Aristotle
Protagoras--"Homo Mensura"--brings forward prominently the
subjective, and is quite distinct from either. Aristotle does indeed
treat the Protagorean theory as substantially identical with that of
Herakleitus, and as standing or falling therewith. This seems a
mistake: the theory of Protagoras is as much opposed to Herakleitus
as to Aristotle.
We have now to see how Aristotle sustains these two Axioms (which he
calls "the firmest of all truths and the most assuredly known")
against theories opposed to them. In the first place, he repeats here
what he had declared in the Analytica Posteriora--that they cannot
be directly demonstrated, though they are themselves the _principia_
of all demonstration. Some persons indeed thought that these Axioms
were demonstrable; but this is an error, proceeding (he says) from
complete ignorance of analytical theory. How, then, are these Axioms
to be proved against Herakleitus? Aristotle had told us in the
Analytica that axioms were derived from particulars of sense by
Induction, and apprehended or approved by the [Greek: Nou=s]. He does
not repeat that observation here; but he intimates that there is only
one process available for defending them, and that process amounts to
an appeal to Induction. You can give no ontological reason in support
of the Axioms, except what will be condemned as a _petitio
principii_; you must take them in their logical aspect, as enunciated
in significant propositions. You must require the Herakleitean
adversary to answer some question affirmatively, in terms significant
both to himself and to others, and in a proposition declaring his
belief on the point. If he will not do this, you can hold no
discussion with him: he might as well be deaf and dumb: he is no
better than a plant (to use Aristotle's own comparison). If he does
it, he has bound himself to something determinate: first, the
signification of the terms is a fact, excluding what is contrary or
contradictory; next, in declaring his belief, he at the same time
declares that he does not believe in the contrary or contradictory,
and is so understood by the hearers. We may grant what his theory
affirms--that the subject of a proposition is continually under some
change or movement; yet the identity designated by its name is still
maintained,[21] and many true predications respecting it remain true
in spite of its partial change. The argument in defence of the Maxim
of Contradiction is, that it is a postulate implied in all the
particular statements as to matters of daily experience, that a man
understands and acts upon when heard from his neighbours; a postulate
such that, if you deny it, no speech is either significant or
trustworthy to inform and guide those who hear it. If the speaker
both affirms and denies the same fact at once, no information is
conveyed, nor can the hearer act upon the words. Thus, in the
Acharnenses of Aristophanes, Dikæopolis knocks at the door of
Euripides, and inquires whether the poet is within; Kephisophon, the
attendant, answers--"Euripides is within and not within." This answer
is unintelligible; Dikæopolis cannot act upon it; until Kephisophon
explains that "not within" is intended metaphorically. Then, again,
all the actions in detail of a man's life are founded upon his own
belief of some facts and disbelief of other facts: he goes to Megara,
believing that the person whom he desires to see is at Megara, and at
the same time disbelieving the contrary: he acts upon his belief both
as to what is good and what is not good, in the way of pursuit and
avoidance. You may cite innumerable examples both of speech and
action in the detail of life, which the Herakleitean must go through
like other persons; and when, if he proceeded upon his own theory, he
could neither give nor receive information by speech, nor ground any
action upon the beliefs which he declares to co-exist in his own
mind. Accordingly, the Herakleitean Kratylus (so Aristotle says)
renounced the use of affirmative speech, and simply pointed with his
finger.[22]
[Footnote 21: This argument is given by Aristotle, Metaph. [Greek:
G]. v. p. 1010, a. 7-25, contrasting change [Greek: kata\ to\ poso/n]
and change [Greek: kata\ to\ poio/n].]
[Footnote 22: Aristot. Metaph. [Greek: G]. v. p. 1010, a. 12. Compare
Plato, Theætêt. pp. 179-180, about the aversion of the Herakleiteans
for clear issues and propositions.]
The Maxim of Contradiction is thus seen to be only the general
expression of a postulate implied in all such particular speeches as
communicate real information. It is proved by a very copious and
diversified Induction, from matters of experience familiar to every
individual person. It is not less true in regard to propositions
affirming changes, motions, or events, than in regard to those
declaring durable states or attributes.
In the long pleading of Aristotle on behalf of the Maxim of
Contradiction against the Herakleiteans, the portion of it that
appeals to Induction is the really forcible portion; conforming as it
does to what he had laid down in the Analytica Posteriora about the
inductive origin of the _principia_ of demonstration. He employs,
however, besides, several other dialectical arguments built more or
less upon theories of his own, and therefore not likely to weigh much
with an Herakleitean theorist; who--arguing, as he did argue, that
(because neither subject nor predicate was ever unchanged or stable
for two moments together) no true proposition could be framed but was
at the same time false, and that contraries were in perpetual
co-existence--could not by any general reasoning be involved in
greater contradiction and inconsistency than he at once openly
proclaimed.[23] It can only be shown that such a doctrine cannot be
reconciled with the necessities of daily speech, as practised by
himself, as well as by others. We read, indeed, one ingenious
argument whereby Aristotle adopts this belief in the co-existence of
contraries, but explains it in a manner of his own, through his much
employed distinction between potential and actual existence. Two
contraries cannot co-exist (he says) in actuality; but they both may
and do co-exist in different senses--one or both of them being
potential. This, however, is a theory totally different from that of
Herakleitus; coincident only in words and in seeming. It does indeed
eliminate the contradiction; but that very contradiction formed the
characteristic feature and keystone of the Herakleitean theory. The
case against this last theory is, that it is at variance with
psychological facts, by incorrectly assuming the co-existence of
contradictory beliefs in the mind; and that it conflicts both with
postulates implied in the daily colloquy of detail between man and
man, and with the volitional preferences that determine individual
action. All of these are founded on a belief in the regular sequence
of our sensations, and in the at least temporary durability of
combined potential aggregates of sensations, which we enunciate in
the language of definite attributes belonging to definite substances.
