Title:The Interlocking Problem for Logical Inferentialism
Abstract:
Logical inferentialism holds that the meaning of a logical expression, like “not”, is fully determined by inference rules governing its use. This metasemantics purely for logical vocabulary is often paired with a distinct, non-inferentialist metasemantics for empirical expressions like “electron”. I argue that the resulting dualist metasemantics faces the Interlocking Problem: a dualist metasemantics is untenable unless it is complete, assigning meanings to all meaningful expressions, and coherent, avoiding incompatible verdicts for a single expression. I show how this problem undermines Jared Warren’s conventionalist version of logical inferentialism, which involves dualist metasemantics that combines logical inferentialism with a causal metasemantics for empirical vocabulary. The framework violates the completeness requirement by underdetermining the meanings of some non-empirical and non-logical terms. It also violates the coherence requirement by overdetermining the meanings of empirical expressions used in inferences and logical expressions used in perceptual judgments. But the troubles Warren faces stem from the general structure of a dualist metasemantics. The Interlocking Problem thus represents a salient obstacle that any logical inferentialist view would have to overcome.
