Aristotle
Errors of simple ignorance (not concluded from false syllogism) may
proceed from defect or failure of sensible perception, in one or
other of its branches. For without sensation there can be no
induction; and it is from induction only that the premisses for
demonstration by syllogism are obtained. We cannot arrive at
universal propositions, even in what are called abstract sciences,
except through induction of particulars; nor can we demonstrate
except from universals. Induction and Demonstration are the only two
ways of learning; and the particulars composing our inductions can
only be known through sense.[54]
[Footnote 54: Analyt. Post. I. xviii. p. 81, a. 38-b. 9. In this
important chapter (the doctrines of which are more fully expanded in
the last chapter of the Second Book of the Analyt. Post.), the text
of Waitz does not fully agree with that of Julius Pacius. In Firmin
Didot's edition the text is the same as in Waitz; but his Latin
translation remains adapted to that of Julius Pacius. Waitz gives the
substance of the chapter as follows (ad Organ. II. p. 347):--
"Universales propositiones omnes inductione comparantur, quum etiam
in iis, quæ a sensibus maxime aliena videntur et quæ, ut mathematica
([Greek: ta\ e)x a)phaire/seôs]), cogitatione separantur à materia
quacum conjuncta sunt, inductione probentur ea quæ de genero (e. g.,
de linea vel de corpore mathematico), ad quod demonstratio pertineat,
prædicentur [Greek: kath' au(ta/] et cum ejus natura conjuncta sint.
Inductio autem iis nititur quæ sensibus percipiuntur; nam res
singulares sentiuntur, scientia vero rerum singularium non datur sine
inductione, non datur inductio sine sensu."]
Aristotle next proceeds to show (what in previous passages he had
assumed)[55] that, if Demonstration or the syllogistic process be
possible--if there be any truths supposed demonstrable, this implies
that there must be primary or ultimate truths. It has been explained
that the constituent elements assumed in the Syllogism are three
terms and two propositions or premisses; in the major premiss, A is
affirmed (or denied) of all B; in the minor, B is affirmed of all C;
in the conclusion, A is affirmed (or denied) of all C.[56] Now it is
possible that there may be some one or more predicates higher than A,
but it is impossible that there can be an infinite series of such
higher predicates. So also there may be one or more subjects lower
than C, and of which C will be the predicate; but it is impossible
that there can be an infinite series of such lower subjects. In like
manner there may perhaps be one or more middle terms between A and B,
and between B and C; but it is impossible that there can be an
infinite series of such intervening middle terms. There must be a
limit to the series ascending, descending, or intervening.[57] These
remarks have no application to reciprocating propositions, in which
the predicate is co-extensive with the subject.[58] But they apply
alike to demonstrations negative and affirmative, and alike to all
the three figures of Syllogism.[59]
[Footnote 55: Analyt. Prior. I. xxvii. p. 43, a. 38; Analyt. Post. I.
ii. p. 71, b. 21.]
[Footnote 56: Analyt. Post. I. xix. p. 81, b. 10-17.]
[Footnote 57: Ibid. p. 81, b. 30-p. 82, a. 14.]
[Footnote 58: Ibid. p. 82, a. 15-20. M. Barthélemy St. Hilaire, p.
117:--"Ceci ne saurait s'appliquer aux termes réciproques, parce que
dans les termes qui peuvent être attribués réciproquement l'un à
l'autre, on ne peut pas dire qu'il y ait ni premier ni dernier
rélativement à l'attribution."]
[Footnote 59: Analyt. Post. I. xx., xxi. p. 82, a. 21-b. 36.]
In Dialectical Syllogism it is enough if the premisses be admitted or
reputed as propositions immediately true, whether they are so in
reality or not; but in Scientific or Demonstrative Syllogism they
must be so in reality: the demonstration is not complete unless it
can be traced up to premisses that are thus immediately or directly
true (without any intervening middle term).[60] That there are and
must be such primary or immediate premisses, Aristotle now undertakes
to prove, by some dialectical reasons, and other analytical or
scientific reasons.[61] He himself thus distinguishes them; but the
distinction is faintly marked, and amounts, at most, to this, that
the analytical reasons advert only to essential predication, and to
the conditions of scientific demonstration, while the dialectical
reasons dwell upon these, but include something else besides, viz.,
accidental predication. The proof consists mainly in the declaration
that, unless we assume some propositions to be true immediately,
indivisibly, undemonstrably,--Definition, Demonstration, and Science
would be alike impossible. If the ascending series of predicates is
endless, so that we never arrive at a highest generic predicate; if
the descending series of subjects is endless, so that we never reach
a lowest subject,--no definition can ever be attained. The essential
properties included in the definition, must be finite in number; and
the accidental predicates must also be finite in number, since they
have no existence except as attached to some essential subject, and
since they must come under one or other of the nine later
Categories.[62] If, then, the two extremes are thus fixed and
finite--the highest predicate and the lowest subject--it is
impossible that there can be an infinite series of terms between the
two. The intervening terms must be finite in number. The
Aristotelian theory therefore is, that there are certain
propositions directly and immediately true, and others derived from
them by demonstration through middle terms.[63] It is alike an error
to assert that every thing can be demonstrated, and that nothing can
be demonstrated.
[Footnote 60: Ibid. xix. p. 81, b. 18-29.]
[Footnote 61: Ibid. xxi. p. 82, b. 35; xxii. p. 84, a. 7: [Greek:
_logikô=s_ me\n ou)=n e)k tou/tôn a)/n tis pisteu/seie peri\ tou=
lechthe/ntos, _a)nalutikô=s_ de\ dia\ tô=nde phanero\n
suntomô/teron.] In Scholia, p. 227, a. 42, the same distinction is
expressed by Philoponus in the terms [Greek: logikô/tera] and [Greek:
pragmatôde/stera]. Compare Biese, Die Philosophie des Aristoteles,
pp. 134, 261; Bassow, De Notionis Definitione, pp. 19, 20; Heyder,
Aristot. u. Hegel. Dialektik, pp. 316, 317.
