DOES THE PRINCIPLE OF CONTRADICTION MERIT THE TITLE OF FUNDAMENTAL; AND
IF SO, IN WHAT SENSE?
204. Having cleared up the true sense of the principle of
contradiction, let us now see whether it merits to be called
fundamental, whether it possesses all the characteristics requisite to
such a dignity. These characteristics are three in number: first, that
it depend on no other principle; secondly, that its fall involve the
ruin of all others; thirdly, that it may, while it remains firm, be
conclusively urged against all who deny the others, and be of avail to
bring them back to the truth by a demonstration at least indirect.
* * * * *
205. In order completely to solve all questions depending on the
principle of contradiction, we shall state a few propositions, and
accompany them with their proper demonstrations:
FIRST PROPOSITION.
If the principle of contradiction be denied, all certainty, all truth,
and all knowledge are at an end.
_Demonstration._--If a thing may be and not be at the same time,
we may be certain and not certain, know and not know, exist and
not exist; affirmation may be joined with negation, contradictory
things united, distinct things identified, and identical things
distinguished: the intellect is a chaos to the full extent of the word;
reason is overturned; language is absurd; subject and object clash
in the midst of frightful darkness, and all intellectual light is
for ever extinguished. All principles are involved in the universal
wreck, and consciousness itself would totter, were it not, when this
absurd supposition is made, upheld by the invincible hand of nature.
Consciousness, indeed, in this absurd hypothesis, does not perish, for
this is impossible, but it sees itself carried away by this violent
whirlwind, which precipitates it and every thing else into chaotic
darkness. In vain does it strive to save its ideas; they all vanish
before the force of contradiction: in vain does it generate new ideas
to be substituted for those it loses; these also disappear: in vain
does it seek new objects, for they, too, disappear in like manner, and
it endures only to feel the radical impossibility of all thought, and
see contradiction lording it over the intellect, and destroying, with
irresistible might, whatever would germinate there.
SECOND PROPOSITION.
206. It is not enough not to suppose the principle of contradiction
false; we must suppose it to be true, if we would not have all
certainty, all knowledge, all truth to perish.
_Demonstration._--The reasons given for the first proposition avail
also to prove this. In the one case the principle of contradiction is
supposed to be denied; in the other, it is neither supposed true nor
false; but this evidently is not enough, for, until the principle of
contradiction is placed beyond all doubt, we remain in darkness, and
must doubt of every thing. We do not mean to say that it is impossible
for us to have certainty of any thing, if we do not think explicitly
of this principle; but that it must be so firmly established, that we
cannot raise the least doubt concerning it, and that, when we see any
thing connected with it, we must, of necessity, consider that thing as
founded upon an immovable basis: the least vacillation, the least doubt
of this principle utterly destroys it; the possibility of an absurdity
is itself an absurdity.
THIRD PROPOSITION.
207. The certainty of the principle of contradiction rests upon no
other principle.
_Demonstration._--It is, as we have seen, necessary in every
cognition to suppose the truth of the principle of contradiction;
therefore, no one can avail to demonstrate it. Every argument, made
to demonstrate this, necessarily involves a vicious circle; the
principle of contradiction is proved by another principle, which,
in its turn, supposes that of contradiction; and so we shall have a
superstructure resting upon a foundation, which foundation rests upon
the superstructure itself.
FOURTH PROPOSITION.
208. Whoever denies the principle of contradiction can neither directly
nor indirectly be refuted by any other.
_Demonstration._--It would be amusing to hear the arguments directed
against a man who admits both affirmation and negation to be at the
same time possible; although forced to admit the affirmative, he will
still hold the negative, and _vice versa_. It is impossible not only to
argue, but even to speak, or to think on such a supposition.
FIFTH PROPOSITION.
209. It is not exact to say, as is generally said, that by the
principle of contradiction, we may argue conclusively against whoever
denies the others.
Here take notice that we only say _it is not exact_, for we believe
it at bottom to be true, although not free from inexactness. To show
this, let us examine the weight of the demonstration ordinarily given.
The reasons, arguments, and replies may be presented most clearly and
strongly in the form of a dialogue. Let us suppose some one to deny
this axiom: the whole is greater than its part.
If you deny this, you admit that the same thing may both be and not be
at the same time. This is what you have to prove. With you the whole is
the whole and not the whole, and the part the part and not the part.
