Aristotle
it is an analogical whole, including several genera distinct from
each other at the beginning, though all of them branches derivative
from one and the same root; all of them connected by some sort of
analogy or common relation to that one root, yet not necessarily
connected with each other by any direct or special tie.
[Footnote 9: Metaphys. [Greek: G]. ii. p. 1003, a. 33-p. 1004, a. 5:
[Greek: to\ d' o)\n le/getai me\n pollachô=s, a)lla\ pro\s e(\n kai\
mi/an tina\ phu/sin, kai\ ou)ch o(mônu/m ôs--u(pa/rchei ga\r
eu)thu\s ge/nê e)/chonta to\ o)\n kai\ to\ e(/n.]
Compare K. iii. p. 1060, b. 32. See also above, ch. iii. p. 60, of
the present work.]
Of these various significations, he enumerates, as we have already
seen, four:--(1) _Ens_ which is merely concomitant with, dependent
upon, or related to, another _Ens_ as terminus; (2) _Ens_ in the
sense of the True, opposed to _Non-Ens_ in the sense of the False;
(3) _Ens_ according to each of the Ten Categories; (4) _Ens_
potentially, as contrasted with _Ens_ actually. But among these four
heads, the two last only are matters upon which science is
attainable, in the opinion of Aristotle. To these two, accordingly,
he **confines Ontology or First Philosophy. They are the only
two that have an objective, self-standing, independent, nature.
That which falls under the first head (_Ens per Accidens_) is
essentially indeterminate; and its causes, being alike indeterminate,
are out of the reach of science. So also is that which falls under
the second head--_Ens tanquam verum_, contrasted with _Non-Ens
tanquam falsum_. This has no independent standing, but results from
an internal act of the judging or believing mind, combining two
elements, or disjoining two elements, in a way conformable to, or
non-conformable to, real fact. The true combination or disjunction is
a variety of _Ens_; the false combination or disjunction is a variety
of _Non-Ens_. This mental act varies both in different individuals,
and at different times with the same individual, according to a
multitude of causes often unassignable. Accordingly, it does not fall
under Ontological Science, nor can we discover any causes or
principles determining it.[10] When Aristotle says that the two first
heads are out of the reach of science, or not proper subjects of
science, he means that their first _principia_, causes, or deepest
foundations, cannot be discovered and assigned; for it is in
determining these _principia_ and causes that true scientific
cognition consists.[11]
[Footnote 10: Aristot. Met. E. iv. p. 1027, b. 17; [Greek: Th]. p.
1051, b. 2; p. 1052, a. 17-30; K. viii. p. 1065, a. 21.
There remains much obscurity about this meaning of _Ens_ (_Ens_
[Greek: ô(s a)lêthe/s]), even after the Scholia of Alexander (p. 701,
a. 10, Sch. Brand.), and the instructive comments of Bonitz,
Schwegler, and Brentano (Ueber die Bedeutung des Seienden nach
Aristoteles, ch. iii. pp. 21-39).
The foundation of this meaning of _Ens_ lies in the legitimate
_Antiphasis_, and the proper division thereof ([Greek: to\ de\
su/nolon peri\ merismo\n a)ntipha/seôs], p. 1027, b. 20). It is a
first principle (p. 1005, b. 30) that, if one member of the
_Antiphasis_ must be affirmed as true, the other must be denied as
false. If we fix upon the right combination to affirm, we say _the
thing that is_: if we fix upon the wrong combination and affirm it,
we say _the thing that is not_ (p. 1012, b. 10). "Falsehood and Truth
(Aristotle says, E. iv. p. 1027, b. 25) are not in things but in our
mental combination; and as regards simple (uncombined) matters and
essences, they are not even in our mental combination:" [Greek: ou)
ga/r e)sti to\ pseu=dos kai\ to\ a)lêthe\s e)n toi=s pra/gmasin,
oi(=on to\ me\n a)gatho\n a)lêthe/s, to\ de\ kako\n eu)thu\s
pseu=dos, a)ll' e)n dianoi/a|; peri\ de\ ta\ a(pla= kai\ ta\ ti/
e)stin ou)d' e)n tê=| dianoi/a|.] Compare Bonitz (ad Ar. Metaph. Z.
iv. p. 1030, a.), p. 310, Comm.
