32. If any part of science ought to be regarded as purely speculative, it is undoubtedly the part which concerns certainty; and this proposition, paradoxical as it may seem at first sight, is true, and can be easily demonstrated.
33. What does philosophy here propose to do? To produce certainty? But it exists independently of all philosophical systems, and mankind were certain of many things before ever any one thought of such questions. Moreover, since the question was first raised, few, compared with the whole human race, have examined it; so it is now, and so it will be; and all the theories invented on this point can have no effect upon the fact of certainty. What has been said of its production may be said of the attempt to consolidate it. When have the generality of men had, or when will they have, time and opportunity to examine these questions?
34. Philosophy could here have produced nothing but skepticism, for the variety and opposition of systems were more calculated to create than to dissipate doubts. Happily nature is the most invincible opponent of skepticism; the sage's dreams pass not from his library to the every day uses of the life of ordinary men, or even of those who labor under or imagine them.
35. Philosophy here can propose to itself no more reasonable object than simply to examine the foundations of certainty, with the sole view of more thoroughly knowing the human mind, not of making any change in practice; just as astronomers observe the course of the stars, investigate and determine the laws to which they are subject, without therefore presuming to be able to modify them.
36. But even this supposition places philosophy in a very unsatisfactory position; for if we recollect what we have already established, we shall see that science observes a real and true phenomenon, but gives it a gratuitous explanation, by making an imaginary analysis of it.
Experience has in fact shown our understanding to be guided by no one of the considerations made by philosophers; its assent, when it is accompanied by the greatest certainty, is a spontaneous product of a natural instinct, not of combinations; it is a firm adhesion exacted by the evidence of the truth, the power of the internal sense, or the impulse of instinct; not a conviction produced by a series of ratiocinations. These combinations and ratiocinations therefore exist only in the mind of philosophers, not in reality; when, therefore, they attempt to designate the foundations of certainty, we are told what could or should have been, but not what is.
If philosophers would only be guided by their own systems, and would not forget them nor set them aside as soon as, or even before, they have finished explaining them, it might be said, that even if no reason can be given for human certainty, one can be given for philosophical certainty; but since these same philosophers make no use of these scientific means save when developing them ex professo, it follows that their pretended foundations are a mere theory, having little or no connection with the reality.
37. This demonstration of the vanity of philosophical systems relating to the foundation of certainty, far from leading to skepticism, has a directly contrary tendency; for it makes us appreciate at their true value, the emptiness of our cavils, compares their impotence with the irresistible force of nature, and thus destroys that foolish pride which would make us superior to the laws imposed upon our understanding by the Creator himself; it places us in the channel through which the torrent of humanity has for ages run; and it disposes us to receive with sound philosophy what the laws of our nature force us to accept.(3)
CHAPTER IV.
EXISTENCE OF TRANSCENDENTAL SCIENCE IN THE ABSOLUTE INTELLECTUAL ORDER
38. Philosophers have sought a first principle of human knowledge; each has assigned his own, and now after so much discussion it is doubtful who is right, or even if any one is right.
Before inquiring what the first principle is, they ought to have ascertained whether there be any such principle. We cannot suppose this last question to be answered affirmatively; for it is, as we shall hereafter see, susceptible of different solutions, according to the aspect under which it is seen.
The first principle of knowledge may be understood in either of two senses; as denoting one first truth from which all others flow, or as expressing a truth which we must suppose if we would not have all other truths disappear. In the former sense it is a spring from which the waters flow, which fertilize the intellect; in the second sense it is a point whereon to rest a great weight.
39. Is there any one truth from which all others flow? There is in reality, in the order of beings, in the universal intellectual order; but in the human intellectual order there is none.
40. There is in the order of beings one truth, the origin of all truths; for truth is reality, and there is one Being, author of all beings. This being is a truth, truth itself, the plenitude of truth, for he is being by essence, the plenitude of being.
