Ansten Klev – On the corner
You are cordially invited to attend a McGill Philosophy Workshop
presented by Ansten Klev this coming Monday, March 8, at 3pm in Leacock 927.
On the corner
Classical presentations of logic in the metamathematical tradition typically make use of special devices to effect discourse about the object language. Among such devices are Quine’s corner notation, ”quasi-quotation” as he called it. This notation has seen many uses since its introduction in Quine’s Mathematical Logic (1940), but few, if any, of these uses have been in accordance with Quine’s intentions.
This might be for good reasons: as used by Quine the device of quasi-quotation is not merely an innocent quotation device, but involves large amounts of semantics. Indeed, quasi-quotation requires a disquotation operator for its precise explication. Quine should therefore not be granted the most important use he makes of quasi-quotation, to wit in stating the formation rules of his logical system. Disquotation is not the mere pruning of quotation marks, but the retrieving of sense; to apply disquotation to the expressions of a system of logic, the system must therefore already have been given, so the use of disquotation, and hence of quasi-quotation, in stating the formation rules is viciously circular.
My argument involves considerations of semantical categories and of variables. I will begin by discussing these notions and their interaction. Then I explain quasi-quotation from what I take to be Quine’s point of view, before I give my argument that the actual use Quine makes of quasi-quotation rests on disquotation. The, admittedly speculative, diagnosis I will make is that Quine was caught between, on the one hand, wanting his system of logic to be a language to talk with, and on the other hand, treating the elements of his system merely as objects to talk about; Quine was thus trapped between, on the one hand, the notion of formal language as a universal character, found in Frege and Russell, and on the other hand, the notion of formal language as formal system, the notion which today is the dominant one.