Aristotle
when Aristotle proceeds to specify those functions of mind wherewith
the inductive _principia_ and the demonstrated conclusions correlate,
he refers both of them to functions wherein (according to him) the
mind is unerring and infallible--Intellect ([Greek: Nou=s]) and
Science. But, between these two he ranks Intellect as the higher, and
he refers the inductive _principia_ to Intellect. He does not mean
that Intellect ([Greek: Nou=s]) generates or produces these
principles. On the contrary, he distinctly negatives such a
supposition, and declares that no generative force of this high order
resides in the Intellect; while he tells us, with equal distinctness,
that they are generated from a lower source--sensible perception, and
through the gradual upward march of the inductive process. To say
that they originate from Sense through Induction, and nevertheless to
refer them to Intellect ([Greek: Nou=s]) as their subjective
correlate,--are not positions inconsistent with each other, in the
view of Aristotle. He expressly distinguishes the two points, as
requiring to be separately dealt with. By referring the _principia_
to Intellect ([Greek: Nou=s]), he does not intend to indicate their
generating source, but their evidentiary value and dignity when
generated and matured. They possess, in his view, the maximum of
dignity, certainty, cogency, and necessity, because it is from them
that even Demonstration derives the necessity of its conclusions;
accordingly (pursuant to the inclination of the ancient philosophers
for presuming affinity and commensurate dignity between the
_cognitum_ and the _cognoscens_), they belong as objective correlates
to the most unerring cognitive function--the Intellect ([Greek:
Nou=s]). It is the Intellect that grasps these principles, and
applies them to their legitimate purpose of scientific demonstration;
hence Aristotle calls Intellect not only the _principium_ of Science,
but the _principium principii_.
In the Analytica, from which we have hitherto cited, Aristotle
explains the structure of the Syllogism and the process of
Demonstration. He has in view mainly (though not exclusively) the
more exact sciences, arithmetic, geometry, astronomy, &c. But he
expressly tells us that all departments of inquiry are not capable of
this exactness; that some come nearer to it than others; that we must
be careful to require no more exactness from each than the subject
admits; and that the method adopted by us must be such as will attain
the admissible maximum of exactness. Now each subject has some
_principia_, and among them definitions, peculiar to itself; though
there are also some _principia_ common to all, and essential to the
march of each. In some departments of study (Aristotle says) we get
our view of _principia_ or first principles by induction; in others,
by sensible perception; in others again, by habitual action in a
certain way; and by various other processes also. In each, it is
important to look for first principles in the way naturally
appropriate to the matter before us; for this is more than half of
the whole work; upon right first principles will mainly depend the
value of our conclusions. For what concerns Ethics, Aristotle tells
us that the first principles are acquired through a course of
well-directed habitual action; and that they will be acquired easily,
as well as certainly, if such a course be enforced on youth from the
beginning. In the beginning of the Physica, he starts from that
antithesis, so often found in his writings, between what is more
knowable to us and what is more knowable absolutely or by nature. The
natural march of knowledge is to ascend from the first of these two
termini (particulars of sense) upward to the second or opposite,[17]
and then to descend downward by demonstration or deduction. The fact
of motion he proves (against Melissus and Parmenides) by an express
appeal to induction, as sufficient and conclusive evidence. In
physical science (he says) the final appeal must be to the things and
facts perceived by sense. In the treatise De Coelo he lays it down
that the _principia_ must be homogeneous with the matters they belong
to: the _principia_ of perceivable matters must be themselves
perceivable; those of eternal matters must be eternal; those of
perishable matters, perishable.
[Footnote 17: See also Aristot. Metaphys. Z. iv. p. 1029, b. 1-14.]
The treatises composing the Organon stand apart among Aristotle's
works. In them he undertakes (for the first time in the history of
mankind) the systematic study of significant propositions enunciative
of truth and falsehood. He analyses their constituent elements; he
specifies the conditions determining the consistency or inconsistency
of such propositions one with another; he teaches to arrange the
propositions in such ways as to detect and dismiss the inconsistent,
keeping our hold of the consistent. Here the signification of terms
and propositions is never out of sight: the facts and realities of
nature are regarded as so signified. Now all language becomes
significant only through the convention of mankind, according to
Aristotle's express declaration: it is used by speakers to
communicate what they mean to hearers that understand them. We see
thus that in these treatises the subjective point of view is brought
into the foreground--the enunciation of what we see, remember,
believe, disbelieve, doubt, anticipate, &c. It is not meant that the
objective point of view is eliminated, but that it is taken in
implication with, and in dependence upon, the subjective. Neither the
one nor the other is dropped or hidden. It is under this double and
conjoint point of view that Aristotle, in the Organon, presents to
us, not only the processes of demonstration and confutation, but also
the fundamental _principia_ or axioms thereof; which axioms in the
Analytica Posteriora (as we have already seen) he expressly declares
to originate from the data of sense, and to be raised and generalized
by induction.
