TRUE SENSE OF THE PRINCIPLE OF CONTRADICTION.--KANT'S OPINION.
189. Before examining the value of the principle of contradiction as
a basis for our cognitions, it will be well to fix its true and exact
sense. This renders necessary some considerations upon an opinion
of Kant, advanced in his _Critic of Pure Reason_, when treating of
the form in which the principle of contradiction has hitherto been
enunciated in all schools of philosophy. The German metaphysician
grants, that whatever may be the matter of our cognitions, and in
whatever manner they may relate to their object, it is a general,
although a purely negative, condition of all our judgments, that they
should not mutually contradict each other; otherwise, even without
reference to their object, they are nothing in themselves. This
doctrine established, he observes that what is called the principle
of contradiction is the following: "A predicate that is opposed to a
subject does not belong to it;" and then goes on to say, that this is
a universal, although purely negative criterion of all truth; that
it moreover belongs exclusively to logic, since it is of use to pure
cognitions as to cognitions in general, without relation to their
object, and he declares that the contradiction makes them completely
disappear. "But of this celebrated principle, although stripped of
all contents, and purely formal," he continues, "there is still a
formula containing a synthesis, which has inadvertently, and quite
unnecessarily, been mixed up therein. It is this: _It is impossible
for the same thing to be and not be at the same time._ Not only has
the apodictic certainty (by the word _impossible_) been unnecessarily
added, which certainty would have been of itself understood from the
proposition; but the proposition is affected by the condition of time,
and says, as it were: a thing = A, which is something = B, cannot at
the same time be not B, but it can very well be both (B as well as not
B) in succession. For example: a man who is young, cannot at the same
time be old; but the same person may very well be young at one time, at
another not young, that is, old. Now, the principle of contradiction,
as a mere logical principle, must not at all restrict its meaning
to the relations of time, and consequently, such a formula is quite
opposed to its intention. The misapprehension arises simply from this:
that we first separate the predicate of a thing from its conception,
and afterwards unite its opposite with this predicate, which never
gives a contradiction with the subject, but only with its predicate,
which is synthetically joined with that subject, and that only when
the first and second predicates are asserted at the same time. If I
say a man who is unlearned is not learned, the condition, _at the same
time_, must be expressed; for he who is unlearned at one time may very
well be learned at another. But if I say no unlearned man is learned,
the proposition is analytic, since the sign (the unlearnedness) now
constitutes the conception of the subject, and then the negative
proposition is evident immediately from the principle of contradiction,
without it being necessary for the condition, _at the same time_, to be
added. This is also the cause why I have so changed the formula of this
principle, that the nature of an analytic proposition might be clearly
expressed."[16]
[16] _Transcendental Logic_, B. ii., C. 2, Sect. 1, pp. 140-141. Ed.
Leipsic. 1828.
190. The reader will not easily comprehend the meaning of this passage,
not very clear of itself, unless he knows what Kant understands by
analytic and synthetic propositions. We will explain this. In all
affirmative judgments, the relation of a predicate to a subject is
possible in two manners: either the predicate belongs to the subject
as contained in it, or is completely extraneous to it although joined
with it. In the former case, the judgment is analytic; in the latter,
it is synthetic. Analytic affirmative judgments are those in which the
union of the predicate with the subject is conceived by identity: those
are called synthetic in which this union is conceived without identity.
Kant illustrates his idea by the following examples: "When I say all
bodies are extended, I express an analytic judgment; for I need not go
out of the conception of body in order to find that of extension, which
I connect with it, but I have only to analyze the conception of body,
that is, to become conscious of the diversity which I always think in
this conception, in order to find the predicate. It is, therefore, an
analytic judgment. But when I say, all bodies are heavy, the predicate
heaviness is by no means included in my conception of the subject, that
is, of body in general. It is a conception added to the conception of
body. The addition in this way of the predicate to the subject gives a
synthetic judgment."[17]
[17] _Critic of Pure Reason._ Introduction, Sect. 4., p. 9.
