description of observations together with the intervention of a mere formula, by recalling our memories of childhood. There is a large audience, a magician comes upon the stage, places a table in front of him, takes off his coat, turns it inside out, shows himself to us, then commences voluble patter with elaborate gestures, and finally produces two rabbits from his hat. We are asked to believe that it was the patter that did it.
The common sense of the matter is, that the mathematical formulae are descriptive of those characteristics of the common external world which are relevant to the transmission of physical states from the band to the bodies of the listeners.
If this be true, we are now a long way from the sweet simplicity of the original doctrine. We have introduced the notion of the external world with its spatio-temporal occurrences, speculatively described by science. We have introduced the notion of potentiality, by substituting the word “observable” for the word “observed.” Also hundreds of millions of dollars have been risked in reliance upon inductive generalization. If we ask what we mean by all this apparatus of vague notions, our only appeal must be to the speculative Reason.
It is quite true that exactly at this point we can damp down any further speculative Reason, and can relapse into the routine of successful methodology. But the claim of science that it can produce an understanding of its procedures within the limits of its own categories, or that those categories