Such is the way that Aristotle represents the fundamental principles
of syllogistic Demonstration, when he deals with them as portions of
Logic. But we also find him dealing with them as portions of Ontology
or First Philosophy (this being his manner of characterizing his own
treatise, now commonly known as the Metaphysica). To that science he
decides, after some preliminary debate, that the task of formulating
and defending the axioms belongs, because the application of these
axioms is quite universal, for all grades and varieties of Entia.
Ontology treats of Ens in its largest sense, with all its properties
_quatenus_ Ens, including Unum, Multa, Idem, Diversum, Posterius,
Prius, Genus, Species, Totum, Partes, &c. Now Ontology is with
Aristotle a purely objective science; that is, a science wherein the
subjective is dropt out of sight and no account taken of it, or
wherein (to state the same fact in the language of relativity) the
believing and reasoning subject is supposed constant. Ontology is the
most comprehensive among all the objective sciences. Each of these
sciences singles out a certain portion of it for special study. In
treating the logical axioms as portions of Ontology, Aristotle
undertakes to show their objective value; and this purpose, while it
carries him away from the point of view that we remarked as
prevailing in the Organon, at the same time brings him into conflict
with various theories, all of them in his time more or less current.
Several philosophers--Herakleitus, Anaxagoras, Demokritus,
Protagoras--had propounded theories which Aristotle here impugns. We
do not mean that these philosophers expressly denied his fundamental
axioms (which they probably never distinctly stated to themselves,
and which Aristotle was the first to formulate), but their theories
were to a certain extent inconsistent with these axioms, and were
regarded by Aristotle as wholly inconsistent.
The two Axioms announced in the Metaphysica, and vindicated by
Aristotle, are--
1. The Maxim of Contradiction: It is impossible for the same thing to
be and not to be; It is impossible for the same to belong and not to
belong to the same, at the same time and in the same sense. This is
the statement of the Maxim as a formula of Ontology. Announced as a
formula of Logic, it would stand thus: The same proposition cannot be
both true and false at the same time; You cannot both believe and
disbelieve the same proposition at the same time; You cannot believe,
at the same time, propositions contrary or contradictory. These
last-mentioned formulae are the logical ways of stating the axiom. They
present it in reference to the believing or disbelieving (affirming
or denying) subject, distinctly brought to view along with the matter
believed; not exclusively in reference to the matter believed, to the
omission of the believer.
2. The Maxim of Excluded Middle: A given attribute either does
belong, or does not belong to a subject (_i.e._, provided that it has
any relation to the subject at all)--there is no medium, no real
condition intermediate between the two. This is the ontological
formula; and it will stand thus, when translated into Logic: Between
a proposition and its contradictory opposite there is no tenable
halting ground; If you disbelieve the one, you must pass at once to
the belief of the other--you cannot at the same time disbelieve the
other.
These two maxims thus teach--the first, that we cannot at the same
time _believe_ both a proposition and its contradictory opposite; the
second, that we cannot at the same time _disbelieve_ them both.[18]
[Footnote 18: We have here discussed these two maxims chiefly in
reference to Aristotle's manner of presenting them, and to the
conceptions of his predecessors and contemporaries. An excellent view
of the Maxims themselves, in their true meaning and value, will be
found in Mr. John Stuart Mill's Examination of the Philosophy of Sir
W. Hamilton, ch. xxi. pp. 406-421.]
Now, Herakleitus, in his theory (a theory propounded much before the
time of Protagoras and the persons called Sophists), denied all
permanence or durability in nature, and recognized nothing except
perpetual movement and change. He denied both durable substances and
durable attributes; he considered nothing to be lasting except the
universal law or principle of change--the ever-renewed junction or
co-existence of contraries and the perpetual transition of one
contrary into the other. This view of the facts of nature was adopted
by several other physical philosophers besides.[19] Indeed it lay at
the bottom of Plato's new coinage--Rational Types or Forms, at once
universal and real. The Maxim of Contradiction is intended by
Aristotle to controvert Herakleitus, and to uphold durable substances
with definite attributes.
[Footnote 19: See 'Plato and other Comp. of Sokr.' I. i. pp. 28-38.]
Again, the theory of Anaxagoras denied all simple bodies (excepting
Noûs) and all definite attributes. He held that everything was
mingled with everything else, though there might be some one or other
predominant constituent. In all the changes visible throughout
nature, there was no generation of anything new, but only the coming
into prominence of some constituent that had before been
comparatively latent. According to this theory, you could neither
wholly affirm, nor wholly deny, any attribute of its subject. Both
affirmation and denial were untrue: the real relation between the two
was something half-way between affirmation and denial. The Maxim of
Excluded Middle is maintained by Aristotle as a doctrine in
opposition to this theory of Anaxagoras.[20]
[Footnote 20: Ibid. pp. 49-57.]
Both the two above-mentioned theories are objective. A third, that of