and just as in the case of colour and size, he would recognise that the first two equalities in no wise compelled the equality of
and
.
But we may wonder why it is that the critic does not realise that all the trouble that has arisen is of his own making. The answer appears perfectly clear. It would be somewhat as follows:
“At no time does he realise that he has introduced an arbitrary assumption and has thereby begged the entire question. The traditional belief in absolute time so dominates his mind that he thinks in terms of it even when he knows that the theory of relativity is not based on any such a priori belief.”
Once again, the theory of relativity as a theory of mathematical physics may survive or may succumb. It is for experiment to give the answer. If the anticipations of the theory should not conform to experiment, if, for instance, the recent experiment of Miller were considered conclusive as detecting velocity through the ether, it would be impossible to save the theory, at least in its present form.[75] But we must not confuse the ability of the theory to portray the workings of nature with its legitimacy as a perfectly consistent and rational doctrine of thought. On this last point no doubt exists. The theory has been scrutinised by the greatest of living mathematicians and not the slightest error of mathematical reasoning, nor therefore of logic, has been found in it.
