Inferential rules as Dynamic Semantic Values
Abstract
What is an inferential rule? Upon consideration of Lewis Carroll’s regress,
philosophers are almost unanimous in taking inferential rules to be something
different from principles, or propositions. For example, it is taken to be the import
of the regress that the rule of modus ponens must be something different from the
principle that if `p’ is true and `if p then q’ is true, then `q’ is true. But if not that
general principle, what is then an inferential rule? We are often told that they are to
be identified with schemata, or forms (see especially Sanford 2011). But these views
do not seem to really clarify the nature of inferential rules and face the objection of
mysteriousness. In this paper, I argue that inferential rules are better understood as
dynamic semantic values. In my proposal, I generalize to the more general logic case
Bernard Nickel (Philosophical studies, forthcoming)’s recent view of inferential
semantics as a special sort of dynamic semantics. I argue that the resulting view has
the advantage of dispelling the mysteriousness objection to the appeal to inferential
rules. In the ending, I discuss my view in “Practical senses” (Philosophers’ Imprint,
2015) in the light of this proposal. In this essay, I claim that practical senses to be
thought on the model of a special sort of inferential rules --- so-called operational
semantic values --- that are ordinarily invoked by operational semantics for
programming languages. I conclude that if inferential rules are quite generally to be
thought of as dynamic semantic values, then operational semantic values
themselves are better thought of as a sort of dynamic semantic values, and so are
practical senses.