Aristotle
diorismo/n.] See xiii. p. 32, a. 33, where [Greek: to\ e)nde/chesthai
u(pa/rchein] is asserted to be equivalent to or convertible with
[Greek: to\ e)nde/chesthai mê\ u(pa/rchein]; and xix. p. 38, a. 35:
[Greek: to\ e)x a)na/gkês ou)k ê)=n _e)ndecho/menon_]. Theophrastus
and Eudemus differed from Aristotle about his theory of the Modals in
several points (Scholia ad Analyt. Priora, pp. 161, b. 30; 162, b.
23; 166, a. 12, b. 15, Brand.). Respecting the want of clearness in
Aristotle about [Greek: to\ e)ndecho/menon], see Waitz's note **ad p.
32, b. 16. Moreover, he sometimes uses [Greek: u(pa/rchon] in the
widest sense, including [Greek: e)ndecho/menon] and [Greek:
a)nagkai=on], xxiii. p. 40, b. 24.]
[Footnote 38: Analyt. Prior. I. xv. p. 34, b. 7.]
Having finished with the Modals, Aristotle proceeds to lay it down,
that all demonstration must fall under one or other of the three
figures just described; and therefore that all may be reduced
ultimately to the two first modes of the First figure. You cannot
proceed a step with two terms only and one proposition only. You must
have two propositions including three terms; the middle term
occupying the place assigned to it in one or other of the three
figures.[39] This is obviously true when you demonstrate by direct or
ostensive syllogism; and it is no less true when you proceed by
_Reductio ad Impossibile_. This last is one mode of syllogizing from
an hypothesis or assumption:[40] your conclusion being disputed, you
prove it indirectly, by assuming its contradictory to be true, and
constructing a new syllogism by means of that contradictory together
with a second premiss admitted to be true; the conclusion of this new
syllogism being a proposition obviously false or known beforehand to
be false. Your demonstration must be conducted by a regular
syllogism, as it is when you proceed directly and ostensively. The
difference is, that the conclusion which you obtain is not that which
you wish ultimately to arrive at, but something notoriously false.
But as this false conclusion arises from your assumption or
hypothesis that the contradictory of the conclusion originally
disputed was true, you have indirectly made out your case that this
contradictory must have been false, and therefore that the conclusion
originally disputed was true. All this, however, has been
demonstration by regular syllogism, but starting from an hypothesis
assumed and admitted as one of the premisses.[41]
[Footnote 39: Ibid. xxiii. p. 40, b. 20, p. 41, a. 4-20.]
[Footnote 40: Ibid. p. 40, b. 25: [Greek: e)/ti ê)\ deiktikô=s ê)\
e)x u(pothe/seôs; tou= d' _e)x u(pothe/seôs_ me/ros to\ dia\ tou=
a)duna/tou.]]
[Footnote 41: Ibid. p. 41, b. 23: [Greek: pa/ntes ga\r oi( dia\ tou=
a)duna/tou perai/nontes to\ me\n pseu=dos sullogi/zontai, to\ d' e)x
a)rchê=s _e)x u(pothe/seôs_ deiknu/ousin, o(/tan a)du/nato/n ti
sumbai/nê| tê=s a)ntipha/seôs tethei/sês.]
It deserves to be remarked that Aristotle uses the phrase [Greek:
sullogismo\s _e)x u(pothe/seôs_], not [Greek: sullogismo\s
u(pothetiko/s]. This bears upon the question as to his views upon
what subsequently received the title of _hypothetical syllogisms_;
a subject to which I shall advert in a future note.]
Aristotle here again enforces what he had before urged--that in every
valid syllogism, one premiss at least must be affirmative, and one
premiss at least must be universal. If the conclusion be universal,
both premisses must be so likewise; if it be particular, one of the
premisses may not be universal. But without one universal premiss at
least, there can be no syllogistic proof. If you have a thesis to
support, you cannot assume (or ask to be conceded to you) that very
thesis, without committing _petitio principii,_ (_i.e._ _quæsiti_ or
_probandi_); you must assume (or ask to have conceded to you) some
universal proposition containing it and more besides; under which
universal you may bring the subject of your thesis as a minor, and
thus the premisses necessary for supporting it will be completed.
