Let us then content ourselves with a more humble and more material philosophy; and by keeping within the sphere Nature has allotted us, let us examine the rash steps and the rapid flight of those who attempt to soar beyond it. All this Pythagorean philosophy, which is purely intellectual, turns entirely on two principles, one of which is false and the other precarious: those are, the real power of abstraction, and the actual existence of final causes. To take numbers for real beings; to say that unity is a general individual, which not only represents every individual, but even communicates existence to them; to pretend that unity has the actual power to engender another unity nearly similar to itself, and constituting two individuals, two sides of a triangle, which can have no bound or perfection without a third side, or by a third individual, which they necessarily engender. To regard numbers, geometrical lines, and metaphysical abstractions, as efficient and real physical causes, on which the formation of the elements, the generation of animals and plants, and all the phenomena of Nature depend, seems to me to be the most absurd abuse of reason, and the greatest obstacle that can be put against the advancement of our knowledge. Besides, what can be more false than such suppositions? Admitting, with Plato and Malebranche, that matter does not exist, that external objects are only ideal images of the creative faculty, and that we perceive every thing in the Deity, must it be concluded from thence that our ideas should be of the same order as those of the Creator, or that they can produce existences? Are not we dependent on our sensations? Whether the objects that cause them are real or not; whether this cause of our sensations exists outwardly or inwardly; whether it be the Creator or matter we perceive, what does it signify to us? Are we less certain of being always affected in the same manner by the same causes? Have not our sensations an invariable order of existence, and a necessary relation between them and the objects? This, therefore, is what must constitute the principles of our philosophy; and what has no relation with it is vain, useless, and false in the application. Can a triangular harmony form the substance of the elements? Is fire, as Plato affirms, an acute triangle, and light and heat properties of this triangle? Air and water, are they rectangular and equilateral triangles? Is the form of the terrestrial element a square, because, being the least perfect of all the four elements, it recedes as much as possible from a triangle without losing its essence? Do the male and female embrace only to complete the triangle of generation? These platonic ideas have two very different aspects. In speculation they seem to flow from noble and sublime principles, but in application nothing but false and puerile consequences can be drawn from them.