Aristotle
Petitio Principii; that is, all real deductive reasoning, in the
syllogistic form, would be a Petitio Principii. To this we may add,
that, from the passage above referred to in the Topica, all inductive
reasoning also (reasoning from parts to whole) would involve Petitio
Principii.
Mr. Poste's explanation of this difficult passage brings into view
the original and valuable exposition made by Mr. John Stuart Mill of
the Functions and Logical Value of the Syllogism.--System of Logic,
Book II. ch. iii. sect 2:--"It must be granted, that in every
syllogism, considered as an argument to prove the conclusion, there
is a Petitio Principii," &c.
Petitio Principii, if ranked among the Fallacies, can hardly be
extended beyond the first of the five distinct varieties enumerated
in the Topica, VIII. xiii.]
[Footnote 23: Analyt. Prior. II. xvi. p. 65, a. 23-27: [Greek: to\
ga\r e)x a)rchê=s ti/ du/natai, ei)/rêtai ê(mi=n, o(/ti to\ di'
au(tou= deiknu/nai to\ mê\ di' au(tou= dê=lon.--tou=to d' e)/sti, to\
mê\ deiknu/nai.]
The meaning of some lines in this chapter (p. 65, a. 17-18) is to me
very obscure, after all the explanations of commentators.]
[Footnote 24: Ibid. p. 65, a. 35; Topic. VIII. xiii. p. 162, b. 31.]
We must be careful to note, that when Aristotle speaks of a
_principium_ as knowable in itself, or true in itself, he does not
mean that it is innate, or that it starts up in the mind ready made
without any gradual building up or preparation. What he means is,
that it is not demonstrable deductively from anything else prior or
more knowable by nature than itself. He declares (as we shall see)
that _principia_ are acquired, and mainly by Induction.
Next to _Petitio Principii_, Aristotle indicates another fallacious
or erroneous procedure in dialectic debate; misconception or
misstatement of the real grounds on which a conclusion rests--_Non
per Hoc_. You may impugn the thesis (set up by the respondent)
directly, by proving syllogistically its contrary or contradictory;
or you may also impugn it indirectly by _Reductio ad Absurdum_;
_i.e._ you prove by syllogism some absurd conclusion, which you
contend to be necessarily true, if the thesis is admitted. Suppose
you impugn it in the first method, or directly, by a syllogism
containing only two premisses and a conclusion: _Non per Hoc_ is
inapplicable here, for if either premiss is disallowed, the
conclusion is unproved; the respondent cannot meet you except by
questioning one or both of the premisses of your impugning
syllogism.[25] But if you proceed by the second method or indirectly,
_Non per Hoc_ may become applicable; for there may then be more than
two premisses, and he may, while granting that the absurd conclusion
is correctly made out, contend that the truth or falsehood of his
thesis is noway implicated in it. He declares (in Aristotle's phrase)
that the absurdity or falsehood just made out does not follow as a
consequence from his thesis, but from other premisses independent
thereof; that it would stand equally proved, even though his thesis
were withdrawn.[26] In establishing the falsehood or absurdity you
must take care that it shall be one implicated with or dependent upon
his thesis. It is this last condition that he (the respondent)
affirms to be wanting.[27]
[Footnote 25: Analyt. Prior. II. xvii. p. 65, b. 4: [Greek: o(/tan
a)naire/thê| ti deiktikôs dia\ tô=n A, B, G], &c.; xviii. 66, a. 17:
[Greek: ê)\ ga\r e)k tô=n du/o prota/seôn ê)\ e)k pleio/nôn pa=s
e)sti\ sullogismo/s; ei) me\n ou)=n e)k tô=n du/o, tou/tôn a)na/gkê
tê\n me\n e(te/ran ê)\ kai\ a)mphote/ras ei)=nai pseudei=s;] &c.
Whoever would understand this difficult chapter xvii., will do well
to study it with the notes of Julius Pacius (p. 360), and also the
valuable exposition of Mr. Poste, who has extracted and illustrated
it in Appendix B. (p. 190) of the notes to his edition of the
Sophistici Elenchi. The six illustrative diagrams given by Julius
Pacius afford great help, though the two first of them appear to me
incorrectly printed, as to the brackets connecting the different
propositions.]
