THE PHILOSOPHY OF MATHEMATICS 



By a. N. whitehead, F.RS. 



The most recent work ^ on this subject suffers from the in- 

 determinateness of its aims and also from its neglect of dis- 

 tinctions vital to the subject. In Part I., which is composed 

 of the first three chapters, the interest is chiefly psychological. 

 The relation of Thought to Language and Language as an 

 instrument of Reason are considered. Then this general subject 

 is narrowed to a consideration of the psychology of mathe- 

 maticians, and of the reasons why mathematicians tend to lapse 

 into what the author calls mysticism. But in the rest of the 

 book the psychology gradually fades, and the substantial investi- 

 gation appears to be concerned with the logical correctness 

 of the statements and explanations of various mathematicians, 

 intermingled with the author's own expositions. These two 

 investigations should be kept sharply distinct : logically it is 

 indifferent whether the error of a mathematician be due to 

 mysticism or to indigestion, nor does a medical knowledge of 

 these two diseases help us in determining the truth or falsehood 

 of his statements. But the facile imputation of mysticism, like 

 the invocation of the supernatural to explain events, has, I 

 think, seriously misled the author by preventing him from 

 apprehending the real points which the mathematicians criticised 

 are endeavouring with more or less success to explain. 



In Part II. the concepts of Algebra and of Imaginary Loci 

 in Geometry are considered. Part III. is headed " Metageo- 

 metry " and deals with the principles of Geometry. The book 

 is written from the prevalent standpoint of fifteen years ago, 

 apparently in complete unconsciousness that great discoveries 

 have since been made by which the subject has been revolu- 

 tionised. The author has read Mr. Bertrand Russell's Principles 

 of Mathematics, but has missed the point that the theory of the 

 " variable " is the key which unlocks the whole subject. Indeed, 



' Mysticism in Modern Maihe^natics, by Hastings Berkeley, Oxford University 

 Press, 19:0, pp. xii, 264 ; 8^-. net. 



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