Aristotle
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