Another and a better criterion, it is true, is also to be found in Helmholtz, and has also been adopted by Erdmann. Whatever might, by a different experience, have been rendered different--so this criterion contends--must itself be dependent on experience, and so empirical. This criterion seems perfectly sound, but Helmholtz's use of it is usually vitiated by his neglecting to prove the possibility of the different experience in question. He says, for example, that if our experience showed us only bodies which changed their shapes in motion, we should not arrive at the axiom of Congruence, which he pronounces accordingly to be empirical. But I shall endeavour to prove, in Chapter III., that without the axiom of Congruence, experience of spatial magnitude would be impossible. If my proof be correct, it follows that no experience can ever reveal spatial magnitudes which contradict this axiom--a possibility which Helmholtz nowhere discusses, in setting up his hypothetical experience. Thus this second criterion, though perfectly sound, requires always an accompanying transcendental argument, as to the conditions of possible experience. But this accompaniment is seldom to be found in Helmholtz. =68.= One of the few cases, in which Helmholtz has attempted such an accompaniment, occurs in connection with our second point, the imaginability of non-Euclidean spaces. The argument on this point was elicited by Helmholtz's Kantian opponents, who maintained that the merely logical possibility of these spaces was irrelevant, since the basis of Geometry was not logic, but intuition. The axioms, they said, are synthetic propositions, and their contraries are, therefore, not self-contradictory; they are nevertheless apodeictic propositions, since no other _intuition_ than the Euclidean is possible to us[87]. I have already criticized this line of argument in the beginning of the present chapter. Helmholtz's criticism, however, was different: admitting the internal consistency of the argument, he denied one of its premisses. We _can_ imagine non-Euclidean spaces, he said, though their unfamiliarity makes this difficult. From this view it followed, of course, that Kant's argument, even if it were formally valid, could not prove the apriority of Euclidean space in particular, but only of that general space which included Euclid and non-Euclid alike[88].