Reduction and Elimination in Philosophy and the Sciences

tual sequences, and relative frequencies therein, is another
matter.” H. Cramér takes a similar stance: “[Limiting
frequencies] involve a mixture of empirical and theoretical
elements, which is usually avoided in modern axiomatic
theories.” (quoted in Gillies 2000, 100)
As the quote by Cramér suggests, the main problem
of limiting frequencies seems the inextricable mixture of
ontic and epistemic elements. This squares badly with the
usual distinction between epistemic and ontic accounts of
probability 2 . Subjective interpretations of probability – in
terms of degrees of belief – can readily account for the
smoothing out of the discrete probability distributions.
However, it seems odd to interpret probabilities as degrees
of belief within objective sciences like physics. But thus far,
nobody has yet managed to justify the infinite limit on the
basis of a purely objective account. Notwithstanding these
difficulties, the scientific practice in statistical reductions
forces us to make sense of the notion of limiting
frequencies. Maybe the lesson is to abandon the hard
distinction between ontic and epistemic accounts
altogether.
2 Excellent overviews of the different accounts of probability are Galavotti
2005 and Gillies 2000.
258
Limiting Frequencies in Scientific Reductions — Wolfgang Pietsch
Literature
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