In regard to _cogitabilia_--simple, indivisible, uncompounded--there
is no combination or disjunction; therefore, strictly speaking,
neither truth nor falsehood (Aristot. De Animâ, III. vi. p. 430, a.
26; also Categor. x. p. 13, b. 10). The intellect either apprehends
these simple elements, or it does not apprehend them; there is no
[Greek: dia/noia] concerned. Not to apprehend them is ignorance,
[Greek: a)/gnoia], which sometimes loosely passes under the title of
[Greek: pseu=dos] (Schwegler, Comm. Pt. II., p. 32).]
[Footnote 11: Metaphys. E. i. p. 1025, b. 3: [Greek: ai( a)rchai\
kai\ ta\ ai)/tia zêtei=tai tô=n o)/ntôn, dê=lon d' o(/ti ê(=|
o)/nta.--o(/lôs de\ pa=sa e)pistê/mê dianoêtikê\ ê)\ mete/chousa/ ti
dianoi/as peri\ ai)ti/as kai\ a)rcha/s e)stin ê)\ a)kribeste/ras ê)\
a(plouste/ras.]
Compare Metaph. K. vii. p. 1063, b. 36; p. 1065, a. 8-26. Analyt.
Post. I. ii. p. 71, b. 9.]
There remain, as matter proper for the investigation of First
Philosophy, the two last-mentioned heads of _Ens_; viz., _Ens_
according to the Ten Categories, and _Ens_ potential and actual. But,
along with these, Aristotle includes another matter also; viz., the
critical examination of the Axioms and highest generalities of
syllogistic proof or Demonstration. He announces as the first
principle of these Axioms--as the highest and firmest of all
Principles--the Maxim of Contradiction:[12] The same predicate cannot
both belong and not belong to the same subject, at the same time and
in the same sense; or, You cannot both truly affirm, and truly deny,
the same predicate respecting the same subject; or, The same
proposition cannot be at once true and false. This Axiom is by nature
the beginning or source of all the other Axioms. It stands first in
the order of knowledge; and it neither rests upon nor involves any
hypothesis.[13]
[Footnote 12: Metaph. [Greek: G]. iii. p. 1005, b. 7, 17, 22, 34:
[Greek: au(/tê dê\ pasô=n e)sti\ bebaiota/tê tô=n
a)rchô=n--phu/sei ga\r a)rchê\ kai\ tô=n a)/llôn a)xiôma/tôn au(/tê
pa/ntôn.]--p. 1011, b. 13: [Greek: bebaiota/tê _do/xa_ pasô=n to\ mê\
ei)=nai a)lêthei=s a(/ma ta\s a)ntikeime/nas pha/seis]--(He here
applies the term [Greek: do/xa] to designate this fundamental maxim.
This deserves notice, because of the antithesis, common with him
elsewhere, between [Greek: do/xa] and [Greek: e)pistê/mê]).]
[Footnote 13: Metaph. [Greek: G]. iii. p. 1005, b. 13-14: [Greek:
gnôrimôta/tên--a)nupo/theton].]
The Syllogism is defined by Aristotle as consisting of premisses and
a conclusion: if the two propositions called premisses be granted as
true, a third as conclusion must for that reason be granted as true
also.[14] The truth of the conclusion is affirmed conditionally on
the truth of the premisses; and the rules of Syllogism set out those
combinations of propositions in which such affirmation may be made
legitimately. The rules of the Syllogism being thus the rules for
such conditional affirmation, the Principle or Axiom thereof
enunciates in the most general terms what is implied in all those
rules, as essential to their validity. And, since the syllogistic or
deductive process is applicable without exception to every variety of
the _Scibile_, Aristotle considers the Axioms or Principles thereof
to come under the investigation of Ontology or First Philosophy. Thus
it is, that he introduces us to the Maxim of Contradiction, and its
supplement or correlative, the Maxim of the Excluded Middle.
[Footnote 14: Analyt. Prior. I. i. p. 24, b. 18-20, et alib.]