This language, the common medium of communication among
non-theorizing men, is accepted as a basis, and is generalized and
regularized, in the logical theories of Aristotle.
[Footnote 23: This is stated by Aristotle himself, Metaph. [Greek:
G]. vi. p. 1011, a. 15: [Greek: oi( d' e)n tô=| lo/gô| tê\n bi/an
mo/non zêtou=ntes a)du/naton zêtou=sin; e)nanti/a ga\r ei)pei=n
a)xiou=sin, eu)thu\s e)nanti/a le/gontes.] He here, indeed, applies
this observation immediately to the Protagoreans, against whom it
does not tell, instead of the Herakleiteans, against whom it does
tell. The whole of the reasoning in this part of the Metaphysica is
directed indiscriminately, and in the same words, against
Protagoreans and Herakleiteans.]
The doctrine here mentioned is vindicated by Aristotle, not only
against Herakleitus, by asserting the Maxim of Contradiction, but
also against Anaxagoras, by asserting the Maxim of Excluded Middle.
Here we have the second _principium_ of Demonstration, which, if it
required to be defended at all, can only be defended (like the first)
by a process of Induction. Aristotle adduces several arguments in
support of it, some of which involve an appeal to Induction, though
not broadly or openly avowed; but others of them assume what
adversaries, and Anaxagoras especially, were not likely to grant. We
must remember that both Anaxagoras and Herakleitus propounded their
theories as portions of Physical Philosophy or of Ontology; and that
in their time no such logical principles and distinctions as those
that Aristotle lays down in the Organon, had yet been made known or
pressed upon their attention. Now, Aristotle, while professing to
defend these Axioms as data of Ontology, forgets that they deal with
the logical aspect of Ontology, as formulated in methodical
propositions. His view of the Axioms cannot be properly appreciated
without a classification of propositions, such as neither Herakleitus
nor Anaxagoras found existing or originated for themselves. Aristotle
has taught us what Herakleitus and Anaxagoras had not been taught--to
distinguish separate propositions as universal, particular and
singular; and to distinguish pairs of propositions as contrary,
sub-contrary, and contradictory. To take the simplest case, that of
a singular proposition, in regard to which the distinction between
contrary and contradictory has no application,--such as the answer
(cited above) of Kephisophon about Euripides. Here Aristotle would
justly contend that the two propositions--Euripides is within,
Euripides is not within--could not be either both of them true, or
both of them false; that is, that we could neither believe both, nor
disbelieve both. If Kephisophon had answered, Euripides is neither
within nor not within, Dikæopolis would have found himself as much at
a loss with the two negatives as he was with the two affirmatives. In
regard to singular propositions, neither the doctrine of Herakleitus
(to believe both affirmation and negation) nor that of Anaxagoras (to
disbelieve both) is admissible. But, when in place of singular
propositions we take either universal or particular propositions, the
rule to follow is no longer so simple and peremptory. The universal
affirmative and the universal negative are _contrary_; the particular
affirmative and the particular negative are _sub-contrary_; the
universal affirmative and the particular negative, or the universal
negative and the particular affirmative, are _contradictory_. It is
now noted in all manuals of Logic, that of two contrary propositions,
both cannot be true, but both may be false; that of two
sub-contraries, both may be true, but both cannot be false; and that
of two contradictories, one must be true and the other false.
III.
METAPHYSICA.
[The following Abstract--when not translation--of six books ([Greek:
G], E, Z, Ê, [Greek: Th], [Greek: L]) out of the fourteen included
under the title 'Metaphysica,' may be said to cover the whole of
Aristotle's dogmatic exposition of First Philosophy. According to the
view of Brandis, now in its main features generally accepted, the
exposition continued through Books [Greek: G], E, Z, Ê, reaches back
to Books A and B, and comes to an end with Book [Greek: Th]. Still it
is only with Book [Greek: G] that the properly didactic treatment
begins, Book A being a historical review of previous opinion, and
Book B a mere collection of [Greek: a)pori/ai] subjected to a
preliminary dialectical handling; while, at the other end, Book
[Greek: L], though it has no direct connection with Book [Greek: Th],
is, especially in its latter part, of undeniable importance for
Aristotle's metaphysical doctrine.