Hayes, P.J.



It is possible to render any theory decidable in a trivial way by invoking a time cutoff on reasonings and having a default mechanism for deciding the values of any expressions still not decided. There does not seem to be any way of avoiding the conclusion that the basic theory must admit an efficient theorem-proving procedure which is close to being a decision procedure. This is what the well-known unification algorithm achieves (Robinson 1965, Prawit11960). By Quine's dictum, anyone who advocates the inclusion of set theory in his theory must admit to the view that sets exist: and set theory is widely held to be at the basis of all of mathematics.