt. Post. I. xviii. p. 81, a. 38-b. 9. In this
important chapter (the doctrines of which are more fully expanded in
the last chapter of the Second Book of the Analyt. Post.), the text
of Waitz does not fully agree with that of Julius Pacius. In Firmin
Didot's edition the text is the same as in Waitz; but his Latin
translation remains adapted to that of Julius Pacius. Waitz gives the
substance of the chapter as follows (ad Organ. II. p. 347):--
"Universales propositiones omnes inductione comparantur, quum etiam
in iis, quæ a sensibus maxime aliena videntur et quæ, ut mathematica
([Greek: ta\ e)x a)phaire/seôs]), cogitatione separantur à materia
quacum conjuncta sunt, inductione probentur ea quæ de genero (e. g.,
de linea vel de corpore mathematico), ad quod demonstratio pertineat,
prædicentur [Greek: kath' au(ta/] et cum ejus natura conjuncta sint.
Inductio autem iis nititur quæ sensibus percipiuntur; nam res
singulares sentiuntur, scientia vero rerum singularium non datur sine
inductione, non datur inductio sine sensu."]
Aristotle next proceeds to show (what in previous passages he had
assumed)[55] that, if Demonstration or the syllogistic process be
possible--if there be any truths supposed demonstrable, this implies
that there must be primary or ultimate truths. It has been explained
that the constituent elements assumed in the Syllogism are three
terms and two propositions or premisses; in the major premiss, A is
affirmed (or denied) of all B; in the minor, B is affirmed of all C;
in the conclusion, A is affirmed (or denied) of all C.[56] Now it is
possible that there may be some one or more predicates higher than A,
but it is impossible that there can be an infinite series of such
higher predicates. So also there may be one or more subjects lower
than C, and of which C will be the predicate; but it is impossible
that there can be an infinite series of such lower subjects. In like
manner there may perhaps be one or more middle terms between A and B,
and between B and C; but it is impossible that there can be an
infinite series of such intervening middle terms. There must be a
limit to the series ascending, descending, or intervening.[57] These
remarks have no application to reciprocating propositions, in which
the predicate is co-extensive with the subject.[58] But they apply
alike to demonstrations negative and affirmative, and alike to all
the three figures of Syllogism.[59]
[Footnote 55: Analyt. Prior. I. xxvii. p. 43, a. 38; Analyt. Post. I.
ii. p. 71, b. 21.]
[Footnote 56: Analyt. Post. I. xix. p. 81, b. 10-17.]
[Footnote 57: Ibid. p. 81, b. 30-p. 82, a. 14.]
[Footnote 58: Ibid. p. 82, a. 15-20. M. Barthélemy St. Hilaire, p.
117:--"Ceci ne saurait s'appliquer aux termes réciproques, parce que
dans les termes qui peuvent être attribués réciproquement l'un à
l'autre, on ne peut pas dire qu'il y ait ni premier ni dernier
rélativement à l'attribution."]
[Footnote 59: Analyt. Post. I. xx., xxi. p. 82, a. 21-b. 36.]
In Dialectical Syllogism it is enough if the premisses be admitted or
reputed as propositions immediately true, whether they are so in
reality or not; but in Scientific or Demonstrative Syllogism they
must be so in reality: the demonstration is not complete unless it
can be traced up to premisses that are thus immediately or directly
true (without any intervening middle term).[60] That there are and
must be such primary or immediate premisses, Aristotle now undertakes
to prove, by some dialectical reasons, and other analytical or
scientific reasons.[61] He himself thus distinguishes them; but the
distinction is faintly marked, and amounts, at most, to this, that
the analytical reasons advert only to essential predication, and to
the conditions of scientific demonstration, while the dialectical
reasons dwell upon these, but include something else besides, viz.,
accidental predication. The proof consists mainly in the declaration
that, unless we assume some propositions to be true immediately,
indivisibly, undemonstrably,--Definition, Demonstration, and Science
would be alike impossible. If the ascending series of predicates is
endless, so that we never arrive at a highest generic predicate; if
the descending series of subjects is endless, so that we never reach
a lowest subject,--no definition can ever be attained. The essential
properties included in the definition, must be finite in number; and
the accidental predicates must also be finite in number, since they
have no existence except as attached to some essential subject, and
since they must come under one or other of the nine later
Categories.[62] If, then, the two extremes are thus fixed and
finite--the highest predicate and the lowest subject--it is
impossible that there can be an infinite series of terms between the
two. The intervening terms must be finite in number. The
Aristotelian theory therefore is, that there are certain
propositions directly and immediately true, and others derived from
them by demonstration through middle terms.[63] It is alike an error
to assert that every thing can be demonstrated, and that nothing can
be demonstrated.
[Footnote 60: Ibid. xix. p. 81, b. 18-29.]
[Footnote 61: Ibid. xxi. p. 82, b. 35; xxii. p. 84, a. 7: [Greek:
_logikô=s_ me\n ou)=n e)k tou/tôn a)/n tis pisteu/seie peri\ tou=
lechthe/ntos, _a)nalutikô=s_ de\ dia\ tô=nde phanero\n
suntomô/teron.] In Scholia, p. 227, a. 42, the same distinction is
expressed by Philoponus in the terms [Greek: logikô/tera] and [Greek:
pragmatôde/stera]. Compare Biese, Die Philosophie des Aristoteles,
pp. 134, 261; Bassow, De Notionis Definitione, pp. 19, 20; Heyder,
Aristot. u. Hegel. Dialektik, pp. 316, 317.
Aristotle, however, does not always adhere closely to the
distinction. Thus, if we compare the _logical_ or _dialectical_
reasons given, p. 82, b. 37, seq., with the _analytical_, announced
as beginning p. 84, a. 8, seq., we find the same main topic dwelt
upon in both, namely, that to admit an infinite series excludes the
possibility of Definition. Both Alexander and Ammonius agree in
announcing this as the capital topic on which the proof turned; but
Alexander inferred from hence that the argument was purely
_dialectical_ ([Greek: logiko\n e)pichei/rêma]), while Ammonius
regarded it as a reason thoroughly convincing and evident: [Greek: o(
me/ntoi philo/sophos] (Ammonius) [Greek: e)/lege mê\ dia\ tou=to
le/gein _logika\_ ta\ e)picheirê/mata; e)narge\s ga\r o(/ti ei)si\n
o(rismoi/, ei) mê\ a)katalêpsi/an ei)saga/gômen] (Schol. p. 227, a.
40, seq., Brand.).]
[Footnote 62: Analyt. Post. I. xxii. p. 83, a. 20, b. 14. Only eight
of the ten Categories are here enumerated.]
[Footnote 63: Ibid. I. xxii. p. 84, a. 30-35. The paraphrase of
Themistius (pp. 55-58, Spengel) states the Aristotelian reasoning in
clearer language than Aristotle himself. Zabarella (Comm. in Analyt.
Post. I. xviii.; context. 148, 150, 154) repeats that Aristotle's
proof is founded upon the undeniable fact that there _are_
definitions, and that without them there could be no demonstration
and no science. This excludes the supposition of an infinite series
of predicates and of middle terms:--"Sumit rationem à definitione; si
in _predicatis in quid_ procederetur ad infinitum, sequeretur auferri
definitionem et omnino essentiæ cognitionem; sed hoc dicendum non
est, quum omnium consensioni adversetur" (p. 466, Ven. 1617).]
It is plain from Aristotle's own words[64] that he intended these
four chapters (xix.-xxii.) as a confirmation of what he had already
asserted in chapter iii. of the present treatise, and as farther
refutation of the two distinct classes of opponents there indicated:
(1) those who said that everything was demonstrable, demonstration in
a circle being admissible; (2) those who said that nothing was
demonstrable, inasmuch as the train of predication upwards,
downwards, and intermediate, was infinite. Both these two classes of
opponents agreed in saying, that there were no truths immediate and
indemonstrable; and it is upon this point that Aristotle here takes
issue with them, seeking to prove that there are and must be such
truths. But I cannot think the proof satisfactory; nor has it
appeared so to able commentators either of ancient or modern
times--from Alexander of Aphrodisias down to Mr. Poste.[65] The
elaborate amplification added in these last chapters adds no force to
the statement already given at the earlier stage; and it is in one
respect a change for the worse, inasmuch as it does not advert to the
important distinction announced in chapter iii., between universal
truths known by Induction (from sense and particulars), and universal
truths known by Deduction from these. The truths immediate and
indemonstrable (not known through a middle term) are the inductive
truths, as Aristotle declares in many places, and most emphatically
at the close of the Analytica Posteriora. But in these chapters, he
hardly alludes to Induction. Moreover, while trying to prove that
there must be immediate universal truths, he neither gives any
complete list of them, nor assigns any positive characteristic
whereby to identify them. Opponents might ask him whether these
immediate universal truths were not ready-made inspirations of the
mind; and if so, what better authority they had than the Platonic
Ideas, which are contemptuously dismissed.
[Footnote 64: Analyt. Post. I. xxii. p. 84, a. 32: [Greek: o(/per
e)/phame/n tinas le/gein kat' a)rcha/s], &c.]
[Footnote 65: See Mr. Poste's note, p. 77, of his translation of this
treatise. After saying that the first of Aristotle's _dialectical_
proofs is faulty, and that the second is a _petitio principii_, Mr.
Poste adds, respecting the so-called _analytical_ proof given by
Aristotle:--"It is not so much a proof, as a more accurate
determination of the principle to be postulated. This postulate, the
existence of first principles, as concerning the constitution of the
world, appears to belong properly to Metaphysics, and is merely
borrowed by Logic. See Metaph. ii. 2, and Introduction." In the
passage of the Metaphysica ([Greek: a]. p. 994) here cited the main
argument of Aristotle is open to the same objection of _petitio
principii_ which Mr. Poste urges against Aristotle's second
_dialectical_ argument in this place.
Mr. John Stuart Mill, in his System of Logic, takes for granted that
there _must_ be immediate, indemonstrable truths, to serve as a basis
for deduction; "that there cannot be a chain of proof suspended from
nothing;" that there must be ultimate laws of nature, though we
cannot be sure that the laws now known to us are ultimate.
On the other hand, we read in the recent work of an acute
contemporary philosopher, Professor Delboeuf (Essai de Logique
Scientifique, Liège, 1865, Pref. pp. v, vii, viii, pp. 46, 47:)--"Il
est des points sur lesquels je crains de ne m'être pas expliqué assez
nettement, entre autres la question du fondement de la certitude. Je
suis de ceux qui repoussent de toutes leurs forces l'axiome si
spécieux qu'on ne peut tout démontrer; cette proposition aurait, à
mes yeux, plus besoin que toute autre d'une démonstration. Cette
démonstration ne sera en partie donnée que quand on aura une bonne
fois énuméré toutes les propositions indémontrables; et quand on aura
bien défini le caractère auquel on les reconnait. Nulle part on ne
trouve ni une semblable énumération, ni une semblable définition. On
reste à cet égard dans une position vague, et par cela même facile à
défendre."
It would seem, by these words, that M. Delboeuf stands in the most
direct opposition to Aristotle, who teaches us that the [Greek:
a)rchai\] or _principia_ from which demonstration starts cannot be
themselves demonstrated. But when we compare other passages of M.
