Quine: `Reference And Modality’
Quine argues that there is no inference from `There is no such thing as Pegasus’ to `(∃ x) (There is no such thing as x)’, which is true. And yet, there is such a generalization from `There is no reference for the term Pegasus’ to `(∃ x) (There is no reference for the term x)’. Since `Pegasus’ does not refer, use of the term can only refer to the name itself. The name can have properties even though the referent of the name, being non-existent, can not.
Similarly, one can question another claim of Quine’s that one exception to existential generalization is given by noting that it is not possible to generalize from `Giorgione was so-called because of his size’ to `(∃ x) (x was so-called because of its size)’. This seems to rely too much on the precise usage of `so-called’, which does indeed, as Quine points out, lack a defining antecedent in the generalization given. Yet there is a perfectly good generalization to `(∃ x) (x was called x because of its size)’, which captures the meaning well, suggesting that Quine has been over-reliant on the properties of `so-called’ here.
If these two substitutions are innocuous in a Wittgensteinian sense such that meaning is use, then their inter-substitution should not change the results that Quine seeks.
Why is `the number of the planets’ a name of the number 9? Surely Quine’s point is that the number nine has certain properties necessarily, while the number of planets is contingent, as indeed demonstrated by the demotion of Pluto from planetary status. Presumably Quine will respond that there is no need for a name to be linked necessarily to its referent. But that merely plays on the unhelpful trope that `9′ could refer to a different number — such that `9′ could be less than 8, if `9′ referred to the number we currently refer to with `2′.
Fine: ‘The Problem Of De Re Modality’
Fine disagrees (p. 218) with Quine’s claim that failure of substitutivity of two terms suffices to show that they are not co-referential. One of his arguments for this is that it is not possible to substitute a co-referring substitute for `nine’ into `canine’ within the laws of grammar. This is true, but the failure of substitutivity is of a different type to the one Quine considers. Quite simply, `can[X]’ is not a word in English for almost all values of X. It is this which prevents the substitution — it is generally not permitted to break words up and make arbitrary replacements of some letters while retaining the original reference or indeed any reference at all. So Fine is wrong to say that this type of failure of substitutivity is a counter-example to Quine’s rule that failure of substitutivity entails failure of co-reference.
Fine’s second complaint here is that a language may be `impoverished’ such that there is no term co-referential with `nine’ that we may use to check for failure of substitutivity and to see whether failure of co-referentiality is invariably entailed. Yet this absence is purely contingent. If we define the neologism `morgon’ to be co-referential with `nine’, we may ask the question whether substitution changes truth value. This seems to be the case because “ `Nine’ has four letters” is true while “ `Morgon’ has four letters’ is false. Yet Quine will surely respond that these quotational contexts are referentially opaque and thus not open for substitution.
Fine addresses this response by allowing his opponents to require that the new sentence after substitution is in fact a sentence according to the language. He allows that this solves the first difficulty but not the second. His preferred solution is to restrict his analysis to languages which do not prevent such substitutions. But then we are no longer talking about natural languages.
Fine’s further complaint is that substitutivity cannot be examined in sentences which are disjuncts with a logical truth. For example, we cannot substitute `Giorgione’ in the sentence “ `Giorgione’ was so called because of his size or 2 + 2 = 4′ to check for changes in truth value because the disjunction is always true. In fact, this is the case whatever we substitute for `Giorgione’. And yet, is this not because in fact we do not consider — or need to consider, at least — the first clause at all? What would we say if the first clause became meaningless, or contained non-referring terms? We would probably conclude that the sentence as a whole remains true, thus showing that in fact the structure has merely removed the first clause from considerations altogether. That is why it fails as a substitutivity test: the relevant element is no longer under consideration.