Konstantin Genin (University of Toronto), Kevin T. Kelly (Carnegie Mellon University)
The distinction between deductive (infallible, monotonic) and inductive (fallible, non-monotonic) inference is fundamental in the philosophy of science. However, virtually all scientific inference is statistical, which falls on the inductive side of the traditional distinction. We propose that deduction should be nearly infallible and monotonic, up to an arbitrarily small, a priori bound on chance of error. A challenge to that revision is that deduction, so conceived, has a structure entirely distinct from ideal, infallible deduction, blocking useful analogies from the logical to the statistical domain. We respond by tracing the logical insights of traditional philosophy of science to the underlying information topology over possible worlds, which corresponds to deductive verifiability. Then we isolate the unique information topology over probabilistic worlds that corresponds to statistical verifiability. That topology provides a structural bridge between statistics and logical insights in the philosophy science.
