group of varieties of _Ens_ (or different meanings of the term _Ens_)
as corresponding to the diversity of the ten Categories; while
recognizing also another variety of _Ens_ as _Truth_, with its
antithesis _Non-Ens_ as _Falsehood_.[1] The former group was dealt
with in the preceding chapter; the latter will form the subject of
the present chapter. In both, indeed, Ontology is looked at as
implicated with Logic; that is, _Ens_ is considered as distributed
under significant names, fit to be coupled in propositions. This is
the common basis both of the Categoriæ and of the treatise De
Interpretatione. The whole classification of the Categories rests on
the assumption of the proposition with its constituent parts, and on
the different relation borne by each of the nine _genera_ of
predicates towards their common Subject. But in the Categoriæ no
account was taken of the distinction between truth and falsehood, in
the application of these predicates to the Subject. If we say of
Sokrates, that he is fair, pug-nosed, brave, wise, &c., we shall
predicate truly; if we say that he is black, high-nosed, cowardly,
stupid, &c., we shall predicate falsely; but in each case our
predicates will belong to the same Category--that of _Quale_. Whether
we describe him as he now is, standing, talking, in the market-place
at Athens; or whether we describe him as he is not, sitting down,
singing, in Egypt--in both speeches, our predicates rank under the
same Categories, _Jacere_, _Agere_, _Ubi_. No account is taken in the
Categoriæ of the distinction between true and false application of
predicates; we are only informed under what number of general heads
all our predicates must be included, whether our propositions be true
or false in each particular case.
[Footnote 1: See above in the preceding chapter, p. 60.]
But this distinction between _true_ and _false_, which remained
unnoticed in the Categoriæ, comes into the foreground in the treatise
De Interpretatione. The Proposition, or enunciative speech,[2] is
distinguished from other varieties of speech (interrogative,
precative, imperative) by its communicating what is true or what is
false. It is defined to be a complex significant speech, composed of
two terms at least, each in itself significant, yet neither of them,
separately taken, communicating truth or falsehood. The terms
constituting the Proposition are declared to be a Noun in the
nominative case, as Subject, and a Verb, as Predicate; this latter
essentially connoting time, in order that the synthesis of the two
may become the enunciation of a fact or quasi-fact, susceptible of
being believed or disbelieved. All this mode of analysing a
proposition, different from the analysis thereof given or implied in
the Categoriæ, is conducted with a view to bring out prominently its
function of imparting true or false information. The treatise called
the Categoriæ is a theory of significant names subjicible and
predicable, fit to serve as elements of propositions, but not yet
looked at as put together into actual propositions; while in the
treatise De Interpretatione they are assumed to be put together, and
a theory is given of Propositions thus completed.
[Footnote 2: Aristot. De Interpret. p. 17, a. 1: [Greek: lo/gos
a)pophantiko/s].]
Words spoken are marks significant of mental impressions associated
with them both by speaker and hearer; words written are symbols of
those thus uttered. Both speech and writing differ in different
nations, having no natural connection with the things signified. But
these last, the affections or modifications of the mind, and the
facts or objects of which they are representations or likenesses, are
the same to all. Words are marks primarily and directly of the first,
secondarily and indirectly of the second.[3] Aristotle thus
recognizes these two aspects--first, the subjective, next the
objective, as belonging, both of them conjointly, to significant
language, yet as logically distinguishable; the former looking to the
proximate _correlatum_, the latter to the ultimate.
[Footnote 3: Ibid. p. 16, a. 3, seq. [Greek: ô(\n me/ntoi tau=ta
sêmei=a prô/tôs, tau)ta\ pa=si pathê/mata tê=s psuchê=s, kai\ ô(=n
tau=ta o(moiô/mata, pra/gmata ê)/dê tau)ta/.]]
For this doctrine, that the mental affections of mankind, and the
things or facts which they represent, are the same everywhere, though
the marks whereby they are signified differ, Aristotle refers us to
his treatise De Animâ, to which he says that it properly belongs.[4]
He thus recognizes the legitimate dependence of Logic on Psychology
or Mental Philosophy.
[Footnote 4: Aristot. De Interpret. p. 16, a. 8: [Greek: peri\ me\n
ou)=n tau/tôn ei)/rêtai e)n toi=s peri\ psuchê=s; a)/llês ga\r
pragmatei/as.] It was upon this reference, mainly, that Andronikus
the Rhodian rested his opinion, that the treatise De Interpretatione
was not the work of Aristotle. Andronikus contended that there was
nothing in the De Animâ to justify the reference. But Ammonius in his
Scholia (p. 97, Brand.) makes a sufficient reply to the objection of
Andronikus. The third book De Animâ (pp. 430, 431) lays down the
doctrine here alluded to. Compare Torstrick's Commentary, p. 210.]
That which is signified by words (either single or in combination) is
some variety of these mental affections or of the facts which they
represent. But the signification of a single Term is distinguished,
in an important point, from the signification of that conjunction of
terms which we call a Proposition. A noun, or a verb, belonging to
the aggregate called a language, is associated with one and the same
phantasm[5] or notion, without any conscious act of conjunction or
disjunction, in the minds of speakers and hearers: when pronounced,
it arrests for a certain time the flow of associated ideas, and
determines the mind to dwell upon that particular group which is
called its meaning.[6] But neither the noun nor the verb, singly
taken, does more than this; neither one of them affirms, or denies,
or communicates any information true or false. For this last purpose,
we must conjoin the two together in a certain way, and make a
Proposition. The signification of the Proposition is thus
specifically distinct from that of either of its two component
elements. It communicates what purports to be matter of fact, which
may be either true or false; in other words, it implies in the
speaker, and raises in the hearer, the state of belief or disbelief,
which does not attach either to the noun or to the verb separately.
Herein the Proposition is discriminated from other significant
arrangements of words (precative, interrogative, which convey no
truth or falsehood), as well as from its own component parts. Each of
these parts, noun and verb, has a significance of its own; but these
are the ultimate elements of speech, for the parts of the noun or of
the verb have no significance at all. The Verb is distinguished from
the Noun by connoting time, and also by always serving as predicate
to some noun as subject.[7]
[Footnote 5: Ibid. p. 16, a. 13: [Greek: ta\ me\n ou)=n o)no/mata
au)ta\ kai\ ta\ r(ê/mata e)/oike tô=| a)/neu diaire/seôs kai\
sunthe/seôs noê/mati, oi(=on to\ a)/nthrôpos kai\ to\ leuko/n, o(/tan
mê\ proste/thê| ti; ou)/te ga\r pseu=dos ou)/te a)lêthe/s pô.]]
[Footnote 6: Ibid. p. 16, b. 19: [Greek: au)ta\ me\n kath' e(auta\
lego/mena ta\ r(ê/mata o)no/mata/ e)sti kai\ sêmai/nei ti (_i(/stêsi
ga\r o( le/gôn tê\n dia/noian_, kai\ _o( a)kou/sas ê)re/mêsen_) a)ll'
ei) e)sti\n ê)\ mê/, ou)/pô sêmai/nei], &c.
Compare Analyt. Poster. II. xix. pp. 99, 100, where the same doctrine
occurs: the movement of association is stopped, and the mind is
determined to dwell upon a certain idea; one among an aggregate of
runaways being arrested in flight, another halts also, and so the
rest in succession, until at length the Universal, or the sum total,
is detained, or "stands still" as an object of attention. Also
Aristot. Problem. p. 956, b. 39.]
[Footnote 7: Aristot. De Interpr. p. 16, b. 2, seq.]
Aristotle intimates his opinion, distinctly and even repeatedly, upon
the main question debated by Plato in the Kratylus. He lays it down
that all significant speech is significant by convention only, and
not by nature or as a natural instrument.[8] He tells us also that,
in this treatise, he does not mean to treat of all significant
speech, but only of that variety which is known as _enunciative_.
This last, as declaring truth or falsehood, is the only part
belonging to Logic as he conceives it; other modes of speech, the
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
exterior sphere of the Kosmos (the _Aplan=es_) with the countless
number of fixed stars fastened into it, was a type of regularity and
uniformity; eternal and ever moving in the same circular orbit, by
necessity of its own nature, and without any potentiality of doing
otherwise. But the earth and the elemental bodies, organized and
unorganized, below the lunar sphere and in the interior of the
Kosmos, were of inferior perfection and of very different nature.
They were indeed in part governed and pervaded by the movement and
influence of the celestial substance within which they were
comprehended, and from which they borrowed their Form or constituent
essence; but they held this Form implicated with Matter, _i.e._ the
principle of potentiality, change, irregularity, generation, and
destruction, &c. There are thus in these sublunary bodies both
constant tendencies and variable tendencies. The _constant_ Aristotle
calls 'Nature;' which always aspires to Good, or to perpetual
renovation of Forms as perfect as may be, though impeded in this work
by adverse influences, and therefore never producing any thing but
individuals comparatively defective and sure to perish. The
_variable_ he calls 'Spontaneity' and 'Chance,' forming an
independent agency inseparably accompanying Nature--always modifying,
distorting, frustrating, the full purposes of Nature. Moreover, the
different natural agencies often interfere with each other, while the
irregular tendency interferes with them all. So far as Nature acts,
in each of her distinct agencies, the phenomena before us are regular
and predictable; all that is uniform, and all that (without being
quite uniform) recurs usually or frequently, is her work. But,
besides and along with Nature, there is the agency of Chance and
Spontaneity, which is essentially irregular and unpredictable. Under
this agency there are possibilities both for and against; either of
two alternative events may happen.
