Note 149 — Introductory material

There remain, however, a few objections and difficulties to be discussed. First, how do we obtain equality in solids, and in Kant's cases of right and left hands, or of right and left-handed screws, where actual superposition is impossible? Secondly, how can we take congruence as the only possible basis of spatial measurement, when we have before us the case of time, where no such thing as congruence is conceivable? Thirdly, it might be urged that we can immediately estimate spatial equality by the eye, with more or less accuracy, and thus have a measure independent of congruence. Fourthly, how is metrical Geometry possible on non-congruent surfaces, if congruence be the basis of spatial measurement? I will discuss these objections successively.