Delboeuf's work, we find that, in rejecting all undemonstrable
propositions, what he really means is to reject all _self-evident
universal truths_, "C'est donc une véritable illusion d'admettre des
vérités évidentes par elles-mêmes. Il n'y a pas de proposition fausse
que nous ne soyons disposés d'admettre comme axiome, quand rien ne
nous a encore autorisés à la repousser" (p. ix.). This is quite true
in my opinion; but the immediate indemonstrable truths for which
Aristotle contends as [Greek: a)rchai\] of demonstration, are not
announced by him as _self-evident_, they are declared to be results
of sense and induction, to be raised from observation of particulars
multiplied, compared, and permanently formularized under the
intellectual _habitus_ called Noûs. By Demonstration Aristotle means
deduction in its most perfect form, beginning from these [Greek:
a)rchai\] which are inductively known but not demonstrable (_i. e._
not knowable deductively). And in this view the very able and
instructive treatise of M. Delboeuf mainly coincides, assigning even
greater preponderance to the inductive process, and approximating in
this respect to the important improvements in logical theory advanced
by Mr. John Stuart Mill.
Among the universal propositions which are not derived from
Induction, but which serve as [Greek: a)rchai\] for Deduction and
Demonstration, we may reckon the religious, ethical, æsthetical,
social, political, &c., beliefs received in each different community,
and impressed upon all newcomers born into it by the force of
precept, example, authority. Here the major premiss is felt by each
individual as carrying an authority of its own, stamped and enforced
by the sanction of society, and by the disgrace or other penalties in
store for those who disobey it. It is ready to be interpreted and
diversified by suitable minor premisses in all inferential
applications. But these [Greek: a)rchai\] for deduction, differing
widely at different times and places, though generated in the same
manner and enforced by the same sanction, would belong more properly
to the class which Aristotle terms [Greek: ta\ e)/ndoxa].]
We have thus recognized that there exist immediate (ultimate or
primary) propositions, wherein the conjunction between predicate and
subject is such that no intermediate term can be assigned between
them. When A is predicated both of B and C, this may perhaps be in
consequence of some common property possessed by B and C, and such
common property will form a middle term. For example, equality of
angles to two right angles belongs both to an isosceles and to a
scalene triangle, and it belongs to them by reason of their common
property--triangular figure; which last is thus the middle term. But
this need not be always the case.[66] It is possible that the two
propositions--A predicated of B, A predicated of C--may both of them
be immediate propositions; and that there may be no community of
nature between B and C. Whenever a middle term can be found,
demonstration is possible; but where no middle term can be found,
demonstration is impossible. The proposition, whether affirmative or
negative, is then an immediate or indivisible one. Such propositions,
and the terms of which they are composed, are the ultimate elements
or _principia_ of Demonstration. Predicate and subject are brought
constantly into closer and closer conjunction, until at last they
become one and indivisible.[67] Here we reach the unit or element of
the syllogizing process. In all scientific calculations there is
assumed an unit to start from, though in each branch of science it is
a different unit; _e.g._ in barology, the pound-weight; in harmonics,
the quarter-tone; in other branches of science, other units.[68]
Analytical research teaches us that the corresponding unit in
Syllogism is the affirmative or negative proposition which is
primary, immediate, indivisible. In Demonstration and Science it is
the Noûs or Intellect.[69]
[Footnote 66: Analyt. Post. I. xxiii. p. 84, b. 3-18. [Greek: tou=to
d' ou)k a)ei\ ou(/tôs e)/chei.]]
[Footnote 67: Ibid. b. 25-37. [Greek: a)ei\ to\ me/son puknou=tai,
e(/ôs a)diai/reta ge/nêtai kai\ e(/n. e)/sti d' e(/n, o(/tan a)/meson
ge/nêtai kai\ mi/a pro/tasis a(plô=s ê( a)/mesos.]]
[Footnote 68: Analyt. Post. I. xxiii. p. 84, b. 37: [Greek: kai\
ô(/sper e)n toi=s a)/llois ê( a)rchê\ a(plou=n, tou=to d' ou) tau)to\
pantachou=, a)ll' e)n barei= me\n mna=, e)n de\ me/lei di/esis,
a)/llo d' e)n a)/llô|, ou(/tôs e)n sullogismô=| to\ e(\n pro/tasis
a)/mesos, e)n d' a)podei/xei kai\ e)pistê/mê| o( nou=s.]]
[Footnote 69: Ibid. b. 35-p. 85, a. 1.]
Having thus, in the long preceding reasoning, sought to prove that
all demonstration must take its departure from primary undemonstrable
_principia_--from some premisses, affirmative and negative, which are
directly true in themselves, and not demonstrable through any middle
term or intervening propositions, Aristotle now passes to a different
enquiry. We have some demonstrations in which the conclusion is
Particular, others in which it is Universal: again, some Affirmative,
some Negative, Which of the two, in each of these alternatives, is
the best? We have also demonstrations Direct or Ostensive, and
demonstrations Indirect or by way of _Reductio ad Absurdum_. Which of
these two is the best? Both questions appear to have been subjected
to debate by contemporary philosophers.[70]
[Footnote 70: Ibid. xxiv. p. 85, a. 13-18. [Greek: a)mphisbêtei=tai
pote/ra belti/ôn; ô(s d' au(/tôs kai\ peri\ tê=s a)podeiknu/nai
legome/nês kai\ tê=s ei)s to\ a)du/naton a)gou/sês a)podei/xeôs.]]
Aristotle discusses these points dialectically (as indeed he points
out in the Topica that the comparison of two things generally, as to
better and worse, falls under the varieties of
**dialectical enquiry[71]), first stating and next refuting
the arguments on the weaker side. Some persons may think (he says)
that demonstration of the Particular is better than demonstration of
the Universal: first, because it conducts to fuller cognition of that
which the thing is in itself, and not merely that which it is
_quatenus_ member of a class; secondly, because demonstrations of the
Universal are apt to generate an illusory belief, that the Universal
is a distinct reality apart from and independent of all its
particulars (_i.e._, that figure in general has a real existence
apart from all particular figures, and number in general apart from
all particular numbers, &c.), while demonstrations of the Particular
do not lead to any such illusion.[72]
[Footnote 71: Aristot. Topic. III. i. p. 116, a. 1, seq.]
[Footnote 72: Analyt. Post. I. xxiv. p. 85, a. 20-b. 3. Themistius,
pp. 58-59, Spengel: [Greek: ou) ga\r o(mô/numon to\ katho/lou
e)sti/n, ou)de\ phônê\ mo/non, a)ll' u(po/stasis, ou) chôristê\ me\n
ô(/sper ou)de\ ta\ sumbebêko/ta, e)nargô=s d' ou)=n emphainome/nê
toi=s pra/gmasin.] The Scholastic doctrine of _Universalia in re_ is
here expressed very clearly by Themistius.]
To these arguments Aristotle replies:--1. It is not correct to say
that cognition of the Particular is more complete, or bears more upon
real existence, than cognition of the Universal. The reverse would be
nearer to the truth. To know that the isosceles, _quatenus_ triangle,
has its three angles equal to two right angles, is more complete
cognition than knowing simply that the isosceles has its three angles
equal to two right angles. 2. If the Universal be not an equivocal
term--if it represents one property and one definition common to many
particulars, it then has a real existence as much or more than any
one or any number of the particulars. For all these particulars are
perishable, but the class is imperishable. 3. He who believes that
the universal term has one meaning in all the particulars, need not
necessarily believe that it has any meaning _apart_ from all
particulars; he need not believe this about Quiddity, any more than
he believes it about Quality or Quantity. Or if he does believe so,
it is his own individual mistake, not imputable to the demonstration.
4. We have shown that a complete demonstration is one in which the
middle term is the cause or reason of the conclusion. Now the
Universal is most of the nature of Cause; for it represents the First
Essence or the _Per Se_, and is therefore its own cause, or has no
other cause behind it. The demonstration of the Universal has thus
more of the Cause or the _Why_, and is therefore better than the
demonstration of the Particular. 5. In the Final Cause or End of
action, there is always some ultimate end for the sake of which the
intermediate ends are pursued, and which, as it is better than they,
yields, when it is known, the only complete explanation of the
action. So it is also with the Formal Cause: there is one highest
form which contains the _Why_ of the subordinate forms, and the
knowledge of which is therefore better; as when, for example, the
exterior angles of a given isosceles triangle are seen to be equal to
four right angles, not because it is isosceles or triangle, but
because it is a rectilineal figure. 6. Particulars, as such, fall
into infinity of number, and are thus unknowable; the Universal tends
towards oneness and simplicity, and is thus essentially knowable,
more fully demonstrable than the infinity of particulars. The
demonstration thereof is therefore better. 7. It is also better, on
another ground; for he that knows the Universal does in a certain
sense know also the Particular;[73] but he that knows the Particular
cannot be said in any sense to know the Universal. 8. The
_principium_ or perfection of cognition is to be found in the
immediate proposition, true _per se_. When we demonstrate, and thus
employ a middle term, the nearer the middle term approaches to that
_principium_, the better the demonstration is. The demonstration of
the Universal is thus better and more accurate than that of the
Particular.[74]
[Footnote 73: Compare Analyt. Post. I. i. p. 71, a. 25; also
Metaphys. A. p. 981, a. 12.]
[Footnote 74: Analyt. Post. I. xxiv. p. 85, b. 4-p. 86, a. 21. Schol.
p. 233, b. 6: [Greek: o(moi/ôs de\ o)/ntôn gnôri/môn, ê( di'
e)latto/nôn me/sôn ai(retôte/ra; ma=llon ga\r e)ggute/rô tê=s tou=
nou= e)nergei/as.]]
Such are the several reasons enumerated by Aristotle in refutation of
the previous opinion stated in favour of the Particular. Evidently he
does not account them all of equal value: he intimates that some are
purely dialectical ([Greek: logika/]); and he insists most upon the
two following:--1. He that knows the Universal knows in a certain
sense the Particular; if he knows that every triangle has its three
angles equal to two right angles, he knows potentially that the
isosceles has its three angles equal to the same, though he may not
know as yet that the isosceles _is_ a triangle. But he that knows the
Particular does not in any way know the Universal, either actually or
potentially.[75] 2. The Universal is apprehended by Intellect or
Noûs, the highest of all cognitive powers; the Particular terminates
in sensation. Here, I presume, he means, that, in demonstration of
the Particular, the conclusion teaches you nothing more than you
might have learnt from a direct observation of sense; whereas in that
of the Universal the conclusion teaches you more than you could have
learnt from direct sensation, and comes into correlation with the
highest form of our intellectual nature.[76]
[Footnote 75: Analyt. Post. I. xxiv. p. 86**, a. 22: [Greek: a)lla\
tô=n me\n ei)rême/nôn e)/nia logika/ e)sti; _ma/lista_ de\ dê=lon
o(/ti ê( katho/lou kuriôte/ra, o(/ti--o( de\ tau/tên e)/chôn tê\n
pro/tasin] (the Particular) [Greek: _to\ katho/lou ou)damô=s oi)=den,
ou)/te duna/mei ou)/t' e)nergei/a|_.]]
[Footnote 76: Ibid. a. 29: [Greek: kai\ ê( me\n katho/lou noêtê/, ê(
de\ kata\ me/ros ei)s ai)/sthêsin teleuta=|.] Compare xxiii. p. 84,
b. 39, where we noticed the doctrine that [Greek: Nou=s] is the
_unit_ of scientific demonstration.]
Next, Aristotle compares the Affirmative with the Negative
demonstration, and shows that the Affirmative is the better. Of two
demonstrations (he lays it down) that one which proceeds upon a
smaller number of postulates, assumptions, or propositions, is better
than the other; for, to say nothing of other reasons, it conducts you
more speedily to knowledge than the other, and that is an advantage.