It is with a view to this doctrine about the variable kosmical
agencies or potentialities that Aristotle lays down the logical
doctrine now before us, distinguishing propositions affirming
particular facts past or present, from propositions affirming
particular facts future. In both cases alike, the disjunctive
antithesis, as a whole, is necessarily true. Either there was a
sea-fight yesterday, or there was not a sea-fight yesterday: Either
there will be a sea-fight to-morrow, or there will not be a sea-fight
to-morrow--both these disjunctives alike are necessarily true. There
is, however, a difference between the one disjunctive couple and the
other, when we take the affirmation separately or the negation
separately. If we say, There will be a sea-fight to-morrow, that
proposition is not necessarily true nor is it necessarily false; to
say that it is either the one or the other (Aristotle argues) would
imply that every thing in nature happened by necessary agency--that
the casual, the potential, the _may be or may not be_, is stopped out
and foreclosed. But this last is really the case, in regard to a past
fact. There was a sea-fight yesterday, is a proposition either
necessarily true or necessarily false. Here the antecedent agencies
have already spent themselves, blended, and become realized in one or
other of the two alternative determinate results. There is no
potentiality any longer open; all the antecedent potentiality has
been foreclosed. The proposition therefore is either necessarily true
or necessarily false; though perhaps we may not know whether it is
the one or the other.
In defending his position regarding this question, Aristotle denies
(what he represents his opponents as maintaining) that all events
happen by necessity. He points to the notorious fact that we
deliberate and take counsel habitually, and that the event is
frequently modified, according as we adopt one mode of conduct or
another; which could not be (he contends), if the event could be
declared beforehand by a proposition necessarily or determinately
true. What Aristotle means by _necessity_, however, is at bottom
nothing else than constant sequence or conjunction, conceived by him
as necessary, because the fixed ends which Nature is aiming at can
only be attained by certain fixed means. To this he opposes
Spontaneity and Chance, disturbing forces essentially inconstant and
irregular; admitting, indeed, of being recorded when they _have_
produced effects in the past, yet defying all power of prediction as
to those effects which they _will_ produce in the future. Hence
arises the radical distinction that he draws in Logic, between the
truth of propositions relating to the past (or present) and to the
future.
But this logical distinction cannot be sustained, because his
metaphysical doctrine (on which it is founded) respecting the
essentially irregular or casual, is not defensible. His opponents
would refuse to grant that there is any agency essentially or in
itself irregular, casual, and unpredictable.[21] The aggregate of
Nature consists of a variety of sequences, each of them constant and
regular, though intermixed, co-operating, and conflicting with each
other, in such manner that the resulting effects are difficult to
refer to their respective causes, and are not to be calculated
beforehand except by the highest scientific efforts; often, not by
any scientific efforts. We must dismiss the hypothesis of Aristotle,
assuming agencies essentially irregular and unpredictable, either as
to the past or as to the future. The past has been brought about by
agencies all regular, however multifarious and conflicting, and the
future will be brought about by the like: there is no such
distinction of principle as that which Aristotle lays down between
propositions respecting the past and propositions respecting the
future.
[Footnote 21: The Stoics were opposed to Aristotle on this point.
They recognized no logical difference in the character of the
Antiphasis, whether applied to past and present, or to future.
Nikostratus defended the thesis of Aristotle against them. See the
Scholia of Simplikius on the Categoriæ, p. 87, b. 30-p. 88, a. 24.
[Greek: ai( ga\r ei)s to\n me/llonta chro/non e)gklino/menai
prota/seis ou)/te a)lêthei=s ei)si\n ou)/te pseudei=s dia\ tê\n tou=
e)ndechome/nou phu/sin.]
The remarks of Hobbes, upon the question here discussed by Aristotle,
well deserve to be transcribed (De Corpore, part II. ch. X. s. 5):--
"But here, perhaps, some man may ask whether those future things,
which are called _contingents_, are necessary. I say, therefore, that
generally all contingents have their necessary causes, but are called
contingents in respect of other events, upon which they do not
depend; as the rain, which shall be to-morrow, shall be necessary,
that is, from necessary causes; but we think and say, it happens by
chance, because we do not yet perceive the causes thereof, though
they exist now. For men commonly call that _casual_ or _contingent_,
whereof they do not perceive the necessary cause; and in the same
manner they use to speak of things past, when not knowing whether a
thing be done or no, they say, it is possible it never was done.
"Wherefore, all propositions concerning future things, contingent or
not contingent--as this, _It will rain to-morrow_, or this,
_To-morrow the sun will rise_--are either necessarily true, or
necessarily false; but we call them contingent, because we do not yet
know whether they be true or false; whereas their verity depends not
upon our knowledge, but upon the foregoing of their causes. But there
are some, who, though they confess this whole proposition, _To-morrow
it will either rain or not rain_, to be true, yet they will not
acknowledge the parts of it, as _To-morrow it will rain_, or
_To-morrow it will not rain_, to be either of them true by itself;
because they say neither this nor that is true _determinately_. But
what is this _determinately true_, but true _upon our knowledge_, or
evidently true? And therefore they say no more, but that it is not
yet known whether it be true or no; but they say it more obscurely,
and darken the evidence of the truth with the same words with which
they endeavour to hide their own ignorance."
Compare also the fuller elucidation of the subject given by Mr. John
Stuart Mill, in his System of Logic, Bk. III. ch. xvii. s. 2:--"An
event occurring by chance may be better described as a coincidence
from which we have no ground to infer an uniformity; the occurrence
of an event in certain circumstances, without our having reason on
that account to infer that it will happen again in those
circumstances. This, however, when looked closely into, implies that
the enumeration of the circumstances is not complete. Whatever the
fact was, since it has occurred once, we may be sure that if all the
circumstances were repeated, it would occur again; and not only if
all, but there is some particular portion of those circumstances, on
which the phenomenon is invariably consequent. With most of them,
however, it is not connected in any permanent manner: its conjunction
with those is said to be the effect of chance, to be merely casual.
Facts casually conjoined are separately the effect of causes, and
therefore of laws; but of different causes, and causes not connected
by any law. It is incorrect then to say that any phenomenon is
produced by chance; but we may say that two or more phenomena are
conjoined by chance, that they co-exist or succeed one another only
by chance."]
There is, indeed, one distinction between inferences as to the past
and inferences as to the future, which may have contributed to
suggest, though it will not justify, the position here laid down by
Aristotle. In regard to the disjunctive--To-morrow there will be a
sea-fight, or there will not be a sea-fight--nothing more trustworthy
than inference or anticipation is practicable: the anticipation of a
sagacious man with full knowledge is more likely to prove correct
than that of a stupid man with little knowledge; yet both are alike
anticipations, unverifiable at the present moment. But if we turn to
the other disjunctive--Yesterday there was a sea-fight, or there was
not a sea-fight--we are no longer in the same position. The two
disputants, supposed to declare thus, may have been far off, and may
have no other means of deciding the doubt than inference. But the
inference here is not unverifiable: there exist, or may exist,
witnesses or spectators of the two fleets, who can give direct
attestation of the reality, and can either confirm or refute the
inference, negative or affirmative, made by an absentee. Thus the
proposition, Yesterday there was a sea-fight, or the other, Yesterday
there was not a sea-fight, will be verifiable or determinably true.
There are indeed many inferences as to the past, in regard to which
no direct evidence is attainable. Still this is an accident; for such
direct evidence may always be supposed or imagined as capable of
being brought into court. But, in respect to the future, verification
is out of the question; we are confined to the region of inference,
well or ill-supported. Here, then, we have a material distinction
between the past and the future. It was probably present to the mind
of Aristotle, though he misconceives its real extent of operation,
and makes it subservient to his still more comprehensive
classification of the different contemporaneous agencies (regular and
irregular) which he supposes to pervade the Kosmos.
In the treatise before us, he next proceeds to state what collocation
of the negative particle constitutes the special or legitimate
negation to any given affirmation, or what are the real forms of
proposition, standing in contradictory opposition to certain other
forms, so as to make up one _Antiphasis_.[22] The simplest
proposition must include a noun and a verb, either definite or
indefinite: _non homo_ is a specimen of an indefinite noun--_non
currit_, of an indefinite verb. There must be, in any one
proposition, one subject and one predicate; even the indefinite noun
or verb signifies, in a certain sense, one thing. Each affirmation
comprises a noun, or an indefinite noun, with a verb; the special
corresponding or contradictory negation (making up the _Antiphasis_
along with the former) comprises a noun (or an indefinite noun) with
an indefinite verb. The simplest proposition is--
_Affirmative_. _Contradictory Negative_.
Est homo ... ... ... ... Non est homo.
Est non homo ... ... ... ... Non est non homo.
Here are only two pairs of antithetic propositions, or one
quaternion. The above is an indefinite proposition (which may be
either universal or not). When we universalize it, or turn it an
universal proposition, we have--
_Affirmative_. _Contradictory Negative_.
Est omnis homo ... ... ... Non est omnis homo.
Est omnis non homo ... ... Non est omnis non homo.
[Footnote 22: Aristot. De Interpr. p. 19, b. 5, seq.]