[Footnote 26: Ibid. II. xvii. p. 65, b. 38, b. 14, p. 66, a. 2, 7:
[Greek: to\ mê\ _para\ tou=to_ sumbai/nein to\ pseu=dos--tou= mê\
_para\ tê\n the/sin_ ei)=nai to\ pseu=dos--ou) _para\ tê\n the/sin_
sumbai/nei to\ pseu=dos--ou)k a)\n ei)/ê _para\ tê\n the/sin_.]
Instead of the preposition [Greek: para/], Aristotle on two occasions
employs [Greek: dia/--ou(/tô ga\r e)/stai _dia\ tê\n
u(po/thesin_]--p. 65, b. 33, p. 66, a. 3.
The preposition [Greek: para/], with acc. case, means _on account
of_, _owing to_, &c. See Matthiæ and Kühner's Grammars, and the
passage of Thucydides i. 141; [Greek: kai\ e(/kastos _ou) para\ tê\n
e(autou= a)me/leian_ oi)etai bla/psein, me/lein de/ tini kai\ a)/llô|
u(pe\r e(autou= ti proi+dei=n], &c., which I transcribe partly on
account of Dr. Arnold's note, who says about [Greek: para\]
here:--"This is exactly expressed in vulgar English, _all along of_
his own neglect, _i. e._ owing to his own neglect."]
[Footnote 27: Ibid. II. xvii. p. 65, b. 33: [Greek: dei= pro\s tou\s
e)x a)rchê=s o(/rous suna/ptein to\ a)du/naton; ou(/tô ga\r e)/stai
dia\ tê\n u(po/thesin.]]
Aristotle tells us that this was a precaution which the defender of a
thesis was obliged often to employ in dialectic debate, in order to
guard against abuse or misapplication of _Reductio ad Absurdum_ on
the part of opponents, who (it appears) sometimes took credit for
success, when they had introduced and demonstrated some absurd
conclusion that had little or no connection with the thesis.[28] But
even when the absurd conclusion is connected with the thesis
continuously, by a series of propositions each having a common term
with the preceding, in either the ascending or the descending scale,
we have here more than three propositions, and the absurd conclusion
may perhaps be proved by the other premisses, without involving the
thesis. In this case the respondent will meet you with _Non per
Hoc_:[29] he will point out that his thesis is not one of the
premisses requisite for demonstrating your conclusion, and is
therefore not overthrown by the absurdity thereof. Perhaps the thesis
may be false, but you have not shown it to be so, since it is not
among the premisses necessary for proving your _absurdum_. An
_absurdum_ may sometimes admit of being demonstrated by several lines
of premisses,[30] each involving distinct falsehood. Every false
conclusion implies falsity in one or more syllogistic or
prosyllogistic premisses that have preceded it, and is _owing to_ or
occasioned by this first falsehood.[31]
[Footnote 28: Analyt. Prior. II. xvii. p. 65, a. 38: [Greek: o(\
polla/kis e)n toi=s lo/gois ei)ô/thamen le/gein], &c. That the
_Reductio ad Absurdum_ was sometimes made to turn upon matters wholly
irrelevant, we may see from the illustration cited by Aristotle, p.
65, b. 17.]
[Footnote 29: In this chapter of the Analytica, Aristotle designates
the present fallacy by the title, _Non per Hoc_, [Greek: ou) para\
tou=to--ou) para\ tê\n the/sin sumbai/nei to\ pseu=dos]. He makes
express reference to the Topica (_i.e._ to the fifth chapter of
Sophist. Elenchi, which he regards as part of the Topica), where the
same fallacy is designated by a different title, _Non Causa pro
Causâ_, [Greek: to\ a)nai/tion ô(s ai)/tion tithe/nai]. We see
plainly that this chapter of the Anal. Priora was composed later than
the fifth chapter of Soph. El.; whether this is true of the two
treatises as wholes is not so certain. I think it probable that the
change of designation for the same fallacy was deliberately adopted.
