Aristotle
precative, imperative, interrogative, &c., belong more naturally to
Rhetoric or Poetic.[9] Enunciative speech may be either simple or
complex; it may be one enunciation, declaring one predicate (either
in one word or in several words) of one subject; or it may comprise
several such.[10] The conjunction of the predicate with the subject
constitutes the variety of proposition called Affirmation; the
disjunction of the same two is Negation or Denial.[11] But such
conjunction or disjunction, operated by the cogitative act, between
two mental states, takes place under the condition that, wherever
conjunction may be enunciated, there also disjunction may be
enunciated, and _vice versâ_. Whatever may be affirmed, it is
possible also to deny; whatever may be denied, it is possible also to
affirm.[12]
[Footnote 8: Ibid. p. 16, a. 26; p. 17, a. 2.]
[Footnote 9: Ibid. p. 17, a. 6: [Greek: _o( de\ a)pophantiko\s tê=s
nu=n theôri/as_]. See the **Scholion of Ammonius, pp. 95, 96, 108, a.
27. In the last passage, Ammonius refers to a passage in one of the
lost works of Theophrastus, wherein that philosopher distinguished
[Greek: to\n a)pophantiko\n lo/gon] from the other varieties of
[Greek: lo/gos], by the difference of [Greek: sche/sis]: the [Greek:
a)pophantiko\s lo/gos] was [Greek: pro\s ta\ pra/gmata], or
_objective_; the others were [Greek: pro\s tou\s a)kroôme/nous],
_i.e._ varying with the different varieties of hearers, or
_subjective_.]
[Footnote 10: Ibid. p. 17, a. 25.]
[Footnote 11: Ibid. p. 17, a. 25.]
[Footnote 12: Ibid. p. 17, a. 30: [Greek: a(/pan a)\n e)nde/choito
kai\ o(\ kate/phêse/ tis a)pophê=sai, kai\ o(\ a)pe/phêse/ tis
kataphê=sai.]]
To every affirmative proposition there is thus opposed a
contradictory negative proposition; to every negative a contradictory
affirmative. This pair of contradictory opposites may be called an
_Antiphasis_; always assuming that the predicate and subject of the
two shall be really the same, without equivocation of terms--a
proviso necessary to guard against troublesome puzzles started by
Sophists.[13] And we must also distinguish these propositions
opposite as _Contradictories_, from propositions opposite as
_Contraries_. For this, it has to be observed that there is a
distinction among things ([Greek: pra/gmata]) as universal or
singular, according as they are, in their nature, predicable of a
number or not: _homo_ is an example of the first, and _Kallias_ is an
example of the second. When, now, we affirm a predicate universally,
we must attach the mark of universality to the subject and not to the
predicate; we must say, Every man is white, No man is white. We
cannot attach the mark of universality to the predicate, and say,
Every man is every animal; this would be untrue.[14] An affirmation,
then, is _contradictorily_ opposed to a negation, when one indicates
that the subject is universally taken, and the other, that the
subject is taken not universally, _e.g. Omnis homo est albus_, _Non
omnis homo est albus_; _Nullus homo est albus_, _Est aliquis homo
albus_. The opposition is _contrary_, when the affirmation is
universal, and the negation is also universal, _i.e._, when the
subject is marked as universally taken in each: for example, _Omnis
homo est albus_, _Nullus homo est albus_. Of these contrary
opposites, both cannot be true, but both may be false. Contradictory
opposites, on the other hand, while they cannot both be true, cannot
both be false; one must be false and the other true. This holds also
where the subject is a singular term, as Sokrates.[15] If, however,
an universal term appear as subject in the proposition
_indefinitely_, that is, without any mark of universality whatever,
_e.g._, Est albus homo_, _Non est albus homo_, then the affirmative
and negative are not necessarily either contrary or contradictory,
though they may be so sometimes: there is no opposition, properly
speaking, between them; both may alike be true. This last observation
(says Aristotle) will seem strange, because many persons suppose that
_Non est homo albus_ is equivalent to _Nullus homo est albus_; but
the meaning of the two is not the same, nor does the truth of the
latter follow from that of the former,[16] since _homo_ in the former
may be construed as not universally taken.
