A reduction of the theory of confirmation to the notions of distance and measure
Karl Schlechta · Logic Journal of IGPL · 1997
We present an analysis and formalization of confirmation of a theory through observation. The basic ideas are, first, to carry the results of single observations over to neighbouring cases by analogy, using an abstract distance relation as in the Stalnaker/Lewis semantics for counterfactual conditionals. A theory is then, in a second step, considered confirmed if we have thus concluded positively for a 'large' part of the universe - where 'large' is interpreted by a weak filter. Formal semantics as well as sound and complete axiomatizations for the (trivial) first order and the propositional case are given.