=181.= I have already indicated, in general terms, the ground for regarding as _à priori_ the properties of any form of externality. This ground is transcendental, _i.e._ it is to be found in the conditions required for the possibility of experience. The form of externality, like Riemann's manifolds, is a general class-conception, including time as well as Euclidean and non-Euclidean spaces. It is not motived, however, like the manifolds, by a _quantitative_ resemblance to space, but by the fact that it fulfils, if it has more than one dimension, all those functions which, in our actual world, are fulfilled by space. But a form of externality, in order to accomplish this, must be, not a mere conception, but an actually experienced intuition. Hence the conception of such a form is the general _conception_, containing under it every logically possible _intuition_ which can fulfil the function actually fulfilled by space. And this function is, to render possible experience of diverse but interrelated things. Some form in sense-perception, then, whose conception is included under our form of externality, is _à priori_ necessary to experience of diversity in relation, and without experience of this, we should, as modern logic shows, have no experience at all. This still leaves untouched the relation of the _à priori_ to the subjective: the form of externality is necessary to experience, but is not, _on that account_, to be declared purely subjective. Of course, necessity for experience can only arise from the nature of the mind which experiences; but it does not follow that the necessary conditions could be fulfilled, unless the objective world had certain properties. The _ground_ of necessity, we may safely say, arises from the mind; but it by no means follows that the _truth_ of what is necessary depends only on the constitution of the mind. Where this is not the case, our conclusion, when a piece of knowledge has been declared _à priori_, can only be: Owing to the constitution of the _mind_, experience will be impossible unless the _world_ accepts certain adjectives. Such, in outline, will be the argument of the first half of this chapter, and such will be the justification for regarding as _à priori_ those axioms of Geometry, which were deduced above from the conception of a form of externality. For these axioms, and these only, are necessarily true of any world in which experience is possible. =182[178].= The view suggested has, obviously, much in common with that of the Transcendental Aesthetic. Indeed the whole of it, I believe, can be obtained by a certain limitation and interpretation of Kant's classic arguments. But as it differs, in many important points, from the conclusions aimed at by Kant, and as the agreement may easily seem greater than it is, I will begin by a brief comparison, and endeavour, by reference to authoritative criticisms, to establish the legitimacy of my divergence from him.