[Footnote 13: Ibid. p. 17, a. 33: [Greek: _kai\ e)/stô a)nti/phasis
tou=to_, kata/phasis kai\ a)po/phasis ai( a)ntikei/menai.]
It seems (as Ammonius observes, Schol. p. 112, a. 33) that [Greek:
a)nti/phasis] in this sense was a technical term, introduced by
Aristotle.]
[Footnote 14: Aristot. De Interpr. p. 17, a. 37-b. 14: [Greek: e)pei\
d' e)sti\ ta\ me\n katho/lou tô=n pragma/tôn, ta\ de\ kath' e(/kaston
(le/gô de\ katho/lou me\n o(\ e)pi\ pleio/nôn pe/phuke
katêgorei=sthai, kath' e(/kaston de\ o(\ mê\, oi(=on a)/nthrôpos me\n
tô=n katho/lou, Kalli/as de\ tô=n kath' e(/kaston);] &c. Ammonius (in
Schol. p. 113, a. 38) says that what is predicated, either of many
subjects or of one, must be [Greek: mi/a phu/sis].
The warning against quantifying the predicate appears in this logical
treatise of Aristotle, and is repeated in the Analytica Priora, I.
xxvii. p. 43, b. 17. Here we have: [Greek: ou)demi/a kata/phasis
a)lêthê\s e)/stai, e)n ê(=| tou= katêgoroume/nou katho/lou to\
katho/lou katêgorei=tai, oi(=on e)/sti pa=s a)/nthrôpos pa=n zô=|on]
(b. 14).]
[Footnote 15: Ibid. b. 16-29.]
[Footnote 16: Ibid. p. 17, b. 29-37. Mr. John Stuart Mill (System of
Logic, Bk. I. ch. iv. s. 4) cites and approves Dr. Whately's
observation, that the recognition of a class of Propositions called
_indefinite_ "is a solecism, of the same nature as that committed by
grammarians when in their list of genders they enumerate the
_doubtful_ gender. The speaker _must mean_ to assert the proposition
either as an universal or as a particular proposition, though he has
failed to declare which."
But Aristotle would not have admitted Dr. Whately's doctrine,
declaring what the speaker "_must mean_." Aristotle fears that his
class, _indefinite_, will appear impertinent, because many speakers
are not conscious of any distinction or transition between the
particular and the general. The looseness of ordinary speech and
thought, which Logic is intended to bring to view and to guard
against, was more present to his mind than to that of Dr. Whately:
moreover, the forms of Greek speech favoured the ambiguity.
Aristotle's observation illustrates the deficiencies of common
speaking, as to clearness and limitation of meaning, at the time when
he began to theorize on propositions.
I think that Whately's assumption--"the speaker _must mean_"--is
analogous to the assumption on which Sir W. Hamilton founds his
proposal for explicit quantification of the predicate, viz., that the
speaker _must_, implicitly or mentally, quantify the predicate; and
that his speech ought to be such as to make such quantification
explicit. Mr. Mill has shewn elsewhere that this assumption of Sir.
W. Hamilton's is incorrect.]
It thus appears that there is always one negation corresponding to
one and the same affirmation; making up together the _Antiphasis_, or
pair of contradictory opposites, quite distinct from contrary
opposites. By _one_ affirmation we mean, that in which there is one
predicate only, and one subject only, whether taken universally or
not universally:--
_E.g._ Omnis homo est albus ... ... Non omnis homo est albus.
Est homo albus ... ... ... Non est homo albus.
Nullus homo est albus ... ... Aliquis homo est albus.
