ABSTRACT

Logical inferentialism is, roughly, the view that the meaning of a logical connective is determined by the inference rules governing that connective. For example, in systems of natural deduction the introduction and elimination rules for a connective fix its meaning. Conversion reductions a way of ensuring that the addition of standard connectives will be conservative extensions. It is natural to think that the idea can be generalized to a template for harmony as a local constraint on inference rules. Dummett, Prawitz, and other intuitionists have argued that the nonconservativeness of classical negation shows that the classical inference rules fail to fix a conceptual content at all. Classical negation provides motivation to adopt multiple conclusion sequents, as it is difficult to add to a single-conclusion system with a conditional in a harmonious way. The rules for tonk present a problem for the logical inferentialist: there needs to be a principled way to separate the acceptable combinations of rules from the unacceptable.