Aristotle
predicable of every subject. Again, if either A or B must necessarily
be predicable of every subject, but never both predicable of the same
at once; and if, either C or D must be predicable of every subject,
but never both predicable of the same at once; then, if A and C
reciprocate, B and D will also reciprocate.[47] When A is predicable
of all B and all C, but of no other subject besides, and when B is
predicable of all C, then A and B must reciprocate with each other,
or be co-extensive with each other; that is, B may be predicated of
every subject of which A can be predicated, though B cannot be
predicated of A itself.[48] Again, when A and B are predicable of all
C, and when C reciprocates with B, then A must also be predicable of
all B.[49]
[Footnote 46: Ibid. II. xxii. p. 67, b. 27, seq. In this chapter
Aristotle introduces us to affirmative universal propositions
convertible _simpliciter_; that is, in which the predicate must be
understood to be distributed as well as the subject. Here, then, the
quantity of the predicate is determined in thought. This is (as
Julius Pacius remarks, p. 371) in order to lay down principles for
the resolution of Induction into Syllogism, which is to be explained
in the next chapter. In these peculiar propositions, the reason urged
by Sir W. Hamilton for his favourite precept of verbally indicating
the quantity of the predicate, is well founded as a fact: though _he_
says that in _all_ propositions the quantity of the predicate is
understood in thought, which I hold to be incorrect.
We may remark that this recognition by Aristotle of a class of
universal affirmative propositions in which predicate and subject
reciprocate, contrived in order to force Induction into the
syllogistic framework, is at variance with his general view both of
reciprocating propositions and of Induction. He tells us (Analyt.
Post. I. iii. p. 73, a. 18) that such reciprocating propositions are
very rare, which would not be true if they are taken to represent
every Induction; and he forbids us emphatically to annex the mark of
universality to the predicate; which he has no right to do, if he
calls upon us to reason on the predicate as distributed (Analyt.
Prior. I. xxvii., p. 43, b. 17; De Interpret. p. 17, b. 14).]
[Footnote 47: Ibid. II. xxii. p. 68, a. 2-15.]
[Footnote 48: Ibid. a. 16-21. [Greek: plê\n au)tou= tou= A]. Waitz
explains these words in his note (p. 531): yet I do not clearly make
them out; and Alexander of Aphrodisias declared them to assert what
was erroneous ([Greek: e)spha/lthai le/gei], Schol. p. 194, a. 40,
Brandis).]
[Footnote 49: Ibid. II. xxii. p. 68, a. 21-25.]
Lastly, suppose two pairs of opposites, A and B, C and D; let A be
more eligible than B, and D more eligible than C. Then, if A C is
more eligible than B D, A will also be more eligible than D. For A is
as much worthy of pursuit as B is worthy of avoidance, they being two
opposites; the like also respecting C and D. If then A and D are
equally worthy of pursuit, B and C are equally worthy of avoidance;
for each is equal to each. Accordingly the two together, A C, will be
equal to the two together, B D. But this would be contrary to the
supposition; since we assumed A to be more eligible than B, and D to
be more eligible than C. It will be seen that on this supposition A
is more worthy of pursuit than D, and that C is less worthy of
avoidance than B; the greater good and the lesser evil being more
eligible than the lesser good and the greater evil. Now apply this to
a particular case of a lover, so far forth as lover. Let A represent
his possession of those qualities which inspire reciprocity of love
towards him in the person beloved; B, the absence of those qualities;
D, the attainment of actual sexual enjoyment; C, the non-attainment
thereof. In this state of circumstances, it is evident that A is more
eligible or worthy of preference than D. The being loved is a greater
object of desire to the lover _qua_ lover than sexual gratification;
it is the real end or purpose to which love aspires; and sexual
gratification is either not at all the purpose, or at best only
subordinate and accessory. The like is the case with our other
appetites and pursuits.[50]
[Footnote 50: Analyt. Prior. II. xxii. p. 68, a. 25-b. 17. Aristotle
may be right in the conclusion which he here emphatically asserts;
but I am surprised that he should consider it to be proved by the
reasoning that precedes.
