The Bayesian Theory of Confirmation, Idealizations and Approximations in Science :: Scientific Papers

The Bayesian Theory of Confirmation, Idealizations and Approximations in Science ABSTRACT: 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 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 relative 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 taking 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. A non-probabilistic analogue of the confirmation condition above that I offer avoids the 'old evidence problem, which has been a headache for classical Bayesianism. Idealizations and approximations like point-masses, perfectly 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 long neglected or misunderstood by philosophers. In standard hypothetico-deductive, bootstrapping and Bayesian accounts of confirmation, idealizations and approximations 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 o f 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 relative 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 taking 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.