Every school of philosophy has in some sense recognized this unity of origin. The atheist talks of the force of nature; the pantheist of an only substance, of the absolute, of the unconditioned; both have abandoned the idea of God, and now labour to replace it by something which may be made the origin of the existence of the universe, and of the development of its phenomena.
41. There is in the universal intellectual order one truth from which all others flow; it is, that the unity of origin of all truths is not only found in realized truths, that is, in beings considered in themselves, but likewise in the concatenation of ideas representing these beings. And thus if our understanding could ascend to the knowledge of all truths, and embrace them in their unity and in all the relations uniting them, it would see them after arriving at a certain height, notwithstanding their dispersion and divergence as now perceived by us, converge to a centre, in which they unite, like rays of light in the luminous object from which they issued.
42. The most profound philosophical doctrines often appear in the treatises of theologians explaining the doctrines of the church. Thus St. Thomas, in his questions on the understanding of angels, and in other parts of his works, has left us a very luminous and interesting theory. According to him, spirits understand by a number of ideas smaller in proportion to the superiority of their order; and so the diminution goes on even to God, who understands by means of a single idea which is his own essence. And thus according to the holy doctor, not only is there one being, author of all beings, but also one infinite idea which includes all ideas. Whoever fully possesses this idea will see every thing in it; but since this full possession, called comprehension in theology, is solely a property of the infinite intelligence of God, creatures, when in the other life they shall have obtained the beatific vision, will see more or fewer objects in God according to the greater or less perfection in which they possess it. How wonderful! The dogma of beatific vision well understood, is also a truth which sheds much light upon philosophical theories. Malebranche's sublime dream about ideas was, perhaps, a reminiscence of his theological studies.
43. The transcendental science which embraces and explains them all, is a chimera to our mind so long as we inhabit this earth, but it is a reality to other spirits of a higher order, and it will also be so to us when, freed from this mortal body, we attain the regions of light.
44. So far as we may conjecture from analogy, we have proofs of the existence of this transcendental science, which includes all sciences, and is in its turn contained in one sole principle, or rather, in one only idea, in one only intuition. If we observe the scale of beings, the grades of distinction between individual intelligences, and the successive progress of science, the image of this truth will be presented to us in a very striking manner.
44. So far as we may conjecture from analogy, we have proofs of the existence of this transcendental science, which includes all sciences, and is in its turn contained in one sole principle, or rather, in one only idea, in one only intuition. If we observe the scale of beings, the grades of distinction between individual intelligences, and the successive progress of science, the image of this truth will be presented to us in a very striking manner.
One of the distinctive characteristics of our mind is its power of generalization, of perceiving the common in the various, of reducing the multiplex to unity; and this power is proportional to its degree of intelligence.
45. The brute is limited to its sensations and the objects causing them. It has no power of generalization or of classification; nothing beyond the impression received or the instinct of satisfying its wants. Man, however, as soon as he opens the eyes of his understanding, perceives unnumbered relations; he applies what he has seen in one case to different cases; he generalizes and infolds very many ideas in a single idea. The child desires an object above his reach; he immediately takes a chair or a stool, and improvises a ladder. A brute will watch the object of its appetite whole hours when placed beyond its reach, without ever thinking of doing like the child, and forming a ladder. If every thing be so disposed as to enable it to climb, it will climb, but it is incapable of thinking that in similar circumstances it ought to act in like manner. In the former case, we see a being having the general idea of a means, and its relation to the end, of which it makes use when necessary: in the latter we see another being having indeed before its eyes the end and the means, but not perceiving their relation, unable to go beyond the material individuality of objects.
In the former there is perception of unity; in the latter there is no bond to join the variety of particular facts.
It is seen by this simple example that the child will reduce all the infinity of cases, in which an object may be placed beyond his reach, to this one case; he possesses, so to speak, the formula of this little problem. True, he does not render himself an account of this formula, that is, does not reflect upon it; but he has it in reality; and if you give him an opportunity he will at once apply it, which proves that he has it. Or speak to him of things placed too high for his reach, and point rapidly from one to another of the objects before him; he will at all times instantly apply the general idea of an auxiliary medium; he will avail himself perhaps of his father's arm, or that of a servant, a chair, if in the house, a heap of stones, if in the fields; he discovers in all things the relation of the means to the end. When he sees the end, he immediately turns his attention to the means of attaining it: the general idea seeks individualization in a particular case.