But this will only hold on the assumption that _album_ signifies one
and the same thing. If there be one name signifying two things not
capable of being generalized into one nature, or not coming under the
same definition, then the affirmation is no longer one.[17] Thus if
any one applies the term _himation_ to signify both horse and man,
then the proposition, _Est himation album_, is not one affirmation,
but two; it is either equivalent to _Est homo albus_ and _Est equus
albus_--or it means nothing at all; for this or that individual man
is not a horse. Accordingly, in this case also, as well as in that
mentioned above, it is not indispensable that one of the two
propositions constituting the _Antiphasis_ should be true and the
other false.[18]
[Footnote 17: Aristot. De Interpr. p. 18, a. 13, seq.: [Greek: mi/a
de/ e)sti kata/phasis kai\ a)po/phasis ê( e(\n kath' e(no\s
sêmai/nousa, ê)\ katho/lou o)/ntos katho/lou ê)\ mê\ o(moi/ôs, oi(=on
pa=s a)/nthrôpos leuko/s e)stin . . . _ei) to\ leuko\n e(\n
sêmai/nei_. ei) de\ duoi=n e(\n o)/noma kei=tai, e)x ô(=n _mê/ e)stin
e(/n_, ou) mi/a kata/phasis], &c., and the Scholion of Ammonius, p.
116, b. 6, seq.]
[Footnote 18: Aristot. De Interpr. p. 18, a. 26. The example which
Aristotle here gives is one of a _subject_ designated by an equivocal
name; when he had begun with the _predicate_. It would have been more
pertinent if he had said at first, [Greek: ei) o( a)/nthrôpos e(\n
sêmai/nei].]
With these exceptions Aristotle lays it down, that, in every
_Antiphasis_, one proposition must be true and the other must be
false. But (he goes on to say) this is only true in regard to matters
past or present; it is not true in regard to events particular and
future. To admit it in regard to these latter, would be to affirm
that the sequences of events are all necessary, and none of them
casual or contingent; whereas we know, by our own personal
experience, that many sequences depend upon our deliberation and
volition, and are therefore not necessary. If all future sequences
are necessary, deliberation on our part must be useless. We must
therefore (he continues) recognize one class of sequences which are
not uniform--not predetermined by antecedents; events which _may_
happen, but which also _may not_ happen, for they will not happen.
Thus, my coat _may_ be cut into two halves, but it never _will_ be so
cut; it will wear out without any such bisection occurring.[19]
[Footnote 19: Aristot. De Interpr. p. 18, a. 28-p. 19, b. 4.]
If you affirm the reality of a fact past or present, your affirmation
is of necessity determinately true, or it is determinately false,
_i.e._ the contradictory negation is determinately true. But if you
affirm the reality of a fact to come, then your affirmation is not by
necessity determinately true, nor is the contradictory negation
determinately true. Neither the one nor the other separately is true:
nothing is true except the disjunctive antithesis as a whole,
including both. If you say, To-morrow there will either be a
sea-fight, or there will not be a sea-fight, this disjunctive or
indeterminate proposition, taken as a whole, will be true. Yet
neither of its constituent parts will be determinately true; neither
the proposition, To-morrow there will be a sea-fight, nor the
proposition, To-morrow there will not be a sea-fight. But if you
speak with regard to past or present--if you say, Yesterday either
there was a sea-fight or there was not a sea-fight--then not only
will the disjunctive as a whole be true, but also one or other of its
parts will be determinately true.[20]
[Footnote 20: Ibid. p. 18, b. 29. Ammonius (Scholia ad De Interpret.
p. 119, bb. 18, 28, seq.) expresses Aristotle's meaning in terms more
distinct than Aristotle himself: [Greek: mê\ pa/ntôs e)/chein to\
e(/teron mo/rion tê=s a)ntipha/seôs _a)phôrisme/nôs a)lêtheu=on_],
&c. (b. 43).]
This remarkable logical distinction is founded on Aristotle's
ontological or physical doctrines respecting the sequence and
conjunction of events. He held (as we shall see more fully in the
Physica and other treatises) that sequences throughout the Kosmos
were to a certain extent regular, to a certain extent irregular. The