Reference and modality means how we refer to items and in what way they exist. Names of non-existent items cause problems here. I will discuss the views of Quine and Fine and raise some questions.
Reference And Modality: Pegasus
Quine argues in “Reference And Modality” 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.
One can question another claim of Quine’s that one exception to existential generalisation is given by noting that it is not possible to generalise 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.” That does indeed, as Quine points out, lack a defining antecedent in the generalisation given.
Yet we can make a perfectly good generalisation to `(∃ x) (x was called x because of its size)”. And that captures the meaning well, suggesting that Quine has been over-reliant on the properties of “so-called” here.
These two substitutions may be innocuous in a Wittgensteinian sense such that meaning is use. Then their inter-substitution should not change the results that Quine seeks.
The Number Of Planets
Why is `the number of the planets’ a name of the number 9? (Or eight in post-Pluto days.)
Quine’s point is that the number nine has certain properties necessarily. However, the number of planets is contingent, as indeed demonstrated by the demotion of Pluto from planetary status. Presumably Quine responds here that he does not need 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. So that “9” could be less than 8. That would happen if the symbol “9” referred to the number we currently refer to with “2.”
Reference And Modality: Failure Of Substitutivity
Fine in “The Problem Of De Re Modality” 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. We cannot 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.” Perhaps no term co-refers with “nine.” We could then not use it to check for failure of substitutivity. We could not see whether failure of substitutivity invariably entails failure of co-referentiality.
Yet this absence is purely contingent. If we define the neologism “morbag” 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 ” ‘Morbag’ 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. He allows 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.
Reference And Modality: Disjunctions With Logical Truths
Fine’s further complaint is that we cannot examine substitutivity 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.