Aristotle
endeavoured, by careful study and multiplied comparison of
propositions, to elicit general truths respecting their ratiocinative
interdependence, and to found thereupon precepts for regulating the
conduct of demonstration and dialectic.[2]
[Footnote 1: See the remarkable passage at the close of the
Sophistici Elenchi, p. 183, b. 34-p. 184, b. 9: [Greek: tau/tês de\
tê=s pragmatei/as ou) to\ me\n ê)=n to\ de\ ou)k ê)=n
proexeirgasme/non, a)ll' ou)de\n pantelô=s u(pê=rche--kai\ peri\ me\n
tô=n r(êtorikô=n u(pê=rche polla\ kai\ palaia\ ta\ lego/mena, peri\
de\ tou= sullogi/zesthai pantelô=s ou)de\n ei)/chomen pro/teron
a)/llo le/gein, a)ll' ê)\ tribê=| zêtou=ntes polu\n chro/non
e)ponou=men.]]
[Footnote 2: Sir Wm. Hamilton, Lectures on Logic, Lect. v. pp. 87-91,
vol. III.:--"The principles of Contradiction and Excluded Middle can
both be traced back to Plato, by whom they were enounced and
frequently applied; though it was not till long after, that either of
them obtained a distinctive appellation. To take the principle of
Contradiction first. This law Plato frequently employs, but the most
remarkable passages are found in the Phædo (p. 103), in the Sophista
(p. 252), and in the Republic (iv. 436, vii. 525). This law was
however more distinctively and emphatically enounced by Aristotle. .
. . . Following Aristotle, the Peripatetics established this law as
the highest principle of knowledge. From the Greek Aristotelians it
obtained the name by which it has subsequently been denominated, the
_principle_, or _law_, or _axiom_, of _Contradiction_ ([Greek:
a)xi/ôma tê=s a)ntipha/seôs]). . . . . The law of Excluded Middle
between two contradictories remounts, as I have said, also to Plato;
though the Second Alcibiades, in which it is most clearly expressed
(p. 139; also Sophista, p. 250), must be admitted to be spurious. . .
. . This law, though universally recognized as a principle in the
Greek Peripatetic school, and in the schools of the middle ages, only
received the distinctive appellation by which it is now known at a
comparatively modern date."
The passages of Plato, to which Sir W. Hamilton here refers, will not
be found to bear out his assertion that Plato "enounced and
frequently applied the principles of Contradiction and Excluded
Middle." These two principles are both of them enunciated,
denominated, and distinctly explained by Aristotle, but by no one
before him, as far as our knowledge extends. The conception of the
two maxims, in their generality, depends upon the clear distinction
between Contradictory Opposition and Contrary Opposition; which is
fully brought out by Aristotle, but not adverted to, or at least
never broadly and generally set forth, by Plato. Indeed it is
remarkable that the word [Greek: A)nti/phasis], the technical term
for Contradiction, never occurs in Plato; at least it is not
recognized in the _Lexicon Platonicum_. Aristotle puts it in the
foreground of his logical exposition; for, without it, he could not
have explained what he meant by Contradictory Opposition. See
Categoriæ, pp. 13-14, and elsewhere in the treatise De
Interpretatione and in the Metaphysica. Respecting the idea of the
Negative as put forth by Plato in the Sophistes (not coinciding
either with Contradictory Opposition or with Contrary Opposition),
see 'Plato and the Other Companions of Sokrates,' vol. II. ch. xxvii.
pp. 449-459. I have remarked in that chapter, and the reader ought to
recollect, that the philosophical views set out by Plato in the
Sophistes differ on many points from what we read in other Platonic
dialogues.]
