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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.

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!

The intimate connection of mathematical and natural science cannot be questioned; and who shall say to what extent both are connected with ontological, psychological, theological, and moral science? The extended scale over which beings are distributed may at first sight seem to be an assemblage of unconnected objects, but seen with the eyes of science, it is perceived to be a delicately worked chain, whose links present, as we advance, greater beauty and perfection. We see the different realms of nature united by close relations: the sciences, of which they are the objects, mutually borrow each other's light, and enter on each other's territory. The complication of objects among themselves involves this complication of science; and the unity of the laws imposed upon different orders of beings makes all sciences approach, and tend to form, one only science. If it were given us to see the identity of their origin, the unity of the end and the simplicity of the means, we should come into the possession of the true transcendental science, the only science which involves all others, or more correctly speaking, the only idea in which every thing is represented as it is, and every thing seen without any necessity of combination, or effort of any kind, just as a magnificent landscape, its outlines, form, and colors are pictured on a perfectly clear mirror. In the meantime, we must rest satisfied with shadows of reality, and must see in the instinctive tendency of our understanding to simplify, to reduce every thing or make it approach as much as possible to unity, the announcement, the sign of this single science, this intuition of the one infinite idea; just as in the desire for happiness which agitates our heart, the thirst after enjoyment which torments us we discover a proof that all is not ended here below, and that our soul has been created for the possession of a good not to be attained in this mortal life.

51. If we compare men with men, and pay attention to the character of genius, the most elevated point of human intelligence, we shall see the truth of what has been said of the scale of human beings, and the progress of science. Men of true genius are distinguished by the unity and extent of their conceptions. If they treat a difficult and complicated question, they simplify it, consider it from a high point of view, and determine one general idea which sheds light upon all the others. If they have a difficulty to solve, they show the root of the error, and with a word dispel all the illusion of sophistry. If they use synthesis, they first establish the principle which is to serve as its basis, and with one dash trace the road to be followed in order to reach the wished-for result. If they make use of analysis, they strike in its secret resort the point where decomposition is to commence, they at once open the object, and reveal to us its most obscure mysteries. If there is question of a discovery, while others are seeking here and there, they strike the ground with their foot, and exclaim, "the treasure is here." They make no long arguments, nor evasions; their thoughts are few but pregnant; their words are not many, but in each of them is set a pearl of inestimable value.

52. No doubt there is in the intellectual order a single truth from which all other truths emanate, one idea which includes all other ideas. This philosophy teaches, and the efforts, the natural and instinctive tendencies of every intelligence, toiling after simplicity and unity, show it: such also is the dictate of common sense, which considers that thought the highest and most noble which is the most comprehensive and the most simple.(4)