Verbal statements often have context dependent or poorly defined truth value, but observations are pretty (not completely) solid. Since useful models eventually shake out into observations, the binary truth values tagging observations “propagate back” through probability theory to make useful statements about models. I am not convinced that we need a fuzzier framework—though I am interested in the philosophical justification for probability theory in the “unrealizable” case where no element of the hypothesis class is true. For instance, it seems that universal distributions mixture is over probabilistic models none of which should necessarily be assumed true, but rather only the widest class we can compute.
Verbal statements often have context dependent or poorly defined truth value, but observations are pretty (not completely) solid. Since useful models eventually shake out into observations, the binary truth values tagging observations “propagate back” through probability theory to make useful statements about models. I am not convinced that we need a fuzzier framework—though I am interested in the philosophical justification for probability theory in the “unrealizable” case where no element of the hypothesis class is true. For instance, it seems that universal distributions mixture is over probabilistic models none of which should necessarily be assumed true, but rather only the widest class we can compute.