The above are specimens of the smallest proposition; but when we
regard larger propositions, such as those (called _tertii
adjacentis_) where there are two terms besides _est_, the collocation
of the negative particle becomes more complicated, and requires
fuller illustration. Take, as an example, the affirmative _Est justus
homo_, the true negation of this is, _Non est justus homo_. In these
two propositions, _homo_ is the subject; but we may join the negative
with it, and we may consider _non homo_, not less than _homo_, as a
distinct subject for predication, affirmative or negative. Farther,
we may attach _est_ and _non est_ either to _justus_ or to _non
justus_ as the predicate of the proposition, with either _homo_, or
_non homo_, as subject. We shall thus obtain a double mode of
antithesis, or two distinct quaternions, each containing two pairs of
contradictory propositions. The second pair of the first quaternion
will not be in the same relation as the second pair of the second
quaternion, to the proposition just mentioned, viz.--(A) _Est justus
homo_; with its negative, (B) _Non est justice homo_.[23]
[Footnote 23: Aristot. De Interpr. p. 19, b. 19. [Greek: o(/tan de\
to\ e)/sti tri/ton proskatêgorê=tai, ê)/dê dichô=s le/gontai ai(
a)ntithe/seis; le/gô de\ oi(=on _e)/sti di/kaios a)/nthrôpos_; to\
_e)/sti_ tri/ton phêmi\ sugkei=sthai o)/noma ê)\ r(ê=ma e)n tê=|
katapha/sei. ô(/ste dia\ tou=to te/ttara e)/stai tau=ta, ô(=n ta\
me\n du/o pro\s tê\n kata/phasin kai\ a)po/phasin e(/xei kata\ to\
stoichou=n ô(s ai( sterê/seis, ta\ de\ du/o, ou)/. [le/gô de\ o(/ti
to\ _e)/stin_ ê)\ tô=| dikai/ô| proskei/setai ê)\ tô=| ou) dikai/ô|],
ô(/ste kai\ ê( a)po/phasis. te/ttara ou)=n e)/stai. noou=men de\ to\
lego/menon e)k tô=n u(pogegramme/nôn.] In this passage the words
which I have enclosed between brackets are altered by Waitz: I shall
state presently what I think of his alteration. Following upon these
words there ought to be, and it seems from Ammonius (Schol. p. 121,
a. 20) that there once was, a scheme or table arranging the four
propositions in the order and disposition which we read in the
Analytica Priora, I. xlvi. p. 51, b. 37, and which I shall here
follow. But no such table now appears in our text; we have only an
enumeration of the four propositions, in a different order, and then
a reference to the Analytica.]
First, let us assume _homo_ as subject. We have then
(QUATERNION I.)
(A) Est justus homo ... ... ... ... (B) Non est justus homo.
(D) Non est non justus homo ... ... ... (C) Est non justus homo.
Examining the relation borne by the last two among these four
propositions (C and D), to the first two (A and B), the simple
affirmative and negative, we see that B is the legitimate negative of
A, and D that of C. We farther see that B is a consequence of C, and
D a consequence of A, but not _vice versâ_: that is, if C is true, B
must certainly be true; but we cannot infer, because B is true, that
C must also be true: while, if A is true, D must also be true; but D
may perhaps be true, though A be not true. In other words, the
relation of D to A and of C to B, is the same as it would be if the
privative term _injustus_ were substituted in place of _non justus_;
_i.e._ if the proposition C (_Est injustus homo_) be true, the other
proposition B (_Non est justus homo_) must certainly be true, but the
inference will not hold conversely; while if the proposition A (_Est
justus homo_) be true, it must also be true to say D (_Non est
injustus homo_), but not _vice versâ_.[24]
[Footnote 24: Referring to the words cited in the preceding note, I
construe [Greek: ta\ de\ du/o, ou)/] as Boethius does (II. pp.
384-385), and not in agreement with Ammonius (Schol. p. 122, a. 26,
Br.), who, however, is followed both by Julius Pacius and Waitz (p.
344). I think it impossible that these words, [Greek: ta\ de\ du/o,
ou)/], can mean (as Ammonius thinks) the [Greek: kata/phasis] and
[Greek: a)po/phasis] themselves, since the very point which Aristotle
is affirming is the relation of these words, [Greek: pro\s tê\n
kata/phasin kai\ a)po/phasin], _i.e._ to the affirmative and negative
started from--
(A) Est justus homo ... ... ... ... (B) Non est justus homo.
As the words [Greek: ta\ me\n du/o] refer to the second contradictory
pair (that is, C and D) in the _first_ Quaternion, so the words
[Greek: ta\ de\ du/o, ou)/] designate the second contradictory pair
(G and H) in the _second_ Quaternion. Though G and H are included in
the second Quaternion, they are here designated by the negative
relation ([Greek: ta\ de\ du/o, ou)/]) which they bear to A and B,
the first contradictory pair of the _first_ Quaternion. [Greek:
dichô=s le/gontai ai( a)ntithe/seis] (line 20) is explained and
illustrated by line 37--[Greek: au(=tai me\n ou)=n du/o
a)nti/keintai, a)/llai de\ du/o pro\s to\ _ou)k a)/nthrôpos_ ô(s
u(pokei/meno/n ti prostethe/n]. Lastly, Aristotle expressly states
that the second Quaternion will stand independently and by itself (p.
20, a. 1), having noticed it in the beginning only in relation to the
first.]
Such is the result obtained when we take _homo_ as the subject of the
proposition; we get four propositions, of which the two last (C and
D) stand to the two first (B and A) in the same relation as if they
(C and D) were privative propositions. But if, instead of _homo_, we
take _non homo_ as Subject of the proposition (_justus_ or _non
justus_ being predicates as before), we shall then obtain two other
pairs of contradictory propositions; and the second pair of this new
quaternion will not stand in that same relation to these same
propositions B and A. We shall then find that, instead of B and A, we
have a different negative and a different affirmative, as the
appropriate correlates to the third and fourth propositions. The new
quaternion of propositions, with _non homo_ as subject, will stand
thus--
(QUATERNION II.)
(E) Est justus non homo ... ... ... (F) Non est justus non homo.
(H) Non est non justus non homo ... (G) Est non justus non homo.[25]
Here we see that propositions G and H do not stand to B and A in the
same relations as C and D stand to B and A; but that they stand in
that same relation to two perfectly different propositions, F and E.
That is, if in place of _non **justus_, in propositions G and H, we
substitute the privative term _injustus_ (thus turning G into _Est
injustus non homo_, and turning H into _Non est injustus non homo_),
the relation of G, when thus altered, to F, and the relation of H,
when thus altered, to E, will be the same as it was before. Or, in
other words, if G be true, F will certainly be true, but not _vice
versâ_; and if E be true, H will certainly be true, but not _vice
versâ_.
[Footnote 25: Aristot. De Interpr. p. 19, b. 36. [Greek: au(=tai me\n
ou)=n du/o a)nti/keintai] (the two pairs--A B and C D--of the first
quaternion), [Greek: a)/llai de\ du/o pro\s to\ _ou)k a)/nthrôpos_
ô(s u(pokei/meno/n ti prostethe/n;]
(E) [Greek: e)/sti di/kaios ou)k a)/nthrôpos] ... ... ... (F)
[Greek: ou)k e)/sti di/kaios ou)k a)/nthrôpos.]
(H) [Greek: ou)k e)/stin ou) di/kaios ou)k a)/nthrôpos] ... (G)
[Greek: e)/stin ou) di/kaios ou)k a)/nthrôpos.]
[Greek: plei/ous de\ tou/tôn ou)k e)/sontai a)ntithe/seis. au(=tai
de\ chôri\s e)kei/nôn au)tai\ kath' e(auta\s e)/sontai, ô(s o)no/mati
tô=| _ou)k a)/nthrôpos_ chrô/menai.] The second [Greek: au(=tai]
alludes to this last quaternion, [Greek: e)kei/nôn] to the first. I
have, as in the former case, transposed propositions three and four
of this second quaternion, in order that the relation of G to F and
of H to E may be more easily discerned.
There are few chapters in Aristotle more obscure and puzzling than
the tenth chapter of the De Interpretatione. It was found so by
Alexander, Herminus, Porphyry, Ammonius, and all the Scholiasts.
Ammonius (Schol. pp. 121, 122, Br.) reports these doubts, and
complains of it as a riddle almost insolvable. The difficulties
remain, even after the long note of Waitz, and the literal
translation of M. Barthélemy St. Hilaire.]
The propositions which we have hitherto studied have been indefinite;
that is, they might be universal or not. But if we attach to them the
sign of universality, and construe them as universals, all that we
have said about them would still continue to be true, except that the
propositions which are diametrically (or diagonally) opposed would
not be both true in so many instances. Thus, let us take the first
quaternion of propositions, in which _est_ is attached to _homo_, and
let us construe these propositions as universal. They will stand
thus--
(A) Omnis est homo justus ... ... (B) Non omnis est homo justus.
(D) Non omnis est homo non justus (C) Omnis est homo non justus.
In these propositions, as in the others before noticed, the same
relation prevails between C and B, and between A and D; if C be true,
B also is true, but not _vice versâ_; if A be true, D also will be
true, but not _vice versâ_. But the propositions diagonally opposed
will not be so often alike true:[26] thus, if A be true (_Omnis est
homo justus_), C cannot be true (_Omnis est homo non justus_);
whereas in the former quaternion of propositions (indefinite, and
therefore capable of being construed as not universal) A and C might
both be alike true.[27]
[Footnote 26: Aristot. De Interpret. p. 19, b. 35. [Greek: plê\n
ou)ch o(moi/ôs ta\s kata\ dia/metron e)nde/chetai sunalêtheu/ein;
e)nde/chetai de\ pote/.] The "diameter" or "diagonal" is to be
understood with reference to the scheme or square mentioned p. 119,
note, the related propositions standing at the angles, as above.]
[Footnote 27: The Scholion of Ammonius, p. 123, a. 17, Br., explains
this very obscure passage: [Greek: a)ll' e)pi\ me\n tô=n
a)prosdiori/stôn] (indefinite propositions, such as may be construed
either as universal or as particular), [Greek: kata\ tê\n
e)ndechome/nên u(/lên ta/s te katapha/seis] (of the propositions
diagonally opposite), [Greek: sunalêtheu/ein a)llê/lais sumbai/nei
kai\ ta\s a)popha/seis, _a(/te tai=s merikai=s i)sodunamou/sas_.
e)pi\ de\ tô=n prosdiôrisme/nôn] (those propositions where the mark
of universality is tacked to the Subject), [Greek: peri\ ô(=n nuni\
au)tô=| o( lo/gos, tê=s katho/lou katapha/seôs kai\ tê=s e)pi\
me/rous a)popha/seôs, ta\s me\n katapha/seis a)du/naton
sunalêtheu=sai kath' oi(andê/pote u(/lên, ta\s me/ntoi a)popha/seis
sumbai/nei sunalêtheu/ein kata\ mo/nên tê\n e)ndechome/nên;] &c.]
