142. The will, although an inseparable companion of the understanding, and even necessary to its existence, is nevertheless a very different faculty from it; for the will offers to our intuition a series of phenomena very unlike the phenomena of the understanding. To understand is not to will; a thing may be known, and yet not willed. One and the same act of the understanding may unite at various times, or in diverse subjects, very different if not contradictory acts of the will; to will and to not will; or inclination and aversion.
The cognition of that series of phenomena called acts of the will, is not a general but a particular, not an abstract but an intuitive, cognition. What necessity is there of abstraction or discursion to ascertain what we will or do not will, what we love or what we abhor? This cognition is intuitive, so far as the acts of our own will are concerned; and although we have no immediate intuition of what the will of others is, we know perfectly well what passes in them, from seeing it in some degree manifested by what we ourselves experience. When we hear the acts of another's will spoken of, have we, by chance, any difficulty in conceiving the object in question? Are we obliged to proceed discursively by abstract ideas? Certainly not! The same occurs in others as in ourselves. When they will, or do not will, they experience just what we ourselves experience when we will or do not will. The consciousness of our will is the image of all others existing or possible. We conceive that will to be more or less perfect, which unites in a higher or lower degree the actual or possible perfections of our own: and if we would conceive a will of infinite perfection, we must elevate to an infinite degree the actual or possible perfection which we discover in the finite will.
143. When the Sacred Text tells us that man is created to the image and likeness of God, it teaches us a truth highly luminous, whether considered in a purely philosophical or in a supernatural aspect. We discover in our soul, in this image of infinite intelligence, not only a multitude of general ideas which carry us beyond the limits of sensibility, but also an admirable representation wherein we contemplate, as in a mirror, every thing that passes in that infinite sea which cannot be known by immediate intuition so long as we remain in this life. This representation is imperfect, is enigmatical; but it is a true representation: in its minutest particles, infinitely increased, we may contemplate the infinite; its feeblest brilliance reflects back to us the splendor of infinity. The slight spark struck from the flint may lead the imagination to that ocean of fire, discovered by astronomers in the orb of day.
CHAPTER XXIII.
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