Now, both in the affirmative and in the negative syllogism, you must
have three terms and two propositions; but in the affirmative you
assume only that something _is_; while in the negative you assume
both that something _is_, and that something _is not_. Here is a
double assumption instead of a single; therefore the negative is the
worse or inferior of the two.[77] Moreover, for the demonstration of
a negative conclusion, you require one affirmative premiss (since
from two negative premisses nothing whatever can be concluded); while
for the demonstration of an affirmative conclusion, you must have two
affirmative premisses, and you cannot admit a negative. This, again,
shows that the affirmative is logically prior, more trustworthy, and
better than the negative.[78] The negative is only intelligible and
knowable through the affirmative, just as _Non-Ens_ is knowable only
through _Ens_. The affirmative demonstration therefore, as involving
better principles, is, on this ground also, better than the
negative.[79] _A fortiori_, it is also better than the demonstration
by way of _Reductio ad Absurdum_, which was the last case to be
considered. This, as concluding only indirectly and from
impossibility of the contradictory, is worse even than the negative;
much more therefore is it worse than the direct affirmative.[80]
[Footnote 77: Analyt. Post. I. xxv. p. 86, a. 31-b. 9.]
[Footnote 78: Ibid. b. 10-30.]
[Footnote 79: Ibid. b. 30-39.]
[Footnote 80: Ibid. I. xxvi. p. 87, a. 2-30. Waitz (II. p. 370),
says: "deductio (ad absurdum), quippe quæ per ambages cogat, post
ponenda, est demonstrationi rectæ."
Philoponus says (Schol. pp. 234-235**, Brand.) that the
Commentators all censured Aristotle for the manner in which he here
laid out the Syllogism [Greek: di' a)duna/tou]. I do not, however,
find any such censure in Themistius. Philoponus defends Aristotle
from the censure.]
If we next compare one Science with another, the prior and more
accurate of the two is, (1) That which combines at once the [Greek:
o(/ti] and the [Greek: dio/ti]; (2) That which is abstracted from
material conditions, as compared with that which is immersed
therein--for example, arithmetic is more accurate than harmonics;
(3) The more simple as compared with the more complex: thus,
arithmetic is more accurate than geometry, a monad or unit is a
substance without position, whereas a point (more concrete) is a
substance with position.[81] One and the same science is that which
belongs to one and the same generic subject-matter. The premisses of
a demonstration must be included in the same genus with the
conclusion; and where the ultimate premisses are heterogeneous, the
cognition derived from them must be considered as not one but a
compound of several.[82] You may find two or more distinct middle
terms for demonstrating the same conclusion; sometimes out of the
same logical series or table, sometimes out of different tables.[83]
[Footnote 81: Analyt. Post. I. xxvii. p. 87, a. 31-37. Themistius,
Paraphras. p. 60, ed. Speng.: [Greek: kat' a)/llon de\ (tro/pon),
e)a\n ê( me\n peri\ u(pokei/mena/ tina kai\ ai)sthêta\
pragmateu/êtai, ê( de\ peri\ noêta\ kai\ katho/lou.]
Philoponus illustrates this (Schol. p. 235, b. 41, Br.): [Greek:
oi(=on ta\ Theodosi/ou sphairika\ a)kribe/stera/ e)stin e)pistê/mê|
tê=s tô=n Au)tolu/kou peri\ kinoume/nês sphai/ras.] &c.]
[Footnote 82: Analyt. Post. I. xxviii. p. 87, a. 38-b. 5. Themistius,
p. 61: [Greek: dê=lon de\ tou=to gi/netai proi+ou=sin e)pi\ ta\s
a)napodei/ktous a)rcha/s; au(=tai ga\r ei) mêdemi/an e)/choien
sugge/neian, e(/terai ai( e)pistê=mai.]]
[Footnote 83: Analyt. Post. I. xxix. p. 87, b. 5-18. Aristotle gives
an example to illustrate this general doctrine: [Greek: ê(/desthai,
to\ kinei=sthai, to\ ê)remi/zesthai, to\ metaba/llein]. As he
includes these terms und this subject among the topics for
demonstration, it is difficult to see where he would draw a distinct
line between topics for Demonstration and topics for Dialectic.]
There cannot be demonstrative cognition of fortuitous events,[84] for
all demonstration is either of the necessary or of the customary. Nor
can there be demonstrative cognition through sensible perception. For
though by sense we perceive a thing as such and such (through its
sensible qualities), yet we perceive it inevitably as _hoc aliquid_,
_hic_, _et nunc_. But the Universal cannot be perceived by sense; for
it is neither _hic_ nor _nunc_, but _semper et ubique_.[85] Now
demonstrations are all accomplished by means of the Universal, and
demonstrative cognition cannot therefore be had through sensible
perception. If the equality of the three angles of a triangle to two
right angles were a fact directly perceivable by sense, we should
still have looked out for a demonstration thereof: we should have no
proper scientific cognition of it (though some persons contend for
this): for sensible perception gives us only particular cases, and
Cognition or Science proper comes only through knowing the
Universal.[86] If, being on the surface of the moon, we had on any
one occasion seen the earth between us and the sun, we could not have
known from that single observation that such interposition is the
cause universally of eclipses. We cannot directly by sense perceive
the Universal, though sense is the _principium_ of the Universal. By
multiplied observation of sensible particulars, we can hunt out and
elicit the Universal, enunciate it clearly and separately, and make
it serve for demonstration.[87] The Universal is precious, because it
reveals the Cause or [Greek: dio/ti], and is therefore more precious,
not merely than sensible observation, but also than intellectual
conception of the [Greek: o(/ti] only, where the Cause or [Greek:
dio/ti] lies apart, and is derived from a higher genus. Respecting
First Principles or _Summa Genera_, we must speak elsewhere.[88] It
is clear, therefore, that no demonstrable matter can be known,
properly speaking, from direct perception of sense; though there are
cases in which nothing but the impossibility of direct observation
drives us upon seeking for demonstration. Whenever we can get an
adequate number of sensible observations, we can generalize the fact;
and in some instances we may perhaps not seek for any demonstrative
knowledge (_i.e._ to explain it by any higher principle). If we could
see the pores in glass and the light passing through them, we should
learn through many such observations why combustion arises on the
farther side of the glass; each of our observations would have been
separate and individual, but we should by intellect generalize the
result that all the cases fall under the same law.[89]
[Footnote 84: Analyt. Post. I. xxx. p. 87, b. 19-27.]
[Footnote 85: Ibid. xxxi. p. 87, b. 28: [Greek: ei) ga\r kai\ e)/stin
ê( ai)/sthêsis tou= toiou=de kai\ mê\ tou=de/ tinos, a)ll'
ai)stha/nesthai/ ge a)nagkai=on to/de ti kai\ pou= kai\ nu=n.]]
[Footnote 86: Ibid. b. 35: [Greek: dê=lon o(/ti kai\ ei) ê)=n
ai)stha/nesthai to\ tri/gônon o(/ti dusi\n o)rthai=s i)/sas e)/chei
ta\s gôni/as, e)zêtou=men a)\n a)po/deixin, kai\ ou)ch (_ô(/sper
phasi/ tines_) ê)pista/metha; ai)stha/nesthai me\n ga\r a)na/gkê
kath' e(/kaston, ê( d' e)pistê/mê tô=| to\ katho/lou gnôri/zein
e)sti/n.]
Euclid, in the 20th Proposition of his first Book, demonstrates that
any two sides of a triangle are together greater than the third side.
According to Proklus, the Epikureans derided the demonstration of
such a point as absurd; and it seems that some contemporaries of
Aristotle argued in a similar way, judging by the phrase [Greek:
ô(/sper phasi/ tines].]
[Footnote 87: Analyt. Post. I. xxxi. p. 88, a. 2: [Greek: ou) mê\n
a)ll' e)k tou= theôrei=n tou=to polla/kis sumbai=non, to\ katho/lou
a)\n thêreu/santes a)po/deixin ei)/chomen; e)k ga\r tô=n kath'
e(/kasta pleio/nôn to\ katho/lou dê=lon.] Themistius, p. 62, Sp.:
[Greek: a)rchê\ me\n ga\r a)podei/xeôs ai)/sthêsis, kai\ to\
katho/lou e)nnoou=men dia\ to\ polla/kis ai)sthe/sthai.]]
[Footnote 88: Analyt. Post. I. xxxi. p. 88, a. 6: [Greek: to\ de\
katho/lou ti/mion, o(/ti dêloi= to\ ai)/tion; ô(/ste peri\ tô=n
toiou/tôn ê( katho/lou timiôte/ra tô=n ai)sthê/seôn kai\ tê=s
noê/seôs, o(/sôn e(/teron to\ ai)/tion; peri\ de\ tô=n prô/tôn
a)/llos lo/gos.]
By [Greek: ta\ prô=ta], he means the [Greek: a)rchai\] of
Demonstration, which are treated especially in II. xix. See Biese,
Die Philos. des Aristoteles, p. 277.]
[Footnote 89: Analyt. Post. I. xxxi. p. 88, a. 9-17. [Greek: e)/sti
me/ntoi e)/nia a)nago/mena ei)s ai)sthê/seôs e)/kleipsin e)n toi=s
problê/masin; e)/nia ga\r ei) e(ô/rômen, ou)k a)\n e)zêtou=men, ou)ch
ô(s ei)do/tes tô=| o(ra=|n, a)ll' ô(s e)/chontes to\ katho/lou e)k
tou= o(ra=|n.]
The text of this and the succeeding words seems open to doubt, as
well as that of Themistius (p. 63). Waitz in his note (p. 374)
explains the meaning clearly:--"non ita quidem ut ipsa sensuum
perceptio scientiam afferat; sed ita ut quod in singulis accidere
videamus, idem etiam in omnibus accidere coniicientes universe
intelligamus."]
Aristotle next proceeds to refute, at some length, the supposition,
that the _principia_ of all syllogisms are the same. We see at once
that this cannot be so, because some syllogisms are true, others
false. But, besides, though there are indeed a few Axioms essential
to the process of demonstration, and the same in all syllogisms, yet
these are not sufficient of themselves for demonstration. There must
farther be other premisses or matters of evidence--propositions
immediately true (or established by prior demonstrations) belonging
to each branch of Science specially, as distinguished from the
others. Our demonstration relates _to_ these special matters or
premisses, though it is accomplished _out of_ or by means of the
common Axioms.[90]
[Footnote 90: Analyt. Post. I. xxxii. p. 88, a. 18-b. 29. [Greek: ai(
ga\r a)rchai\ dittai/, e)x ô(=n te kai\ peri\ o(\; ai( me\n ou)=n e)x
ô(=n koinai/, ai( de\ peri\ o(/ i)/diai, oi(=on a)rithmo/s,
me/gethos.] Compare xi. p. 77, a. 27. See Barthélemy St. Hilaire,
Plan Général des Derniers Analytiques, p. lxxxi.]
Science or scientific Cognition differs from true Opinion, and the
_cognitum_ from the _opinatum_, herein, that Science is of the
Universal, and through necessary premisses which cannot be otherwise;
while Opinion relates to matters true, yet which at the same time may
possibly be false. The belief in a proposition which is immediate
(_i. e._, undemonstrable) yet not necessary, is Opinion; it is not
Science, nor is it Noûs or Intellect--the _principium_ of Science or
scientific Cognition. Such beliefs are fluctuating, as we see every
day; we all distinguish them from other beliefs, which we cannot
conceive not to be true and which we call cognitions.[91] But may
there not be Opinion and Cognition respecting the same matters? There
may be (says Aristotle) in different men, or in the same man at
different times; but not in the same man at the same time. There may
also be, respecting the same matter, true opinion in one man's mind,
and false opinion in the mind of another.[92]
[Footnote 91: Analyt. Post. I. xxxiii. p. 88, b. 30-p. 89, a. 10.]