He begins the Analytica Priora by setting forth his general purpose,
and defining his principal terms and phrases. His manner is one of
geometrical plainness and strictness. It may perhaps have been common
to him with various contemporary geometers, whose works are now lost;
but it presents an entire novelty in Grecian philosophy and
literature. It departed not merely from the manner of the
rhetoricians and the physical philosophers (as far as we know them,
not excluding even Demokritus), but also from Sokrates and the
Sokratic school. For though Sokrates and Plato were perpetually
calling for definitions, and did much to make others feel the want of
such, they neither of them evinced aptitude or readiness to supply
the want. The new manner of Aristotle is adapted to an undertaking
which he himself describes as original, in which he has no
predecessors, and is compelled to dig his own foundations. It is
essentially didactic and expository, and contrasts strikingly with
the mixture of dramatic liveliness and dialectical subtlety which we
find in Plato.
The terminology of Aristotle in the Analytica is to a certain extent
different from that in the treatise De Interpretatione. The
Enunciation ([Greek: A)po/phanis]) appears under the new name of
[Greek: Pro/tasis], _Proposition_ (in the literal sense) or
_Premiss_; while, instead of Noun and Verb, we have the word _Term_
([Greek: O(/ros]), applied alike both to Subject and to Predicate.[3]
We pass now from the region of _declared_ truth, into that of
_inferential_ or _reasoned_ truth. We find the proposition looked at,
not merely as communicating truth in itself, but as generating and
helping to guarantee certain ulterior propositions, which communicate
something additional or different. The primary purpose of the
Analytica is announced to be, to treat of Demonstration and
demonstrative Science; but the secondary purpose, running parallel
with it and serving as illustrative counterpart, is, to treat also of
Dialectic; both of them[4] being applications of the inferential or
ratiocinative process, the theory of which Aristotle intends to
unfold.
[Footnote 3: Aristot. Analyt. Prior. I. i. p. 24, b. 16: [Greek:
o(/ron de\ kalô= ei)s o(\n dialu/etai ê( pro/tasis, oi(=on to/ te
katêgorou/menon kai\ to\ kath' ou(= katêgorei=tai], &c.
[Greek: O(/ros]--_Terminus_--seems to have been a technical word
first employed by Aristotle himself to designate subject and
predicate as the _extremes_ of a proposition, which latter he
conceives as the _interval_ between the _termini_--[Greek:
_dia/stêma_]. (Analyt. Prior. I. xv. p. 35, a. 12. [Greek:
sterêtikô=n diastêma/tôn], &c. See Alexander, Schol. pp. 145-146.)
In the Topica Aristotle employs [Greek: o(/ros] in a very different
sense--[Greek: lo/gos o( to\ ti/ ê)=n ei)=nai sêmai/nôn] (Topic. I.
v. p. 101, b. 39)--hardly distinguished from [Greek: o(rismo/s]. The
Scholia take little notice of this remarkable variation of meaning,
as between two treatises of the Organon so intimately connected (pp.
256-257, Br.).]
[Footnote 4: Analyt. Prior. I. i. p. 24, a. 25.]
The three treatises--1, Analytica Priora, 2, Analytica Posteriora, 3,
Topica with Sophistici Elenchi--thus belong all to one general
scheme; to the theory of the Syllogism, with its distinct
applications, first, to demonstrative or didactic science, and, next,
to dialectical debate. The scheme is plainly announced at the
commencement of the Analytica Priora; which treatise discusses the
Syllogism generally, while the Analytica Posteriora deals with
Demonstration, and the Topica with Dialectic. The first chapter of
the Analytica Priora and the last chapter of the Sophistici Elenchi
(closing the Topica), form a preface and a conclusion to the whole.
The exposition of the Syllogism, Aristotle distinctly announces,
precedes that of Demonstration (and for the same reason also precedes
that of Dialectic), because it is more general: every demonstration
is a sort of syllogism, but every syllogism is not a
demonstration.[5]
[Footnote 5: Ibid. I. iv. p. 25, b. 30.]
