Aristotle
destined to re-appear in the conclusion. If the qualification be
attached to the middle term, it cannot appear in the conclusion, and
any conclusion that embraces it will not be proved. Suppose the
conclusion to be proved is. The wholesome is knowledge _quatenus
bonum_ or _quod bonum est_; the three terms of the syllogism must
stand thus:--
_Major_--_Bonum_ is knowable, _quatenus bonum_ or _quod bonum est_.
_Minor_--The wholesome is _bonum_.
_Ergo_--The wholesome is knowable, _quatenus bonum_, &c.
For every syllogism in which the conclusion is qualified, the terms
must be set out accordingly.[80]
[Footnote 78: Analyt. Prior. I. xxxvi. p. 48, a. 40-p. 49, a. 5.
[Greek: a(plô=s le/gomen ga\r tou=to kata\ pa/ntôn, o(/ti tou\s me\n
o(/rous a)/ei thete/on kata\ ta\s klê/seis tô=n o)noma/tôn--ta\s de\
prota/seis lêpte/on kata\ ta\s e(ka/stou ptô/seis.] Several examples
are given of this precept.]
[Footnote 79: Ibid. I. xxxvii. p. 49, a. 6-10. Alexander remarks in
the Scholia (p. 183, a. 2) that the distinction between simple and
compound predication has already been adverted to by Aristotle in De
Interpretatione (see p. 20, b. 35); and that it was largely treated
by Theophrastus in his work, [Greek: Peri\ Katapha/seôs], not
preserved.]
[Footnote 80: Ibid. I. xxxviii. p. 49, a. 11-b. 2. [Greek: phanero\n
ou)=n o(/ti e)n toi=s e)n me/rei sullogismoi=s ou(/tô lêpte/on tou\s
o(/rous.] Alexander explains [Greek: oi( e)n me/rei sullogismoi/]
(Schol. p. 183, b. 32, Br.) to be those in which the predicate has a
qualifying adjunct tacked to it.]
We are permitted, and it is often convenient, to exchange one phrase
or term for another of equivalent signification, and also one word
against any equivalent phrase. By doing this, we often **facilitate
the setting out of the terms. We must carefully note the different
meanings of the same substantive noun, according as the definite
article is or is not prefixed. We must not reckon it the same term,
if it appears in one premiss with the definite article, and in the
other without the definite article.[81] Nor is it the same
proposition to say B is predicable of C (indefinite), and B is
predicable of _all_ C (universal). In setting out the syllogism, it
is not sufficient that the major premiss should be indefinite; the
major premiss must be universal; and the minor premiss also, if the
conclusion is to be universal. If the major premiss be universal,
while the minor premiss is only affirmative indefinite, the
conclusion cannot be universal, but will be no more than indefinite,
that is, counting as particular.[82]
[Footnote 81: Analyt. Prior. I. xxxix.-xl. p. 49, b. 3-13. [Greek:
ou) tau)to\n e)sti to\ ei)=nai tê\n ê(donê\n a)gatho\n kai\ to\
ei)=nai tê\n ê(donê\n to\ a)gatho/n], &c.]
[Footnote 82: Ibid. I. xli. p. 49, b. 14-32. The Scholion of
Alexander (Schol. p. 184, a. 22-40) alludes to the peculiar mode,
called by Theophrastus [Greek: kata\ pro/slêpsin], of stating the
premisses of the syllogism: two terms only, the major and the middle,
being enunciated, while the third or minor was included potentially,
but not enunciated. Theophrastus, however, did not recognize the
distinction of meaning to which Aristotle alludes in this chapter. He
construed as an universal minor, what Aristotle treats as only an
indefinite minor. The liability to mistake the Indefinite for an
Universal is here again adverted to.]