[Footnote 92: Ibid. p. 89, a. 11-b. 6. That eclipse of the sun is
caused by the interposition of the moon was to the astronomer
Hipparchos scientific Cognition; for he saw that it _could not_ be
otherwise. To the philosopher Epikurus it was Opinion; for he thought
that it _might_ be otherwise (Themistius, p. 66, Spengel).]
With some remarks upon Sagacity, or the power of divining a middle
term in a time too short for reflection (as when the friendship of
two men is on the instant referred to the fact of their having a
common enemy), the present book is brought to a close.[93]
[Footnote 93: Ibid. xxxiv. p. 89, b. 10-20.]
CHAPTER VIII.
ANALYTICA POSTERIORA II.
Aristotle begins the Second Book of the Analytica Posteriora by an
enumeration and classification of Problems or Questions suitable for
investigation. The matters knowable by us may be distributed into
four classes:--
[Greek: O(/ti]. [Greek: Dio/ti]. [Greek: Ei) e)/sti]. [Greek: Ti/
e)sti].
1. Quod. 2. Cur. 3. An sit. 4. Quid sit.
Under the first head come questions of Fact; under the second head,
questions of Cause or Reason; under the third, questions of
Existence; under the fourth, questions of Essence. Under the first
head we enquire, Whether a fact or event is so or so? Whether a given
subject possesses this or that attribute, or is in this or that
condition? enumerating in the question the various supposable
alternatives. Under the second head, we assume the first question to
have been affirmatively answered, and we proceed to enquire, What is
the cause or reason for such fact, or such conjunction of subject and
attribute? Under the third head, we ask, Does a supposed subject
exist? And if the answer be in the affirmative, we proceed to
enquire, under the fourth head, What is the essence of the
subject?[1]
[Footnote 1: Analyt. Post. II. i. p. 89, b. 23, seq. Themistius
observes, p. 67, Speng.: [Greek: zêtou=men ti/nun ê)\ peri\ a(plou=
tino\s kai\ a)sunthe/tou, ê)\ peri\ sunthe/tou kai\ e)n prota/sei.]
Themistius has here changed Aristotle's order, and placed the third
and fourth heads before the first and second. Compare Schol. p. 240,
b. 30; p. 241, a. 18. The Scholiast complains of the enigmatical
style of Aristotle: [Greek: tê=| griphô/dei tou= r(êtou= e)paggeli/a]
(p. 240, b. 25).]
We have here two distinct pairs of _Quæsita_: Obviously the second
head presupposes the first, and is consequent thereupon; while the
fourth also presupposes the third. But it might seem a more suitable
arrangement (as Themistius and other expositors have conceived) that
the third and fourth heads should come first in the list, rather than
the first and second; since the third and fourth are simpler, and
come earlier in the order of philosophical exposition, while the
first and second are more complicated, and cannot be expounded
philosophically until after the philosophical exposition of the
others. This is cleared up by adverting to the distinction, so often
insisted on by Aristotle, between what is first in order of cognition
relatively to us (_nobis notiora_), and what is first in order of
cognition by nature (_naturâ notiora_). _To us_ (that is to men taken
individually and in the course of actual growth) the phenomena of
nature[2] present themselves as particulars confused and complicated
in every way, with attributes essential and accidental implicated
together: we gradually learn first to see and compare them as
particulars, next to resolve them into generalities, bundles,
classes, and partially to explain the _Why_ of some by means of
others. Here we start from facts embodied in propositions, that
include subjects clothed with their attributes. But in the _order of
nature_ (that is, in the order followed by those who know the
_scibile_ as a whole, and can expound it scientifically) that which
comes first is the Universal or the simple Subject abstracted from
its predicates or accompaniments: we have to enquire, first, whether
a given subject exists; next, if it does exist, what is its real
constituent essence or definition. We thus see the reason for the
order in which Aristotle has arranged the two co-ordinate pairs of
_Quæsita_ or Problems, conformable to the different processes
pursued, on the one hand, by the common intellect, growing and
untrained--on the other, by the mature or disciplined intellect,
already competent for philosophical exposition and applying itself to
new _incognita_.
[Footnote 2: **Schol. Philopon. p. 241, a. 18-24: [Greek:
tou/tôn to\ ei) e)/sti kai\ to\ ti/ e)stin ei)si\n a(pla=, to\ de\
o(/ti kai\ to\ dio/ti su/ntheta--pro/tera ga\r ê(mi=n kai\
gnôrimô/tera ta\ su/ntheta, ô(s tê=| phu/sei ta\ a(pla=.]
Mr. Poste observes upon this quadruple classification by Aristotle
(p. 96):--"The two last of these are problems of Inductive, but first
principles of Deductive, Science; the one being the hypothesis, the
other the definition. The **attribute as well as the subject
must be defined (I. x.), so that to a certain degree the second
problem also is assumed among the principles of Demonstration."]
Comparing together these four _Quæsita_, it will appear that in the
first and third (_Quod_ and _An_), we seek to find out whether there
is or is not any middle term. In the second and fourth (_Cur_ and
_Quid_), we already know or assume that there is a middle term; and
we try to ascertain what that middle term is.[3] The enquiry _Cur_,
is in the main analogous to the enquiry _Quid_; in both cases, we aim
at ascertaining what the cause or middle term is. But, in the enquiry
_Cur_, what we discover is perhaps some independent fact or event,
which is the cause of the event _quæsitum_; while, in the enquiry
_Quid_, what we seek is the real essence or definition of the
substance--the fundamental, generating, immanent cause of its
concomitant attributes. Sometimes, however, the _Quid_ and the _Cur_
are only different ways of stating the same thing. _E.g._, _Quid est
eclipsis lunæ_? Answer: The essence of an eclipse is a privation of
light from the moon, through intervention of the earth between her
and the sun. _Cur locum habet eclipsis lunæ_? Answer: Because the
light of the sun is prevented from reaching the moon by intervention
of the earth. Here it is manifest that the answers to the enquiries
_Quid_ and _Cur_ are really and in substance the same fact, only
stated in different phrases.[4]
[Footnote 3: Analyt. Post. II. i. p. 889, b. 37-p. 90, a. 7. [Greek:
sumbai/nei a)/ra e)n a(pa/sais tai=s zêtê/sesi zêtei=n ê)\ ei) e)/sti
me/son, ê)\ ti/ e)sti to\ me/son; to\ me\n ga\r ai)/tion to\ me/son,
e)n a(/pasi de\ tou=to zêtei=tai.] Compare Schol. p. 241, b. 10, Br.]
[Footnote 4: Analyt. Post. II. ii. p. 90, a. 14-23, 31: [Greek: to\
ti/ e)stin ei)de/nai tau)to/ e)sti kai\ dia\ ti/ e)stin.]]
That the _quæsitum_ in all these researches is a middle term or
medium, is plain from those cases wherein the medium is perceivable
by sense; for then we neither require nor enter upon research. For
example, if we were upon the moon, we should see the earth coming
between us and the sun, now and in each particular case of eclipse.
Accordingly, after many such observations, we should affirm the
universal proposition, that such intervention of the earth was the
cause of eclipses; the universal becoming known to us through
induction of particular cases.[5] The middle term, the Cause, the
_Quid_, and the _Cur_, are thus all the same enquiry, in substance;
though sometimes such _quæsitum_ is the quiddity or essential nature
of the thing itself (as the essence of a triangle is the cause or
ground of its having its three angles equal to two right angles, as
well as of its other properties), sometimes it is an extraneous
fact.[6]
[Footnote 5: Ibid. a. 24-30. [Greek: e)k ga\r tou= ai)sthe/sthai kai\
to\ katho/lou e)ge/neto a)\n ê(mi=n ei)de/nai; ê( me\n ga\r
ai)/sthêsis o(/ti nu=n a)ntiphra/ttei; kai\ ga\r dê=lon o(/ti nu=n
e)klei/pei; e)k de\ tou/tou to\ katho/lou a)\n e)ge/neto.]
The purport and relation of this quadruple classification of problems
is set forth still more clearly in the sixth book of the Metaphysica
(Z. p. 1041) with the explanations of Bonitz, Comm. pp. 358, 359.]
[Footnote 6: Analyt. Post. II. ii. p. 90, a. 31.]
But how or by what process is this _quæsitum_ obtained and made
clear? Is it by Demonstration or by Definition? What is Definition,
and what matters admit of Definition?[7] Aristotle begins by treating
the question dialectically; by setting out a series of doubts and
difficulties. First, Is it possible that the same cognition, and in
the same relation, can be obtained both by Definition and by
Demonstration? No; it is not possible. It is plain that much that is
known by Demonstration cannot be known by Definition; for we have
seen that conclusions both particular and negative are established by
Demonstration (in the Third and Second figures), while every
Definition is universal and affirmative. But we may go farther and
say, that even where a conclusion universal and affirmative is
established (in the First figure) by Demonstration, that same
conclusion can never be known by Definition; for if it could be known
by Definition, it might have been known without Demonstration. Now we
are assured, by an uncontradicted induction, that this is not the
fact; for that which we know by Demonstration is either a proprium of
the subject _per se_, or an accident or concomitant; but no
Definition ever declares either the one or the other: it declares
only the essence.[8]
[Footnote 7: Ibid. iii. p. 90, a. 37: [Greek: ti/ e)stin o(rismo/s,
kai\ ti/nôn, ei)/pômen, diaporê/santes prô=ton peri\ au)tô=n.]]
[Footnote 8: Analyt. Post. II. iii. p. 90, b. 13: [Greek: i(kanê\ de\
pi/stis kai\ e)k tê=s e)pagôgê=s; ou)de\n ga\r pô/pote o(risa/menoi
e)/gnômen, ou)/te tô=n kath' au(to\ u(parcho/ntôn ou)/te tô=n
sumbebêko/tôn. e)/ti ei) o( o(rismo\s ou)si/as tis gnôrismo/s, ta\ ge
toiau=ta phanero\n o(/ti ou)k ou)si/ai.]]
Again, let us ask, _vice versâ_, Can everything that is declared by
Definition, or indeed anything that is declared by Definition, be
known also by Demonstration? Neither is this possible. One and the
same _cognitum_ can be known only by one process of cognition.
Definitions are the _principia_ from which Demonstration departs; and
we have already shown that in going back upon demonstrations, we must
stop somewhere, and must recognize some _principia_
undemonstrable.[9] The Definition can never be demonstrated, for it
declares only the essence of the subject, and does not predicate
anything concerning the subject; whereas Demonstration assumes the
essence to be known, and deduces from such assumption an attribute
distinct from the essence.[10]
[Footnote 9: Ibid. b. 18-27.]
[Footnote 10: Ibid. b. 33, seq.: [Greek: e)/ti pa=sa a)po/deixis ti\
kata/ tinos dei/knusin, oi(=on o(/ti e)/stin ê)\ ou)k e)/stin; e)n
de\ tô=| o(rismô=| ou)de\n e(/teron e(te/rou katêgorei=tai, oi(=on
ou)/te to\ zô=|on kata\ tou= di/podos ou)de\ tou=to kata\ tou=
zô=|ou--o( me\n ou)=n o(rismo\s ti/ e)sti dêloi=, ê( de\ a)po/deixis
o(/ti ê)\ e)/sti to/de kata\ tou=de ê)\ ou)k e)/stin.]