It is thus that Aristotle explains the distinctions of meaning in
propositions, arising out of the altered collocation of the negative
particle; the distinction between (1) _Non est justus_, (2) _Est non
justus_, (3) _Est injustus_. The first of the three is the only true
negative, corresponding to the affirmative _Est Justus_. The second
is not a negative at all, but an affirmative ([Greek: e)k
metathe/seôs], or by transposition, as Theophrastus afterwards called
it). The third is an affirmative, but privative. Both the second and
the third stand related in the same manner to the first; that is, the
truth of the first is a necessary consequence either of the second or
of the third, but neither of these can be certainly inferred from the
first. This is explained still more clearly in the Prior Analytics;
to which Aristotle here makes express reference.[28]
[Footnote 28: Aristot. De Interpr. p. 19, b. 31. [Greek: tau=ta me\n
ou)=n, ô(/sper e)n toi=s A)nalutikoi=s le/getai, ou(/tô te/taktai.]
Waitz in his note suggests that instead of [Greek: te/taktai] we
ought to read [Greek: teta/chthô]. But if we suppose that the formal
table once existed in the text, in an order of arrangement agreeing
with the Analytica, this conjectural change would be unnecessary.
Waitz has made some changes in the text of this chapter, which appear
to me partly for the better, partly not for the better. Both Bekker
and Bussemaker (Firmin Didot) retain the old text; but this old text
was a puzzle to the ancient commentators, even anterior to Alexander
of Aphrodisias. I will here give first the text of Bekker, next the
changes made by Waitz: my own opinion does not wholly coincide with
either. I shall cite the text from p. 19, b. 19, leaving out the
portion between lines 30 and 36, which does not bear upon the matter
here discussed, while it obscures the legitimate sequence of
Aristotle's reasoning.
(Bekker.)--[Greek: O(/tan de\ to\ _e)/sti_ tri/ton proskatêgorê=tai,
ê)/dê dichô=s le/gontai ai( a)ntithe/seis. le/gô de\ oi(=on _e)/sti
di/kaios a)/nthrôpos_; to\ _e)/sti_ tri/ton phêmi\ sugkei=sthai
o)/noma ê)\ r(ê=ma e)n tê=| katapha/sei. ô(/ste dia\ tou=to te/ttara
e)/stai tau=ta, ô(=n ta\ me\n du/o pro\s tê\n kata/phasin kai\
a)po/phasin e(/xei kata\ to\ stoichou=n ô(s ai( sterê/seis, ta\ de\
du/o, ou)/. le/gô d' o(/ti to\ _e)/stin_ ê)\ _tô=| dikai/ô|
proskei/setai_ ê)\ tô=| _ou) dikai/ô|_] (25), [Greek: ô(/ste kai\ ê(
a)po/phasis. te/ttara ou)=n e)/stai.] (Here follow the first pairs of
Antitheses, or the first Quaternion of propositions in the order as
given)--
(A) [Greek: e)/sti di/kios a)/nthrôpos] ... ... (B) [Greek: ou)k
e)/sti di/kios a)/nthrôpos.]y
(C) [Greek: e)/stin ou) di/kaios a)/nthrôpos] ... (D) [Greek: ou)k
e)/stin ou) di/kaios a)/nthrôpos.]
[Greek: to\ ga\r _e)/stin_ e)ntau=tha kai\ to\ _ou)k e)/sti tô=|
dikai/ô| proskei/setai kai\ tô=| ou) dikai/ô|]_ (30).--[Greek:
Au(=tai me\n ou)=n du/o a)nti/keintai, a)/llai de\ du/o pro\s to\
ou)k _a)/nthrôpos_ ô(s u(pokei/meno/n ti] (38) [Greek:
_prostethe/n_.] (Here follow the second pairs of Antitheses, or the
second Quaternion of propositions, again in the order from which I
have departed above)--
(E) [Greek: e)/sti di/kaios ou)k a)/nthrôpos] ... ... (F) [Greek:
Ou)k e)/sti di/kaios ou)k a)/nthrôpos.]
(G) [Greek: e)/stin ou) di/kaios ou)k a)/nthrôpos] ... (H) [Greek:
Ou)k e)/stin ou) di/kaios ou)k a)/nthrôpos.]
[Greek: plei/ous de\ tou/tôn ou)k e)/sontai a)ntithe/seis. au(=tai
de\] (the second Quaternion) [Greek: chôri\s e)kei/nôn] (first
Quaternion) [Greek: au)tai\ kath' e(auta\s e)/sontai, ô(s o)no/mati
tô=| _ou)k a)/nthrôpos_ chrô/menai.]
In this text Waitz makes three alterations:--1. In line 24, instead
of [Greek: ê)\ tô=| dikai/ô| proskei/setai ê)\ tô=| ou) dikai/ô|]--he
reads, [Greek: ê)\ tô=| a)nthrô/pô| proskei/setai ê)\ tô=| ou)k
a)nthrô/pô|].
2. In line 30 he makes a similar change; instead of [Greek: tô=|
dikai/ô| proskei/setai kai\ tô=| ou) dikai/ô|]--he reads, [Greek:
tô=| a)nthrô/pô| proskei/setai kai\ tô=| ou)k a)nthrô/pô|].
In line 38, instead of [Greek: prostethe/n], he reads [Greek:
prostethe/ntos].
Of these three alterations the first appears to me good, but
insufficient; the second not good, though the passage as it stands in
Bekker requires amendment; and the third, a change for the worse.
The purpose of Aristotle is here two-fold. First, to give the reason
why, when the propositions were _tertii adjacentis_, there were two
Quaternions or four couples of antithetical propositions; whereas in
propositions _secundi adjacentis_, there was only one Quaternion or
two couples of antithetical propositions. Next, to assign the
distinction between the first and the second Quaternion in
propositions _tertii adjacentis_.
Now the first of these two purposes is marked out in line 25, which I
think we ought to read not by substituting the words of Waitz in
place of the words of Bekker, but by retaining the words of Bekker
and inserting the words of Waitz as an addition to them. The passage
after such addition will stand thus--[Greek: le/gô d' o(/ti to\
_e)/stin_ ê)\ tô=| dikai/ô| proskei/setai ê)\ tô=| ou) dikai/ô|, kai\
ê)\ tô=| a)nthrô/pô| ê)\ tô=| ou)k a)nthrô/pô|, ô(/ste kai\ ê(
a)po/phasis. te/ttara _ou)=n_ e)/stai.] Here Aristotle declares the
_reason why_ ([Greek: ou)=n]) there come to be four couples of
propositions; that reason is, because [Greek: e)/sti] and [Greek:
ou)k e)/sti] may be joined either with [Greek: di/kaios] or [Greek:
ou) di/kaios] and either with [Greek: a)/nthrôpos] or with [Greek:
ou)k a)/nthrôpos]. Both these alternatives must be specified in order
to make out a reason why there are two Quaternions or four couples of
antithetical propositions. But the passage, as read by Bekker, gives
only one of these alternatives, while the passage, as read by Waitz,
gives only the other. Accordingly, neither of them separately is
sufficient; but both of them taken together furnish the reason
required, and thus answer Aristotle's purpose.
Aristotle now proceeds to enunciate the first of the two Quaternions,
and then proceeds to line 30, where the reading of Bekker is
irrelevant and unmeaning; but the amendment of Waitz appears to me
still worse, being positively incorrect in statement of fact. Waitz
reads [Greek: to\ ga\r _e)/stin_ e)ntau=tha] (in the first
Quaternion, which has just been enunciated) [Greek: kai\ to\ _ou)k
e)/stin_ tô=| a)nthrô/pô| proskei/setai kai\ _tô=| ou)k
a)nthrô/pô|_]. These last words are incorrect in fact, for [Greek:
ou)k a)/nthrôpos] does not appear in the first Quaternion, but is
reserved for the second. While the reading of Waitz is thus evidently
wrong, that of Bekker asserts nothing to the purpose. It is useless
to tell us merely that [Greek: e)/sti] and [Greek: ou)k e)/stin]
attach both to [Greek: di/kaios] and to [Greek: ou) di/kaios] in this
first Quaternion ([Greek: e)ntau=tha]), because that characteristic
is equally true of the second Quaternion (presently to follow), and
therefore constitutes no distinction between the two. To bring out
the meaning intended by Aristotle I think we ought here also to
retain the words of Bekker, and to add after them some, though not
all, of the words of Waitz. The passage would then stand
thus--[Greek: to\ ga\r e)/stin e)ntau=tha kai\ to\ ou)k e)/sti tô=|
dikai/ô| proskei/setai kai\ tô=| ou) dikai/ô|, kai\ tô=| a)nthrô/pô|,
_a)ll' ou)_ tô=| ou)k a)nthrô/pô|.] Or perhaps [Greek: _kai\ ou)_
tô=| ou)k a)nthrô/pô|] might suffice in the last clause (being a
smaller change), though [Greek: a)ll' ou)] seem the proper terms to
declare the meaning. In the reading which I propose, the sequence
intended by Aristotle is clear and intelligible. Having first told us
that [Greek: e)/stin] and [Greek: ou)k e)/sti] being joined
alternately with [Greek: di/kaios] and with [Greek: ou) di/kaios] and
also with [Greek: a)/nthrôpos] and [Greek: ou)k a)/nthrôpos], make up
two Quaternions, he proceeds to enunciate the distinctive character
belonging to the first Quaternion of the two, viz., that in it
[Greek: e)/sti] and [Greek: ou)k e)/stin] are joined both with
[Greek: di/kaios] and [Greek: ou) di/kaios], and also with [Greek:
a)/nthrôpos] _but not with_ [Greek: _ou)k a)/nthrôpos_], This is
exactly the truth.