46. Art is the collection of rules for doing any thing well; and is the more perfect in proportion as each rule embraces a greater number of cases, and consequently as the number of these rules is smaller. Doubtless, buildings that were solid, well proportioned, and adapted to the purpose for which they were destined, had been constructed before the rules of architecture were reduced to formulas; but the great progress of intelligence in the construction of buildings consisted in ascertaining what there was common to all well-built houses, in determining the cause of beauty and of solidity, in themselves considered, by passing from the individual to the universal, that is, by forming general ideas of beauty and solidity applicable to an indefinite number of particular cases, by simplifying.
47. The same may be said of all other liberal and mechanical arts: the progress of intelligence in all of them consists in reducing multiplicity to unity, and including the greatest possible number of applications in the least possible number of ideas. This is why lovers of literature and the fine arts labor to discover an idea of beauty in general, in order to attain a type applicable to all literary and artistic objects. It is also obvious that those engaged in mechanical arts always endeavor to govern their proceedings by a few rules, and he is held to be the most skilful who succeeds in combining the greatest variety of results with the greatest simplicity of means, by making that, which others connect with many ideas, depend upon one idea alone. When we see a machine produce wonderful effects by a very simple process, we praise the artificer not less for the means than for the end: this we say, is grand, and the simplicity with which it works is the most astonishing.
48. Let us apply this doctrine to the natural and exact sciences.
The merit of our actual system of numeration consists in including the expression of all numbers in a single idea, making the value of each figure ten times that to the right, and filling all intervals with zeros. The expression of infinite numbers is reduced to the simplicity of a single rule based upon a single idea; the relation of position with a tenfold value. Logarithms have enabled arithmetic to make a great advance by diminishing the number of its fundamental operations, since, with them it reduces multiplication and division to addition and subtraction. Algebra is only the generalization of arithmetical expressions and operations, their simplification. The application of algebra to geometry is the generalization of geometrical expressions; formulas of lines, figures, bodies, only the expression of their universal idea. In this idea as in a type, geometry preserves its first and generative idea, and it requires only the simplest applications in order to form an exact calculation of all lines belonging to the same class, which can possibly be met with in practice. In the simple expression dz/dx = A, called the differential coefficient, is contained the whole idea of infinitesimal calculus. It originated in geometrical considerations, but so soon as its universality was conceived, it poured a flood of light upon every branch of mathematical and natural science, and led to the discovery of a new world, whose confines are still unknown. The prodigious fecundity of this calculus emanates from its simplicity, its prompt generalization of both algebra and geometry, and its uniting them in a single point which is the relation of the limits of the differentials of any function.
49. It is to this unity of idea that the human intellect in its ambition aspires, and once obtained, it proves the cause of great progress. The glory of the greatest geniuses is that they discovered it: the advance of science has consisted in profiting by it. Vieta explained and applied the principle of the general expression of arithmetical quantities; Descartes extended this to geometrical quantities. Newton established the principle of universal gravitation; and he, at the same time with Leibnitz, invented the infinitesimal calculus; and the exact and natural sciences march, by the light of a vast flambeau, with gigantic strides along paths never before trodden. And all this because intelligence has approached unity, and become possessed of a generative idea, involving infinite other ideas.
50. It is worthy of remark, that as we advance in science, we meet numerous points of contact, close relations, which no one at first sight would have suspected. Ancient mathematicians discussed the conic sections, but were far from imagining that the idea of the ellipse could be the basis of a system of astronomy: the foci to them were simple points, the curve a line, and the relations of both the object of combinations at once profitless and without application. Ages pass away, and these foci are the sun, the curve the orbit of planets. The lines on the geometrician's table represented a world!