It is easy to see the reason of the new nomenclature employed by the
German philosopher. He calls those judgments analytical, in which
it suffices to decompose the subject to find therein the predicate,
without the necessity of adding any thing not already thought, at
least obscurely, in the very conception of the subject; and he calls
synthetic those in which it is necessary to add something to the
conception of subject, since the predicate is not found in this
conception however much we decompose it.
191. This division of judgment, into analytic and synthetic, is much
used in modern philosophy, above all among the Germans; certainly there
are some who may imagine this to be a discovery made by the author of
the _Critic of Pure Reason_; and the very novelty of the name may give
occasion to equivocation. Yet, in all the scholastic writers who lie
forgotten, and covered with dust, in the recesses of libraries, we find
analytic and synthetic judgments, though not under these names. They
said there were two kinds of judgments; some, in which the predicate
was contained in the idea of subject, and others, in which it was not.
They called the propositions which expressed judgments of the former
class, _per se notæ_, or known by themselves, because, the meaning of
the terms being understood, the predicate was seen to be contained in
the idea, or the conception of the subject. They also called them first
principles, and the perception of them, _intelligence_, _intellectus_,
to distinguish them from _reason_, which is conversant about the
cognitions of mediate evidence, or ratiocination.
See if the following texts of St. Thomas leave any thing to be desired
in clearness or precision: "A proposition is known by itself, _per
se notæ_, when the predicate is contained in the subject, as; _man
is an animal_; for animal is of the essence of man. If, then, it is
known to all, what the subject and the predicate are, that proposition
will be known by itself to all, as is seen in the first principles
of demonstration, which are certain, common things, not unknown to
any one, as being and not-being, the whole, the part, and others
similar."[18]
[18] _Summa Theologica._ P. 1^a, Q. 2^a, A. 1^o, in corp.
"Any proposition the predicate of which is of the essence of the
subject, is known by itself, although such a proposition is not known
by itself for any one who is ignorant of the definition of the subject.
Thus this proposition, _man is rational_, is by its nature known by
itself, because _whoever says man, says rational_."[19]
[19] 1^a 2^{dae}, Q. 94^a, A. 2^o, in corp.
192. By these, and many other examples, which it would be easy to
adduce, it is seen that the distinction between analytic and synthetic
judgments was common in the schools centuries before Kant flourished.
Analytic judgments were all those formed by immediate evidence; and
synthetic, those resulting from mediate evidence, whether of the
purely ideal order, or in some sense depending on experience. It
was well known that there were conceptions of the subject, in which
the predicate was thought, at least confusedly; and thus union, or
identity, was explained by saying that the propositions, in which it
was found, were _per se notæ ex terminis_. In analytic judgments, the
predicate is in the subject; nothing is added, according to Kant, it is
only unfolded. _Whoever says man says rational_, are the words of St.
Thomas: the idea is the same as that of the German philosopher.
193. But let us see if it is necessary to change the formula by which
the principle of contradiction has hitherto been expressed.
The first observation of Kant refers to the word _impossible_, which he
considers unnecessarily added, since the apodictic certainty, which we
wish to express, should be contained in the proposition itself. Kant's
formula of the principle is this: "a predicate which is _opposed_ to
a subject, does not belong to it." What is the meaning of the word
_impossible_? "Possible and impossible absolutely, are said in relation
to the terms. Possible, because the predicate is not opposed to the
subject; impossible, because the predicate is opposed to the subject;"
says St. Thomas,[20] and with him agree all the schools. Therefore,
impossibility is the opposition of the predicate to the subject, and to
be repugnant is the same thing as to be impossible, and Kant uses the
very language which he blames in others. The common formula might be
expressed in this manner: "there is opposition in the same thing being
and not-being at the same time," or, "being is opposed to not-being,"
or, "being excludes not-being," or, "every thing is equal to itself;"
and Kant expresses nothing more when he says: "a predicate which is
opposed to a subject does not belong to it."
[20] P. 1^a, Q. 25^a, A. 3.
