Kant, who first emphasised this contradiction, deduced the impossibility of space and time, which he declared to be merely subjective; and since his time very many philosophers have believed that space and time are mere appearance, not characteristic of the world as it really is. Now, however, owing to the labours of the mathematicians, notably Georg Cantor, it has appeared that the impossibility of infinite collections was a mistake. They are not in fact self-contradictory, but only contradictory of certain rather obstinate mental prejudices. Hence the reasons for regarding space and time as unreal have become inoperative, and one of the great sources of metaphysical constructions is dried up.
The mathematicians, however, have not been content with showing that space as it is commonly supposed to be is possible; they have shown also that many other forms of space are equally possible, so far as logic can show. Some of Euclid's axioms, which appear to common sense to be necessary, and were formerly supposed to be necessary by philosophers, are now known to derive their appear-
