IMPOSSIBILITY OF FINDING THE FIRST PRINCIPLE IN THE IDEAL ORDER.
138. We shall in vain seek in the region of ideas for that which we
could not find in that of facts, for there is no ideal truth, the
origin of all other truths.
Ideal truth only expresses the necessary relation of ideas, abstracting
the existence of the objects to which they relate: hence it follows,
first of all, that ideal truths are absolutely incapable of producing
the knowledge of reality.
No ideal truth can lead to any result in the order of existences,
unless there be some fact to which it applies. Otherwise, however
fruitful it may be in the order of ideas, it will be absolutely sterile
in that of facts. The fact without the ideal truth remains in its
isolated individuality, incapable of producing any thing more than
cognition of itself: but in return, the ideal truth, apart from the
fact, remains purely objective in the logical world, and has no means
of descending to that of existences.
139. Let us apply this doctrine to the most certain and most evident
ideal principles, to those which contain the most general ideas, and
which ought, therefore, to possess the fecundity in question, if,
indeed, it be anywhere to be encountered.
"It is impossible for the same thing to be and not be at the same
time." This is the famous principle of contradiction, which may
undoubtedly claim to be regarded as one source of truth to the human
understanding. The ideas contained in it are the clearest and most
simple conceivable; in it is affirmed the repugnance of being to
not-being, and of not-being to being, at the same time, which is most
evident. But what advance can we make with this principle alone?
Present it to the most penetrating mind, to the most powerful genius;
leave them alone with it, and there will result only a sterile,
although pure and most clear intuition. Since it does not affirm that
any thing is or is not, nothing can be inferred either for or against
any existence: it only offers to the mind this conditional relation:
that if any thing does exist, it is repugnant for it not to exist at
the same time that it exists, or to exist at the same time that it does
not exist. But if the condition of existence or non-existence be not
given, _yes_ and _no_ in the real order are indifferent; nothing is
known concerning them, however great the evidence in the ideal order.
To pass from the logical world to that of reality, all that is required
is a fact to serve as a bridge. If this fact be offered to the
understanding, the two banks are joined, and science commences. I feel,
I think, I exist: these are facts of consciousness; combine any one of
them with the principle of contradiction, and what before were sterile
intuitions become prolific ratiocinations, embracing at once the world
of ideas, and that of reality.
140. Even in the purely ideal order, the principle of contradiction
is sterile unless joined with particular truths of the same order. In
geometry, for example, it is often argued thus: such a quantity is
either greater or less than another, or equal to it; for otherwise it
would be both greater and less, equal and unequal, at the same time,
which is absurd. Here the principle of contradiction is effectively
applied, not alone, but together with a particular truth which makes
such an application available. Thus, in the above argument, no use
could be made of the principle of contradiction, to prove equality or
inequality were not the existence or non-existence of one of the two
previously proved or supposed: since this neither does nor can result
from the principle of contradiction which includes, not a particular
idea, but the most general ideas presented to the human mind.
141. General truths, of themselves, even in the purely ideal order,
lead to nothing, because of the indeterminateness of the ideas which
they contain; and, on the other hand, particular truths of themselves
produce no result, because they are limited to what they are, making
reasoning, which cannot take one step without the aid of general ideas
and propositions, impossible. Light results from the union of one with
the other; separated they afford only an abstract and vague intuition,
or the contemplation of a particular truth, which, limited to a
contracted sphere, can give no knowledge of beings considered under a
scientific aspect.
142. We shall see when we come to treat of ideas, that our mind has
two very distinct classes of them; the one supposes space, and cannot
abstract it, such are all geometrical ideas: the other does not relate
to space, and includes all non-geometrical ideas. These two orders of
ideas are separated by an impassable abyss, if the two orders are not
approximated by a simultaneous use of both. The ideal order is not
complete without this approximation; and the real order of the universe
is turned into a chaos, or rather disappears, if real and ideal truths
are not combined, in both the geometrical and non-geometrical orders.
From all geometrical ideas imaginable, considered in all their ideal
purity, nothing would result for the ideal non-geometrical order, for
the world of material, much less of immaterial realities; and, on the
other hand, from non-geometrical ideas alone we could not get so much
as the idea of a right line. This observation shows that there is for
us in the ideal order no one truth, the origin of all other truths; for
if we take the geometrical order, we are limited to those combinations
which do not go out of it; if the non-geometrical order, we lack the
idea of space, without which we lose even the possibility of conceiving
the corporeal world.(14)