194. As a universal criterion, there is more exactness in the common
formula than in that of Kant. The latter restricts the principle
to the relation of predicate and subject, and consequently to the
purely ideal order, making it of no value for the real, unless by
a sort of enlargement. This enlargement, although legitimate and
easy, is not needed in the common formula: by saying being excludes
not-being, we embrace the ideal and the real, and present to the mind
the impossibility, not only of contradictory judgments, but also of
contradictory things.
Kant admits that the principle is the condition _sine qua non_ of
the truth of our cognitions, so that we must take care not to place
ourselves in contradiction with it, under pain of annihilating all
cognition. Let us put this to the proof. Give a man, unacquainted with
these matters, although not ignorant of what is meant by predicate and
subject, these two formulas; which will appear to him the best for all
uses in the external as in the internal? Certainly not that of Kant.
He sees in an instant, in all its generality, that a thing cannot
both be and not be at the same time; and he applies the principle to
all uses as well in the real as in the ideal order. Treating of an
external object, he says, this cannot both be and not be at the same
time; treating of contradictory judgments, of ideas which exclude one
another, he says, without any difficulty, this cannot be, because it
is impossible for the same thing to be and not be at the same time.
But it is not so easily and so readily seen how transition is made
from the ideal to the real order, or how the purely logical ideas of
predicate and subject can be used in the order of facts. The common
formula, then, besides being fully as exact as that of Kant, is more
simple, more intelligible, and more easy of application. Are there any
qualities more desirable than these in a universal criterion, in the
condition _sine qua non_ of the truth of our cognitions?
195. We have thus far supposed Kant's formula really to express the
principle of contradiction; but this supposition is far from being
exact. Undoubtedly there would be a contradiction, were a predicate
opposed to a subject, and yet to belong to it; and in this sense it
may be said that the principle of contradiction is in some manner
expressed in Kant's formula. But this is not enough; for we should
then be obliged to say that every axiom expresses the principle of
contradiction, since no axiom can be denied without a contradiction.
The formula of the principle must _directly_ express reciprocal
exclusion, opposition between being and not-being; this is what
was intended, and nothing else was ever meant by the principle of
contradiction. Kant, in his new formula, does not directly express
this exclusion: what he expresses is, that when the predicate is
excluded from the idea of the subject, it does not belong to it. So
far from expressing the principle of contradiction, it is the famous
principle of the Cartesians: "whatever is contained in the clear and
distinct idea of any thing may be affirmed of it with all certainty."
In substance the two formulas express the same thing, and are only
distinguished by these purely accidental differences: first, that
Kant's formula is the more concise; second, that it is negative, and
that of the Cartesians affirmative.
196. Kant says: "whatever is _excluded_ from the clear and distinct
idea of any thing, may be denied of it." A _predicate which is opposed_
to a subject "is the same thing as that which is _excluded_ from
the idea of any thing;" "does not belong to it" is the same as "may
be denied of it." And as, on the other hand, the principle of the
Cartesians must be understood in both senses, the affirmative and the
negative, because when they say that whatever is contained in the clear
and distinct idea of any thing may be affirmed of it, they mean also
that when any thing is excluded, it may be denied; it follows that
Kant says the same thing as the Cartesians; and thus, in attempting to
correct all the schools, he has fallen into an equivocation not of a
nature to acquire him any great credit for perspicacity.
It is clear that Kant's formula implies this: the predicate contained
in the idea of a subject belongs to it. This condition is equally
the condition _sine qua non_ of all analytic affirmative judgments;
for these disappear if that does not belong to the subject which is
contained in its idea. In this case there is not even an apparent
difference between Kant's formula and that of the Cartesians; the only
difference is in terms; the propositions are exactly the same. Hence we
see that instead of affirming that the schools expressed themselves
inaccurately in the clearest and most fundamental point of human
knowledge, we ought to proceed with great circumspection; witness the
originality of Kant's formula.
197. The author of the _Critic of Pure Reason_ was not more fortunate
in censuring the condition, _at the same time_, which is generally
added to the formula of the principle of contradiction. Since he
took the liberty of believing that no philosopher before himself had
expressed this formula in the proper manner, we beg to say that he did
not himself well understand what the others intended to express, and
we do not, in saying this, deem ourselves guilty of a philosophical
profanation. If Kant is an oracle for certain persons, all philosophers
together and all mankind are also oracles to be heard and respected.
