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THE NATURE OF NUMBER, by Joshua C. Gregory, B.Sc, F.I.C. : 

 on an Introduction to Mathematical Philosophy, by Bertrand 

 Russell. [Pp. viii + 208.] (London : George Allen & Unwin ; New- 

 York: The Macmillan Co., 1919. Price 10s. 6d. net.) 



Thomas HOBBES reminded us that, in the opinion of Pythagoras, men are 

 distinguished from other animals by their ability to number and use numbers. 

 Since a writer can select from many distinctions between humans and animals, 

 from wearing collars to puzzling over metaphysics, he intimates his own interests 

 by the distinction he chooses. Pythagoras was desperately interested in numbers, 

 and he made many other philosophers desperately interested in them also. The 

 Pythagorean enthusiasm for numbers must have been very great and very 

 catching for Xenocrates to define the soul as a " number which moves itself.' 

 Xenocrates did not mean that the soul is X-fold, or divisible by other numbers, 

 or in any way specially numerical : he called the soul a number as a lover calls 

 his beloved a rose. The beloved is as fragrant and as beautiful as a rose ; for 

 Xenocrates numbers were so mysterious and wonderful that the word "number" 

 meant for him "the most exalted objects of knowledge," and so appropriately 

 denoted the soul. Aristotle perceived in this apparently absurd definition a 

 legacy to Xenocrates from the ecstasy that led Mr. Bertrand Russell to remark, 

 in his Introduction to Mathematical Philosophy, that Pythagoras "believed that 

 not only mathematics, but everything else could be deduced from numbers." 



This mysteriousness and significance of numbers, amounting to a sense of 

 the ineffable in many mystics, has always haunted the human mind. The 

 Pythagoreans developed the mystic qualities attached to numbers by primitive 

 men, and systematised them into a philosophy and a religion. They discovered 

 also a new source of astonishment and further mystic qualities in the more purely 

 mathematical qualities of numbers. They observed, for example, that 10 is the 

 sum of the first four integers, 1 + 2 + 3 + 4 = 10, and the tetraktys became a 

 celebrated figure because it represented a pyramid with four balls © 



or dots as its, base, three balls or dots as its second tier, two ® ft @ 

 as its third tier, and one at its apex. This arrangement of dots ® ® «> © 

 long remained famous as a "figurate number," representing a pattern after which 

 many natural objects were made. The Pythagorean discovery that the note of a 

 plucked wire alters with its length, so that different notes correspond to distances 

 expressible by numbers, associated numbers with the magic of music and con- 

 firmed their status as the most abstract and most exalted objects of knowledge. 

 Number became a name to denote the inmost essences of things, and we can 

 understand, staggering though the idea may be to the modern mind, why a 

 fundamental Pythagorean doctrine declared that all things were numbers. 



No renascence is only a renascence, just as believers in reincarnation regard 

 the soul as in some sense remade at each birth : the early Greek preoccupation 

 with numbers was no mere repetition of primitive thought. Primitives, says 



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