Aristotle
contemporaries, Antisthenes among them, who declared contradiction to
be an impossibility;[59] an opinion coinciding at bottom with what I
have just cited from Plato himself. We see, in the Theætêtus, the
Euthydêmus, the Sophistes, and elsewhere, how great was the
difficulty felt by philosophers of that age to find a proper _locus
standi_ for false propositions, so as to prove them theoretically
possible, to assign a legitimate function for the negative, and to
escape from the interdict of Parmenides, who eliminated _Non-Ens_ as
unmeaning and incogitable. Even after the death of Aristotle, the
acute disputation of Stilpon suggested many problems, but yielded few
solutions; and Menedêmus went so far as to disallow negative
propositions altogether.[60]
[Footnote 56: Plato, Sophistes, pp. 261-262. [Greek: pha/sin kai\
a)po/phasin].--ib. p. 263 E. In the so-called Platonic 'Definitions,'
we read [Greek: e)n katapha/sei kai\ a)popha/sei] (p. 413 C); but
these are probably after Aristotle's time. In another of these
Definitions (413 D.) we read [Greek: a)po/phasis], where the word
ought to be [Greek: a)po/phansis].]
[Footnote 57: Plato, Sophist. p. 263 A-C.]
[Footnote 58: Ibid. p. 257, B: [Greek: Ou)k a)r', e)nanti/on o(/tan
a)po/phasis le/gêtai sêmai/nein, sugchôrêso/metha, tosou=ton de\
mo/non, o(/ti _tô=n a)/llôn ti mênu/ei to\ mê\ kai\ to\ ou)/_
protithe/mena tô=n e)pio/ntôn o)noma/tôn, ma=llon de\ tô=n
pragma/tôn, peri\ a(/tt' a)\n ke/êtai ta\ e)piphtheggo/mena u(/steron
tê=s a)popha/seôs o)no/mata.]
The term [Greek: a)nti/phasis], and its derivative [Greek:
a)ntiphatikô=s], are not recognized in the Platonic Lexicon. Compare
the same dialogue, Sophistes, p. 263; also Euthydêmus, p. 298, A.
Plato does not seem to take account of negative propositions as such.
See 'Plato and the Other Companions of Sokrates,' vol. II. ch. xxvii.
pp. 446-455.]
[Footnote 59: Aristot. Topica, I. xi. p. 104, b. 20; Metaphys.
[Greek: D]. p. 1024, b. 32; Analytic. Poster. I. xxv. p. 86, b. 34.]
[Footnote 60: Diogon. Laert. ii. 134-135. See the long discussion in
the Platonic Theætêtus (pp. 187-196), in which Sokrates in vain
endeavours to produce some theory whereby [Greek: pseudê\s do/xa] may
be rendered possible. Hobbes, also, in his Computation or Logic (De
Corp. c. iii. § 6), followed by Destutt Tracy, disallows the negative
proposition _per se_, and treats it as a clumsy disguise of the
affirmative [Greek: e)k metathe/seôs], to use the phrase of
Theophrastus. Mr. John Stuart Mill has justly criticized this part of
Hobbes's theory (System of Logic, Book I. ch. iv. § 2).]
Such being the conditions under which philosophers debated in the age
of Aristotle, we can appreciate the full value of a positive theory
of propositions such as that which we read in his treatise De
Interpretatione. It is, so far as we know, the first positive theory
thereof that was ever set out; the first attempt to classify
propositions in such a manner that a legitimate _Antiphasis_ could be
assigned to each; the first declaration that to each affirmative
proposition there belonged one appropriate negative, and to each
negative proposition one appropriate counter-affirmative, and one
only; the earliest effort to construct a theory for this purpose,
such as to hold ground against all the puzzling questions of acute
disputants.[61] The clear determination of the _Antiphasis_ in each
case--the distinction of Contradictory antithesis from Contrary
antithesis between propositions--this was an important logical
doctrine never advanced before Aristotle; and the importance of it
becomes manifest when we read the arguments of Plato and Antisthenes,
the former overleaping and ignoring the contradictory opposition, the
latter maintaining that it was a process theoretically indefensible.
But in order that these two modes of antithesis should be clearly
contrasted, each with its proper characteristic, it was requisite
that the distinction of quantity between different propositions
should also be brought to view, and considered in conjunction with
the distinction of quality. Until this was done, the Maxim of
Contradiction, denied by some, could not be shown in its true force
or with its proper limits. Now, we find it done,[62] for the first
time, in the treatise before us. Here the Contradictory antithesis
(opposition both in quantity and quality) in which one proposition
must be true and the other false, is contrasted with the Contrary
(propositions opposite in quality, but both of them universal).
Aristotle's terminology is not in all respects fully developed; in
regard, especially, to the quantity of propositions it is less
advanced than in his own later treatises; but from the theory of the
De Interpretatione all the distinctions current among later
logicians, take their rise.
[Footnote 61: Aristot. De Interpr. p. 17, a. 36: [Greek: pro\s ta\s
sophistika\s e)nochlê/seis].]
[Footnote 62: We see, from the argument in the Metaphysica of
Aristotle, that there were persons in his day who denied or refused
to admit the Maxim of Contradiction; and who held that contradictory
propositions might both be true or both false (Aristot. Metaph.
[Greek: G]. p. 1006, a. 1; p. 1009, a. 24). He employs several pages
in confuting them.
See the Antinomies in the Platonic Parmenides (pp. 154-155), some of
which destroy or set aside the Maxim of Contradiction ('Plato and the
Other Companions of Sokrates,' vol. II. ch. xxv. p. 306).]