According to Kant, the principle of contradiction is the condition
_sine qua non_ of all human cognitions. If, then, this condition is
to serve as their object, it must be so expressed as to be applicable
to all cases. Our cognitions are not composed solely of necessary
elements, but admit, to a great extent, ideas connected with the
contingent; since, as we have seen, purely ideal truths lead to nothing
positive, unless brought down to the ground of reality. Contingent
beings are subject to the condition of time, and all cognitions
relating to them must always depend on this condition. Their existence
is limited to a determinate space of time; and it is necessary to think
and speak of it conformably to this determination. Even their essential
properties are in some manner affected by the condition of time;
because if abstracted from it, and considered in general, they are
not as they are when realized; that is, when they cease to be a pure
abstraction, and become something positive. Here, then, is the reason,
and a very profound and cogent reason, why all the schools joined the
idea of time to the formula of the principle of contradiction: the
reason, we repeat, is very profound, and it is strange how it escaped
the German philosopher's penetration.
198. The importance of this subject requires still further explanation.
What is essential to the principle of contradiction, is the exclusion
of being by not-being, and of not-being by being. The formula must
express this fact, this truth, which is presented by immediate
evidence, and is contemplated by the intellect in a most clear
intuition, admitting neither doubt nor obscurity of any kind.
The word _being_ may be taken in two senses: _substantively_, inasmuch
as it signifies existence; and _copulatively_, as it expresses the
relation of predicate to subject. Peter _is_: here the verb _is_
signifies the existence of Peter, and is equivalent to this: Peter
exists. The equilateral triangle is equiangular: here the verb _is_
is taken copulatively, since it is not affirmed that any equilateral
triangle exists; merely the relation of equality of angles to equality
of sides is established absolutely, abstraction made from the existence
of either.
The principle of contradiction must extend to the cases in which
_being_ is copulative, and to those in which it is substantive; for
when we say it is impossible for the same thing to be and not be,
we speak not only of the ideal order, or of the relations between
predicates and subjects, but also of the real order. Were no reference
made to this last, we should hold the entire world of existences
to be deprived of this indispensable condition of all cognitions.
Moreover this condition is not only necessary to every cognition, but
also to every being in itself, abstracting its being known, or being
intelligent. What would a being be that could both be and not be? What
is the meaning of a contradiction realized? The principle must extend
to the word being, not only as copulative, but also as substantive.
All finite existences, our own included, are measured by a successive
duration; therefore, if the formula of the principle of contradiction
is to be applicable to whatever we know in the universe, it must be
accompanied by the condition of time. All finite things, which now
exist, at one time did not exist, and it may again be true that they
do not exist. Of no one can it be truly said that its non-existence
is impossible; this impossibility springs from existence in a given
time, and can only be asserted with respect to that time. Therefore,
the condition of time is absolutely necessary in the formula of the
principle of contradiction, if this formula is to serve for the
existent, that is, for that which is the real object of our cognitions.
199. Let us now see what happens in the purely ideal order, where the
word _being_ is taken copulatively. Propositions of the purely ideal
order are of two classes; in the first, the subject is a generic idea,
which, by the union of the specific difference, becomes a determinate
species; in the second, the subject is this determinate species, or the
generic idea joined with the difference. The word _angle_ expresses
the generic idea comprehending all angles, which, united with the
corresponding difference, constitutes the species of acute, obtuse,
or right angle. At every step we modify the generic idea in various
ways, and as a succession, in which are represented to us distinct
conceptions, all having for their basis the generic idea, necessarily
enters into it, it follows that we consider this idea as a being which
is successively transformed. To express this succession, which is
purely intellectual, we employ the idea of time; and here is one of
the reasons which justify the use of this condition even in the purely
ideal order. Thus we say, an angle cannot at the same time be both
a right angle and a not-right angle; for the idea of angle may be
successively determined by the difference which constitutes it a right
angle, and a not-right angle; but these determinations cannot co-exist
even in our conception, for which reason we do not assert the union of
the difference with the genus to be absolutely impossible, but limit
the impossibility to the condition of simultaneousness.