Aristotle illustrates this by giving a demonstration that the angles
at the base of an isosceles triangle are equal; justifying every step
in the reasoning by an appeal to some universal proposition.[42]
[Footnote 42: Analyt. Prior. I. xxiv. p. 41, b. 6-31. The
demonstration given (b. 13-22) is different from that which we read
in Euclid, and is not easy to follow. It is more clearly explained by
Waitz (p. 434) than either by Julius Pacius or by M. Barth. St.
Hilaire (p. 108).]
Again, every demonstration is effected by two propositions (an _even_
number) and by three terms (an _odd_ number); though the same
proposition may perhaps be demonstrable by more than one pair of
premisses, or through more than one middle term;[43] that is, by two
or more distinct syllogisms. If there be more than three terms and
two propositions, either the syllogism will no longer be one but
several; or there must be particulars introduced for the purpose of
obtaining an universal by induction; or something will be included,
superfluous and not essential to the demonstration, perhaps for the
purpose of concealing from the respondent the real inference
meant.[44] In the case (afterwards called _Sorites_) where the
ultimate conclusion is obtained through several mean terms in
continuous series, the number of terms will always exceed by one the
number of propositions; but the numbers may be odd or even, according
to circumstances. As terms are added, the total of intermediate
conclusions, if drawn out in form, will come to be far greater than
that of the terms or propositions, multiplying as it will do in an
increasing ratio to them.[45]
[Footnote 43: Ibid. I. xxv. p. 41, b. 36, seq.]
[Footnote 44: Ibid. xxv. p. 42, a. 23: [Greek: ma/tên e)/stai
ei)lêmme/na, ei) mê\ e)pagôgê=s ê)\ kru/pseôs ê)/ tinos a)/llou tô=n
toiou/tôn cha/rin.] Ib. a. 38: [Greek: ou(=tos o( lo/gos ê)\ ou)
sullelo/gistai ê)\ plei/ô tô=n a)nagkai/ôn ê)rô/têke pro\s tê\n
the/sin.]]
[Footnote 45: Ibid. p. 42, b. 5-26.]
It will be seen clearly from the foregoing remarks that there is a
great difference between one thesis and another as to facility of
attack or defence in Dialectic. If the thesis be an Universal
Affirmative proposition, it can be demonstrated only in the First
figure, and only by one combination of premisses; while, on the other
hand, it can be impugned either by an universal negative, which can
be demonstrated both in the First and Second figures, or by a
particular negative, which can be demonstrated in all the three
figures. Hence an Universal Affirmative thesis is at once the hardest
to defend and the easiest to oppugn: more so than either a Particular
Affirmative, which can be proved both in the First and Third figures;
or a Universal Negative, which can be proved either in First or
Second.[46] To the opponent, an universal thesis affords an easier
victory than a particular thesis; in fact, speaking generally, his
task is easier than that of the defendant.
[Footnote 46: Analyt. Prior. I. xxvi. p. 42, b. 27, p. 43, a. 15.]
In the Analytica Priora, Aristotle proceeds to tell us that he
contemplates not only theory, but also practice and art. The reader
must be taught, not merely to understand the principles of Syllogism,
but likewise where he can find the matter for constructing syllogisms
readily, and how he can obtain the principles of demonstration
pertinent to each thesis propounded.[47]
[Footnote 47: Ibid. I. xxvii. p. 43, a. 20: [Greek: pô=s d'
eu)porê/somen au)toi\ pro\s to\ tithe/menon a)ei\ sullogismô=n, kai\
dia\ poi/as o(dou= lêpso/metha ta\s peri\ e(/kaston a)rcha/s, nu=n
ê)/dê lekte/on; ou) ga\r mo/non i)/sôs dei= tê\n ge/nesin theôrei=n
tô=n sullogismô=n, a)lla\ kai\ tê\n du/namin e)/chein tou= poiei=n.]
