Some remarks on Quine's arguments against modal logic.
John Robert Baker · Notre Dame Journal of Formal Logic · 1978
In the process of investigating Quine's charge that quantified modal logic is committed to essentialism, I discovered several problems with his arguments which have not heretofore been presented.The first such problem concerns Quine's claim that terms in all alethic modal contests do not occur purely referentially.The second concerns the claim that his argument denying the intelligibility of quantifying into modal contexts goes through without recourse to singular terms.* 1 Quine's argument that modal contexts are referentially opaque is familiar.1 It may be stated as follows:(1) Given a true statement of identity, either of its two terms may be substituted for the other in any true statement and the result will be true.(2) The principle embodied in (1) does not extend to contexts in which the term to be supplanted does not occur purely referentially.(3) Given a true statement of identity, and given that a term of the identity occurs purely referentially in the true statement S, then either of the two terms of the identity may be substituted for the other in S, and the resultant sentence S* will be true.(4) If there is a true statement of identity, and if either one of the two terms of the identity is substituted for the other in a true statement S, and if S* is false, then the term does not occur purely referentially in S.(5) In alethic modal contexts terms of an identity are not substitutible salva veritate, that is, supplanting one term of a true identity for another in S results in the falsity of S*. .'.(6) Terms in alethic modal contexts do not occur purely referentially.Counterinstances to (1) are readily at hand.For example, it is false that