Themistius (p. 71, Speng.) distinguishes the [Greek: o(rismo/s]
itself from [Greek: ê( pro/tasis ê( to\n o(rismo\n katêgorou/menon
e)/chousa].]
Prosecuting still farther the dialectical and dubitative
treatment,[11] Aristotle now proceeds to suggest, that the Essence
(that is, the entire Essence or Quiddity), which is declared by
Definition, can never be known by Demonstration. To suppose that it
could be so known, would be inconsistent with the conditions of the
syllogistic proof used in demonstrating. You prove by syllogism,
through a middle term, some predicate or attribute; _e.g._ because A
is predicable of all B, and B is predicable of all C, therefore A is
predicable of all C. But you cannot prove, through the middle term B,
that A is the essence or quiddity of C, unless by assuming in the
premisses that B is the essence of C, and that A is the essence of B;
accordingly, that the three propositions, AB, BC, AC, are all
co-extensive and reciprocate with each other. Here, then, you have
assumed as your premisses two essential propositions, AB, BC, in
order to prove as an essential proposition the conclusion AC. But
this is inadmissible; for your premisses require demonstration as
much as your conclusion. You have committed a _Petitio
Principii_;[12] you have assumed in your minor premiss the very point
to be demonstrated.
[Footnote 11: Analyt. Post. II. iv. p. 91, a. 12: [Greek: tau=ta me\n
ou)=n me/chri tou/tou diêporê/sthô]. One would think, by these words,
that [Greek: to\ diaporei=n] (or the dubitative treatment) finished
here. But the fact is not so: that treatment is continued for four
chapters more, to the commencement of ch. viii. p. 93.]
[Footnote 12: Analyt. Post. II. iv. p. 91, a. 12-32: [Greek: tau=ta
d' a)na/gkê antistre/phein; ei) ga\r to\ A tou= G i)/dion, dê=lon
o(/ti kai\ tou= B kai\ tou=to tou= G, ô(/ste pa/nta
a)llê/lôn.--lamba/nei ou)=n o(\ dei= dei=xai; kai\ ga\r to\ B e)/sti
ti/ e)stin a)/nthrôpos.] Themistius, pp. 72, 73: [Greek: to\n
a)podeiknu/nta to\ ti/ ê)=n ei)=nai tou= a)nthrô/pou, a)/llo ti dei=
prolabei=n tou= au)tou= to\ ti/ ê)=n ei)=nai.--ou(= ga\r bou/letai
to\n o(rismo\n a)podei=xai, tou/tou prolamba/nei tina\ o(rismo\n
ei)=nai chôti\s a)podei/xeôs.]
M. Barthélemy St. Hilaire, notes, p. 205:--"Il faut donc, pour
conclure par syllogisme que A est la définition essentielle de C, que
A soit la définition essentielle de B, et que B soit lui-même la
définition essentielle de C. Mais alors la définition de la chose
sera dans le moyen terme lui-même, avant d'être dans la conclusion;
en effet, la mineure: B est la définition essentielle de C, donne la
définition essentielle de C, sans qu'il soit besoin d'aller jusqu'**à
la conclusion. Donc la démonstration de l'essence ainsi entendue est
absurde."]
If you cannot obtain Definition as the conclusion of syllogistic
Demonstration, still less can you obtain it through the method of
generic and specific Division; which last method (as has been already
shown in the Analytica Priora) is not equal even to the Syllogism in
respect of usefulness and efficacy.[13] You cannot in this method
distinguish between propositions both true and essential, and
propositions true but not essential; you never obtain, by asking
questions according to the method of generic subdivision, any
premisses from which the conclusion follows by necessity. Yet this is
what you ought to obtain for the purpose of Demonstration; for you
are not allowed to enunciate the full actual conclusion among the
premisses, and require assent to it. Division of a genus into its
species will often give useful information, as Induction also
will;[14] but neither the one nor the other will be equivalent to a
demonstration. A definition obtained only from subdivisions of a
genus, may always be challenged, like a syllogism without its middle
term.
[Footnote 13: Analyt. Post. II. v. p. 91, b. 12, seq.; Analyt. Prior.
I. xxxi. p. 46, a. 31. Aristotle here alludes to the method pursued
by Plato in the Sophistes and Politicus, though he does not name
Plato: [Greek: ê( dia\ tô=n diaire/seôn o(do/s], &c.]
[Footnote 14: Analyt. Post. II. v. p. 91, b. 15-33: [Greek: ou)de\
ga\r o( e)pa/gôn i)/sôs a)podei/knusin, a)ll' o(/môs dêloi= ti.]
Compare Themistius, p. 74.]
Again, neither can you arrive at the definition of a given subject,
by assuming in general terms what a definition ought to be, and then
declaring a given form of words to be conformable to such assumption;
because your minor premiss must involve _Petitio Principii_. The same
logical fault will be committed, if you take your departure from an
hypothesis in which you postulate the definition of a certain
subject, and then declare inferentially what the definition of its
contrary must be. The definition which you here assume requires proof
as much as that which you infer from it.[15] Moreover, neither by
this process, nor by that of generic subdivision, can you show any
reason why the parts of the definition should coalesce into one
essential whole. If they do not thus coalesce--if they be nothing
better than distinct attributes conjoined in the same subject, like
_musicus_ and _grammaticus_--the real essence is not declared, and
the definition is not a good one.[16]
[Footnote 15: Analyt. Post. II. vi. p. 92, a. 6-28. Themist. p. 76.
Rassow renders [Greek: e)x u(pothe/seôs]--"assumptâ generali
definitionis notione;" and also says: "[Greek: to\ ti/ ê)=n
ei)=nai]--generalem definitionis notionem; [Greek: to\ ti/
e)stin]--certam quandam definitionem, significare perspicuum est."
(Aristotelis de Notionis Definitione Doctrina, p. 65).]
[Footnote 16: Analyt. Post. II. vi. p. 92, a. 32. That the parts of
the definition must coalesce into one unity is laid down again in the
Metaphysica, Z. pp. 1037, 1038, where Aristotle makes reference to
the Analytica as haying already treated the same subject, and
professes an intention to complete what has been begun in the
Analytica; [Greek: e)ph' o(/son e)n toi=s A)nalutikoi=s peri\
o(rismou= mê\ ei)/rêtai.]]
After stating some other additional difficulties which seem to leave
the work of Definition inexplicable, Aristotle relinquishes the
dubitative treatment, and looks out for some solution of the puzzle:
How may it be possible that the Definition shall become known?[17] He
has already told us that to know the essence of a thing is the same
as to know the cause or reason of its existence; but we must first
begin by knowing that the _definiendum_ exists; for there can be no
definition of a non-entity, except a mere definition of the word, a
nominal or verbal definition. Now sometimes we know the existence of
the subject by one or other of its accidental attributes; but this
gives us no help towards finding the definition.[18] Sometimes,
however, we obtain a partial knowledge of its essence along with the
knowledge of its existence; when we know it along with some constant
antecedent, or through some constant, though derivative, consequent.
Knowing thus much, we can often discover the cause or fundamental
condition thereof, which is the essence or definition of the
subject.[19] Indeed, it may happen that the constant derivative, and
the fundamental essence on which it depends, become known both
together; or, again, the cause or fundamental condition may perhaps
not be the essence of the subject alone, but some fact including
other subjects also; and this fact may then be stated as a middle
term. Thus, in regard to eclipse of the moon, we know the constant
phenomenal fact about it, that, on a certain recurrence of the time
of full moon, the moon casts no light and makes no shadow. Hence we
proceed to search out the cause. Is it interposition of the earth, or
conversion of the moon's body, or extinction of her light, &c.? The
new fact when shown, must appear as a middle term, throwing into
syllogistic form (in the First figure) the cause or rational
explanation of a lunar eclipse; showing not merely that there is an
eclipse, but what an eclipse is, or what is its definition.[20]
[Footnote 17: Analyt. Post. II. vii. p. 92, a. 34, seq. The [Greek:
a)po/riai] continue to the end of ch. vii. He goes on, ch. viii. p.
93, a. 1-2: [Greek: pa/lin de\ skepte/on ti/ tou/tôn le/getai kalô=s,
kai\ ti/ ou) kalô=s], &c. "Tout ce qui précède ne représente pas la
théorie proprement dite; ce n'est qu'une discussion préliminaire"
(Barth. St. Hilaire, not. p. 222). These difficult chapters are well
illustrated by Hermann Rassow, ch, i. pp. 9-14.]
[Footnote 18: Analyt. Post. II. viii. p. 93, a. 3: [Greek: e)pei\ d'
e)sti/n, ô(s e)/phamen, tau)to\n to\ ei)de/nai ti/ e)sti kai\ to\
ei)de/nai to\ ai)/tion tou= ei) e)/sti;] Ibid. a. 24: [Greek: o(/sa
me\n ou)=n kata\ sumbebêko\s oi)/damen o(/ti e)/stin, a)nagkai=on
mêdamô=s e)/chein pro\s to\ ti/ e)stin; **ou)de\ ga\r o(/ti
e)/stin i)/smen; to\ de\ zêtei=n ti/ e)sti mê\ e)/chontas o(/ti
e)/sti, mêde\n zêtei=n e)sti/n. kath' o(/sôn d' e)/chome/n ti,
r(a=|on; ô(/ste ô(s e)/chomen o(/ti e)/stin, ou(/tôs e)/chomen kai\
pro\s to\ ti/ e)stin.] Compare Brentano, Ueber die Bedeutung des
Seienden nach Aristoteles, p. 17.]
[Footnote 19: Analyt. Post. II. viii. p. 93, a. 21. Themistius, p.
79, Speng.: [Greek: o(/sa de\ a)po\ tô=n oi)kei/ôn te kai\ e)x
au)tou= tou= pra/gmatos, a)po\ tou/tôn ê)/dê r(a=|on ei)s to\ ti/
e)sti metabai/nomen.]]
[Footnote 20: Ibid. p. 93, a. 30-b. 14.]
Aristotle has thus shown how the Essence or Quiddity ([Greek: ti/
e)sti]) may become known in this class of cases. There is neither
syllogism nor demonstration thereof, yet it is declared through
syllogism and demonstration: though no demonstration thereof is
possible, yet you cannot know it without demonstration, wherever
there is an extraneous cause.[21]
[Footnote 21: Ibid. b. 15-20: [Greek: ô(/ste sullogismo\s me\n tou=
ti/ e)stin ou) gi/netai ou)d' a)po/deixis, dê=lon me/ntoi dia\
sullogismou= kai\ di' a)podei/xeôs.]
Mr. Poste translates an earlier passage (p. 93, a. 5) in this very
difficult chapter as follows (p. 107): "If one cause is demonstrable,
another indemonstrable cause must be the intermediate; and the proof
is in the first figure, and the conclusion affirmative and universal.
In this mode of demonstrating the essence, we prove one definition by
another, for the intermediate that proves an essence or a peculiar
predicate must itself be an essence or a peculiar predicate. Of two
definitions, then, one is proved and the other assumed; and, as we
said before, this is not a demonstration but a dialectical proof of
the essence." Mr. Poste here translates [Greek: logiko\s
sullogismo/s] "dialectical proof." I understand it rather as meaning
a syllogism, [Greek: tou= u(pa/rchein] simply (Top. I. v. p. 102, b.