Aristotle next proceeds to the second Quaternion, where he points
out, as the characteristic distinction, that [Greek: ou)k
a)/nthrôpos] comes in and [Greek: a)/nthrôpos] disappears, while
[Greek: di/kaios] and [Greek: ou) di/kaios] remain included, as in
the first. This is declared plainly by Aristotle in line 37:--[Greek:
au(=tai me\n ou)=n du/o a)nti/keintai] (referring to the two pairs of
antithetical propositions in the first Quaternion), [Greek: _a)/llai
de\ pro\s to\ ou)k a)/nthrôpos_ ô(s u(pokei/meno/n ti prostethe/n;
e)/sti di/kaios ou)k a)/nthrôpos, e)/stin ou) di/kaios ou)k
a)/nthrôpos-ou)k e)/sti di/kaios ou)k a)/nthrôpos, e)/stin ou)
di/kaios ou)k a)/nthrôpos-ou)k e)/stin ou) di/kaios ou)k
a)/nthrôpos.] When we read these words, [Greek: a)/llai de\ du/o
pro\s to\ ou)k a)/nthrôpos ô(s u(pokei/meno/n ti prostethe/n], as
applied to the second Quaternion, we see that there must have been
some words preceding which excluded [Greek: _ou)k a)/nthrôpos_] from
the first Quaternion. Waitz contends for the necessity of changing
[Greek: prostethe/n] into [Greek: prostethe/ntos]. I do not concur
with his reasons for the change; the words that follow, p. 20, line
2, [Greek: ô(s o)no/mati tô=| _ou)k a)/nthrôpos_ chrô/menai
(proschrô/menai)], are a reasonable justification of [Greek:
prostethe/n--_ou)k a)/nthrôpos_ ô(s _u(pokei/meno/n ti_ prostethe/n]
being very analogous to [Greek: ou)k a)/nthrôpos ô(s o)/noma].
This long note, for the purpose of restoring clearness to an obscure
text, will appear amply justified if the reader will turn to the
perplexities and complaints of the ancient Scholiasts, revealed by
Ammonius and Boethius. Even earlier than the time of Alexander
(Schol. p. 122**, b. 47) there was divergence in the MSS. of
Aristotle; several read [Greek: tô=| dikai/ô|] (p. 19, b. 25),
several others read [Greek: tô=| a)nthrô/pô|]. I think that all of
them were right in what they retained, and wrong by omission only
or mainly.]
After this very subtle and obscure distinction between propositions
_secundi adjacentis_, and those _tertii adjacentis_, in respect to
the application of the negative, Aristotle touches on the relation of
_contrariety_ between propositions. The universal affirmation _Omne
est animal justum_ has for its contrary _Nullum est animal justum_.
It is plain that both these propositions will never be true at once.
But the negatives or contradictories of both may well be true at
once: thus, _Non omne animal est justum_ (the contradictory of the
first) and _Est aliquid animal justum_ (the contradictory of the
second) may be and are both alike true. If the affirmative
proposition _Omnis homo est non justus_ be true, the negative _Nullus
est homo justus_ must also be true; if the affirmative _Est aliquis
homo justus_ be true, the negative _Non omnis homo est non justus_
must also be true. In singular propositions, wherever the negative or
denial is true, the indefinite affirmative ([Greek: e)k
metathe/seôs], in the language of Theophrastus) corresponding to it
will also be true; in universal propositions, the same will not
always hold. Thus, if you ask, Is Sokrates wise? and receive for
answer No, you are warranted in affirming, Sokrates is not wise (the
indefinite affirmation). But if you ask, Are all men wise? and the
answer is No, you are not warranted in affirming, All men are not
wise. This last is the contrary of the proposition, All men are wise;
and two contraries may both be false. You are warranted in declaring
only the contradictory negative, Not all men are wise.[29]
[Footnote 29: Aristot. De Interpret. p. 20, a. 16-30.]
Neither the indefinite noun ([Greek: ou)k a)/nthrôpos]) nor the
indefinite verb ([Greek: ou) tre/chei--ou) di/kaios]) is a real and
true negation, though it appears to be such. For every negation ought
to be either true or false; but _non homo_, if nothing be appended to
it, is not more true or false (indeed less so) than _homo_.[30]
[Footnote 30: Ibid. a. 31, seq.]
The transposition of substantive and adjective makes no difference in
the meaning of the phrase; _Est albus homo_ is equivalent to _Est
homo albus_. If it were not equivalent, there would be two negations
corresponding to the same affirmation; but we have shown that there
can be only one negation corresponding to one affirmation, so as to
make up an _Antiphasis_.[31]
[Footnote 31: Ibid. b. 1-12. That [Greek: e)sti\ leuko\s
a)/nthrôpos], and [Greek: e)sti\n a)/nthrôpos leuko/s], mean exactly
the same, neither more nor less--we might have supposed that
Aristotle would have asserted without any proof; that he would have
been content [Greek: a)po\ tô=n pragma/tôn pistou=sthai] (to use the
phrase of Ammonius in a portion of the Scholia, p. 121, a. 27). But
he prefers to deduce it as a corollary from a general doctrine much
less evident than the statement itself; and after all, his deduction
is not conclusive, as Waitz has already remarked (ad Organ. I. p.
351).]
In one and the same proposition, it is indispensable that the subject
be one and the predicate one; if not, the proposition will not be
one, but two or more. Both the subject and the predicate indeed may
consist of several words; but in each case the several words must
coalesce to make one total unity; otherwise the proposition will not
be one. Thus, we may predicate of man--_animal_, _bipes_,
_mansuetum_; but these three coalesce into one, so that the
proposition will be a single one. On the other hand the three terms
_homo_, _albus_, _ambulans_, do not coalesce into one; and therefore,
if we predicate all respecting the same subject, or if we affirm the
same predicate respecting all three, expressing them all by one word,
the proposition will not be one, but several.[32]
[Footnote 32: Aristot. De Interpr. p. 20, b. 13-22.]
Aristotle follows this up by a remark interesting to note, because we
see how much his generalities were intended to bear upon the actual
practice of his day, in regard to dialectical disputation. In
dialectic exercise, the respondent undertook to defend a thesis, so
as to avoid inconsistency between one answer and another, against any
questions which might be put by the opponent. Both the form of the
questions, and the form of the answers, were determined beforehand.
No question was admissible which tended to elicit information or a
positive declaration from the respondent. A proposition was tendered
to him, and he was required to announce whether he affirmed or denied
it. The question might be put in either one of two ways: either by
the affirmative alone, or by putting both the affirmative and the
negative; either in the form, Is Rhetoric estimable? or in the form,
Is Rhetoric estimable or not? To the first form the respondent
answered Yes or No: to the second form, he replied by repeating
either the affirmative or the negative, as he preferred. But it was
not allowable to ask him, _What_ is Rhetoric? so as to put him under
the necessity of enunciating an explanation of his own.[33]
[Footnote 33: See the Scholia of Ammonius, p. 127, Br.]
Under these canons of dialectic debate, each question was required to
be really and truly one, so as to admit of a definite answer in one
word. The questioner was either unfair or unskilful, if he wrapped up
two questions really distinct in the same word, and thus compelled
the respondent either to admit them both, or to deny them both, at
once. Against this inconvenience Aristotle seeks to guard, by
explaining what are the conditions under which one and the same word
does in fact include more than one question. He had before brought to
view the case of an equivocal term, which involves such duplication:
if _himation_ means both horse and man, it will often happen that
questions respecting _himation_ cannot be truly answered either by
Yes or No. He now brings to view a different case in which the like
ambiguity is involved. To constitute one proposition, it is essential
both that the subject should be one, and that the predicate should be
one; either of them indeed may be called by two or three names, but
these names must coalesce into one. Thus, _animal_, _bipes_,
_mansuetum_, coalesce into _homo_, and may be employed either as one
subject or as one predicate; but _homo_, _albus_, _ambulans_, do not
coalesce into one; so that if we say, _Kallias est homo, albus,
ambulans_, the proposition is not one but three.[34] Accordingly, the
respondent cannot make one answer to a question thus complicated. We
thus find Aristotle laying down principles--and probably no one had
ever attempted to do so before him--for the correct management of
that dialectical debate which he analyses so copiously in the Topica.
[Footnote 34: Aristot. De Interpret. p. 20, b. 2. seq.; Ammonius,
Schol. pp. 127-128, a. 21, Br. Compare De Sophist. Elench. p. 169, a.
6-15.]
There are cases (he proceeds to state) in which two predicates may be
truly affirmed, taken separately, respecting a given subject, but in
which they cannot be truly affirmed, taken together.[35] Kallias is a
_currier_, Kallias is _good_--both these propositions may be true;
yet the proposition, Kallias is a _good currier_, may not be true.
The two predicates are both of them accidental co-inhering in the
same individual; but do not fuse themselves into one. So, too, we may
truly say, Homer _is a poet_; but we cannot truly say, Homer
_is_.[36] We see by this last remark,[37] how distinctly Aristotle
assigned a double meaning to _est_: first, _per se_, as meaning
existence; next, relatively, as performing the function of copula in
predication. He tells us, in reply either to Plato or to some other
contemporaries, that though we may truly say, _Non-Ens est
opinabile_, we cannot truly say _Non-Ens est_, because the real
meaning of the first of these propositions is, **_Non-Ens est
opinabile non esse_.[38]
[Footnote 35: Aristot. De Interpr. p. 21, a. 7, seq.]
[Footnote 36: Ibid. a. 27.]
[Footnote 37: Compare Schol. (ad Anal. Prior. I.) p. 146, a. 19-27;
also Eudemi Fragment. cxiv. p. 167, ed. Spengel.
Eudemus considered [Greek: e)/stin] as one term in the proposition.
Alexander dissented from this, and regarded it as being only a copula
between the terms, [Greek: sunthe/seôs mênutiko\n mo/rion tô=n e)n
tê=| prota/sei o(/rôn.]]
[Footnote 38: Aristot. De Interpr. p. 21, a. 32; compare Rhetorica,
ii. p. 1402, a. 5. The remark of Aristotle seems to bear upon the
doctrine laid down by Plato in the Sophistes, p. 258--the close of
the long discussion which begins, p. 237, about [Greek: to\ mê\
o)/n], as Ammonius tells us in the Scholia, p. 112, b. 5, p. 129, b.
