Aristotle
commentators ascribe to [Greek: ta\ pa=sin e(po/mena] is given in its
own special and appropriate terms, and thus the same supposition
unnecessarily repeated--I cannot help suspecting that Aristotle
intends [Greek: ta\ pa=sin e(po/mena] to mean something different; to
mean such wide and universal predicates as [Greek: to\ e(\n] and
[Greek: to\ o)/n] which soar above the Categories and apply to every
thing, but denote no real _genera_.]
Thus, when the thesis to be maintained is an universal affirmative
(_e.g._ A is predicable of all E), you will survey all the subjects
to which A will apply as predicate, and all the predicates applying
to E as subject. If these two lists coincide in any point, a middle
term will be found for the construction of a good syllogism in the
First figure. Let B represent the list of predicates belonging
universally to A; D, the list of predicates which cannot belong to
it; C, the list of subjects to which A pertains universally as
predicate. Likewise, let F represent the list of predicates belonging
universally to E; H, the list of predicates that cannot belong to E;
G, the list of subjects to which E is applicable as predicate. If,
under these suppositions, there is any coincidence between the list C
and the list F, you can construct a syllogism (in _Barbara_, Fig. 1),
demonstrating that A belongs to _all_ E; since the predicate in F
belongs to all E, and A universally to the subject in C. If the list
C coincides in any point with the list G, you can prove that A
belongs to _some_ E, by a syllogism (in _Darapti_, Fig. 3). If, on
the other hand, the list F coincides in any point with the list D,
you can prove that A cannot belong to any E: for the predicate in D
cannot belong to any A, and therefore (by converting simply the
universal negative) A cannot belong as predicate to any D; but D
coincides with F, and F belongs to all E; accordingly, a syllogism
(in _Celarent_, Fig. 1) may be constructed, shewing that A cannot
belong to any E. So also, if B coincides in any point with H, the
same conclusion can be proved; for the predicate in B belongs to all
A, but B coincides with H, which belongs to no E; whence you obtain a
syllogism (in _Camestres_, Fig. 2), shewing that no A belongs to
E.[54] In collecting the predicates and subjects both of A and of E,
the highest and most universal expression of them is to be preferred,
as affording the largest grasp for the purpose of obtaining a
suitable middle term.[55] It will be seen (as has been declared
already) that every syllogism obtained will have three terms and two
propositions; and that it will be in one or other of the three
figures above described.[56]
[Footnote 54: Analyt. Prior. I. xxviii. p. 43, b. 39-p. 44, a. 35.]
[Footnote 55: Ibid. p. 44, a. 39. Alexander and Philoponus (Scholia,
p. 177, a. 19, 39, Brandis) point out an inconsistency between what
Aristotle says here and what he had said in one of the preceding
paragraphs, dissuading the inquirer from attending to the highest
generalities, and recommending him to look only at both subject and
predicate in their special place on the logical scale. Alexander's
way of removing the inconsistency is not successful: I doubt if there
be an inconsistency. I understand Aristotle _here_ to mean only that
the universal expression KZ ([Greek: to\ katho/lou Z]) is to be
preferred to the indefinite or indeterminate (simply Z, [Greek:
a)dio/riston]), also K[Greek: G] ([Greek: to\ katho/lou G]) to simple
[Greek: G (a)dio/riston)]. This appears to me not inconsistent with
the recommendation which Aristotle had given before.]
[Footnote 56: Ibid. p. 44, b. 6-20.]
The way just pointed out is the only way towards obtaining a suitable
middle term. If, for example, you find some predicate applicable both
to A and E, this will not conduct you to a valid syllogism; you will
only obtain a syllogism in the Second figure with two affirmative
premisses, which will not warrant any conclusion. Or if you find some
predicate which cannot belong either to A or to E, this again will
only give you a syllogism in the Second figure with two negative
premisses, which leads to nothing. So also, if you have a term of
which A can be predicated, but which cannot be predicated of E, you
derive from it only a syllogism in the First figure, with its minor
negative; and this, too, is invalid. Lastly, if you have a subject,
of which neither A nor E can be predicated, your syllogism
constructed from these conditions will have both its premisses
negative, and will therefore be worthless.[57]
[Footnote 57: Analyt. Prior. I. xxviii. p. 44, b. 25-37.]
In the survey prescribed, nothing is gained by looking out for
predicates (of A and E) which are different or opposite: we must
collect such as are identical, since our purpose is to obtain from
them a suitable middle term, which must be the same in both
premisses. It is true that if the list B (containing the predicates
universally belonging to A) and the list F (containing the predicates
universally belonging to E) are incompatible or contrary to each
other, you will arrive at a syllogism proving that no A can belong to
E. But this syllogism will proceed, not so much from the fact that B
and F are incompatible, as from the other fact, distinct though
correlative, that B will to a certain extent coincide with H (the
list of predicates which cannot belong to E). The middle term and the
syllogism constituted thereby, is derived from the coincidence
between B and H, not from the opposition between B and F. Those who
derive it from the latter, overlook or disregard the real source, and
adopt a point of view merely incidental and irrelevant.[58]
[Footnote 58: Ibid. p. 44, b. 38-p. 45, a. 22. [Greek: sumbai/nei dê\
toi=s ou(/tôs e)piskopou=si prosepible/pein a)/llên o(do\n tê=s
a)nagkai/as, dia\ to\ lantha/nein tê\n tau)to/têta tô=n B kai\ tô=n
Th.]]
