Note 2 — ON THE ORIGIN AND SIGNIFICANCE OF GEOMETRICAL AXIOMS.

In his book, On the Limits of Philosophy, Mr. W. Tobias maintains that axioms of a kind which I formerly enunciated are a misunderstanding of Kant’s opinion. But Kant specially adduces the axioms, that the straight line is the shortest (Kritik der reinen Vernunft, Introduction, v. 2nd ed. p. 16); that space has three dimensions (Ibid. part i. sect. i. § 3, p. 41); that only one straight line is possible between two points (Ibid. part ii. sect. i. ‘On the Axioms of Intuition’), as axioms which express a priori the conditions of intuition by the senses. It is not here the question, whether these axioms were originally given as intuition of space, or whether they are only the starting-points from which the understanding can develop such axioms a priori on which my critic insists.