20, Br. Ammonius also alludes to the Republic; as if Plato had
delivered the same doctrine in both; which is not the fact. See
'Plato and the Other Companions of Sokrates,' vol. II. ch. xxvii. pp.
447-458, seq.]
Aristotle now discusses the so-called Modal Propositions--the
Possible and the Necessary. What is the appropriate form of
_Antiphasis_ in the case of such propositions, where _possible to
be_, or _necessary to be_, is joined to the simple _is_. After a
chapter of some length, he declares that the form of _Antiphasis_
suitable for the Simple proposition will not suit for a Modal
proposition; and that in the latter the sign of negation must be
annexed to the modal adjective--_possible_, _not possible_, _&c._ His
reasoning here is not merely involved, but substantially incorrect;
for, in truth, both in one and in the other, the sign of
contradictory negation ought to be annexed to the copula.[39] From
the _Antiphasis_ in Modals Aristotle proceeds to legitimate sequences
admissible in such propositions, how far any one of them can be
inferred from any other.[40] He sets out four tables, each containing
four modal determinations interchangeable with each other.
1.
1. Possible (physically) to be.
2. Possible (logically) to be.
3. Not impossible to be.
4. Not necessary to be.
2.
1. Possible (physically) not to be.
2. Possible (logically) not to be.
3. Not impossible not to be.
4. Not necessary not to be.
3.
1. Not possible (physically) to be.
2. Not possible (logically) to be.
3. Impossible to be.
4. Necessary not to be.
4.
1. Not possible (physically) not to be.
2. Not possible (logically) not to be.
3. Impossible not to be.
4. Necessary to be.
Aristotle canvasses these tables at some length, and amends them
partly by making the fourth case of the second table change place
with the fourth of the first.[41] He then discusses whether we can
correctly say that the _necessary to be_ is also _possible to be_. If
not, then we might say correctly that the _necessary to be_ is _not
possible to be_; for one side or other of a legitimate _Antiphasis_
may always be truly affirmed. Yet this would be absurd: accordingly
we must admit that the _necessary to be_ is also _possible to be_.
Here, however, we fall seemingly into a different absurdity; for the
_possible to be_ is also _possible not to be_; and how can we allow
that what is _necessary to be_ is at the same time _possible not to
be_? To escape from such absurdities on both sides, we must
distinguish two modes of the Possible: one, in which the affirmative
and negative are alike possible; the other in which the affirmative
alone is possible, because it is always and constantly realized. If a
man is actually walking, we know that it is possible for him to walk;
and even when he is not walking, we say the same, because we believe
that he may walk if he chooses. He is not always walking; and in his
case, as in all other intermittent realities, the affirmative and the
negative are alike possible. But this is not true in the case of
necessary, constant, and sempiternal realities. With them there is no
alternative possibility, but only the possibility of their doing or
continuing to do. The celestial bodies revolve, sempiternally and
necessarily; it is therefore possible for them to revolve; but there
is no alternative possibility; it is not possible for them not to
revolve. Perpetual reality thus includes the unilateral, but not the
bilateral, possibility.[42]
[Footnote 39: Aristot. De Interpret. p. 21, a. 34-p. 22, a. 13. See
the note of Waitz, ad Organ. I. p. 359, who points out the error of
Aristotle, partly indicated by Ammonius in the Scholia.
The rule does not hold in propositions with the sign of universality
attached to the subject; but it is at least the same for Modals and
Non-modals.]
[Footnote 40: Aristot. De Interpr. p. 22, a. 14-b. 28.]
[Footnote 41: Aristot. De Interpr. p. 22, b. 22, [Greek: lei/petai
toi/nun] &c.; Ammonius, Schol. p. 133, b. 5-27-36.
Aristotle also intimates (p. 23, a. 18) that it would be better to
reverse the order of the propositions in the tables, and to place the
Necessary before the Possible. M. Barthélemy St. Hilaire has inserted
(in the note to his Translation, p. 197) tables with this reversed
order.]
[Footnote 42: Aristot. De Interpret. p. 22, b. 29-p. 23, a. 15.]
Having thus stated that _possible to be_, in this unilateral and
equivocal sense but in no other, is a legitimate consequence of
_necessary to be_, Aristotle proceeds to lay down a tripartite
distinction which surprises us in this place. "It is plain from what
has been said that that which is by Necessity, is in Act or
Actuality; so that if things sempiternal are prior, Actuality is
prior to Possibility. Some things, like the first (or celestial)
substances, are Actualities without Possibility; others (the
generated and perishable substances) which are prior in nature but
posterior in generation, are Actualities along with Possibility;
while a third class are Possibilities only, and never come into
Actuality" (such as the largest number, or the least magnitude).[43]
[Footnote 43: Ibid. p. 23, a. 21-26.]
Now the sentence just translated (enunciating a doctrine of
Aristotle's First Philosophy rather than of Logic) appears decidedly
to contradict what he had said three lines before, viz., that in one
certain sense, the _necessary to be_ included and implied the
_possible to be_; that is, a possibility or potentiality unilateral
only, not bilateral; for we are here told that the celestial
substance is Actuality without Possibility (or Potentiality), so that
the unilateral sense of this last term is disallowed. On the other
hand, a third sense of the same term is recognized and distinguished;
a sense neither bilateral nor unilateral, but the negation of both.
This third sense is hardly intelligible, giving as it does an
_impossible_ Possible; it seems a self-contradictory description.[44]
At best, it can only be understood as a limit in the mathematical
sense; a terminus towards which potentiality may come constantly
nearer and nearer, but which it can never reach. The first, or
bilateral potentiality, is the only sense at once consistent,
legitimate, and conformable to ordinary speech. Aristotle himself
admits that the second and third are equivocal meanings,[45]
departing from the first as the legitimate meaning; but if equivocal
departure to so great an extent were allowed, the term, put to such
multifarious service, becomes unfit for accurate philosophical
reasoning. And we find this illustrated by the contradiction into
which Aristotle himself falls in the course of a few lines. The
sentence of First Philosophy (which I translated in the last page) is
a correction of the logical statement immediately preceding it, in so
far as it suppresses the _necessary_ Possible, or the unilateral
potentiality. But on the other hand the same sentence introduces a
new confusion by its third variety--the _impossible_ Potential,
departing from all clear and consistent meaning of potentiality, and
coinciding only with the explanation of _Non-Ens_, as given by
Aristotle elsewhere.[46]
[Footnote 44: M. Barthélemy St. Hilaire, in the note to his
translation (p. 197) calls it justly--"le possible qui n'est jamais;
et qui par cela même, porte en lui une sorte d'impossibilité." It
contradicts both the two explanations of [Greek: dunato\n] which
Aristotle had given a few lines before. 1. [Greek: dunato\n o(/ti
e)nergei=]. 2. [Greek: dunato\n o(/ti e)nergê/seien a)/n] (p. 23, a.
10).]
[Footnote 45: Aristot. De Interpr. p. 23, a. 5. [Greek: tou=to me\n
tou/tou cha/rin ei)/rêtai, o(/ti ou) pa=sa du/namis tô=n
a)ntikeime/nôn, ou)d' o(/sai le/gontai kata\ to\ au)to\ ei)=dos.
e)/niai de\ duna/meis o(mô/numoi/ ei)sin; to\ ga\r dunato\n ou)ch
a(plô=s le/getai, a)lla\ to\ me\n o(/ti a)lêthe\s ô(s e)nergei/a|
o)/n], &c.
If we read the thirteenth chapter of Analytica Priora I. (p. 32, a.
18-29) we shall see that [Greek: to\ e)ndecho/menon] is declared to
be [Greek: ou)k a)nagkai=on], and that in the definition of [Greek:
to\ e)ndecho/menon], the words [Greek: ou(= mê\ o)/ntos a)nagkai/ou]
are expressly inserted. When [Greek: to\ a)nagkai=on] is said [Greek:
e)nde/chesthai], this is said only in an _equivocal_ sense of [Greek:
e)nde/chesthai--to\ ga\r a)nagkai=on _o(mônu/môs_ e)nde/chesthai
le/gomen.]
On the meaning of [Greek: to\ e)ndecho/menon], translated above, in
the table, "possible (logically) to be," and its relation to [Greek:
to\ dunato/n], see Waitz, ad Organ. I. pp. 375-8. Compare Prantl.
Gescht. der Logik, I. pp. 166-8.]
[Footnote 46: Aristot. De Interpr. p. 21, a. 32: [Greek: to\ de\ mê\
o)/n, o(/ti doxasto/n, ou)k a)lêthe\s ei)pei=n o)/n ti; do/xa ga\r
au)tou= ou)k e)/stin o(/ti e)/stin, a)ll' o(/ti ou)k e)/stin. To\ mê\
o)/n] is the true description of that which Aristotle improperly
calls [Greek: du/namis ê(\ ou)de/pote e)ne/rgeia/ e)stin].
The triple enumeration given by Aristotle (1. Actuality without
Potentiality. 2. Actuality with Potentiality. 3. Potentiality without
Actuality) presents a neat symmetry which stands in the place of
philosophical exactness.]
The contrast of Actual and Potential stands so prominently forward in
Aristotle's First Philosophy, and is, when correctly understood, so
valuable an element in First Philosophy generally, that we cannot be
too careful against those misapplications of it into which he himself
sometimes falls. The sense of Potentiality, as including the
alternative of either affirmative or negative--_may be or may not
be_--is quite essential in comprehending the ontological theories of
Aristotle; and when he professes to drop the _may not be_ and leave
only the _may be_, this is not merely an equivocal sense of the word,
but an entire renunciation of its genuine sense. In common parlance,
indeed, we speak elliptically, and say, _It may be_, when we really
mean, _It may or may not be_. But the last or negative half, though
not expressly announced, is always included in the thought and belief
of the speaker and understood by the hearer.[47]
[Footnote 47: See Trendelenburg ad Aristot. De Animâ, pp. 303-307.]
