AND ON LOGIC IN GENERAL. 175 



Of the two philosophers who might have made the distinction of form and matter exercise 

 a strong influence over their systems, Aristotle did it, and Plato did not. Plato's writings do 

 not convince any mathematician that their author was strongly addicted to geometry ; they 

 shew at most that he may have been well versed in it : I have no objection to say that geo- 

 metry helped him in his colouring. We know that he encouraged mathematics, that his 

 followers form a school, and that the reputation of the school has given the character of a 

 geometer to the founder. But if — which nobody believes — the /uj/^e/sr dyew/jieTptjTo^ e'lcriTw 

 of Tzetzes had been written over his gate, it would no more have indicated the geometry 

 within than a warning not to forget to bring a packet of sandwiches would now give promise 

 of a good dinner. But Aristotle was a mathematician, versed in that science and addicted to 

 it : geometry aided him in the tracing of his outline. This appears throughout his writings, 

 even after rejection of those which are doubtful, some of which, supposing him to be only a 

 putative father, show that a very positive mathematical character was assigned to him by his 

 successors. To him we owe such perpetual indication of the distinction of form and matter 

 that many, including some who should have known better, have assigned the form of thought 

 to him as his definition of logic, giving him the word into the bargain. But the definition was 

 never distinctly conceived in that character until the last century, when it was propounded by 

 a philosopher whose earliest studies had been in mathematics, which be had taught in conjunc- 

 tion with logic for fifteen years before he gave himself up to the study of the pure reason. If, 

 between Kant* and Aristotle, there were one leader of philosophical opinion who more nearly 

 than another caught the conception, it was the mathematician Leibnitz. And the history of 

 man in species analogises with what we have seen of man in individuals : we trace our mathe- 

 matics to the Greeks and the Hindoos, the two independent cultivators of systems of logic in 

 which form is investigated for its own sake, though the separation is indistinctly conceived by 

 both. Of the Romans, we only know that they originated nothing, either in mathematics or in 

 logic : and it is just worth notice here that Boethius, the only Roman who gave us a summary 

 of Aristotle, was the only Roman who gave us a summary of Euclid. 



The separation of mathematics and logic which has gradually arrived in modern times has 

 been accompanied, as separations between near relations generally are, with a good deal of 

 adverse feeling. Great names in each have writtenj- and spoken contemptuously of the other; 

 while those who have attended to both are aware that they have a joint as well as a separate 

 value. This alienation of the two sciences has furnished two magazines to those who would 

 put down all education except that which immediately conduces to production of wealth : in 



• It is only of late years that, in this country at least, Kant's ! distinction.' 



definition has been clearly apprehended, and its trutli sincerely 

 felt. If the inquirer will look out for English works preceding 

 1848, or thereabouts, which state Kant's definition as an exist- 

 ing thing, not to speak of adopting it, he will have some diffi- 

 culty in finding one. In some old notes of my own, made after 

 comparison of Aristotle, some of the mediasvals, and Kant, I 

 find the following sentence : " I should say [of formal and 

 material] that the great leader saw the distinction, that the 

 .schoolmen made the distinction, and that Kant built upon the 



t There is no occasion to refer to any of the ordinary exhi- 

 bitions, whether dissertations in favour of ignorance, or orations 

 in contempt of knowledge. But there is one which deserves 

 preservation for its humour, and which may be lost with an 

 ephemeral pamphlet, if not elsewhere recorded. An Oxford 

 M.A. writing on education, about ten years ago, advocated 

 some pursuit of mathematics : for, said he, man is an arith- 

 metical, geometrical, and mechanical animal, as well as a ratio- 

 nal soul. 