5), in which all that you really know is that the predicate belongs
to the subject, but in which you _assume_ besides that it belongs to
the subject _essentially_. It is not a demonstration because, in
order to obtain Essence in the conclusion, you are obliged to
postulate Essence in your premiss. (See Alexander ad Topic. I. p.
263, Br.). You have therefore postulated a premiss which required
proof as much as the conclusion.]
But the above doctrine will hold only in cases where there _is_ a
distinct or extraneous cause; it will not hold in cases where there
is none. It is only in the former (as has been said) that a middle
term can be shown; rendering it possible that Quiddity or Essence
should be declared by a valid formal syllogism, though it cannot be
demonstrated by syllogism. In the latter, where there is no distinct
cause, no such middle term can be enunciated: the Quiddity or Essence
must be assumed as an immediate or undemonstrable principium, and
must be exposed or set out in the best manner practicable as an
existent reality, on Induction or on some other authority. The
arithmetician makes his first steps by assuming both what a monad is
and that there exists such a monad.[22]
[Footnote 22: Analyt. Post. II. ix. p. 93, b. 21. [Greek: e)/sti de\
tô=n me\n e(/tero/n ti ai)/tion, tô=n d' ou)k e)/stin. ô(/ste dê=lon
o(/ti kai\ tô=n ti/ e)sti ta\ me\n a)/mesa kai\ a)rchai/ ei)sin, a(\
kai\ ei)=nai kai\ ti/ e)stin u(pothe/sthai dei= ê)\ a)/llon tro/pon
phanera\ poiê=sai. o(/per o( a)rithmêtiko\s poiei=; kai\ ga\r ti/
e)sti tê\n mona/da u(poti/thetai, kai\ o(/ti e)/stin.]
Themistius, p. 80: [Greek: a(\ kai\ ei)=nai kai\ ti/ e)stin
u(pothe/sthai dei=, ê)\ a)/llon tro/pon phanera\ poiê=sai e)x
e)pagôgê=s ê)\ pi/steôs ê)\ e)mpeiri/as.] Rassow, De Notionis
Definitione, pp. 18-22.]
We may distinguish three varieties of Definition. 1. Sometimes it is
the mere explanation what a word signifies; in this sense, it has
nothing to do with essence or existence; it is a nominal definition
and nothing more.[23] 2. Sometimes it enunciates the Essence, cause,
or reason of the _definitum_; this will happen where the cause is
distinct or extraneous, and where there is accordingly an intervening
middle term: the definition will then differ from a demonstration
only by condensing into one enunciation the two premisses and the
conclusion which together constitute the demonstration.[24] 3.
Sometimes it is an immediate proposition, an indemonstrable
hypothesis, assuming Essence or Quiddity; the essence itself being
cause, and no extraneous cause--no intervening middle term--being
obtainable.[25]
[Footnote 23: Analyt. Post. II. x. p. 93, b. 29-37.]
[Footnote 24: Ibid. p. 93, b. 38, seq. [Greek: oi(=on a)po/deixis
tou= ti/ e)stin, tê=| the/sei diaphe/rôn tê=s
a)podei/xeôs;--sullogismo\s tou= ti/ e)sti, ptô/sei diaphe/rôn tê=s
a)podei/xeôs]--differing "situ et positione terminorum" (Julius
Pacius, p. 493).]
[Footnote 25: Ibid. p. 94, a. 9: [Greek: o( de\ tô=n a)me/sôn
o(rismo/s, the/sis e)sti\ tou= ti/ e)stin a)napo/deiktos.] Compare I.
xxiv. p. 85, b. 24: [Greek: ô(=| ga\r kath' au(to\ u(pa/rchei ti,
tou=to au)to\ au(tô=| ai)/tion.] See Kampe, Die Erkenntniss-theorie
des Aristoteles, p. 212, seq.]
To know or cognize is, to know the Cause; when we know the Cause, we
are satisfied with our cognition. Now there are four Causes, or
varieties of Cause:--
1. The Essence or Quiddity (Form)--[Greek: to\ ti/ ê)=n ei)=nai].
2. The necessitating conditions (Matter)--[Greek: to/ ti/nôn o)/ntôn
a)na/gkê tou=t' ei)=nai].
3. The proximate mover or stimulator of change (Efficient)--[Greek:
ê( ti/ prô=ton e)ki/nêse].
4. That for the sake of which (Final Cause or End)--[Greek: to\
ti/nos e(/neka].
All these four Causes (Formal, Material, Efficient, Final) appear as
middle terms in demonstrating. We can proceed through the medium
either of Form, or of Matter, or of Efficient, or of End. The first
of the four has already been exemplified--the demonstration by Form.
The second appears in demonstrating that the angle in a semi-circle
is always a right angle; where the middle term (or matter of the
syllogism, ([Greek: to\ e)x ou(=]) is, that such angle is always the
half of two right angles.[26] The Efficient is the middle term, when
to the question, Why did the Persians invade Athens? it is answered
that the Athenians had previously invaded Persia along with the
Eretrians. (All are disposed to attack those who have attacked them
first; the Athenians attacked the Persians first; _ergo_, the
Persians were disposed to attack the Athenians.) Lastly, the Final
Cause serves as middle term, when to the question, Why does a man
walk after dinner? the response is, For the purpose of keeping up his
health. In another way, the middle term here is digestion: walking
after dinner promotes digestion; digestion is the efficient cause of
health.[27]
[Footnote 26: Analyt. Post. II. xi. p. 94, a. 21-36. Themistius, p.
83: [Greek: ma/lista me\n ga\r e)pi\ pa/sês a)podei/xeôs o( me/sos
e)/stin oi(=on ê( u(/lê tô=| sullogismô=|; ou(/tos ga\r o( poiô=n
ta\s du/o prota/seis, e)ph' ai(=s to\ sumpe/rasma.]]
[Footnote 27: Analyt. Post. II. xi. p. 94, a. 36-b. 21.]
The Final Cause or End is prior in the order of nature, but posterior
to the terms of the conclusion in the order of time or generation;
while the Efficient is prior in the order of time or generation. The
Formal and Material are simultaneous with the effect, neither prior
nor posterior.[28] Sometimes the same fact may proceed both from a
Final cause, and from a cause of Material Necessity; thus the light
passes through our lantern for the purpose of guiding us in the dark,
but also by reason that the particles of light are smaller than the
pores in the glass. Nature produces effects of finality, or with a
view to some given end; and also effects by necessity, the necessity
being either inherent in the substance itself, or imposed by
extraneous force. Thus a stone _falls_ to the ground by necessity of
the first kind, but _ascends_ by necessity of the second kind. Among
products of human intelligence some spring wholly from design without
necessity; but others arise by accident or chance and have no final
cause.[29]
[Footnote 28: Analyt. Post. II. xi. p. 94, a. 21-26. Themistius, p.
83: [Greek: ê( ge/nesis ou)=n tou= me/sou kai\ ai)ti/ou tê\n au)tê\n
ou)k e)/chei ta/xin e)ph' a(pa/ntôn, a)ll' ou(= me\n prô/tên ô(s
e)pi\ tô=n kinêtikô=n, ou(= de\ teleutai/an ô(s e)pi\ tô=n telô=n
kai\ ô(=n e(/neka, ou(= d' a(/ma ô(s e)pi\ tô=n o(rismô=n kai\ tou=
ti/ ê)=n ei)=nai.]]
[Footnote 29: Analyt. Post. II. p. 94, b. 27-p. 95, a. 9.]
That the middle term is the Cause, is equally true in respect to
_Entia_, _Fientia_, _Præterita_, and _Futura_; only that in respect
to _Entia_, the middle term or Cause must be an _Ens_; in respect to
_Fientia_ it must be a _Fiens_; in respect to _Præterita_, a
_Præteritum_; and in respect to _Futura_, a _Futurum_; that is, in
each case, it must be generated at the corresponding time with the
major and minor terms in the conclusion.[30] What is the cause of an
eclipse of the moon? The cause is, that the earth intervenes between
moon and sun; and this is true alike of eclipses past, present, and
future. Such an intervention is the essence or definition of a lunar
eclipse: the cause is therefore Formal, and cause and effect are
simultaneous, occurring at the same moment of time. But in the other
three Causes--Material, Efficient, Final--where phenomena are
successive and not simultaneous, can we say that the antecedent is
cause and the consequent effect, time being, as seems to us, a
_continuum_? In cases like this, we can syllogize from the consequent
backward to the antecedent; but not from the antecedent forward to
the consequent. If the house has been built, we can infer that the
foundations have been laid; but, if the foundations have been laid,
we cannot infer that the house has been built.[31] There must always
be an interval of time during which inference from the antecedent
will be untrue; perhaps, indeed, it may never become true. Cause and
_causatum_ in these three last varieties of Cause, do not universally
and necessarily reciprocate with each other, as in the case of the
Formal cause. Though time is continuous, events or generations are
distinct points marked in a continuous line, and are not continuous
with each other.[32] The number of these points that may be taken is
indeed infinite; yet we must assume some of them as ultimate and
immediate _principia_, in order to construct our syllogism, and
provide our middle term.[33] Where the middle term reciprocates and
is co-extensive with the major and the minor, in such cases we have
generation of phenomena in a cycle; _e.g._, after the earth has been
made wet, vapour rises of necessity: hence comes a cloud, hence
water; which again falls, and the earth again becomes wet.[34]
Finally, wherever our conclusion is not universally and necessarily
true, but true only in most cases, our immediate _principia_ must
also be of the same character, true in most cases, but in most cases
only.[35]
[Footnote 30: Analyt. Post. II. xii. p. 95, a. 10, 36: [Greek: to\
ga\r me/son o(mo/gonon dei= ei)=nai], &c.]
[Footnote 31: Ibid. a. 24 seq., b. 32; Julius Pacius, ad loc.; Biese,
Die Philosophie des Aristot. pp. 302-303.]
[Footnote 32: Analyt. Post. II. xii. p. 95, a. 39-b. 8; Themistius,
p. 86.]
[Footnote 33: Analyt. Post. II. xii. p. 95, b. 14-31: [Greek: a)rchê\
de\ kai\ e)n tou/tois a)/mesos lêpte/a].]
[Footnote 34: Ibid. b. 38-p. 96, a**. 7.]
[Footnote 35: Ibid. p. 96, a. 8-19.]
How are we to proceed in hunting out those attributes that are
predicated _in Quid_,[36] as belonging to the Essence of the subject?
The subject being a lowest species, we must look out for such
attributes as belong to all individuals thereof, but which belong
also to individuals of other species under the same genus. We shall
thus find one, two, three, or more, attributes, each of which,
separately taken, belongs to various individuals lying out of the
species; but the assemblage of which, collectively taken, does not
belong to any individual lying out of the species. The Assemblage
thus found is the Essence; and the enunciation thereof is the
Definition of the species. Thus, the triad is included in the genus
number; in searching for its definition, therefore, we must not go
beyond that genus, nor include any attributes (such as _ens_, &c.)
predicable of other subjects as well as numbers. Keeping within the
limits of the genus, we find that every triad agrees in being an odd
number. But this oddness belongs to other numbers also (pentad,
heptad, &c.). We therefore look out for other attributes, and we find
that every triad agrees in being a prime number, in two distinct
senses; first, that it is not measured by any other number; secondly,
that it is not compounded of any other numbers. This last attribute
belongs to no other odd number except the triad. We have now an
assemblage of attributes, which belong each of them to every triad,
universally and necessarily, and which, taken all together, belong
_exclusively_ to the triad, and therefore constitute its essence or
definition. The triad is a number, odd, and prime in the two
senses.[37] The _definitum_ and the definition are here exactly
co-extensive.
