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Statistical Data and Mathematical Propositions
Author(s) -
Juhl Cory
Publication year - 2015
Publication title -
pacific philosophical quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.914
H-Index - 32
eISSN - 1468-0114
pISSN - 0279-0750
DOI - 10.1111/papq.12061
Subject(s) - frequentist inference , mathematical economics , frequentist probability , statistical hypothesis testing , statement (logic) , prima facie , statistical model , epistemology , statistical theory , impossibility , mathematics , computer science , econometrics , statistics , philosophy , bayesian probability , political science , law , bayesian inference
Statistical tests of the primality of some numbers look similar to statistical tests of many nonmathematical, clearly empirical propositions. Yet interpretations of probability prima facie appear to preclude the possibility of statistical tests of mathematical propositions. For example, it is hard to understand how the statement that n is prime could have a frequentist probability other than 0 or 1. On the other hand, subjectivist approaches appear to be saddled with ‘coherence’ constraints on rational probabilities that require rational agents to assign extremal probabilities to logical and mathematical propositions. In the light of these problems, many philosophers have come to think that there must be some way to generalize a B ayesian statistical account. In this article I propose that a classical frequentist approach should be reconsidered. I conclude that we can give a conditional justification of statistical testing of at least some mathematical hypotheses: if statistical tests provide us with reasons to believe or bet on empirical hypotheses in the standard situations, then they also provide us with reasons to believe or bet on mathematical hypotheses in the structurally similar mathematical cases.