His vindication of these Axioms is very illustrative of the
philosophy of his day. It cannot be too often impressed that he was
the first either to formulate the precepts; or to ascend to the
theory, of deductive reasoning; that he was the first to mark by
appropriate terms the most important logical distinctions and
characteristic attributes of propositions; that before his time,
there was abundance of acute dialectic, but no attempt to set forth
any critical scheme whereby the conclusions of such dialectic might
be tested. Anterior to Sokrates, the cast of Grecian philosophy had
been altogether either theological, or poetical, or physical, or at
least some fusion of these three varieties into one. Sokrates was the
first who broke ground for Logic--for testing the difference between
good and bad ratiocination. He did this by enquiry as to the
definition of general terms,[15] and by dialectical exposure of the
ignorance generally prevalent among those who familiarly used them.
Plato in his Sokratic dialogues followed in the same negative track;
opening up many instructive points of view respecting the erroneous
tendencies by which reasoners were misled, but not attempting any
positive systematic analysis, nor propounding any intelligible scheme
of his own for correction or avoidance of the like. If Sokrates and
Plato, both of them active in exposing ratiocinative error and
confusion, stopped short of any wide logical theory, still less were
the physical philosophers likely to supply that deficiency. Aristotle
tells us that several of them controverted the Maxim of
Contradiction.[16] Herakleitus and his followers maintained the
negative of it, distinctly and emphatically;[17] while the disciples
of Parmenides, though less pronounced in their negative, could not
have admitted it as universally true. Even Plato must be reckoned
among those who, probably without having clearly stated to himself
the Maxim in its universal terms, declared doctrines quite
incompatible with it: the Platonic Parmenides affords a conspicuous
example of contradictory conclusions deduced by elaborate reasoning
and declared to be both of them firmly established.[18] Moreover, in
the Sophistes,[19] Plato explains the negative proposition as
expressing what is different from that which is denied, but nothing
beyond; an explanation which, if admitted, would set aside the Maxim
of Contradiction as invalid.
[Footnote 15: Aristot. Metaph. A. vi. p. 987, b. 1: [Greek: S
ôkra/tous de\ peri\ me\n ta\ ê)thika\ pragmateuome/nou, peri\ de\
tê=s o(/lês phu/seôs ou)the/n, e)n me/ntoi tou/tois to\ katho/lou
zêtou=ntos, kai\ peri\ o(rismô=n e)pistê/santos _prô/tou_ tê\n
dia/noian.]]
[Footnote 16: Aristot. Metaph. [Greek: G]. iv. p. 1005, b. 35:
[Greek: ei)si\ de/ tines, oi(/, katha/per ei)/pomen, au)toi/ te
e)nde/chesthai/ phasi to\ au)to\ ei)=nai kai\ mê\ ei)=nai, kai\
u(polamba/nein ou(/tôs. chrô=ntai de\ tô=| lo/gô| tou/tô|
polloi\ kai\ tô=n peri\ phu/seôs.]]
[Footnote 17: Ibid. iii. p. 1005, b. 25; v. p. 1010, a. 13; vi. p.
1011, a. 24.]
[Footnote 18: Plato, Republic. v. p. 479, A.; vii. p. 538, E. Compare
also the conclusion of the Platonic Parmenides, and the elaborate
dialectic or antinomies by which the contradictions involved in it
are proved.]
[Footnote 19: Plato, Sophistes, p. 257, B.]
While Aristotle mentions these various dissentients, and especially
Herakleitus, he seems to imagine that they were not really in
earnest[20] in their dissent. Yet he nevertheless goes at length into
the case against them, as well as against others, who agreed with him
in affirming the Maxim, but who undertook also to demonstrate it. Any
such demonstration Aristotle declares to be impossible. The Maxim is
assumed in all demonstrations; unless you grant it, no demonstration
is valid; but it cannot be itself demonstrated. He had already laid
down in the Analytica that the premisses for demonstration could not
be carried back indefinitely, and that the attempt so to carry them
back was unphilosophical.[21] There must be some primary,
undemonstrable truths; and the Maxim of Contradiction he ranks among
the first. Still, though in attempting any formal demonstration of
the Maxim you cannot avoid assuming the Maxim itself and thus falling