History of Western Philosophy - Bertrand Russell [408]
The gist of this argument is the denial of plurality in space itself.
What we call 'spaces' are neither instances of a general concept 'a space', nor parts of an aggregate. I do not know quite what, according to Kant, their logical status is, but in any case they are logically subsequent to space. To those who take, as practically all moderns do, a relational view of space, this argument becomes incapable of being stated, since neither 'space' nor 'spaces' can survive as a substantive.
The fourth metaphysical argument is chiefly concerned to prove that space is an intuition, not a concept. Its premiss is 'space is imagined [or presented, vorgestellt] as an infinite given magnitude'. This is the view of a person living in a flat country, like that of Königsberg; I do not see how an inhabitant of an Alpine valley could adopt it. It is difficult to see how anything infinite can be 'given'. I should have thought it obvious that the part of space that is given is that which is peopled by objects of perception, and that for other parts we have only a feeling of possibility of motion. And if so vulgar an argument may be intruded, modern astronomers maintain that space is in fact not infinite, but goes round and round, like the surface of the globe.
The transcendental (or epistemological) argument, which is best stated in the Prolegomena, is more definite than the metaphysical arguments, and is also more definitely refutable. 'Geometry', as we now know, is a name covering two different studies. On the one hand, there is pure geometry, which deduces consequences from axioms, without inquiring whether the axioms are 'true'; this contains nothing that does not follow from logic, and is not 'synthetic', and has no need of figures such as are used in geometrical textbooks. On the other hand, there is geometry as a branch of physics, as it appears, for example, in the general theory of relativity; this is an empirical science, in which the axioms are inferred from measurements, and are found to differ from Euclid's. Thus of the two kinds of geometry one is a priori but not synthetic, while the other is synthetic but not a priori. This disposes of the transcendental argument.
Let us now try to consider the questions raised by Kant as regards space in a more general way. If we adopt the view, which is taken for granted in physics, that our percepts have external causes which are (in some sense) material, we are led to the conclusion that all the actual qualities in percepts are different from those in their unperceived causes, but that there is a certain structural similarity between the system of percepts and the system of their causes. There is, for example, a correlation between colours (as perceived) and wave-lengths (as inferred by physicists). Similarly there must be a correlation between space as an ingredient in percepts and space as an ingredient in the system of unperceived causes of percepts. All this rests upon the maxim 'same cause, same effect', with its obverse, 'different effects, different causes'. Thus, e.g. when a visual percept A appears to the left of a visual percept B, we shall suppose that there is some corresponding relation between the cause of A and the cause of B.
We have, on this view, two spaces, one subjective and one objective, one known in experience and the other merely inferred. But there is no difference in this respect between space and other aspects of perception, such as colours and sounds. All alike, in their subjective forms, are known empirically; all alike, in their objective forms, are inferred by means of a maxim as to causation. There is no reason whatever for regarding our knowledge of space as in any way different from our knowledge of colour and sound and smell.
With regard to time, the matter is