Many logicians, and Sir William Hamilton very emphatically, have
considered the Modality of propositions as improper to be included in
the province of Logic, and have treated the proceeding of Aristotle
in thus including it, as one among several cases in which he had
transcended the legitimate boundaries of the science.[48] This
criticism, to which I cannot subscribe, is founded upon one peculiar
view of the proper definition and limits of Logic. Sir W. Hamilton
lays down the limitation peremptorily, and he is warranted in doing
this for himself; but it is a question about which there has been
great diversity of view among expositors, and he has no right to
blame others who enlarge it. My purpose in the present volume is to
explain how the subject presented itself to Aristotle. He was the
first author that ever attempted to present Logic in a scientific
aspect; and it is hardly fair to try him by restrictions emanating
from critics much later. Yet, if he is to be tried upon this point, I
think the latitude in which he indulges preferable to the restricted
doctrine of Sir W. Hamilton.
[Footnote 48: See pp. 143-5 of the article, "Logic," in Sir William
Hamilton's Discussions on Philosophy--a very learned and instructive
article, even for those who differ from most of its conclusions.
Compare the opposite view, as advocated by M. Barthélemy St. Hilaire,
Logique d'Aristote, Préface, pp. **lxii.-lxviii.]
In the treatise now before us (De Interpretatione) Aristotle
announces his intention to explain the Proposition or Enunciative
Speech, the conjunction of a noun and a verb; as distinguished,
first, from its two constituents (noun and verb) separately taken;
next, from other modes of speech, also combining the two (precative,
interrogative, &c.). All speech (he says), the noun or verb
separately, as well as the proposition conjointly, is, in the first
instance, a sign of certain mental states common to the speaker with
his hearers; and, in the second instance, a sign of certain things or
facts, resembling (or correlating with) these mental states.[49] The
noun, pronounced separately, and the verb, pronounced separately, are
each signs of a certain thought in the speaker's mind, without either
truth or falsehood; the Proposition, or conjunction of the two, goes
farther and declares truth or falsehood. The words pronounced (he
says) follow the thoughts in the mind, expressing an opinion (_i.e._
belief or disbelief) entertained in the mind; the verbal affirmation
or negation gives utterance to a mental affirmation or negation--a
feeling of belief or disbelief--that something _is_, or that
something _is not_.[50] Thus, Aristotle intends to give a theory of
the Proposition, leaving other modes of speech to Rhetoric or
Poetry:[51] the Proposition he considers under two distinct aspects.
In its first or _subjective_ aspect, it declares the state of the
speaker's mind, as to belief or disbelief. In its second or
_objective_ aspect, it declares a truth or falsehood correlating with
such belief or disbelief, for the information of the hearer. Now the
Mode belonging to a proposition of this sort, in virtue of its
_form_, is to be _true_ or _false_. But there are also other
propositions--other varieties of speech enunciative--which differ
from the Simple or Assertory Proposition having the form _is_ or _is
not_, and which have distinct modes belonging to them, besides that
of being true or false. Thus we have the Necessary Proposition,
declaring that a thing _is_ so _by necessity_, that it _must be_ so,
or _cannot but be_ so; again, the Problematical Proposition,
enunciating that a thing _may or may not be so_. These two modes
attach to the _form_ of the proposition, and are quite distinct from
those which attach to its _matter_ as simply affirmed or denied; as
when, instead of saying, John is sick, we say, John is sick _of a
fever_, John is _dangerously_ sick, with a merely material
modification. Such adverbs, modifying the _matter_ affirmed or
denied, are numerous, and may be diversified almost without limit.
But they are not to be placed in the same category with the two just
mentioned, which modify the _form_ of the proposition, and correspond
to a state of mind distinct from simple belief or disbelief,
expressed by a simple affirmation or negation.[52] In the case of
each of the two, Aristotle has laid down rules (correct or incorrect)
for constructing the legitimate _Antiphasis_, and for determining
other propositions equipollent to, or following upon, the
propositions given; rules distinct from those applying to the simple
affirmation. When we say of anything, _It may be or may not be_, we
enunciate here only one proposition, not two; we declare a state of
mind which is neither belief nor disbelief, as in the case of the
Simple Proposition, but something wavering between the two; yet which
is nevertheless frequent, familiar to every one, and useful to be
made known by a special form of proposition adapted to it--the
Problematical. On the other hand, when we say, _It is by
necessity--must be--cannot but be_--we declare our belief, and
something more besides; we declare that the supposition of the
opposite of what we believe, would involve a contradiction--I would
contradict some definition or axiom to which we have already sworn
adherence. This again is a state of mind known, distinguishable, and
the same in all, subjectively; though as to the objective
correlate--what constitutes the Necessary, several different
opinions have been entertained.
[Footnote 49: Aristot. De Interpr. p. 16, a. 3-8: [Greek: e)/sti me\n
ou)=n ta\ e)n tê=| phônê=| tô=n e)n tê=| psuchê=| pathêma/tôn
su/mbola--ô(=n me/ntoi tau=ta sêmei=a _prô/tôs_, tau)ta\ pa=si
pathê/mata tê=s psuchê=s, kai\ ô(=n tau=ta o(moiô/mata, pra/gmata
ê)/dê tau)ta/.] Ibid. a. 13: [Greek: ta\ me\n ou)=n o)no/mata au)ta\
kai\ ta\ r(ê/mata e)/oike tô=| a)/neu sunthe/seôs kai\ diaire/seôs
noê/mati--ou)/te ga\r pseu=dos ou)/t' a)lêthe/s pô.] Ib. p. 17, a. 2:
[Greek: lo/gos a)pophantiko\s, e)n ô(=| to\ a)lêtheu/ein ê)\
pseu/desthai u(pa/rchei]. Compare p. 20, a. 34.]
[Footnote 50: Aristot. De Interpret. p. 23, a. 32: [Greek: ta\ me\n
e)n tê=| phônê=| a)kolouthei= toi=s e)n tê=| dianoi/a|, e)kei= de\
e)nanti/a do/xa ê( tou= e)nanti/ou], &c. Ib. p. 24, b. 1: [Greek:
ô(/ste ei)/per e)pi\ do/xês ou(/tôs e)/chei, ei)si\ de\ ai( e)n tê=|
phônê=| katapha/seis kai\ a)popha/seis su/mbola tô=n e)n tê=|
psuchê=|, dê=lon o(/ti kai\ katapha/sei e)nanti/a me\n a)po/phasis
ê(/ peri\ tou= au)tou= katho/lou], &c. Ib. p. 17, a. 22: [Greek:
e)/sti de\ ê( a(plê= a)po/phansis phônê\ sêmantikê\ peri\ tou=
u(pa/rchein ti ê)\ mê\ u(pa/rchein], &c.]
[Footnote 51: Ibid. p. 17, a. 5. [Greek: oi( me\n ou)=n a)/lloi
(lo/goi) a)phei/sthôsan; r(êtorikê=s ga\r ê)\ poiêtikê=s oi)keiote/ra
ê( ske/psis; o( de\ a)pophantiko\s tê=s nu=n theôri/as.]]
[Footnote 52: Ammonius (in the Scholia on De Interpret. p. 130, a.
16, seq., Brand.) ranks all modal propositions under the same
category, and considers the number of them to be, not indeed
infinite, but very great. He gives as examples: "The moon changes
_fast_; Plato loves Dion _vehemently_." Sir W. Hamilton adopts the
same view as Ammonius: "Modes may be conceived without end--all must
be admitted, if any are; the line of distinction attempted to be
drawn is futile." (Discussions on Phil. ut sup. p. 145.) On the other
hand, we learn from Ammonius that most of the Aristotelian
interpreters preceding him reckoned the simple proposition [Greek:
to\ u(pa/rchein] as a modal; and Aristotle himself seems so to
mention it (Analytica Priora, I. ii. p. 25, a. 1); besides that he
enumerates _true_ and _false_, which undoubtedly attach to [Greek:
to\ u(pa/rchein], as examples of modes (De Interpret. c. 12, p. 22,
a. 13). Ammonius himself protests against this doctrine of the former
interpreters.
Mr. John Stuart Mill (System of Logic, Bk. I. ch. iv. s. 2) says:--"A
remark of a similar nature may be applied to most of those
distinctions among propositions which are said to have reference to
their _modality_; as difference of tense or time; the sun _did_ rise,
_is_ rising, _will_ rise. . . . The circumstance of time is properly
considered as attaching to the copula, which is the sign of
predication, and not to the predicate. If the same cannot be said of
such modifications as these, Cæsar is _perhaps_ dead; it is
_possible_ that Cæsar is dead; it is only because these fall together
under another head; being properly assertions not of anything
relating to the fact itself, but of the state of our own mind in
regard to it; namely, our absence of disbelief of it. Thus, _Cæsar
may be dead_, means, _I am not sure that Cæsar is alive_."
I do not know whether Mr. Mill means that the function of the copula
is different in these problematical propositions, from what it is in
the categorical propositions: I think there is no difference. But his
remark that the problematical proposition is an assertion of the
state of our minds in regard to the fact, appears to me perfectly
just. Only, we ought to add, that this is equally true about the
categorical proposition. It is equally true about all the three
following propositions:--1. The three angles of a triangle may or may
not be equal to two right angles. 2. The three angles of a triangle
are equal to two right angles. 3. The three angles of a triangle are
necessarily equal to two right angles. In each of these three
propositions, an assertion of the state of our minds is involved, and
a different state of mind in each. This is the subjective aspect of
the proposition; it belongs to the form rather than to the matter,
and may be considered as a mode. The commentators preceding Ammonius
did so consider it, and said that the categorical proposition had its
mode as well as the others. Ammonius differed from them, treating the
categorical as having no mode--as the standard unit or point of
departure.
