Probabilistic logic as a unified framework for inference
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I argue that a probabilistic logical language incorporates all the features of deductive, inductive, and abductive inference with the exception of how to generate hypotheses ex nihilo. In the context of abduction, it leads to the Bayes theorem for confirming hypotheses, and naturally captures the theoretical virtue of quantitative parsimony. I address common criticisms against this approach, including how to assign probabilities to sentences, the problem of the catch-all hypothesis, and the problem of auxiliary hypotheses. Finally, I make a tentative argument that mathematical deduction fits in the same probabilistic framework as a deterministic limiting case.