It is probable that Aristotle here understood the object of [Greek:
e)/rôs] (as it is conceived through most part of the Symposion of
Plato) to be a beautiful youth: (see Plato, Sympos. pp. 218-222; also
Xenophon, Sympos. c. viii., Hiero, c. xi. 11, Memorab. I. ii. 29,
30). Yet this we must say--what the two women said when they informed
Simætha of the faithlessness of Delphis (Theokrit. Id. ii.
149)--[Greek: Kê)=|pe/ moi a)/lla te polla/, kai\ ô(s a)/ra De/lphis
e)/ratai;
Kê)/|te min au)=te gunaiko\s e)/chei po/thos, ei)/te kai\ a)ndro/s,
Ou)k e)/phat' a)treke\s i)/dmen.]]
Such is the relation of the terms of a syllogism in regard to
reciprocation and antithesis. Let it next be understood that the
canons hitherto laid down belong not merely to demonstrative and
dialectic syllogisms, but to rhetorical and other syllogisms also;
all of which must be constructed in one or other of the three
figures. In fact, every case of belief on evidence, whatever be the
method followed, must be tested by these same canons. We believe
everything either through Syllogism or upon Induction.[51]
[Footnote 51: Ibid. II. xxiii. p. 68, b. 13: [Greek: a(/panta ga\r
pisteu/omen ê)\ dia\ sullogismou= ê)\ e)x e)pagôgê=s.]]
Though Aristotle might seem, even here, to have emphatically
contrasted Syllogism with Induction as a ground of belief, he
proceeds forthwith to indicate a peculiar form of Syllogism which may
be constructed out of Induction. Induction, and the Syllogism from or
out of Induction (he says) is a process in which we invert the order
of the terms. Instead of concluding from the major through the middle
to the minor (_i.e._ concluding that the major is predicable of the
minor), we now begin from the minor and conclude from thence through
the middle to the major (_i.e._ we conclude that the major is
predicable of the middle).[52] In Syllogism as hitherto described, we
concluded that A the major was predicable of C the minor, through the
middle B; in the Syllogism from Induction we begin by affirming that
A the major is predicable of C the minor; next, we affirm that B the
middle is also predicable of C the minor. The two premisses, standing
thus, correspond to the Third figure of the Syllogism (as explained
in the preceding pages) and would not therefore by themselves justify
anything more than a _particular_ affirmative conclusion. But we
reinforce them by introducing an extraneous assumption:--That the
minor C is co-extensive with the middle B, and comprises the entire
aggregate of individuals of which B is the universal or class-term.
By reason of this assumption the minor proposition becomes
convertible simply, and we are enabled to infer (according to the
last preceding chapter) an universal affirmative conclusion, that the
major term A is predicable of the middle term B. Thus, let A (the
major term) mean the class-term, long-lived; let B (the middle term)
mean the class-term, bile-less, or the having no bile; let C (the
minor term) mean the individual animals--man, horse, mule, &c.,
coming under the class-term B, bile-less.[53] We are supposed to
know, or to have ascertained, that A may be predicated of all C;
(_i.e._ that all men, horses, mules, &c., are long-lived); we farther
know that B is predicable of all C (_i.e._ that men, horses, mules,
&c., belong to the class bile-less). Here, then, we have two
premisses in the Third syllogistic figure, which in themselves would
warrant us in drawing the particular affirmative conclusion, that A
is predicable of _some_ B, but no more. Accordingly, Aristotle
directs us to supplement these premisses[54] by the extraneous
assumption or postulate, that C the minor comprises all the
