MATHEMATICS AND THE 

 METAPHYSICIANS 



npHE nineteenth century, which prided itself upon 

 ^ the invention of steam and evolution, might have 

 derived a more legitimate title to fame from the discovery 

 of pure mathematics. This science, like most others, 

 \vas baptised long before it was born ; and thus we find 

 writers before the nineteenth century alluding to what 

 they called pure mathematics. But if they had been 

 asked what this subject was, they would only have been 

 able to say that it consisted of Arithmetic, Algebra, 

 Geometry, and so on. As to what these studies had in 

 common, and as to what distinguished them from applied 

 mathematics, our ancestors were completely in the dark. 

 Pure mathematics was discovered by Boole, in a work 

 which he called the Laws of Thought {1854). This work 

 abounds in asseverations that it is not mathematical, 

 the fact being that Boole was too modest to suppose his 

 book the first ever written on mathematics. He was also 

 mistaken in supposing that he was dealing with the laws 

 of thought : the question how people actually think was 

 quite irrelevant to him, and if his book had really con- 

 tained the laws of thought, it was curious that no one 

 should ever have thought in such a way before. His 

 book was in fact concerned with formal logic, and this 

 is the same thing as mathematics. 



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