The distinction of Contradictory and Contrary is fundamental in
ratiocinative Logic, and lies at the bottom of the syllogistic theory
as delivered in the Analytica Priora. The precision with which
Aristotle designates the Universal proposition with its exact
contradictory antithesis, is remarkable in his day. Some, however, of
his observations respecting the place and functions of the negative
particle ([Greek: ou)]), must be understood with reference to the
variable order of words in a Greek or Latin sentence; for instance,
the distinction between _Kallias non est justus_ and _Kallias est non
justus_ does not suggest itself to one speaking English or
French.[63] Moreover, the Aristotelian theory of the Proposition is
encumbered with various unnecessary subtleties; and the introduction
of the Modals (though they belong, in my opinion, legitimately to a
complete logical theory) renders the doctrine so intricate and
complicated, that a judicious teacher will prefer, in explaining the
subject, to leave them for second or ulterior study, when the simpler
relations between categorical propositions have been made evident and
familiar. The force of this remark will be felt more when we go
through the Analytica Priora. The two principal relations to be
considered in the theory of Propositions--Opposition and
Equipollence--would have come out far more clearly in the treatise De
Interpretatione, if the discussion of the Modals had been reserved
for a separate chapter.
[Footnote 63: The diagram or parallelogram of logical antithesis,
which is said to have begun with Apuleius, and to have been
transmitted through Boethius and the Schoolmen to modern times
(Ueberweg, System der Logik, sect. 72, p. 174) is as follows:--
A. Omnis homo est justus. --- E. Nullus homo est justus.
|X|
I. Aliquis homo est justus. --- O. Aliquis homo non est justus.
But the parallelogram set out by Aristotle in the treatise De
Interpretatione, or at least in the Analytica Priora, is different,
and intended for a different purpose. He puts it thus:--
1. Omnis homo est justus . . . . . 2. Non omnis homo est justus.
4. Non omnis homo est non justus . 3. Omnis homo est non justus.
Here Proposition (1) is an affirmative, of which (2) is the direct
and appropriate negative: also Proposition (3) is an affirmative
(Aristotle so considers it), of which (4) is the direct and
appropriate negative. The great aim of Aristotle is to mark out
clearly what is the appropriate negative or [Greek: A)po/phasis] to
each [Greek: Kata/phasis (mi/a a)po/phasis mia=s katapha/seôs], p.
17, b. 38), making up together the pair which he calls [Greek:
A)nti/phasis], standing in Contradictory Opposition; and to
distinguish this appropriate negative from another proposition which
comprises the particle of negation, but which is really a new
affirmative.
The true negatives of _homo est justus--Omnis homo est justus_ are,
_Homo non est justus--Non omnis homo est justus_. If you say, _Homo
est non justus--Omnis homo est non justus_, these are not negative
propositions, but new affirmatives ([Greek: e)k metathe/seôs] in the
language of Theophrastus).]
CHAPTER V.
ANALYTICA PRIORA I.
Reviewing the treatise De Interpretatione, we have followed Aristotle
in his first attempt to define what a Proposition is, to point out
its constituent elements, and to specify some of its leading
varieties. The characteristic feature of the Proposition he stated to
be--That it declares, in the first instance, the mental state of the
speaker as to belief or disbelief, and, in its ulterior or final
bearing, a state of facts to which such belief or disbelief
corresponds. It is thus significant of truth or falsehood; and this
is its logical character (belonging to Analytic and Dialectic), as
distinguished from its rhetorical character, with other aspects
besides. Aristotle farther indicated the two principal discriminative
attributes of propositions as logically regarded, passing under the
names of quantity and quality. He took great pains, in regard to the
quality, to explain what was the special negative proposition in true
contradictory antithesis to each affirmative. He stated and enforced
the important separation of contradictory propositions from contrary;
and he even parted off (which the Greek and Latin languages admit,
though the French and English will hardly do so) the true negative
from the indeterminate affirmative. He touched also upon equipollent
propositions, though he did not go far into them. Thus commenced with
Aristotle the systematic study of propositions, classified according
to their meaning and their various interdependences with each other
as to truth and falsehood--their mutual consistency or
incompatibility. Men who had long been talking good Greek fluently
and familiarly, were taught to reflect upon the conjunctions of words
that they habitually employed, and to pay heed to the conditions of
correct speech in reference to its primary purpose of affirmation and
denial, for the interchange of beliefs and disbeliefs, the
communication of truth, and the rectification of falsehood. To many
of Aristotle's contemporaries this first attempt to theorize upon the
forms of locution familiar to every one would probably appear hardly
less strange than the interrogative dialectic of Sokrates, when he
declared himself not to know what was meant by justice, virtue,
piety, temperance, government, &c.; when he astonished his hearers by
asking them to rescue him from this state of ignorance, and to
communicate to him some portion of their supposed plenitude of
knowledge.
Aristotle tells us expressly that the theory of the Syllogism, both
demonstrative and dialectic, on which we are now about to enter, was
his own work altogether and from the beginning; that no one had ever
attempted it before; that he therefore found no basis to work upon,
but was obliged to elaborate his own theory, from the very rudiments,
by long and laborious application. In this point of view, he
contrasts Logic pointedly with Rhetoric, on which there had been a
series of writers and teachers, each profiting by the labours of his
predecessors.[1] There is no reason to contest the claim to
originality here advanced by Aristotle. He was the first who