The second section of Book I. here begins.]
A thesis being propounded in appropriate terms, with subject and
predicate, how are you the propounder to seek out arguments for its
defence? In the first place, Aristotle reverts to the distinction
already laid down at the beginning of the Categoriæ.[48] Individual
things or persons are subjects only, never appearing as
predicates--this is the lowest extremity of the logical scale: at
the opposite extremity of the scale, there are the highest
generalities, predicates only, and not subjects of any predication,
though sometimes supposed to be such, as matters of dialectic
discussion.[49] Between the lowest and highest we have intermediate
or graduate generalities, appearing sometimes as subjects, sometimes
as predicates; and it is among these that the materials both of
problems for debate, and of premisses for proof, are usually
found.[50]
[Footnote 48: Ibid. I. xxvii. p. 43, a. 25, seq.]
[Footnote 49: Ibid. p. 43, a. 39: [Greek: plê\n ei) mê\ kata\
do/xan]. Cf. Schol. of Alexander, p. 175, a. 44, Br.: [Greek:
e)ndo/xôs kai\ dialektikô=s, ô(/sper ei)=pen e)n toi=s Topikoi=s],
that even the _principia_ of science may be debated; for example, in
book B. of the Metaphysica. Aristotle does not recognize either
[Greek: to\ o)/n] or [Greek: to\ e(/n] as true genera, but only as
predicates.]
[Footnote 50: Ibid. a. 40-43.]
You must begin by putting down, along with the matter in hand itself,
its definition and its _propria_; after that, its other predicates;
next, those predicates which _cannot_ belong to it; lastly, those
other subjects, of which it may itself be predicated. You must
classify its various predicates distinguishing the essential, the
_propria_, and the accidental; also distinguishing the true and
unquestionable, from the problematical and hypothetical.[51] You must
look out for those predicates which belong to it as subject
universally, and not to certain portions of it only; since universal
propositions are indispensable in syllogistic proof, and indefinite
propositions can only be reckoned as particular. When a subject is
included in some larger genus--as, for example, man in animal--you
must not look for the affirmative or negative predicates which belong
to animal universally (since all these will of course belong to man
also) but for those which distinguish man from other animals; nor
must you, in searching for those lower subjects of which man is the
predicate, fix your attention on the higher genus animal; for animal
will of course be predicable of all those of which man is predicable.
You must collect what pertains to man specially, either as predicate
or subject; nor merely that which pertains to him necessarily and
universally, but also usually and in the majority of cases; for most
of the problems debated belong to this latter class, and the worth of
the conclusion will be co-ordinate with that of the premisses.[52]**
Do not select predicates that are predicable[53] both of the
predicate and subject; for no valid affirmative conclusion can be
obtained from them.
[Footnote 51: Analyt. Prior. I. xxvii. p. 43, b. 8: [Greek: kai\
tou/tôn poi=a doxastikô=s kai\ poi=a kat' a)lê/theian.]]
[Footnote 52: Ibid. I. xxvii. p. 43, b. 10-35.]
[Footnote 53: Ibid. b. 36: [Greek: e)/ti ta\ pa=sin e(po/mena ou)k
e)klekte/on; ou) ga\r e)/stai sullogismo\s e)x au)tô=n.] The phrase
[Greek: ta\ pa=sin e(po/mena], as denoting predicates applicable both
to the predicate and to the subject, is curious. We should hardly
understand it, if it were not explained a little further on, p. 44,
b. 21. Both the Scholiast and the modern commentators understand
[Greek: ta\ pa=sin e(po/mena] in this sense; and I do not venture to
depart from them. At the same time, when I read six lines afterwards
(p. 44, b. 26) the words [Greek: oi(=on ei) ta\ e(po/mena e(kate/rô|
tau)ta/ e)stin]--in which the same meaning as that which the