Abstract
Some theorems of CQC=, such as those of the form (1.1) \(\exists x(x = \tau )\) and (1.2)\(\phi [\tau /x] \to \exists x\phi \), are often accused of introducing into that theory — and thus into the very core of ‘our logic’ — undesired ‘existential commitments’. However, the mere derivability of these sequences of symbols can hardly accomplish such a major feat by itself, and even when the theory is supplied with the usual ‘referential’ semantics, metaphysics is still far from being determined one way or another. (1.1) and (1.2) certainly require — by means of this semantics — that every singular term of the language receive an interpretation in the domain of quantification, but so what? The formal instrument does not specify the metaphysical counterpart of the relation between a symbol and its interpretation, nor does it tell you which things can or cannot belong to a domain of quantification. The formal instrument is neutral with respect to ail these questions, and thus by itself cannot introduce any metaphysical commitments, existential or otherwise.
Work for the completion of this paper was partly supported by aFaculty Fellowship of the School of Humanities, University of Califonia at Irvine. Thanks are due to Nuel belnap, Gerald Charlwood, Wilfrid Hodges, Karel Lambert and Brian Skyrms for comments on earlier drafts of the paper.
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Bencivenga, E. (1986). Free Logics. In: Gabbay, D., Guenthner, F. (eds) Handbook of Philosophical Logic. Synthese Library, vol 166. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5203-4_6
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