stars, and teaches him how to make use of a ray of light to discover the nature of those distant substances, and to make sure that they are the same in the celestial bodies as they are in the terrestrial globe, which is also celestial in its turn.
It is not satisfied with overcoming the obstacle of distance, which seems to be insurmountable. If to economize time is the most effective way of enriching men and states, physics has the best right to aspire to the glory of being the peerless servant of all administrations, both of public and private affairs. The physiologist also has physics to thank for giving him the means, through the decomposition of light, of perceiving in an instant whether the coloring-matter of the blood is more or less oxidized, while chemical analysis can make it clear only after long and difficult experiments.
But, while different sciences assist one another by reciprocally facilitating, checking, and perfecting each other's work, there is one that has a superior part, at once foundation and summit, elementary and transcendent. This science is the base of all the others, and distributes to the most positive of its sisters crowns, the precious stones of which are touchstones. All of my learned hearers will divine that I am speaking of mathematics, the Dutch name of which (Wiskunde) signifies the science of the certain, the positive science, absolutely science. This science guides our first steps in the highway of thought; it is so blended with the premises of every deduction, that its truths, accepted by the ages, seem to have imposed themselves as axioms, or theses a priori innate to the faculty which we call intelligence, and thereby independent of all demonstration. Now, this hypothesis, widely prevailing as it may be (and it is as universal as the belief that the sun rises), the psychologist shows to be erroneous.[1]
The possibility even of error proves the initiative which we take in the formation of these axioms. They are merely the summary of our first and quite simple observations—a summary which has taken the mathematical form, and seems, under that form, to approach the absolute. It is mathematics which, in all the sciences of observation, conducts to the most precise conclu-
- ↑ Moleschott says, in his "Der Kreislauf des Lebens": "We yet teach children that they can reach the highest summits of thought, without any aid from the senses, by starting from certain premises which they have brought with them at birth as an integral part of their intellect, and for the knowledge of which they have only to appeal to their memory. The mathematician calls these premises axioms, and he persuades children as well as men, when he submits them to them, as, for instance, that the whole is greater than a part, and that the whole is equal to the sum of its parts. And yet no child knows it until he has seen, say a hundred times, that an apple disappears when it is cut into four pieces and these pieces are divided among four persons." See also Helmholtz, "Ueber den Ursprung und die Bedeutung der geometrlschen Axiome" ("On the Origin and Signification of the Geometrical Axioms").