In this proposition, a right angle cannot be obtuse; the subject is not
the generic idea alone, but is united with the difference expressed by
the word _right_. In the conception formed of these two ideas, right
and angle, we see the impossibility of uniting the idea _obtuse_ with
them. This is without any condition of time, and here there is none
expressed. We frequently say, an angle cannot be at the same time right
and obtuse; but we never say, a right angle can never _at the same
time_ be obtuse, but, absolutely, a right angle cannot be obtuse.
200. Kant observes that the equivocation proceeds from commencing by
separating the predicate of a thing from the conception of this thing,
and afterwards joining to this same predicate its opposite, which
never makes a contradiction to the subject, but to the predicate,
which is synthetically united with it; a contradiction which happens
only when the first and second predicates are supposed at the same
time. This observation of Kant is at bottom very true, but it has its
defects: first, it pretends to be original, when it only says things
already well known; and secondly, it is used to combat an equivocation
existing only in the mind of the philosopher who wants to free others
from it. The two propositions analyzed in the last paragraph confirm
what we have just said. An angle cannot be both right and not right.
Here the condition of time is necessary, because the opposition is not
between the predicate and the subject, but between the two predicates.
The angle may be right or not right, only at different times. A
right angle cannot be obtuse; here the condition of time must not be
expressed, because the idea _right_ entering into the conception of the
subject, entirely excludes the idea obtuse.
201. If the principle of contradiction were to serve only for analytic
judgments, that is, for those in which the predicate is contained
in the idea of the subject, the condition of time should never be
expressed; but as this principle is to guide us in all other judgments,
it follows that, in the general formula, we cannot abstract a condition
absolutely indispensable in most cases. In the present state of our
understanding, while we are in this life, non-abstraction of time is
the rule, abstraction the exception; and would you have a general
formula conform to the exception and neglect the rule?
202. We cannot conceive what reason Kant had to illustrate this
subject with the examples above cited. Nothing can be more common
and inopportune than what he adds in illustration of this matter
by examples. "If I say a man who is unlearned is not learned, the
condition _at the same time_ must be understood; for he who is
unlearned at one time, may very well be learned at another." This is
not only very common and inopportune, but it is exceedingly inexact.
If the proposition were: a man cannot be ignorant and instructed; then
the condition _at the same time_ should be added, because not giving
preference to either predicate over the other indicates the manner
of the opposition, which is of predicate to predicate, and not of
predicate to subject. But in the example adduced by Kant, "the man that
is ignorant is not instructed." The subject is not man alone, but an
ignorant man; the predicate _instructed_ devolves on man modified by
the predicate _ignorant_, and, consequently, the expression of time is
not necessary, nor is it used in ordinary language.
There is a great difference between these two propositions: a man that
is ignorant _is not_ instructed; and a man that is ignorant _cannot
be_ instructed. The condition of time must not be expressed in the
former, for the reason already given; it must be in the latter, because
speaking of the impossibility in an absolute manner, we should deny the
ignorant man even the _power_ to be instructed.
203. Kant's other example is the following: "But if I say no unlearned
man is learned, the proposition is analytical, since the sign of
unlearnedness now constitutes the conception of the subject, and then
the negative proposition is immediately evident from the principle
of contradiction, without it being necessary for the condition _at
the same time_ to be added." We cannot see why Kant makes so great
difference between these two propositions: a man who is unlearned is
not learned, and no unlearned man is learned; in both, the predicate
relates not only to man, but to an unlearned man; and it is the same
to say, a man that is unlearned, as, an unlearned man. If, then, the
expression of time is not necessary in the one, neither is it in the
other.
If the idea of unlearned affects the subject, the predicate is
necessarily excluded, because the ideas, learned and unlearned, are
contradictory; and we encounter the rule of logic, that in necessary
matters, an indefinite is equivalent to a universal proposition.
The principle of contradiction must, therefore, be preserved as it is;
the condition of time must not be suppressed, for this would render the
formula, in many cases, inapplicable.(20)