corners

corners also called corner quotes, quasi-quotes, a notational device (] ^) introduced by Quine (Mathematical Logic, 1940) to provide a conveniently brief way of speaking generally about unspecified expressions of such and such kind. For example, a logician might want a conveniently brief way of saying in the metalanguage that the result of writing a wedge ‘7’ (the dyadic logical connective for a truth-functional use of ‘or’) between any two well-formed formulas (wffs) in the object language is itself a wff. Supposing the Greek letters ‘f’ and ‘y’ available in the metalanguage as variables ranging over wffs in the object language, it is tempting to think that the formation rule stated above can be succinctly expressed simply by saying that if f and y are wffs, then ‘f 7 y’ is a wff. But this will not do, for ‘f 7 y’ is not a wff. Rather, it is a hybrid expression of two variables of the metalanguage and a dyadic logical connective of the object language. The problem is that putting quotation marks around the Greek letters merely results in designating those letters themselves, not, as desired, in designating the context of the unspecified wffs. Quine’s device of corners allows one to transcend this limitation of straight quotation since quasi-quotation, e.g., ]f 7 y^, amounts to quoting the constant contextual background, ‘# 7 #’, and imagining the unspecified expressions f and y written in the blanks. See also USE – MENTION DISTINCTIO. R.F.G.

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