Aristotle
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.]