OF THE NECESSITY INVOLVED IN IDEAS.
144. In all ideas, even in those that relate to contingent facts, there
is something of the necessary, something from which science may spring,
but something which cannot emanate from experience, however multiplied
we suppose it. Every induction resulting from experience is confined to
a limited number of facts,--a number, which, even if augmented by all
the experience of all men of all ages, would still remain infinitely
below universality, which extends to all that is possible.
Moreover, however little we reflect upon the certainty of the truths
intimately connected with experience, such as are arithmetical and
geometrical truths, we cannot fail to perceive that the confidence with
which we build upon them is not founded upon induction, but that we
assent to them independently of any particular fact, and consider their
truth as absolutely necessary, although we cannot verify it by the
touchstone of experience.
145. The verification of ideas by facts is in many cases impossible,
because the weakness of our perception and of our senses, and the
coarseness of the instruments we use, fail to render us certain that
the facts correspond exactly to the ideas. It is sometimes absolutely
impossible to establish this proof, since geometrical truth supposes
conditions such as cannot be realized in practice.
146. Let us apply these observations to the simplest truths of
geometry. Certainly no one will doubt the solidity of the proof called
superposition: that is to say, if one of two lines, or surfaces, be
placed upon the other, and they exactly correspond, they will be equal.
This truth cannot depend upon experience: first, because experience
is limited to a certain number of cases, whereas the proposition
is general. To say that one serves for all is to say that there
is a general principal, independent of experience, since, without
recognizing an intrinsic necessity in this truth, the universal could
in no other way be deduced from the particular. Secondly, because even
where experience avails, it is impossible for us to make it exact,
since superposition made in the most delicate manner imaginable, can
never attain to geometrical exactness, which repudiates the minutest
difference in any point.
It is an elementary theorem, that the three angles of a triangle are
equal to two right angles. This truth does not rest upon experience:
first, because the universal cannot be deduced from the particular;
secondly, because, however delicate be the instruments for measuring
angles, they cannot measure them with geometrical exactness; thirdly,
because geometry supposes conditions which we cannot realize in
practice; lines have no thickness, and the vertices of angles are
indivisible points.
147. If general principles depended upon experience they would cease
to be general, and would be limited to a certain number of cases.
Neither would their enunciation be absolute, even for the cases
already observed; for it would of necessity be reduced to what had
been observed, that is to say, to a little more or less, but never be
perfect exactness. Consequently we could not assert that the three
angles of every triangle are equal to two right angles; all that
we could say would be, that so far as our experience goes, we have
observed that in all triangles the three angles are very nearly equal
to two right angles.
This would obviously destroy all necessary truths; and even
mathematical truths would be no more certain than the reports of adepts
in any profession who recount to us their observations concerning their
respective objects.
148. There can be no science without necessary truths; and even the
cognition of contingent truths would become exceedingly difficult
without them. How do we collect the facts furnished by observation, and
adjust them? Is it not by applying certain general truths to them, as,
for example, those of numeration? Otherwise we could have no perfect
confidence in them, nor in the results of observation.
149. Human reason cannot live, if it abandon this treasure of necessary
truths which constitute its common patrimony. Individual reason could
take no more than a few short steps, overwhelmed as it constantly
would be with the mass of observations; distracted unceasingly by the
verifications to which it would always have to recur; in want of some
light to serve for all objects; and prohibited ever from simplifying,
by uniting the rays of science in a common centre.
General reason would also cease to be, and men would no longer
understand each other: every one would be confined to his own
experience: and since there would be in the experiences of all men,
nothing necessary, nothing to connect them, there would be no unity
in them all together: all the sciences would be a field of confusion,
to which all restoration of order would be utterly impossible. No
language could have been formed; or even if formed could be preserved.
We meet in the simplest enunciations of language, as well as in the
complication of a long discourse, an abundance of general and necessary
truths, which serve as the woof for the weaving-in of contingent truths.
150. To inquire, therefore, if there are necessary truths, is to
inquire, if individual, if general reason exists; if what we call
reason, and discover in all men, really exists, or is but a fantastical
illusion. This reason does exist: to deny it is to deny ourselves: not
to wish to admit it, is to reject the testimony of our consciousness,
which assures us that it is in the depth of our soul; it is to make
impotent efforts to destroy a conviction irresistibly imposed by nature.
151. And here I would remark that this community of reason among all
men of all ages and of all climes; this admirable unity, discoverable
in the midst of so much variety; this fundamental accord which neither
the diversity nor the contradiction of views can destroy, evidently
proves that all human souls have one common origin; that thought is not
a work of chance; that, besides human intelligences, there is another
which serves as their support, illuminates them, and has, from the
first moment of their existence, endowed them with all the faculties
needed to perceive, and to know what they perceived. The admirable
order which reigns throughout the material world, the concert, the
unity of plan discoverable in it, are not a more conclusive proof of
the existence of God, than are the order, the concert, the unity,
offered by reason in its assent to necessary truths.
For our own part, we ingenuously confess, that we can discover no more
solid, more conclusive, or more clear proof of the existence of God,
than that deduced from the world of intelligences. Beyond this it has
another advantage, which is, that it takes for its point of departure
the act most immediate to us, the consciousness of our own acts. It is
true, the proof best adapted to the capacity of ordinary men, is the
one founded on the admirable order reigning over the corporeal world:
but this is because they are unaccustomed to meditate upon insensible
objects, upon what passes within themselves; wherefore it is that they
abound more in direct cognitions than in power of reflection.
The atheist asks how we can be certain of the existence of God, and
demands an apparition of the divinity: very well, this apparition
exists, not without, but within us: and although it may be pardonable
for men of little reflection not to perceive it, most certainly it
is not pardonable for those who pretend to be adepts in metaphysical
science, not even to endeavor to discover it. The system of
Malebranche, which makes men see every thing in God, cannot be
sustained, but it shows a very profound thinker.