The propositions now known as Hypothetical and Disjunctive, which may
also be regarded as in a certain sense Modals, are not expressly
considered by Aristotle. In the Anal. Prior. I. xliv. p. 50 a. 16-38,
he adverts to hypothetical syllogisms, and intimates his intention of
discussing them more at length: but this intention has not been
executed, in the works that we possess.]
In every complete theory of enunciative speech, these modal
propositions deserve to be separately explained, both in their
substantive meaning and in their relation to other propositions.
Their characteristic property as Modals belongs to _form_ rather than
to _matter_; and Aristotle ought not to be considered as
unphilosophical for introducing them into the Organon, even if we
adopt the restricted view of Logic taken by Sir W. Hamilton, that it
takes no cognizance of the matter of propositions, but only of their
form. But though I dissent from Hamilton's criticisms on this point,
I do not concur with the opposing critics who think that Aristotle
has handled the Modal Propositions in a satisfactory manner. On the
contrary, I think that the equivocal sense which he assigns to the
Potential or Possible, and his inconsistency in sometimes admitting,
sometimes denying, a Potential that is always actual, and a Potential
that is never actual--are serious impediments to any consistent
Logic. The Problematical Proposition does not admit of being cut in
half; and if we are to recognize a _necessary_ Possible, or an
_impossible_ Possible, we ought to find different phrases by which to
designate them.
We must observe that the distinction of Problematical and Necessary
Propositions corresponds, in the mind of Aristotle, to that capital
and characteristic doctrine of his Ontology and Physics, already
touched on in this chapter. He thought, as we have seen, that in the
vast circumferential region of the Kosmos, from the outer sidereal
sphere down to the lunar sphere, celestial substance was a necessary
existence and energy, sempiternal and uniform in its rotations and
influence; and that through its beneficent influence, pervading the
concavity between the lunar sphere and the terrestrial centre (which
included the four elements with their compounds) there prevailed a
regularizing tendency called Nature: modified, however, and partly
counteracted by independent and irregular forces called Spontaneity
and Chance, essentially unknowable and unpredictable. The irregular
sequences thus named by Aristotle were the objective correlate of the
Problematical Proposition in Logic. In these sublunary sequences, as
to future time, _may or may not_ was all that could be attained, even
by the highest knowledge; certainty, either of affirmation or
negation, was out of the question. On the other hand, the necessary
and uniform energies of the celestial substance, formed the objective
correlate of the Necessary Proposition in Logic; this substance was
not merely an existence, but an existence necessary and unchangeable.
I shall say more on this when I come to treat of Aristotle as a
kosmical and physical philosopher; at present it is enough to remark
that he considers the Problematical Proposition in Logic to be not
purely subjective, as an expression of the speaker's ignorance, but
something more, namely, to correlate with an objective essentially
unknowable to all.
The last paragraph of the treatise De Interpretatione discusses the
question of Contraries and Contradictories, and makes out that the
greatest breadth of opposition is that between a proposition and its
contradictory (Kallias is just--Kallias is not just), not that
between, a proposition and what is called its contrary (Kallias is
just--Kallias is unjust); therefore, that according to the definition
of contrary, the true contrary of a proposition is its
contradictory.[53] This paragraph is not connected with that which
precedes; moreover, both the reasoning and the conclusion differ from
what we read as well in this treatise as in other portions of
Aristotle. Accordingly, Ammonius in the Scholia, while informing us
that Porphyry had declined to include it in his commentary, intimates
also his own belief that it is not genuine, but the work of another
hand. At best (Ammonius thinks), if we must consider it as the work
of Aristotle, it has been composed by him only as a dialectical
exercise, to debate an unsettled question.[54] I think the latter
hypothesis not improbable. The paragraph has certainly reference to
discussions which we do not know, and it may have been composed when
Aristotle had not fully made up his mind on the distinction between
Contrary and Contradictory. Considering the difficult problems that
he undertook to solve, we may be sure that he must have written down
several trains of thought merely preliminary and tentative. Moreover,
we know that he had composed a distinct treatise 'De Oppositis,'[55]
which is unfortunately lost, but in which he must have included this
very topic--the distinction between Contrary and Contradictory.
[Footnote 53: Aristot. De Interpr. p. 23, a. 27, seq.]
[Footnote 54: Scholia ad Arist. pp. 135-139, Br. [Greek: gumna/sai
mo/non boulêthe/ntos tou\s e)ntugcha/nontas pro\s tê\n e)pi/krisin
tô=n pithanô=s me\n ou) me/ntoi a)lêthô=s legome/nôn lo/gôn] &c. (p.
135, b. 15; also p. 136, a. 42).]
[Footnote 55: Scholia ad Categorias, p. 83, a. 17-19, b. 10, p. 84,
a. 29, p. 86, b. 42, p. 88, a. 30. It seems much referred to by
Simplikius, who tells us that the Stoics adopted most of its
principles (p. 83, a. 21, b. 7).]
Whatever may have been the real origin and purpose of this last
paragraph, I think it unsuitable as a portion of the treatise De
Interpretatione. It nullifies, or at least overclouds, one of the
best parts of that treatise, the clear determination of _Anaphasis_
and its consequences.
If, now, we compare the theory of the Proposition as given by
Aristotle in this treatise, with that which we read in the Sophistes
of Plato, we shall find Plato already conceiving the proposition as
composed indispensably of noun and verb, and as being either
affirmative or negative, for both of which he indicates the technical
terms.[56] He has no technical term for either subject or predicate;
but he conceives the proposition as belonging to its subject:[57] we
may be mistaken in the predicates, but we are not mistaken in the
subject. Aristotle enlarges and improves upon this theory. He not
only has a technical term for affirmation and negation, and for
negative noun and verb, but also for subject and predicate; again,
for the mode of signification belonging to noun and verb, each
separately, as distinguished from the mode of signification belonging
to them conjointly, when brought together in a proposition. He
follows Plato in insisting upon the characteristic feature of the
proposition--aptitude for being true or false; but he gives an ampler
definition of it, and he introduces the novel and important
distribution of propositions according to the quantity of the
subject. Until this last distribution had been made, it was
impossible to appreciate the true value and bearing of each
_Antiphasis_ and the correct language for expressing it, so as to say
neither more nor less. We see, by reading the Sophistes, that Plato
did not conceive the _Antiphasis_ correctly, as distinguished from
Contrariety on the one hand, and from mere Difference on the other.
He saw that the negative of any proposition does not affirm the
contrary of its affirmative; but he knew no other alternative except
to say, that it affirms only something different from the
affirmative. His theory in the Sophistes recognizes nothing but
affirmative propositions, with the predicate of contrariety on one
hand, or of difference on the other;[58] he ignores, or jumps over,
the intermediate station of propositions affirming nothing at all,
but simply denying a pre-understood affirmative. There were other
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
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
considers the premisses alone as constituting the Syllogism; the
conclusion is not a part thereof, but something distinct and
superadded. It appears to me that the _vulgus logicorum_ are here in
the right.]
In the Analytica Priora, we find ourselves involved, from and after
the second chapter, in the distinction of Modal propositions, the
necessary and the possible. The rules respecting the simple Assertory
propositions are thus, even from the beginning, given in conjunction
and contrast with those respecting the Modals. This is one among many
causes of the difficulty and obscurity with which the treatise is
beset. Theophrastus and Eudemus seem also to have followed their
master by giving prominence to the Modals:[11] recent expositors
avoid the difficulty, some by omitting them altogether, others by
deferring them until the simple assertory propositions have been
first made clear. I shall follow the example of these last; but it
deserves to be kept in mind, as illustrating Aristotle's point of
view, that he regards the Modals as principal varieties of the
proposition, co-ordinate in logical position with the simple
assertory.
[Footnote 11: Eudemi Fragmenta, cii.-ciii. p. 145, ed. Spengel.]
Before entering on combinations of propositions, Aristotle begins by
shewing what can be done with single propositions, in view to the
investigation or proving of truth. A single proposition may be
_converted_; that is, its subject and predicate may be made to change
places. If a proposition be true, will it be true when thus
converted, or (in other words) will its converse be true? If false,
will its converse be false? If this be not always the case, what are
the conditions and limits under which (assuming the proposition to be
true) the process of conversion leads to assured truth, in each
variety of propositions, affirmative or negative, universal or
particular? As far as we know, Aristotle was the first person that
ever put to himself this question; though the answer to it is
indispensable to any theory of the process of proving or disproving.
He answers it before he enters upon the Syllogism.
The rules which he lays down on the subject have passed into all
logical treatises. They are now familiar; and readers are apt to
fancy that there never was any novelty in them--that every one knows
them without being told. Such fancy would be illusory. These rules
are very far from being self-evident, any more than the maxims of
Contradiction and of the Excluded Middle. Not one of the rules could
have been laid down with its proper limits, until the discrimination
of propositions, both as to quality (affirmative or negative), and as
to quantity (universal or particular), had been put prominently
forward and appreciated in all its bearings. The rule for trustworthy
conversion is different for each variety of propositions. The
Universal Negative may be converted simply; that is, the predicate
may become subject, and the subject may become predicate--the
proposition being true after conversion, if it was true before. But
the Universal Affirmative cannot be thus converted simply. It admits
of conversion only in the manner called by logicians _per accidens_:
if the predicate change places with the subject, we cannot be sure
that the proposition thus changed will be true, unless the new
subject be lowered in quantity from universal to particular; _e.g._
the proposition, All men are animals, has for its legitimate converse
not, _All_ animals are men, but only, _Some_ animals are men. The
Particular Affirmative may be converted simply: if it be true that
Some animals are men, it will also be true that Some men are animals.
But, lastly, if the true proposition to be converted be a Particular
Negative, it cannot be converted at all, so as to make sure that the
converse will be true also.[12]
[Footnote 12: Aristot. Analyt. Prior. I. ii. p. 25, a. 1-26.]