Abstract
This paper draws together four perspectives that contribute to a new understanding of probability and solving problems involving probability. The first is the Subjective Bayesian perspective that probability is affected by one’s knowledge, and that it is updated as one’s knowledge changes. The main criticism of the Bayesian perspective is the problem of assigning prior probabilities; this problem disappears with our Information Theory perspective, in which we take the bold new step of equating probability with information. The main point of the paper is that the formal perspective (formalize, calculate, unformalize) is beneficial to solving probability problems. And finally, the programmer’s perspective provides us with a suitable formalism. To illustrate the benefits of these perspectives, we completely solve the hitherto open problem of the two envelopes.
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I. Hayes and J. Woodcock
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Hehner, E.C.R. A probability perspective. Form Asp Comp 23, 391–419 (2011). https://doi.org/10.1007/s00165-010-0157-0
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DOI: https://doi.org/10.1007/s00165-010-0157-0