A Fallacy in Ramsey

Abstract

At the end of 'Facts and Propositions',1 Frank Ramsey argued in favour of Wittgenstein's thesis that universal (existential) quantifications were equivalent in meaning to the (probably infinite) conjunctions (disjunctions) of their instances, and against Russell's contention that they were true in virtue of sui generis general (or existential) facts.2 The positive argument is simple enough: if Wittgenstein's extension of the notion of truth-functional composition to cover quantification is accepted, then his semantic account of validity in propositional logic can be extended to cover such quantificational inferences as universal instantiation and existential generalization, whereas a semantic account like Russell's, in terms of sui generis facts, would leave the validity of these inferences unexplained. On the other side, however, the Russellian has an apparently telling objection to the Wittgensteinian account, and Ramsey answers this objection with an interesting but, I will argue, subtly circular argument. Russell's objection is that the conjunction of all its instances, even if it could be enunciated, does not exhaust the content of a universal quantification: the quantification cannot validly be inferred from the conjunction without an additional premiss to the effect that the conjunction is complete, that the names in the conjunct instances exhaust the domain over which the quantified variable ranges. In reply, Ramsey first canvasses the Wittgensteinian position, that the supposed added premiss is without meaning, but declines to defend it in detail, and contents himself with an ad hominem response. If the added premiss is tautologous, it adds nothing to the conjunction and can be omitted without affecting the validity of the inference, but, he claims, it can be shown, on the basis of assumptions acceptable to the (unnamed-he doesn't appear to have Russell in mind here) advancers of the objection, that it is a tautology. At this point there is a change of terminology. 'The objectors will claim that [the added premiss] is not a tautology, or in their terminology not a necessary proposition....' We who have read Kripke may find the identification of necessity with tautologousness, or in general with any sort of analyticity, dubious, but Ramsey felt comfortable enough with it to use in the remainder of the paragraph only the modal terminology. (His conclusion-that the added premiss is, if true, necessarily true, and, if false, necessarily false-is surprising enough for the objectors to be expected to retreat in confusion before it whatever their opinions on