Empirical Adequacy

Abstract

In his book, The Scientific Image, Bas van Fraassen argues for an anti-realist view of science according to which the sole epistemological aim of science is to “save the phenomena”. As originally conceived, his constructive empiricism is strongly extensional, but in his account of the empirical adequacy of probabilistic theories, van Fraassen reluctantly abandons this extensional position, arguing that modal (intensional) notions are unavoidable in interpreting probability. I argue in this paper that van Fraassen has not presented the strongest possible case for a fully extensional account of empirical adequacy. On the present account, a probabilistic theory is empirically adequate just in case there is no theory that has a higher likelihood relative to all the phenomena in the actual world. I prove that a theory is empirically adequate if and only if the probability attributed to each observable event that occurs in the actual world is its limiting relative frequency. Thus, in so far as one is concerned with the empirical adequacy (rather than with the literal truth) of probabilistic theories, strict relative frequencies provide an adequate basis for “interpreting probability”. Probabilistic theories are treated in a genuine measurement context. In this connection I distinguish between worlds that are “strongly infinite” and worlds that are only “weakly infinite”. It is characteristic of the former worlds that there is no limit to the precision of actual measurements. I show by example that in some “strongly infinite” worlds, theories will be empirically adequate only if observables are represented by continuous (rather than discrete) random variables. The range of such examples is clarified by a theorem which states necessary and sufficient conditions under which the “phenomena can be saved” without recourse to continuous random variables and real numbers.

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