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Theories of Parallelism : an Historical Critique. By William Barrett FranklandM.A. , sometime Fellow of Clare College, Cambridge; Vicar of Wrawby. Pp. xviii + 70. 3s. net. 1910. (Cambridge Univ. Press.)

Published online by Cambridge University Press:  03 November 2016

Philip E. B. Jourdain
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Reviews
Information
The Mathematical Gazette , Volume 5 , Issue 87 , July 1910 , pp. 310 - 311
Copyright
Copyright © Mathematical Association 1910

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References

page 310 note * The “implicit definitions” (or “definitions by postulates”) so frequently used by Hilbert do not, in general, define things, and, though axioms are necessary at the beginning of logic, they have shown themselves to be unnecessary at the beginnings of arithmetic and geometry (cf. Russell, The Principles of Mathematics, Cambridge, 1903, pp. v, 4-5, 11, 429-430; Couturat, Les Principes des Mathématiques, Paris, 1905, pp. 157-159).

page 310 note † Cf. Couturat, Eev. de Métaphys. et de Morale, xiv., 190fi, pp. 210-211.