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.
CHAPTER XXIV.
EXISTENCE OF UNIVERSAL REASON
152. General truths have some relation to particular truths; for since they are not a vain illusion, they must of necessity be connected with some object either existing or possible. Whatever exists is particular; not even possible being can be conceived of, if it be not, so to speak, particularized in the regions of possibility. God himself, being by essence, is not a being in abstract, but an infinite reality. In him, the general idea of the plenitude of being, of all perfection, of infinity, is, so to speak, particularized.
General truths would then be vain illusions did they not refer to something particular either existing or possible. Without this relation, cognition would be a purely subjective phenomenon; science would have no object; knowledge would be had, but there would be nothing known.
The appearance of knowing is never offered to us as a purely subjective fact; that is to say, when we think we know, we think we know something either within or without us, according to the matters which occupy us. Supposing, then, the phenomenon of cognition to be purely subjective, and to become objective for itself, we should have what would constantly lead us into error; for the human reason would be