As a foundation for the syllogistic theory, propositions are
classified according to their quantity (more formally than in the
treatise De Interpretatione) into Universal, Particular, and
Indefinite or Indeterminate;[6] Aristotle does not recognize the
Singular Proposition as a distinct variety. In regard to the
Universal Proposition, he introduces a different phraseology
according as it is looked at from the side of the Subject, or from
that of the Predicate. The Subject is, or is not, in the whole
Predicate; the Predicate is affirmed or denied respecting all or
every one of the Subject.[7] The minor term of the Syllogism (in the
first mode of the first figure) is declared to be in the whole middle
term; the major is declared to belong to, or to be predicable of, all
and every the middle term. Aristotle says that the two are the same;
we ought rather to say that each is the concomitant and correlate of
the other, though his phraseology is such as to obscure the
correlation.
[Footnote 6: Ibid. I. i. p. 24, a. 17. The Particular ([Greek: e)n
me/rei]), here for the first time expressly distinguished by
Aristotle, is thus defined:--[Greek: e)n me/rei de\ to\ tini\ ê)\ mê\
tini\ ê)\ mê\ panti\ u(pa/rchein.]]
[Footnote 7: Ibid. b. 26: [Greek: to\ d' e)n o(/lô| ei)nai e(/teron
e(te/rô|, kai\ to\ kata\ panto\s katêgorei=sthai thate/rou tha/teron,
tau)to/n e)sti--tau)to\n], _i.e._ [Greek: _a)ntestramme/nôs_], as
Waitz remarks in note. Julius Pacius says:--"Idem re, sed ratione
differunt ut ascensus et descensus; nam subjectum dicitur esse vel
non esse in toto attributo, quia attributum dicitur de omni vel de
nullo subjecto" (p. 128).]
The definition given of a Syllogism is very clear and
remarkable:--"It is a speech in which, some positions having been
laid down, something different from these positions follows as a
necessary consequence from their being laid down." In a _perfect_
Syllogism nothing additional is required to make the necessity of the
consequence obvious as well as complete. But there are also
_imperfect_ Syllogisms, in which such necessity, though equally
complete, is not so obviously conveyed in the premisses, but requires
some change to be effected in the position of the terms in order to
render it conspicuous.[8]
[Footnote 8: Aristot. Anal. Prior. I. i. p. 24, b. 18-26. The same,
with a little difference of wording, at the commencement of Topica,
p. 100, a. 25. Compare also Analyt. Poster. I. x. p. 76, b. 38:
[Greek: o(/sôn o)/ntôn tô=| e)kei=na ei)=nai gi/netai to\
sumpe/rasma.]]
The term Syllogism has acquired, through the influence of Aristotle,
a meaning so definite and technical, that we do not easily conceive
it in any other meaning. But in Plato and other contemporaries it
bears a much wider sense, being equivalent to reasoning generally, to
the process of comparison, abstraction, generalization.[9] It was
Aristotle who consecrated the word, so as to mean exclusively the
reasoning embodied in propositions of definite form and number.
Having already analysed propositions separately taken, and
discriminated them into various classes according to their
constituent elements, he now proceeds to consider propositions in
combination. Two propositions, if properly framed, will conduct to a
third, different from themselves, but which will be necessarily true
if they are true. Aristotle calls the three together a Syllogism.[10]
He undertakes to shew how it must be framed in order that its
conclusion shall be necessarily true, if the premisses are true. He
furnishes schemes whereby the cast and arrangement of premisses,
proper for attaining truth, may be recognized; together with the
nature of the conclusion, warrantable under each arrangement.
[Footnote 9: See especially Plato, Theætêt. p. 186, B-D., where
[Greek: o( sullogismo\s] and [Greek: ta\ a)nalogi/smata] are
equivalents.]
[Footnote 10: Julius Pacius (ad Analyt. Prior. I. i.) says that it is
a mistake on the part of most logicians to treat the Syllogism as
including three propositions (ut vulgus logicorum putat). He