George Frederick James Temple - Logical Quotes

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Mathematics has also been developed as a philosophy, in the sense in which this term is defined by A. N. Whitehead as 'the endeavor to frame a coherent, logical and necessary system of general ideas in terms of which every element of our experience can be interpreted'. Substitute 'mathematics' for 'experience' and we have an admirable description of its speculative and philosophic development.... Philosophy of mathematics... has its paradoxes and antimonies, and also diverse schools of thought...

George Frederick James Temple
As a science mathematics has been adapted to the description of natural phenomena, and the great practitioners in this field... have never concerned themselves with the logical foundations of mathematics, but have boldly taken a pragmatic view of mathematics as an intellectual machine which works successfully. Description has been verified by further observation, still more strikingly be prediction, and sometimes, more ominously, by control of natural forces. Happily, unresolved problems... still remain as challenges.

George Frederick James Temple
Logical analysis is indispensable for an examination of the strength of a mathematical structure, but it is useless for its conception and design. The great advances in mathematics have not been made by logic but by creative imagination.

George Frederick James Temple