Kant, Euclid, and the Non-Euclideans

Extract

There are styles in thinking just as there are in dress. Their justification is often as slight, and once a style in thought has been established, it is followed with the same unconscious readiness. The possibility of styles lies, of course, in a lack of fixed criterions. In dress, the choice to a large extent is a matter of taste, and because taste varies from individual to individual and from time to time, styles also change. Although the foundations of science are far more stable than those of taste, they yet have some touch of uncertainty. We live in a relative world, not an absolute one, and thus there is always room for the point of view to shift. We like to feel that we ourselves and the world in general are growing wiser, and thus that while there were errors in the thinking of the past, they are now being rapidly eliminated. The discovery that some philosopher of several thousand years ago held almost our identical views is always disconcerting.