individual animals that are bile-less, or all those that correspond
to the class-term B; in other words, the assumption, that B the
middle does not denote any more individuals than those which are
covered by C the minor--that B the middle does not stretch beyond or
overpass C the minor.[55] Having the two premisses, and this
postulate besides, we acquire the right to conclude that A is
predicable of _all_ B. But we could not draw that conclusion from the
premisses alone, or without the postulate which declares B and C to
be co-extensive. The conclusion, then, becomes a particular
exemplification of the general doctrine laid down in the last
chapter, respecting the reciprocation of extremes and the
consequences thereof. We thus see that this very peculiar Syllogism
from Induction is (as indeed Aristotle himself remarks) the opposite
or antithesis of a genuine Syllogism. It has no proper middle term;
the conclusion in which it results is the first or major proposition,
the characteristic feature of which it is to be _immediate_, or not
to be demonstrated through a middle term. Aristotle adds that the
genuine Syllogism, which demonstrates through a middle term, is by
nature prior and more effective as to cognition; but that the
Syllogism from Induction is _to us_ plainer and clearer.[56]
[Footnote 52: Analyt. Prior. II. xxiii. p. 68, b. 15: [Greek:
e)pagôgê\ me\n ou)=n e)sti\ kai\ o( e)x e)pagôgê=s sullogismo\s to\
dia\ tou= e(te/rou tha/teron a)/kron tô=| me/sô| sullogi/sasthai;
oi(=on ei) tô=n AG me/son to\ B, dia\ tou= G dei=xai to\ A tô=| B
u(pa/rchon; ou(/tô ga\r poiou/metha ta\s e)pagôga/s.]
Waitz in his note (p. 532) says: "Fit Inductio, cum per minorem
terminum demonstratur _medium prædicari de majore_." This is an
erroneous explanation. It should have been: "demonstratur _majorem
prædicari de medio_." Analyt. Prior. II. xxiii. 68, b. 32: [Greek:
kai\ tro/pon tina\ a)ntikei=tai ê( e)pagôgê\ tô=| sullogismô=|; o(
me\n ga\r dia\ tou= me/sou to\ a)/kron tô=| tri/tô| dei/knusin, ê(
de\ dia\ tou= tri/tou to\ a)/kron tô=| me/sô|.]]
[Footnote 53: Ibid. II. xxiii. p. 68, b. 18: [Greek: oi(=on e)/stô
to\ A makro/bion, to\ d' e)ph' ô(=| B, to\ cholê\n mê\ e)/chon, e)ph'
ô(=| de\ G, to\ kath' e(/kaston _makro/bion_, oi(=on a)/nthrôpos kai\
i(/ppos kai\ ê(mi/onos. tô=| dê\ G o(/lô| u(pa/rchei to\ A; pa=n ga\r
to\ a)/cholon makro/bion; a)lla\ kai\ to\ B, to\ mê\ e)/chein
cholê/n, panti\ u(pa/rchei tô=| G. ei) ou)=n a)ntistre/phei to\ G
tô=| B kai\ mê\ u(pertei/nei to\ me/son, a)na/gkê to\ A tô=| B
u(pa/rchein.]
I have transcribed this Greek text as it stands in the editions of
Buhle, Bekker, Waitz, and F. Didot. Yet, notwithstanding these high
authorities, I venture to contend that it is not wholly correct; that
the word [Greek: _makro/bion_], which I have emphasized, is neither
consistent with the context, nor suitable for the point which
Aristotle is illustrating. Instead of [Greek: _makro/bion_], we ought
in that place to read [Greek: a)/cholon]; and I have given the sense
of the passage in my English text as if it did stand [Greek:
a)/cholon] in that place.
I proceed to justify this change. If we turn back to the edition by
Julius Pacius (1584, p. 377), we find the text given as follows after
the word [Greek: ê(mi/onos] (down to that word the text is the same):
[Greek: tô=| dê\ G o(/lô| u(pa/rchei to\ A; pa=n ga\r to\ G
makro/bion; a)lla\ kai\ to\ B, to\ mê\ e)/chon cholê/n, panti\
u(pa/rchei tô=| G. ei) ou)=n a)ntistre/phei to\ G tô=| B, kai\ mê\
u(pertei/nei to\ me/son, a)na/gkê to\ A tô=| B u(pa/rchein.] Earlier
than Pacius, the edition of Erasmus (Basil. 1550) has the same text