How to Establish Non-Conventional Isochrony

Abstract

Like verificationism, conventionalism begins-or generally does so-with this premise: If it is in principle impossible to learn empirically whether a given assertion is true, then there is no genuine fact to be asserted. Unlike the verificationist, however, the conventionalist does not conclude, concerning the sort of sentence that concerns him, that it is mere meaningless nonsense, and hence neither true nor false. It may be meaningful, he says, but since there are no facts about the world to make it true or false, its truth-value can be stipulated freely. It is made true or false simply by convention. Such is often claimed to be the case in general with geochronometrical statements-for example, a statement to the effect that some pair of temporally separated time intervals are congruent. After all, we can not move one of them through time and bring it into coincidence with the other for comparison, so how can we know whether or not they are of equal duration? And if we can not know it, the conclusion runs, then no statement asserting it or denying it is either true or false-unless, once again, we make it so by sheer arbitrary stipulation. (See Reichenbach [1958], pp. I13-19.) From this it follows that no clock-i.e. a physical system undergoing cyclic change-is 'factually' (non-conventionally) isochronous. We can discover empirically whether two periodic processes are 'equivalent'; that is, whether every m cycles of one coincide in time with exactly n cycles of the other. But we have no way of knowing whether either of them is (to use Carnap's phrase) strongly periodic, having cycles of equal length. Says Carnap, 'We cannot know that a process is periodic in the strong sense unless we already have a method for determining equal intervals of time! It is precisely such a method that we are trying to establish by our rules. How can we escape this vicious circle?' And he concludes that brute fiat is the only way out. (Carnap [1966], pp. 80-85.) Now, it is widely accepted these days that the Verifiability Principle must, if it is to be saved at all, be understood in the weak sense that is satisfied by the possibility of inductive (or ampliative) evidence. And I should think that this goes for conventionalist views as well. But believers