Why so? First, it is the whole by supposition. Admitted. And at the
same time it is not. Denied. It is not the whole because it is not
greater than its part. An excellent way of arguing! This is a _petitio
principii_. I commence by asserting that the whole is not greater than
its part, and you argue on the contrary supposition; for you tell me
the whole would not be the whole were it not greater than its part. If
I had conceded that the whole is greater than its part, and then denied
this property, I should indeed fall into a contradiction, making that
a whole, which, according to my principles, is not a whole; but as I
now deny that the whole must be greater than its part, I must also deny
that it ceases to be a whole by not being greater than its part.
210. What will you reply to one reasoning thus. Certainly nothing in
the form of an argument: all that you can do is to call his attention
to the absurdity of his position; but this is to be done not by
argument, but by exactly determining the meaning of the words and
analyzing the conceptions which they express. This is all that can
or should be done. The contradiction exists; this is certain; but
what is wanted is, that he see that he has fallen into it; and if the
explanation of the terms, and the analysis of the conceptions do not
suffice, nothing else will.
Let us see how this may be done in the same example. The whole is
greater than its part. What is the whole? The collection of the parts,
the parts themselves united. The idea of the parts then enters into the
idea of the whole. What is the meaning of greater? One thing is said to
be greater than another, when, besides containing an equal quantity,
it also contains something else. Seven is greater than five, because,
besides the same five, it contains also two. The whole contains one
part and also the other parts; therefore, the idea of _greater than
its part_ enters into the idea of whole. Thus it is that we must
refute whoever denies this principle; and this method, better than
that of argumentation, may be said to explain the terms and analyze
the conceptions, for it clearly does nothing but define the former and
decompose the latter.
SIXTH PROPOSITION.
211. The principle of contradiction is known only by immediate evidence.
_Demonstration._--Two things are here to be proved: that the knowledge
is by evidence, and that the evidence is immediate. As regards the
former we will remark that the principle of contradiction is not a
simple fact of consciousness, but a purely ideal truth. Every fact of
consciousness involves reality, and cannot be expressed without the
assertion of some existence: the principle of contradiction neither
affirms nor denies any thing positive; that is, it does not say that
any thing exists or does not exist; it only expresses the opposition of
being to not-being, and of not-being to being, abstraction made from
our taking the word being copulatively or substantively.
212. Every fact of consciousness is not only something existent, but
something determinate; it is not a thought in the abstract, but is
this or that thought. The principle of contradiction contains nothing
determinate; it abstracts not only the existence, but also the essence
of things, since it relates not only to existing things, but also to
things possible: it distinguishes no species among them, but embraces
them all in their greatest generality. When we say, "it is impossible
for the same thing to be and not be," the word _thing_ does not at all
restrict the meaning; it expresses being in general, in its greatest
indeterminateness. In the _to be_ or _not be_, the word _be_ expresses
not only existence, but also every class of essences in their most
complete indeterminateness. Thus the principle is equally applicable
in these two propositions: it is impossible for the moon to be and not
be; it is impossible for a circle to be and not be a circle; although
the first is in the real order, and there the word _be_ expresses
existence, and the second is in the ideal order, and the word _be_
expresses only the relation of predicate to subject.
213. Every fact of consciousness is individual; the principle of
contradiction is the most universal imaginable: every fact of
consciousness is contingent; the principle of contradiction is
absolutely necessary, a necessity which is a mark of truths known by
evidence.
214. The principle of contradiction is a law of all intelligence; it is
of absolute necessity for the finite as for the infinite; not even the
infinite intelligence is beyond this necessity, for infinite perfection
cannot be an absurdity. Every fact of consciousness as purely
individual, relates only to the being that experiences it; neither the
order of intelligences, nor that of truth suffers any mutation from my
existence or non-existence.
215. The principle of contradiction, besides the marks of necessity and
universality, which distinguish truths of evidence, possesses also that
of being seen with that immediate, intellectual clearness, of which we
have already treated. In the idea of being we see most clearly the
exclusion of not-being.
Hence the proof of the second part of the proposition: because there
is immediate evidence of the relation of the predicate to the subject,
when the sole idea of the subject, without the necessity of combination
with other ideas, enables us to perceive this relation: this is so
in the present case, for not only no combination is needed, but all
combinations are impossible if the truth of this principle be not
supposed.(21)