Abstract

Inferential expressivism makes a systematic distinction between inferences that are valid qua preserving commitment and inferences that are valid qua preserving evidence. I argue that the characteristic inferences licensed by the principle of comprehension, from "x is P" to "x is in the extension of P" and vice versa, fail to preserve evidence, but do preserve commitment. Taking this observation into account allows one to phrase inference rules for unrestricted comprehension without running into Russell’s paradox. In the resulting logic, one can derive full second-order arithmetic. Thus, it is possible to derive classical arithmetic in a consistent logic with unrestricted comprehension.