The argument, so stated, is undeniably plausible. Nevertheless, examination of it reveals two fatal defects. In the first place, its starting-point is false. To Kant the paradox of geometrical judgements lies in the fact that they are not based upon an appeal to experience of the things to which they relate. It is implied, therefore, that judgements which are based on experience involve no paradox, and for the reason that in experience we apprehend things as they are.[48] In contrast with this, it is implied that in geometrical judgements the connexion which we apprehend is not real, i. e. does not relate to things as they are. Otherwise, there would be no difficulty; if in geometry we apprehended rules of connexion relating to things as they are, we could allow without difficulty that the things must conform to them. No such distinction, however, can be drawn between _a priori_ and empirical judgements. For the necessity of connexion, e. g. between being a three-sided figure and being a three-angled figure, is as much a characteristic of things as the empirically-observed shape of an individual body, e. g. a table. Geometrical judgements, therefore, cannot be distinguished from empirical judgements on the ground that in the former the mind remains within itself, and does not immediately apprehend fact or a real characteristic of reality.[49] Moreover, since in a geometrical judgement we do in fact think that we are apprehending a real connexion, i. e. a connexion which applies to things and to things as they are in themselves, to question the reality of the connexion is to question the validity of thinking altogether, and to do this is implicitly to question the validity of our thought about the nature of our own mind, as well as the validity of our thought about things independent of the mind. Yet Kant's argument, in the form in which it has just been stated, presupposes that our thought is valid at any rate when it is concerned with our perceptions of things, even if it is not valid when concerned with the things as they are in themselves. [48] Cf. p. 17. [49] For the reasons which led Kant to draw this distinction between empirical and _a priori_ judgements, cf. pp. 21-2.