III. Dimensions in space and time.

Before entering upon them we must repeat that the question of number

and series in mathematics is independent of the assumptions of space

and time. As a science, mathematics could exist outside them: order

is not necessarily spatial or temporal. Our conclusions, therefore,

cannot be attacked on the ground that they are based on Euclidean

conceptions of space: they are based on the laws of logic.

On the theory of the infinite in modern thought · 第 17 / 22 题