Aristotle
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.]
The major term of the syllogism will in point of extension be larger
than any particular minor, but equal or co-extensive with the sum
total of the particulars. Thus the predicate deciduous, affirmable of
all plants with broad leaves, is greater in extension than the
subject vines, also than the subject fig-trees; but it is equal in
extension to the sum total of vines and fig-trees (the other
particular broad-leaved plant). The middle also, in an universal
demonstration, reciprocates with the major, being its definition.
Here the true middle or cause of the effect that vines and fig-trees
shed their leaves, is not that they are broad-leaved plants, but
rather a coagulation of sap or some such fact.[61]
[Footnote 61: Ibid. a. 16 seq.]
The last chapter of the present treatise is announced by Aristotle as
the appendix and completion of his entire theory of Demonstrative
Science, contained in the Analytica Priora, which treats of
Syllogism, and the Analytica Posteriora, which treats of
Demonstration. After formally winding up the whole enquiry, he
proceeds to ask regarding the _principia_ of Demonstrative Science:
What are they? How do they become known? What is the mental habit or
condition that is cognizant of them?[62]
[Footnote 62: Analyt. Post. II. xix. p. 99, b. 15-19: [Greek: peri\
me\n ou)=n sullogismou= kai\ a)podei/xeôs, ti/ te e(ka/tero/n e)sti
kai\ pô=s gi/netai, phanero/n, a(/ma **de\ kai\ peri\ e)pistê/mês
a)podeiktikê=s; tau)to\n ga/r e)stin. peri\ de\ tô=n a)rchô=n, pô=s
te gi/nontai gnô/rimoi, kai\ _ti/s ê( gnôri/zousa e(/xis_,
e)nteu=the/n e)sti dê=lon proaporê/sasi prô=ton.]
Bekker and Waitz, in their editions, include all these words in ch.