The Logic of Commands

rescher logic of commands.jpg

I picked up a cheap paperback copy of Rescher's Logic of Commands and have been enjoying it so far. In one of the chapters of my dissertation I'm arguing that Pearl's intervention operation - $do(X=x)$ - is best understood as an imperative. I think this has several theoretical benefits, from explaining why the language of probability is insufficient for capturing our causal judgments to helping settle problems in modal metaphysics involving the do-operator (such as the failure of modus ponens).

But imperative logic is a funny thing, and while many philosophers have tried to develop a logic of commands there doesn't seem to be the kind of consensus that we see in propositional logic, even about the basic parts of the language. Peter Vranas at UW-Madison goes in for a three-valued logic of 'satisfaction' in which imperatives are tuples of sets of propositions (roughly, sets of the propositions describing how the imperative could be satisfied or violated). These sets need not be mutually exclusive and exhaustive, in which case one can avoid the command altogether. Rescher represents commands as having a target, duration, description, and precondition. So, Jones, go to the store when you get back becomes [Jones! going to the store / Jones gets back]. These kinds of conditional commands turn out to be especially difficult to handle, and Rescher makes use of flow diagrams and operational scenarios in order to capture the complexity here.

One of my main interests in imperative logic is for the work it can do in supplying a logic of intervention and experimentation. If interventions of the $do(X=x)$ sort are imperatives, then experiments are (surprisingly!) imperative arguments. As are many other abstract objects like symphonies, recipes, algorithms, and many computer programs. I think this has consequences for the ontology of experiments, which will affect what we should say about the experimenter's regress, stopping rules for experimental design, and the difference between experiments and simulations.