[Footnote 36: Ibid. xiii. p. 96, a. 22: [Greek: pô=s dei=
_thêreu/ein_ ta\ e)n tô=| ti/ e)sti katêgorou/mena?]]
[Footnote 37: Analyt. Post. II. xiii. p. 96, a. 24-b. 14. [Greek: ei)
toi/nun mêdeni\ u(pa/rchei a)/llô| ê)\ tai=s a)to/mois tria/si,
tou=t' a)\n ei)/ê to\ tria/di ei)=nai. u(pokei/sthô ga\r kai\ tou=to,
ê( ou)si/a ê( e(ka/stou ei)=nai ê( e)pi\ tai=s a)to/mois e)/schatos
toiau/tê katêgori/a. ô(/ste o(moi/ôs kai\ a)/llô| o(tô|ou=n tô=n
ou(/tô deichthe/ntôn to\ _au)tô=| ei)=nai_ e)/stai.]]
Where the matter that we study is the entire genus, we must begin by
distributing it into its lowest species; _e.g._ number into dyad,
triad, &c.; in like manner, taking straight line, circle, right
angle, &c.[38] We must first search out the definitions of each of
these lowest species; and these having been ascertained, we must next
look above the genus, to the Category in which it is itself
comprised, whether _Quantum_, _Quale_, &c. Having done thus much we
must study the derivative attributes or propria of the lowest species
through the common generalities true respecting the larger. We must
recollect that these derivative attributes are derived from the
essence and definition of the lowest species, the complex flowing
from the simple as its _principium_: they belong _per se_ only to the
lowest species thus defined; they belong to the higher genera only
through those species.[39] It is in this way, and not in any other,
that the logical Division of genera, according to specific
differences, can be made serviceable for investigation of essential
attributes; that is, it can only be made to demonstrate what is
derivative from the essence. We have shown already that it cannot
help in demonstrating essence or Definition itself. We learn to
marshal in proper order the two constituent elements of our
definition, and to attach each specific difference to the genus to
which it properly belongs. Thus we must not attempt to distribute the
genus animal according to the difference of having the wing divided
or undivided: many animals will fall under neither of the two heads;
the difference in question belongs to the lower genus winged animal,
and distributes the same into two species. The characteristic or
specific difference must be enunciated and postulated by itself, and
must be attached to its appropriate genus in order to form the
definition. It is only by careful attention to the steps of
legitimate logical Division that we can make sure of including all
the particulars and leaving out none.[40]
[Footnote 38: Ibid. b. 18. The straight line is the first or lowest
of all lines: no other line can be understood, unless we first
understand what is meant by a straight line. In like manner the right
angle is the first of all angles, the circle the first of all
curvilinear figures (Julius Pacius, ad loc. p. 504).]
[Footnote 39: Analyt. Post. II. xiii. p. 96, b. 19-25: [Greek: meta\
de\ tou=to, la/bo/nta ti/ to\ ge/nos, oi(=on po/teron tô=n posô=n ê)\
tô=n poiô=n, ta\ i)/dia pa/thê theôrei=n dia\ tô=n koinô=n prô/tôn.
toi=s ga\r suntitheme/nois e)k tô=n a)to/môn] (speciebus infimis)
[Greek: ta\ sumbai/nonta e)k tô=n o(rismô=n e)/stai dê=la, dia\ to\
a)rchê\n ei)=nai pa/ntôn to\n o(rismo/n kai\ to\ a(plou=n, kai\ toi=s
a(ploi=s kath' au(ta\ u(pa/rchein ta\ sumbai/nonta mo/nois, toi=s d'
a)/llois kat' e)kei=na.]
Themistius illustrates this obscure passage, p. 89. The definitions
of [Greek: eu)thei=a grammê/, keklasme/nê grammê/, peripherê\s
grammê/], must each of them contain the definition of [Greek: grammê/
(= mê=kos a)plate/s)], since it is in the Category [Greek: Poso/n
(poso\n mê=kos a)plate/s)]. But the derivative properties of the
circle ([Greek: peripherê\s grammê/]) are deduced from the definition
of a circle, and belong to it in the first instance _quâ_ [Greek:
peripherê\s grammê/], in a secondary way _quâ_ [Greek: grammê/].]
[Footnote 40: Analyt. Post. II. xiii. p. 96, b. 25-p. 97, a. 6.]
Some contemporaries of Aristotle, and among them Speusippus,
maintained that it was impossible either to define, or to divide
logically, unless you knew all particulars without exception. You
cannot (they said) know any one thing, except by knowing its
differences from all other things; which would imply that you knew
also all these other things.[41] To these reasoners Aristotle
replies: It is not necessary to know _all_ the differences of every
thing; you know a thing as soon as you know its essence, with the
properties _per se_ which are derivative therefrom. There are many
differences not belonging to the essence, but distinguishing from
each other two things having the same essence: you may know the
thing, without knowing these accidental differences.[42] When you
divide a genus into two species, distinguished by one proximate
specific difference, such that there cannot be any thing that does
not fall under one or other of these _membra condividentia_, and when
you have traced the subject investigated under one or other of these
members, you can always follow this road until no lower specific
difference can be found, and you have then the final essence and
definition of the subject; even though you may not know how many
_other_ subjects each of the two members may include.[43] Thus does
Aristotle reply to Speusippus, showing that it is not necessary, for
the definition of one thing, that you should know _all_ other things.
His reply, as in many other cases, is founded on the distinction
between the Essential and the Accidental.
[Footnote 41: Ibid. p. 97, a. 6-10; Themistius, p. 92. Aristotle does
not here expressly name Speusippus, but simply says [Greek: phasi/
tines]. It is Themistius who names Speusippus; and one of the
Scholiasts refers to Eudemus as having expressly indicated Speusippus
(Schol. p. 248, a. 24, Br.).]
[Footnote 42: Analyt. Post. II. xiii. p. 97, a. 12: [Greek: pollai\
ga\r diaphorai\ u(pa/rchousi toi=s au)toi=s tô=| ei)/dei, a)ll' ou)
kat' ou)si/an ou)de\ kath' au(ta/.]]
[Footnote 43: Ibid. a. 18-22: [Greek: phanero\n ga\r o(/ti a)\n
ou(/tô badi/zôn e)/lthê| ei)s tau=ta ô(=n mêke/ti e)sti\ diaphora/,
e(/xei to\n lo/gon tê=s ou)si/as.]]
To obtain or put together a definition through logical Division,
three points are to be attended to.[44] Collect the predicates _in
Quid_; range them in the proper order; make sure that there are no
more, or that you have collected all. The essential predicates are
genera, to be obtained not otherwise than by the method (dialectical)
used in concluding accidents. As regards order, you begin with the
highest genus, that which is predicable of all the others, while none
of these is predicable of it, determining in like fashion the
succession of the rest respectively. The collection will be complete,
if you divide the highest genus by an exhaustive specific difference,
such that every thing must be included in one or other of the two
proximate and opposed portions; and then taking the species thus
found as your _dividendum_, subdivide it until no lower specific
difference can be found, or you obtain from the elements an exact
equivalent to the subject.[45]
[Footnote 44: Ibid. a. 23: [Greek: ei)s de\ to\ kataskeua/zein o(/ron
dia\ diaire/seôn]. The Scholiast, p. 248, a. 41, explains [Greek:
kataskeua/zein] by [Greek: eu(rei=n, sunthei=nai, a)podou=nai]. He
distinguishes it from [Greek: a)podeiknu/nai]; demonstration of the
definition being impracticable.]
[Footnote 45: Analyt. Post. II. xiii. p. 97, a. 23 seq. See Waitz,
Comm. p. 418.]
When the investigation must proceed by getting together a group of
similar particulars, you compare them, and note what is the same in
all; then turn to another group which are the same _in genere_ yet
differ _in specie_ from the first group, and have a different point
of community among themselves. You next compare the point of
community among the members of the first group, and that among the
members of the second group. If the two points of community can be
brought under one rational formula, that will be the definition of
the subject; but if at the end of the process, the distinct points of
community are not found resolvable into any final one, this proves
that the supposed _definiendum_ is not one but two or more.[46] For
example, suppose you are investigating, What is the essence or
definition of magnanimity? You must study various magnanimous
individuals, and note what they have in common _quâ_ magnanimous.[47]
Thus, Achilles, Ajax, Alkibiades were all magnanimous. Now, that
which the three had in common was, that they could not endure to be
insulted; on that account Alkibiades went to war with his countrymen,
Achilles was angry and stood aloof from the Greeks, Ajax slew
himself. But, again, you find two other magnanimous men, Sokrates and
Lysander. These two had in common the quality, that they maintained
an equal and unshaken temper both in prosperity and adversity. Now
when you have got thus far, the question to be examined is, What is
the point of identity between the temper that will not endure insult,
and the temper that remains undisturbed under all diversities of
fortune? If an identity can be found, this will be the essence or
definition of magnanimity; to which will belong equanimity as one
variety, and intolerance of insult as another. If, on the contrary,
no identity can be found, you will then have two distinct mental
dispositions, without any common definition.[48]
[Footnote 46: Analyt. Post. II. xiii. p. 97, b. 7-15. [Greek: pa/lin
skopei=n ei) tau)to\n e(/ôs a)\n ei)s e(/na e)/lthê| lo/gon; ou(=tos
ga\r e)/stai tou= pra/gmatos o(rismo/s. e)a\n de\ mê\ badi/zê| ei)s
e(/na a)ll' ei)s du/o ê)\ plei/ô, dê=lon o(/ti ou)k a)\n ei)/ê e(/n
ti ei)=nai to\ zêtou/menon, a)lla\ plei/ô.]]
[Footnote 47: Ibid. b. 16: [Greek: skepte/on e)pi/ tinôn
megalopsu/chôn, ou(\s i)/smen, ti/ e)/chousin e(\n pa/ntes ê(=|
_toiou=toi_.]]
[Footnote 48: Ibid. b. 17-25. [Greek: tau=ta du/o labô\n skopô= ti/
to\ au)to\ e)/chousin ê(/ te a)pa/theia ê( peri\ ta\s tu/chas kai\ ê(
mê\ u(pomonê\ a)timazome/nôn. ei) de\ mêde/n, du/o ei)/dê a)\n ei)/ê
tê=s megalopsuchi/as.]
Æquam memento rebus in arduis
Servare mentem: non secus in bonis
Ab insolenti temperatam
Lætitiâ.--Horace. _Ode_, ii. 3.
Aristotle says that there will be two species of magnanimity. But
surely if the two so-called species connote nothing in common they
are not rightly called species, nor is magnanimity rightly called a
genus. Equanimity would be distinct from magnanimity; Sokrates and
Lysander would not properly be magnanimous but equanimous.]
