Hypothesis-Discharging Rules in Atomic Bases

Abstract

This paper investigates the idea, familiar inter alia from Prawitz, that an inference is to be deemed valid, relative to a basis of inference rules for atomic sentences, just in case every extension of that basis supporting the premisses of the inference also supports its conclusion. Specifically, we try to carry out this idea in a setting where atomic bases are allowed to contain rules that license the discharging of hypotheses. The results are mixed. While the ensuing concept of validity appears to be an extensionally adequate one, from a conceptual point of view the theory is deemed unsatisfactory in that certain inferences come out valid, as it were, for the wrong reason. So, for instance, an atomic rule contained in a basis will qualify as valid relative to that basis, but not simply in virtue of the fact that it occurs there; its validity also depends on the assumption that all bases conform to a particular format, thus lending a peculiarly holistic character to the theory.