The precept here delivered--That in order to obtain middle terms and
good syllogisms, you must study and collect both the predicates and
the subjects of the two terms of your thesis--Aristotle declares to
be equally applicable to all demonstration, whether direct or by way
of _Reductio ad Impossibile_. In both the process of demonstration is
the same--involving two premisses, three terms, and one of the three
a suitable middle term. The only difference is, that in the direct
demonstration, both premisses are propounded as true, while in the
_Reductio ad Impossibile_, one of the premisses is assumed as true
though known to be false, and the conclusion also.[59] In the other
cases of hypothetical syllogism your attention must be directed, not
to the original _quæsitum_, but to the condition annexed thereto; yet
the search for predicates, subjects, and a middle term, must be
conducted in the same manner.[60] Sometimes, by the help of a
condition extraneous to the premisses, you may demonstrate an
universal from a particular: _e.g._, Suppose C (the list of subjects
to which A belongs as predicate) and G (the list of subjects to which
E belongs as predicate) to be identical; and suppose farther that the
subjects in G are the _only_ ones to which E belongs as predicate
(this seems to be the _extraneous_ or _extra-syllogistic_ condition
assumed, on which Aristotle's argument turns); then, A will be
applicable to all E. Or if D (the list of predicates which cannot
belong to A) and G (the list of subjects to which E belongs as
predicate) are identical; then, assuming the like extraneous
condition, A will not be applicable to any E.[61] In both these
cases, the conclusion is more universal than the premisses; but it is
because we take in an hypothetical assumption, in addition to the
premisses.
[Footnote 59: Ibid. I. xxix. p. 45, a. 25-b. 15.]
[Footnote 60: Ibid. I. xxix. p. 45, b. 15-20. This paragraph is very
obscure. Neither Alexander, nor Waitz, nor St. Hilaire clears it up
**completely. See Schol. pp. 178, b., 179, a. Brandis.
Aristotle concludes by saying that syllogisms from an hypothesis
ought to be reviewed and classified into varieties--[Greek:
e)piske/psasthai de\ dei= kai\ dielei=n posachô=s oi( e)x
u(pothe/seôs] (b. 20). But it is doubtful whether he himself ever
executed this classification. It was done in the Analytica of his
successor Theophrastus (Schol. p. 179, a. 6, 24). Compare the note of
M. Barthélemy St. Hilaire, p. 140.]
[Footnote 61: Analyt. Prior. I. xxix. p. 45, b. 21-30.]
Aristotle has now shown a method of procedure common to all
investigations and proper for the solution of all problems, wherever
soluble. He has shown, first, all the conditions and varieties of
probative Syllogism, two premisses and three terms, with the place
required for the middle term in each of the three figures; next, the
quarter in which we are to look for all the materials necessary or
suitable for constructing valid syllogisms. Having the two terms of
the thesis given, we must study the predicates and subjects belonging
to both, and must provide a large list of them; out of which list we
must make selection according to the purpose of the moment. Our
selection will be different, according as we wish to prove or to
refute, and according as the conclusion that we wish to prove is an
universal or a particular. The lesson here given will be most useful
in teaching the reasoner to confine his attention to the sort of
materials really promising, so that he may avoid wasting his time
upon such as are irrelevant.[62]
[Footnote 62: Ibid. b. 36-xxx. p. 46, a. 10.]
This method of procedure is alike applicable to demonstration in
Philosophy or in any of the special sciences,[63] and to debate in
Dialectic. In both, the premisses or _principia_ of syllogisms must
be put together in the same manner, in order to make the syllogism
valid. In both, too, the range of topics falling under examination is
large and varied; each topic will have its own separate premisses or
_principia_, which must be searched out and selected in the way above
described. Experience alone can furnish these _principia_, in each
separate branch or department. Astronomical experience--the observed
facts and phenomena of astronomy--have furnished the data for the
scientific and demonstrative treatment of astronomy. The like with
every other branch of science or art.[64] When the facts in each
branch are brought together, it will be the province of the logician
or analytical philosopher to set out the demonstrations in a manner
clear and fit for use. For if nothing in the way of true matter of
fact has been omitted from our observation, we shall be able to
discover and unfold the demonstration, on every point where
demonstration is possible; and, wherever it is not possible, to make
the impossibility manifest.[65]
[Footnote 63: Ibid. p. 46, a. 8**: [Greek: kata\ me\n a)lê/theian e)k
tô=n kat' a)lê/theian _diagegramme/nôn_ u(pa/rchein, ei)s de\ tou\s
dialektikou\s sullogismou\s e)k tô=n kata\ do/xan prota/seôn.]
Julius Pacius (p. 257) remarks upon the word [Greek: diagegramme/nôn]
as indicating that Aristotle, while alluding to special sciences
distinguishable from philosophy on one side, and from dialectic on
the other, had in view geometrical demonstrations.]
[Footnote 64: Analyt. Prior. I. xxx. p. 46, a. 10-20**: [Greek: ai(
d' a)rchai\ tô=n sullogismô=n katho/lou me\n ei)/rêntai--i)/diai de\
kath' e(ka/stên ai( plei=stai. dio\ ta\s me\n a)rcha\s ta\s peri\
e(/kaston e)mpeiri/as e)/sti paradou=nai. le/gô d' oi(=on tê\n
a)strologikê\n me\n e)mpeiri/an tê=s a)strologikê=s e)pistê/mês;
lêphthe/ntôn ga\r i(kanô=s tô=n phainome/nôn ou(/tôs eu(re/thêsan ai(
a)strologikai\ a)podei/xeis. o(moi/ôs de\ kai\ peri\ a)/llên
o(poianou=n e)/chei te/chnên te kai\ e)pistê/mên.]
What Aristotle says here--of astronomical observation and experience