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Towards an Expanded Epistemology for Approximations

By stressing the act rather than the relation of approximation, I argue that the magnitude of the error introduced should not be used as the sole criterion for judging the worth of the approximation. Magnitude is a necessary but not sufficient condition for such a judgement. Controllability, the absence of cancelling errors, and the approximation's justification are also important criteria to consider when praising or blaming an approximation. Boltzmann's discussion of the types of approximations used in the kinetic theory of gases at the turn of the century illustrates the use of these criteria.