Aristotle, however, does not always adhere closely to the
distinction. Thus, if we compare the _logical_ or _dialectical_
reasons given, p. 82, b. 37, seq., with the _analytical_, announced
as beginning p. 84, a. 8, seq., we find the same main topic dwelt
upon in both, namely, that to admit an infinite series excludes the
possibility of Definition. Both Alexander and Ammonius agree in
announcing this as the capital topic on which the proof turned; but
Alexander inferred from hence that the argument was purely
_dialectical_ ([Greek: logiko\n e)pichei/rêma]), while Ammonius
regarded it as a reason thoroughly convincing and evident: [Greek: o(
me/ntoi philo/sophos] (Ammonius) [Greek: e)/lege mê\ dia\ tou=to
le/gein _logika\_ ta\ e)picheirê/mata; e)narge\s ga\r o(/ti ei)si\n
o(rismoi/, ei) mê\ a)katalêpsi/an ei)saga/gômen] (Schol. p. 227, a.
40, seq., Brand.).]
[Footnote 62: Analyt. Post. I. xxii. p. 83, a. 20, b. 14. Only eight
of the ten Categories are here enumerated.]
[Footnote 63: Ibid. I. xxii. p. 84, a. 30-35. The paraphrase of
Themistius (pp. 55-58, Spengel) states the Aristotelian reasoning in
clearer language than Aristotle himself. Zabarella (Comm. in Analyt.
Post. I. xviii.; context. 148, 150, 154) repeats that Aristotle's
proof is founded upon the undeniable fact that there _are_
definitions, and that without them there could be no demonstration
and no science. This excludes the supposition of an infinite series
of predicates and of middle terms:--"Sumit rationem à definitione; si
in _predicatis in quid_ procederetur ad infinitum, sequeretur auferri
definitionem et omnino essentiæ cognitionem; sed hoc dicendum non
est, quum omnium consensioni adversetur" (p. 466, Ven. 1617).]
It is plain from Aristotle's own words[64] that he intended these
four chapters (xix.-xxii.) as a confirmation of what he had already
asserted in chapter iii. of the present treatise, and as farther
refutation of the two distinct classes of opponents there indicated:
(1) those who said that everything was demonstrable, demonstration in
a circle being admissible; (2) those who said that nothing was
demonstrable, inasmuch as the train of predication upwards,
downwards, and intermediate, was infinite. Both these two classes of
opponents agreed in saying, that there were no truths immediate and
indemonstrable; and it is upon this point that Aristotle here takes
issue with them, seeking to prove that there are and must be such
truths. But I cannot think the proof satisfactory; nor has it
appeared so to able commentators either of ancient or modern
times--from Alexander of Aphrodisias down to Mr. Poste.[65] The
elaborate amplification added in these last chapters adds no force to
the statement already given at the earlier stage; and it is in one
respect a change for the worse, inasmuch as it does not advert to the
important distinction announced in chapter iii., between universal
truths known by Induction (from sense and particulars), and universal
truths known by Deduction from these. The truths immediate and
indemonstrable (not known through a middle term) are the inductive
truths, as Aristotle declares in many places, and most emphatically
at the close of the Analytica Posteriora. But in these chapters, he
hardly alludes to Induction. Moreover, while trying to prove that
there must be immediate universal truths, he neither gives any
complete list of them, nor assigns any positive characteristic
whereby to identify them. Opponents might ask him whether these
immediate universal truths were not ready-made inspirations of the
mind; and if so, what better authority they had than the Platonic
Ideas, which are contemptuously dismissed.
[Footnote 64: Analyt. Post. I. xxii. p. 84, a. 32: [Greek: o(/per
e)/phame/n tinas le/gein kat' a)rcha/s], &c.]
[Footnote 65: See Mr. Poste's note, p. 77, of his translation of this
treatise. After saying that the first of Aristotle's _dialectical_
proofs is faulty, and that the second is a _petitio principii_, Mr.
Poste adds, respecting the so-called _analytical_ proof given by
Aristotle:--"It is not so much a proof, as a more accurate
determination of the principle to be postulated. This postulate, the
existence of first principles, as concerning the constitution of the
world, appears to belong properly to Metaphysics, and is merely
borrowed by Logic. See Metaph. ii. 2, and Introduction." In the
passage of the Metaphysica ([Greek: a]. p. 994) here cited the main
argument of Aristotle is open to the same objection of _petitio
principii_ which Mr. Poste urges against Aristotle's second
_dialectical_ argument in this place.
Mr. John Stuart Mill, in his System of Logic, takes for granted that
there _must_ be immediate, indemonstrable truths, to serve as a basis
for deduction; "that there cannot be a chain of proof suspended from
nothing;" that there must be ultimate laws of nature, though we
cannot be sure that the laws now known to us are ultimate.
On the other hand, we read in the recent work of an acute
contemporary philosopher, Professor Delboeuf (Essai de Logique
Scientifique, Liège, 1865, Pref. pp. v, vii, viii, pp. 46, 47:)--"Il
est des points sur lesquels je crains de ne m'être pas expliqué assez
nettement, entre autres la question du fondement de la certitude. Je
suis de ceux qui repoussent de toutes leurs forces l'axiome si
spécieux qu'on ne peut tout démontrer; cette proposition aurait, à
mes yeux, plus besoin que toute autre d'une démonstration. Cette