Rejoinder to Dejnožka’s Reply

Abstract

66 Discussion REJOINDER TO DEJNOZKA'S REPLY GARY OSTERTAG Philosophy/ New YorkU. New York,NY 10003, USA G02@NYU.EDU It is common knowledge that Russell does not explicitly endorse modal logic in any of his major logical writings. Nor does my review of BertrandRusseli onModalityand LogicalRelevance' suggest that Jan Dejnozka denies or is somehow unaware of this. On the contrary, I assume it to be obvious that any commitment Russell may have had to modal logic must be implicitin his writings, nor explicit. The real issue is whether there is evidence of any such commitment . I will state, briefly,why I remain sceptical. First, Dejnozka's book lacks any interpretive methodology. When the question arises, In whichcontextsis itpermissibleto translateRusseli's language(formal orinformal)intoa modalsystem?, we get the following: amibute a modal logic to Russell if "it is more reasonable than not to paraphrase Russell's thinking into the modal logic." This condition, we are told, "is met to the extent that acertain modal logic is logicallyimplicit in Russell's thinking." All of which goes without saying, but it simply delays the inevitable question: when is a modal logic logicallyimplicit in a text? Dejnozka's current answer: a modal logic is logically implicit in a text when the text logically implies the paraphrase.2 But the final suggestion is incoherent, since we cannot tell what a text logical1y implies until we have discerned its logicalform-i.e. until we havealready paraphrased it into some formal idiom or other. A related problem is that Dejnozka consistently failsto distinguish two sorts of claims: • Certain passagesin Russell lend themselves to a modal interpretationthey can be captured in a given system of modal logic, e.g. S13. • Such an interpretation reflects Russell'sintentions. That a modal system captures one or another of Russell's accounts of logical truth in itself entails nothing regarding Russell'sintentions. The modal system G described by George Boolos in a munber of publications provides an alterna- ' "Russell's Modal Logic?", Russelin.s. 20 (2000): 165-72. 2 "Reply to Ostertag", Russell, n.s. 21 (2001): 63-5 (at 65). Discussion 67 rive formalization of Peano Arithmetic, enabling the derivation of Godel's incompleteness theorems. Yet the fact that this is possible does not in any way suggest that Godel himself was implicitly committed to G. Unfortunately, Dejnozka often writes as if the mere possibility of a modal interpretation is genuinely revealing as to Russell's intemions. Bm it is just as implausible to maintain this as it is to claim that it was Gi:idel'sintention to present Boolos's G.3 Second, as I maintain in my review, Dejnozka fails to take seriously the many comexts in which Russell is explicitly critical of modality. Dejnozka responds that he has quoted these very passagesand that he "embraces them as half-but only half-of [his] basic message" ("Reply", p. 64). But citing contexts in which Russell appears to find modality congenial does nothing to mitigate the force of the contexts in which Russell explicitly repudiates modality. It is Dejnozka's responsibility to explain how the latter are to cohere with his interpretation. To avoid this issue is to skirt the real philosophical and interpretive challenge that the project entails. Finally, we come to Dejnozka's confusions surrounding MDL-the triad of equivalences that underwrite the interpretation of Principiaas a modal logic. In light of Dejnozka's steadfast refusal to formalize the various modal systems he amibmes to Russell, it hardly makes a differencewhether MDLis a modal logic or merely, to use his terminology, a "modal theory" (assuming that the latter ultimately amounts to something other than a modal logic).4What is importam is whether MDLis trivial. If it is, then it is quite beside the point to pursue the various extensions of MDL.Since I maimain that Russell is not commined, implicitly or otherwise, to a substantive reading of MDL-one in which the modal operators have their conventional meanings-then he is not committed to these extensions, so there is no need for detailed discussion. What remains central is my argtunent for the claim that MDL is trivial. Bm this argmnent (unacknowledged by Dejnozka) is there for...