George Frederick James Temple - Sense 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

The concept of 'number' in its most elementary sense as the signless integer appears to be an immediate abstraction from quantitative reality subjected to processes of counting and measurement. Vulgar fractions arise from division of a quantity into equal parts. But in what sense is zero a number? Are there negative numbers? Are there numbers corresponding to incommensurable ratios? Each question requires for its solution a fresh exercise of that kind of creative imagination which we call mathematical abstraction.

George Frederick James Temple