There is no fear of our being misled by setting out a particular case
for the purpose of the general demonstration; for we never make
reference to the specialties of the particular case, but deal with it
as the geometer deals with the diagram that he draws. He calls the
line A B, straight, a foot long, and without breadth, but he does not
draw any conclusion from these assumptions. All that syllogistic
demonstration either requires or employs, is, terms that are related
to each other either as whole to part or as part to whole. Without
this, no demonstration can be made: the exposition of the particular
case is intended as an appeal to the senses, for facilitating the
march of the student, but is not essential to demonstration.[83]
[Footnote 83: Ibid. I. xli. p. 50, a. 1: [Greek: tô=| d'
e)kti/thesthai ou(/tô chrô/metha ô(/sper kai\ tô=| ai)stha/nesthai
to\n mantha/nonta le/gontes; ou) ga\r ou(/tôs ô(s a)/neu tou/tôn
ou)ch oi(=o/n t' a)podeichthê=nai, ô(/sper e)x ô(=n o(
sullogismo/s.]
This chapter is a very remarkable statement of the Nominalistic
doctrine; perceiving or conceiving all the real specialties of a
particular case, but attending to, or reasoning upon, only a portion
of them.
Plato treats it as a mark of the inferior scientific value of
Geometry, as compared with true and pure Dialectic, that the geometer
cannot demonstrate through Ideas and Universals alone, but is
compelled to help himself by visible particular diagrams or
illustrations. (Plato, Repub. vi. pp. 510-511, vii. p. 533, C.)]
Aristotle reminds us once more of what he had before said, that in
the Second and Third figures, not all varieties of conclusion are
possible, but only some varieties; accordingly, when we are reducing
a piece of reasoning to the syllogistic form, the nature of the
conclusion will inform us which of the three figures we must look
for. In the case where the question debated relates to a definition,
and the reasoning which we are trying to reduce turns upon one part
only of that definition, we must take care to look for our three
terms only in regard to that particular part, and not in regard to
the whole definition.[84] All the modes of the Second and Third
figures can be reduced to the First, by conversion of one or other of
the premisses; except the fourth mode (_Baroco_) of the Second, and
the fifth mode (_Bocardo_) of the Third, which can be proved only by
_Reductio ad Absurdum_.[85]
[Footnote 84: Analyt. Prior. I. xlii., xliii. p. 50, a. 5-15. I
follow here the explanation given by Philoponus and Julius Pacius,
which M. Barthélemy St. Hilaire adopts. But the illustrative example
given by Aristotle himself (the definition of _water_) does not
convey much instruction.]
[Footnote 85: Ibid. xlv. p. 50, b. 5-p. 51, b. 2.]
No syllogisms from an Hypothesis, however, are reducible to any of
the three figures; for they are not proved by syllogism alone: they
require besides an extra-syllogistic assumption granted or understood
between speaker and hearer. Suppose an hypothetical proposition
given, with antecedent and consequent: you may perhaps prove or
refute by syllogism either the antecedent separately, or the
consequent separately, or both of them separately; but you cannot
directly either prove or refute by syllogism the conjunction of the
two asserted in the hypothetical. The speaker must ascertain
beforehand that this will be granted to him; otherwise he cannot
proceed.[86] The same is true about the procedure by _Reductio ad
Absurdum_, which involves an hypothesis over and above the syllogism.
In employing such _Reductio ad Absurdum_, you prove syllogistically a
certain conclusion from certain premisses; but the conclusion is
manifestly false; therefore, one at least of the premisses from which
it follows must be false also. But if this reasoning is to have
force, the hearer must know _aliunde_ that the conclusion is false;
your syllogism has not shown it to be false, but has shown it to be
hypothetically true; and unless the hearer is prepared to grant the
conclusion to be false, your purpose is not attained. Sometimes he
will grant it without being expressly asked, when the falsity is
glaring: _e.g._ you prove that the diagonal of a square is
incommensurable with the side, because if it were taken as
commensurable, an odd number might be shown to be equal to an even
number. Few disputants will hesitate to grant that this conclusion is
false, and therefore that its contradictory is true; yet this last
(viz. that the contradictory is true) has not been proved
syllogistically; you must assume it by hypothesis, or depend upon the
hearer to grant it.[87]
[Footnote 86: Ibid. xliv. p. 50, a. 16-28.]
