THE UNITY OF SCIENCE. 523 



stars, and teaches him how to make use of a ray of light to dis- 

 cover 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 physi- 

 ologist 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, ele- 

 mentary 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 in- 

 nate to the faculty which we call intelligence, and thereby inde- 

 pendent of all demonstration. Now, this hypothesis, widely pre- 

 vailing as it may be (and it is as universal as the belief that the 

 sun rises), the psychologist shows to be erroneous.* 



The possibility even of error proves the initiative which we 

 take in the formation of these axioms. They are merely the sum- 

 mary 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 Lcbcns" : "Wc 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 appenl 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 Ilelmholtz, " iJeber den Ursprung 

 und die Bedeutung der geometrlschen Axiome " (" On the Origin and Signification of the 

 Geometrical Axioms "). 



