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Herbert Spencer 145 



would be many shorter lines between the same two points 

 if there were two poles. Moreover, he tells us, such beings 

 * would not be able to form the notion of parallel geodetical 

 hues, because every pair of their geodetical Hues, when 

 sufficiently prolonged, would intersect in two points,' etc. 

 This passage is not only interesting as demonstrating our 

 power of transcending experience by conception, but even 

 more so as the solemn enunciation of a transparent fallacy 

 by a man of eminence. Professor Helmholtz concludes : — 

 'We may resume the results of these investigations by 

 saying that the axioms on which our geometrical system is 

 based are no necessary truths.' And Professor Clifford 1 cites 

 with approval the article here quoted, and adopts its con- 

 clusions. Nevertheless the fallacy is surely transparent. 

 Unless geometrical axioms were necessary truths, it would 

 be impossible for these professors to declare what would or 

 would not be the necessary results attending such imaginary 

 conditions. And ' other systems ' could not, as Professor 

 Helmholtz admits 2 they may, ' be developed analytically 

 with perfect logical consistency.' If such beings as are 

 supposed, called the lines referred to ' straight,' they would 

 mean by that word what we should call 'arcs of great 

 circles.' Whether such beings could conceive of parallel lines 

 or not, there is no evidence to show, but there is no shadow of 

 foundation for asserting that, if they covM conceive of them, 

 they would not perceive the impossibility of their ever meet- 

 ing, as we can perceive the necessary relations of their 

 supposed space conditions which, by the hypothesis, are not 

 ours. 



Our author, as we have seen, deems it absolutely incon- 

 ceivable that an unextended object can offer resistance or 

 exercise pressure. Nevertheless Mr. Spencer himself is able 

 to conceive ' body ' as really apart from extension, and in 



1 Macmillan's Magazine, Oct. 1872, p. 504. 2 The Academy, vol. i. p. 130. 

 VOL. II. K 