Every definition must be an universal proposition, applicable, not
exclusively to one particular object, but to a class of greater or
less extent. The lowest species is easier to define than the higher
genus; this is one reason why we must begin with particulars, and
ascend to universals. It is in the higher genera that equivocal terms
most frequently escape detection.[49] When you are demonstrating,
what you have first to attend to is, the completeness of the form of
syllogizing: when you are defining, the main requisite is to be
perspicuous and intelligible; _i.e._ to avoid equivocal or
metaphorical terms.[50] You will best succeed in avoiding them, if
you begin with the individuals, or with examples of the lowest
species, and then proceed to consider not their resemblances
generally, but their resemblances in certain definite ways, as in
colour or figure. These more definite resemblances you will note
first; upon each you will found a formula of separate definition;
after which you will ascend to the more general formula of less
definite resemblance common to both. Thus, in regard to the acute or
sharp, you will consider the acute in sound, and in other matters
(tastes, pains, weapons, angles, &c.), and you will investigate what
is the common point of identity characterizing all. Perhaps there may
be no such identity; the transfer of the term from one to the other
may be only a metaphor: you will thus learn that no common definition
is attainable. This is an important lesson; for as we are forbidden
to carry on a dialectical debate in metaphorical terms, much more are
we forbidden to introduce metaphorical terms in a definition.[51]
[Footnote 49: Analyt. Post. II. xiii. p. 97, b. 29: [Greek: kai\ ga\r
ai( o(mônumi/ai **lantha/nousi ma=llon e)n toi=s katho/lou
ê)\ e)n toi=s a)diapho/rois.]]
[Footnote 50: Analyt. Post. II. xiii. p. 97, b. 31: [Greek: ô(/sper
de e)n tai=s a)podei/xesi dei= to/ ge sullelogi/sthai u(pa/rchein,
ou(/tô kai\ e)n toi=s o(/rois _to\ saphe/s_.]
By [Greek: to\ saphe/s], he evidently means the avoidance of
equivocal or metaphorical terms, and the adherence to true genera and
species. Compare Biese, Die Philosophie des Aristot. pp. 308-310.]
[Footnote 51: Analyt. Post. II. xiii. p. 97, b. 35-39.--([Greek:
diale/gesthai/ phêsi, to\ dialektikô=s o(milei=n].--Schol. p. 248, b.
23, Brand.). Aristotle considers it metaphorical when the term
_acute_ is applied both to a sound and to an angle.
The treatment of this portion of the Aristotelian doctrine by Prantl
(Geschichte der Logik, vol. I. ch. iv. pp. 246, 247, 338), is
instructive. He brings out, in peculiar but forcible terms, the idea
of "notional causality" which underlies Aristotle's Logic. "So also
ist die Definition das Aussprechen _des schöpferischen
Wesensbegriffes_. . . . . Soweit der schöpferische Wesensbegriff
erreicht werden kann, ist durch denselben die begriffliche Causalität
erkannt; und die Einsicht in diese _primitive Ursächlichkeit_ wird in
dem Syllogismus vermittelst des Mittelbegriffes erreicht. Ueber den
schöpferischen Wesensbegriff hinauszugehen, ist nicht möglich. . . .
. Sobald die Definition mehr als eine blosse Namenserklärung ist--und
sie muss mehr seyn--erkennt sie den Mittelbegriff als schöpferische
Causalität. . . . . Die ontologische Bedeutung des Mittelbegriffes
ist, dass er schöpferischer Wesensbegriff ist." Rassow (pp. 51, 63,
&c.) adopts a like metaphorical phrase:--"Definitionem est, explicare
notionem; quæ quidem est _creatrix rerum causa_."]
To obtain and enunciate correctly the problems suitable for
discussion in each branch of science, you must have before you tables
of dissection and logical division, and take them as guides;[52]
beginning with the highest genus and proceeding downward through the
successively descending scale of sub-genera and species. If you are
studying animals, you first collect the predicates belonging to all
animals; you then take the highest subdivision of the genus animal,
such as bird, and you collect the predicates belonging to all birds;
and so on to the next in the descending scale. You will be able to
show cause why any of these predicates must belong to the man
Sokrates, or to the horse Bukephalus; because it belongs to the genus
animal, which includes man and horse. Animal will be the middle term
in the demonstration.[53] This example is taken from the class-terms
current in vulgar speech. But you must not confine yourself to these;
you must look out for new classes, bound together by the possession
of some common attribute, yet not usually talked of as classes, and
you must see whether other attributes can be found constantly
conjoined therewith. Thus you find that all animals having horns,
have also a structure of stomach fit for rumination, and teeth upon
one jaw only. You know, therefore, what is the cause that oxen and
sheep have a structure of stomach fit for rumination. It is because
they have horns. Having-horns is the middle term of the
demonstration.[54] Cases may also be found in which several objects
possess no common nature or attribute to bind them into a class, but
are yet linked together, by analogy, in different ways, to one and
the same common term.[55] Some predicates will be found to accompany
constantly this analogy, or to belong to all the objects _quâ_
analogous, just as if they had one and the same class-nature.
Demonstration may be applied to these, as to the former cases.
[Footnote 52: Analyt. Post. II. xiv. p. 98**, a. 1. [Greek: pro\s de\
to\ e)/chein ta\ problê/mata, le/gein dei= ta/s te _a)natoma\s_ kai\
ta\s diaire/seis, ou(/tô de\ diale/gein, u(pothe/menon to\ ge/nos to\
koino\n a(pa/ntôn.] This is Waitz's text, which differs from Julius
Pacius and from Firmin Didot.
Themistius (pp. 94-95) explains [Greek: ta\s a)natoma\s] to be
anatomical drawings or exercises prepared by Aristotle for teaching:
[Greek: kai\ ta\s a)natoma\s e)/chein dei= prochei/rôs, o(/sai
pepoi/êntai A)ristote/lei].
The collection of Problems or questions for investigation was much
prosecuted, not merely by Aristotle but by Theophrastus (Schol. p.
249, a. 12, Br.).]
[Footnote 53: Analyt. Post. II. xiv. p. 98, a. 5-12.]
[Footnote 54: Ibid. a. 13-19. Aristotle assumes that the material
which ought to have served for the upper teeth, is appropriated by
Nature for the formation of horns.]
[Footnote 55: Ibid. a. 20-23: [Greek: e)/ti d' a)/llos tro/pos e)sti\
_kata\ to\ a)na/logon_ e)kle/gein]. He gives as examples, [Greek:
sê/pion, a)/kantha, o)stou=n].]
Problems must be considered to be the same, when the middle term of
the demonstration is the same for each, or when the middle term in
the one is a subordinate or corollary to that in the other. Thus, the
cause of echo, the cause of images in a mirror, the cause of the
rainbow, all come under the same general head or middle term
(refraction), though with a specific difference in each case. Again,
when we investigate the problem, Why does the Nile flow with a more
powerful current in the last half of the (lunar) month? the reason is
that the month is then more wintry. But why _is_ the month then more
wintry? Because the light of the moon is then diminishing. Here are
two middle terms, the one of which depends upon the other. The
problem for investigation is therefore the same in both.[56]
[Footnote 56: Analyt. Post. II. xv. p. 98, a. 24-34. Theophrastus is
said to have made collections of "_like problems_," problems of which
the solution depended upon the same middle term (Schol. p. 249, a.
11**, Brand.).]
Respecting _Causa_ and _Causatum_ question may be made whether it is
necessary that when the _causatum_ exists, the _causa_ must exist
also? The answer must be in the affirmative, if you include the cause
in the definition of _causatum_. Thus, if you include in the
definition of a lunar eclipse, the cause thereof, viz., intervention
of the earth between moon and sun--then, whenever an eclipse occurs,
such intervention must occur also. But it must not be supposed that
there is here a perfect reciprocation, and that as the _causatum_ is
in this case demonstrable from the cause, so there is the like
demonstration of the cause from the _causatum_. Such a demonstration
is never a demonstration of [Greek: dio/ti]; it is only a
demonstration of [Greek: o(/ti]. The _causatum_ is not included in
the definition of the cause; if you demonstrate that because the moon
is eclipsed, therefore the earth is interposed between the moon and
the sun, you prove the fact of the interposition, but you learn
nothing about the cause thereof. Again, in a syllogism the middle
term is the cause of the conclusion (_i.e._, it is the reason why the
major term is predicated of the minor, which predication is the
conclusion); and in this sense the cause and _causatum_ may sometimes
reciprocate, so that either may be proved by means of the other. But
the _causatum_ here reciprocates with the _causa_ only as premiss and
conclusion (_i.e._, we may know either by means of the other), not as
cause and effect; the _causatum_ is not cause of the _causa_ as a
fact and reality, as the _causa_ is cause of the _causatum_.[57]
[Footnote 57: Analyt. Post. II. xvi. p. 98, a. 35, seq. Themistius,
pp. 96-97: [Greek: ou) ga/r e)stin ai)/tion tou= tê\n gê=n e)n me/sô|
ei)=nai to\ tê\n selê/nên e)klei/pein, a)lla\ me/son tou=
sullogismou=; kai\ tou= sumpera/smatos i)/sôs ai)/tion, _tou=
pra/gmatos de\ ou)damô=s_.] Themistius here speaks with a precision
which is not always present to the mind of Aristotle; for he
discriminates the cause of _the fact_ from the cause of the _affirmed
fact_ or _conclusion_. M. Barthélemy St. Hilaire says (Plan Général
des Derniers Analytiques, p. cxl.):--"Ainsi, la démonstration de
l'effet par la cause apprend pourquoi la chose est; la démonstration
par l'effet apprend seulement que la chose est. On sait que la terre
s'interpose, mais on ne sait pas pourquoi elle s'interpose: et ce qui
le montre bien, c'est que l'idée de l'interposition de la terre est
indispensable à la définition essentielle de l'éclipse tandis que
l'idée de l'éclipse n'a que faire dans la définition de
l'interposition. L'interposition de la terre fait donc comprendre
l'éclipse; tandis que l'éclipse ne fait pas du tout comprendre
l'interposition de la terre."]
The question then arises, Can there be more than one cause of the
same _causatum_? Is it necessary that the same effect should be
produced in all cases by the same cause? In other words, when the
same predicate is demonstrated to be true of two distinct minors, may
it not be demonstrated in one case by one middle term, and in the
other case by a different middle term?[58] Answer: In genuine and
proper scientific problems the middle term is the rational account
(definition, interpretation) of the major extreme; this middle term
therefore, or the cause, must in all cases be one and the same. The
demonstration in these cases is derived from the same essence; it is
_per se_, not _per accidens_. But there are other problems, not
strictly and properly scientific, in which cause and _causatum_ are
connected merely _per accidens_; the demonstration being operated by
a middle term which is not of the essence of the major, but is only a
sign or concomitant.[59] According as the terms of the conclusion are
related to each other, so also will the middle term be related to
both. If the conclusion be equivocal, the middle term will be
equivocal also; if the predicate in the conclusion be in generic
relation to the subject, the major also will be in generic relation
to the middle. Thus, if you are demonstrating that one triangle is
similar to another, and that one colour is similar to another, the
word similar in these two cases is not univocal, but equivocal;
accordingly, the middle term in the demonstration will also be
equivocal. Again, if you are demonstrating that four proportionals
will also be proportionals alternately, there will be one cause or
middle term, if the subject of the conclusion be lines; another, if
the subject be numbers. Yet the middle term or cause in both is the
same, in as far as both involve a certain fact of increment.[60]
[Footnote 58: Analyt. Post. II. xvi. p. 98, b. 25.]
[Footnote 59: Ibid. xvii. p. 99, a. 4: [Greek: e)/sti de\ kai\ ou(=
ai)/tion kai\ ô(=| skopei=n kata\ sumbebêko/s; ou) mê\n dokei=
problê/mata ei)=nai.]
"Veluti si probemus grammaticum esse aptum ad ridendum, quia homo est
aptus ad ridendum." (Julius Pacius, p. 514.)]
[Footnote 60: Analyt. Post. II. xvii. p. 99, a. 8-16.]