Lectures On the Philosophy of Mathematics

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Its equations in finite form are the well-known equations for transforming to new rectangular axes. In other words, those properties of figures that do not depend upon a choice of axes are the ones with which Euclid is concerned.
However, we can scarcely agree that the notion of group had ever emerged into human consciousness and had become so familiar that it was ignored. The Greek, of course, observed that handling figures of material objects and moving them around did not disturb their size
...and shape, but the observation brought no intellectual response from him, any more than it did from a beaver who carried his logs of wood around, or from a bird who placed twigs in a nest. It took several centuries for the race to develop to the point where it could conceive experience as other than it is. Until this happened, the notion of group could not have existed. Such notions are simply not existent at all rather than stored up in an inherited mental storehouse.
We may loose our fancy again and suppose the school of Euclid of Alexandria discussing the question as to what operators and Reduction to Algorithms 89 right they had to move their figures around and to super- pose them on each other.


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