Abstract

A common reaction among idealist philosophers to the classical syntactic characterization of proof so crisply articulated by Tarski is an urgent but inchoate Angst that something momentous is missing, an awesome intimation of bereftness. The simple fact is that in many pursuits proof involves an empirical appeal, an operation that Tarski excludes from the domain of proof and assigns to the company of confirmation. In Tarski’s terms, empirical statements never even admit of the predicate true, let alone proved, unless perhaps they hanker after truth or proof in the limit in some dimly understood and always unsuccessful way. Some sources of queasiness about the syntactic account are not hard to pinpoint. On the syntactic account, the injunction “Prove it!” can never be fulfilled, or even well-formedly uttered, in regard to an empirical statement, ┏∅, therefore ∅┓ is valid for any well-formed ∅ in a given first-order language, for any theorem, t, ┏∅, therefore t┓ is an impeccable proof for any well-formed ∅ in the classical languages. It is easy to think, with Bradley, that there is an important and legitimate, if not formally well-articulated sense of proof, characteristic of much of philosophical reasoning and argumentation, which is badly misrepresented by the syntactic conception. The kind of proof often sought after in theology, and sought after and found in the law, and the experimental and social sciences, is not purely syntactic. Idealists, of course, have frequently expressed dissatisfaction with the Tarski conception of truth. We will here extend this skepticism to the Tarski notion of proof.