It is an improvement to dismiss the vague term Cause.]
[Footnote 30: Ibid. II. xvii. p. 66, a. 11: [Greek: e)pei\ tau)to/ ge
pseu=dos sumbai/nein dia\ pleio/nôn u(pothe/seôn ou)de\n i)/sôs
a)/topon, oi(=on ta\s parallê/lous sumpi/ptein], &c.]
[Footnote 31: Ibid. II. xviii. p. 66, a. 16-24: [Greek: o( de\
pseudê\s lo/gos gi/netai para\ to\ prô=ton pseu=dos], &c.]
In impugning the thesis and in extracting from your opponent the
proper concessions to enable you to do so, you will take care to put
the interrogations in such form and order as will best disguise the
final conclusion which you aim at establishing. If you intend to
arrive at it through preliminary syllogisms (prosyllogisms), you will
ask assent to the necessary premisses in a confused or inverted
order, and will refrain from enunciating at once the conclusion from
any of them. Suppose that you wish to end by showing that A may be
predicated of F, and suppose that there must be intervening steps
through B, C, D, E. You will not put the questions in this regular
order, but will first ask him to grant that A may be predicated of B;
next, that D may be predicated of E; afterwards, that B may be
predicated of C, &c. You will thus try to obtain all the concessions
requisite for your final conclusion, before he perceives your drift.
If you can carry your point by only one syllogism, and have only one
middle term to get conceded, you will do well to put the middle term
first in your questions. This is the best way to conceal your purpose
from the respondent.[32]
[Footnote 32: Analyt. Prior. II. xix. p. 66, a. 33-b. 3: [Greek:
chrê\ d' o(/per phila/ttesthai paragge/llomen a)pokrinome/nous,
au)tou\s e)picheirou=ntas peira=sthai lantha/nein.--ka)\n di' e(no\s
me/sou gi/nêtai o( sullogismo/s, a)po\ tou= me/sou a)/rchesthai;
ma/lista ga\r a)\n ou(/tô la/nthanoi to\n a)pokrino/menon.] See the
explanation of Pacius, p. 385. Since the middle term does not appear
in the conclusion, the respondent is less likely to be prepared for
the conclusion that you want to establish. To put the middle term
first, in enunciating the Syllogism, is regarded by Aristotle as a
perverted and embarrassing order, yet it is the received practice
among modern logicians.]
It will be his business to see that he is not thus tripped up in the
syllogistic process.[33] If you ask the questions in the order above
indicated, without enunciating your preliminary conclusions, he must
take care not to concede the same term twice, either as predicate, or
as subject, or as both; for you can arrive at no conclusion unless he
grants you a middle term; and no term can be employed as middle,
unless it be repeated twice. Knowing the conditions of a conclusion
in each of the three figures, he will avoid making such concessions
as will empower you to conclude in any one of them.[34] If the thesis
which he defends is affirmative, the _elenchus_ by which you impugn
it must be a negative; so that he will be careful not to concede the
premisses for a negative conclusion. If his thesis be negative, your
purpose will require you to meet him by an affirmative; accordingly
he must avoid granting you any sufficient premisses for an
affirmative conclusion. He may thus make it impossible for you to
prove syllogistically the contrary or contradictory of his thesis;
and it is in proving this that the _elenchus_ or refutation consists.
If he will not grant you any affirmative proposition, nor any
universal proposition, you know, by the rules previously laid down,
that no valid syllogism can be constructed; since nothing can be
inferred either from two premisses both negative, or from two
premisses both particular.[35]
[Footnote 33: Analyt Prior. II. xix. p. 66, a. 25-32: [Greek: pro\s
de\ to\ mê\ katasullogi/zesthai paratêrête/on, o(/tan a)/neu tô=n
sumperasma/tôn e)rôta=| to\n lo/gon], &c.
Waitz (p. 520) explains [Greek: katasullogi/zesthai], "disputationum
et interrogationum laqueis aliquem irretire." This is, I think, more
correct than the distinction which M. Barthélemy St. Hilaire seeks to
draw, "entre le Catasyllogisme et la Réfutation," in the valuable