Aristotle
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