Wednesday, February 6, 2019
The Bayesian Theory of Confirmation, Idealizations and Approximations in Science :: Scientific Papers
The Bayesian Theory of Confirmation, Idealizations and Approximations in loreABSTRACT My focus in this paper is on how the rudimentary Bayesian model can be amended to reflect the office staff of idealizations and approximations in the substantiation or dis proof of any hypothesis. I suggest the following as a plausible way of incorporating idealizations and approximations into the Bayesian condition for incremental confirmation Theory T is confirmed by observation P congenator to background knowledge where I is the conjunction of idealizations and approximations used in etymologizing the prediction PT from T, PD expresses the discrepancy between the prediction PT and the actual observation P, and stands for logical entailment. This formulation has the virtue of explicitly victorious into account the essential use made of idealizations and approximations as well as the point that theoretically based predictions that utilize such assumptions will not, in general, exactly fit the data. A non-probabilistic analogue of the confirmation condition to a higher place that I offer avoids the old evidence problem, which has been a headache for classical Bayesianism. Idealizations and approximations akin point-masses, suddenly elastic springs, parallel conductors crossing at infinity, assumptions of linearity, of negligible masses, of perfectly spherical shapes, are commonplace in science. Use of such simplifying assumptions as catalysts in the process of deriving testable predictions from theories complicates our picture of confirmation and disconfirmation. Underlying the difficulties is the fact that idealizing and approximating assumptions are already known to be false statements, and yet they are often indispensable when testing theories for truth. This aspect of theory testing has been desire neglected or misunderstood by philosophers. In standard hypothetico-deductive, bootstrapping and Bayesian accounts of confirmation, idealizations and approximatio ns are simply ignored. My focus in this paper is on how the basic Bayesian model can be amended to reflect the role of idealizations and approximations in the confirmation or disconfirmation of an hypothesis. I suggest the following as a plausible way of incorporating idealizations and approximations into the Bayesian condition for incremental confirmation Theory T is confirmed by observation P coition to background knowledge where I is the conjunction of idealizations and approximations used in deriving the prediction PT from T, PD expresses the discrepancy between the prediction PT and the actual observation P, and stands for logical entailment. This formulation has the virtue of explicitly pickings into account the essential use made of idealizations and approximations as well as the fact that theoretically based predictions that utilize such assumptions will not, in general, exactly fit the data.
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