[Footnote 87: Analyt. Prior. I. xliv. p. 50, a. 29-38. See above,
xxiii. p. 40, a. 25.
M. Barthélemy St. Hilaire remarks in the note to his translation of
the Analytica Priora (p. 178): "Ce chapitre suffit à prouver
qu'Aristote a distingué très-nettement les syllogismes par l'absurde,
des syllogismes hypothétiques. Cette dernière dénomination est tout à
fait pour lui ce qu'elle est pour nous." Of these two statements, I
think the _latter_ is more than we can venture to affirm, considering
that the general survey of hypothetical syllogisms, which Aristotle
intended to draw up, either never was really completed, or at least
has perished: the _former_ appears to me incorrect. Aristotle
decidedly reckons the _Reductio ad Impossibile_ among hypothetical
proofs. But he understands by _Reductio ad Impossibile_ something
rather wider than what the moderns understand by it. It now means
only, that you take the contradictory of the conclusion together with
one of the premisses, and by means of these two demonstrate a
conclusion contradictory or contrary to the other premiss. But
Aristotle understood by it this, and something more besides, namely,
whenever, by taking the contradictory of the conclusion, together
with some other incontestable premiss, you demonstrate, by means of
the two, some new conclusion notoriously false. What I here say, is
illustrated by the very example which he gives in this chapter. The
incommensurability of the diagonal (with the side of the square) is
demonstrated by _Reductio ad Impossibile_; because if it be supposed
commensurable, you may demonstrate that an odd number is equal to an
even number; a conclusion which every one will declare to be
inadmissible, but which is not the contradictory of either of the
premisses whereby the true proposition was demonstrated.]
Here Aristotle expressly reserves for separate treatment the general
subject of Syllogisms from Hypothesis.[88]
[Footnote 88: The expressions of Aristotle here are remarkable,
Analyt. Prior. I. xliv. p. 50, a. 39-b. 3: [Greek: polloi\ de\ kai\
e(/teroi perai/nontai e)x u(pothe/seôs, ou(\s e)piske/psasthai dei=
kai\ diasêmê=nai katharô=s. ti/nes me\n ou)=n ai( diaphorai\ tou/tôn,
kai\ posachô=s gi/netai to\ e)x u(pothe/seôs, u(/steron e)rou=men;
nu=n de\ tosou=nton ê(mi=n e)/stô phanero/n, o(/ti ou)k e)/stin
a)nalu/ein ei)s ta\ schê/mata tou\s toiou/tous sullogismou/s. kai\
di' ê(\n ai)ti/an, ei)rê/kamen.]
Syllogisms from Hypothesis were many and various, and Aristotle
intended to treat them in a future treatise; but all that concerns
the present treatise, in his opinion, is, to show that none of them
can be reduced to the three Figures. Among the Syllogisms from
Hypothesis, two varieties recognized by Aristotle (besides [Greek:
oi) dia\ tou= a)duna/tou]) were [Greek: oi( kata\ meta/lêpsin] and
[Greek: oi( kata\ poio/têta]. The same proposition which Aristotle
entitles [Greek: kata\ meta/lêpsin], was afterwards designated by the
Stoics [Greek: kata\ pro/slêpsin] (Alexander ap. Schol. p. 178,
b. 6-24).
It seems that Aristotle never realized this intended future treatise
on Hypothetical Syllogisms; at least Alexander did not know it. The
subject was handled more at large by Theophrastus and Eudêmus after
Aristotle (Schol. p. 184, b. 45. Br.; Boethius, De Syllog.
Hypothetico, pp. 606-607); and was still farther expanded by
Chrysippus and the Stoics.
Compare Prantl, Geschichte der Logik, I. pp. 295, 377, seq. He treats
the Hypothetical Syllogism as having no logical value, and commends
Aristotle for declining to develop or formulate it; while Ritter
(Gesch. Phil. iii. p. 93), and, to a certain extent, Ueberweg (System