In “Semantic Relationism”, Kit Fine proposes to solve Frege’s puzzle by including some irreducibly relational semantic facts. Fine argues that this approach permits him to maintain a) a directly referential semantics for proper names, b) the transparency of meaning, and c) semantic compositionality (of a sort). Fine thus takes his view to have a strong advantage over rival Millian proposals, which typically deny (b).
Fine presents the puzzle as the following inconsistent set of claims (concerning the sentences “Cicero = Cicero” and “Cicero = Tully”):
1a Cognitive Difference: The two identity sentences are cognitively different.
1b Cognitive Link: If the sentences are cognitively different, then they are semantically different.
2 Compositionality: If the sentences are semantically different, then the names “Cicero” and “Tully” are semantically different.
3 Referential Link: If the names “Cicero” and “Tully” are semantically different, they are referentially different.
4 Referential Identity: The names “Cicero” and “Tully” are not referentially different.
For some purposes, Fine collapses 1a and 1b into a single claim:
1 Semantic difference: The two identity sentences are semantically different.
Fine identifies the two major lines of response to this puzzle as the Referentialist response (which denies 1), and the Fregean response (which denies 3). Fine’s own response can most naturally be understood as a denial of 2. Fine argues that the problem with Referentialism is the denial of 2, and that the problem with Fregeanism is the denial of 3. Consequently, Fine’s view only has an advantage as a solution to Frege’s puzzle over Fregeanism or to Referentialism if it avoids the denial of 1 and the denial of 3. However, in order to address all Frege puzzle cases, Fine will have to reject one of those two principles.
Fine’s solution to the puzzle involves the rejection of 2. Fine does so by accepting a weaker version of compositionality. The following two principles entail 2, but Fine only accept
2a Compositionality Proper: If the identity-sentences “Cicero = Cicero” and “Cicero = Tully” are semantically different, then so are the pairs of names “Cicero”, “Cicero” and “Cicero”, “Tully”.
2b Intrinsicality: If the pairs of names “Cicero”, “Cicero” and “Cicero”, “Tully” are semantically different, then so are the names “Cicero” and “Tully”.
Fine accepts 2a, but rejects 2b. Now, the point of Fine’s rejection of compositionality is to make room for a view according to which “Cicero” and “Tully” do not differ semantically, even though the pairs “Cicero”, “Cicero” and “Cicero”, “Tully” do. This is where the irreducibly relational semantic facts enter Fine’s picture. On his view, “Cicero = Cicero” differs semantically from “Cicero = Tully” because the pairs of names differ semantically despite the names themselves not differing semantically.
The trouble is, understood as an attempt to solve Frege’s puzzle, it is insufficient. To address Frege’s puzzle, it really is necessary to reject 1 or 3. In order to see this, we can consider two variations of Frege’s puzzle: I call the first variant “Too Few Occurrences” because in it, there are not enough occurrences of names to use the maneuver Fine invokes here. I call variant 2 “Too Many Types” because it involves more types of names than the maneuver just mentioned can deal with.
Too Few Occurrences:
Consider the sentences “Cicero is an orator” and “Tully is an orator”.
On Fine’s view (through Chapter 2, at least), the two sentences have the same semantic content. This is because Fine accepts Referential link (no semantic difference for names without a referential difference), and a version of compositionality that would require a semantic difference between “Cicero” and “Tully” for these two sentences to differ in semantic value.
However, the sentences are cognitively different (both intuitively and by Fine’s standards), and Fine accepts Cognitive Link (no cognitive difference without a semantic difference). So, we have a version of Frege’s puzzle that does not invoke the richer version of compositionality that Fine rejects. It does still require the assumption of Referential Link and Semantic Difference, though, so one could resolve this problem by rejecting one of those two principles. However, if we reject one of those to deal with Too Few Instances, there is no reason to reject Compositionality in the original case.
Too Many Types:
Consider the sentences “Cicero is Tully” and “Marcus is Tully”.
On Fine’s view, the two sentences have the same semantic content. This is because Fine’s semantic theory for the irreducibly relational facts about pairs of names is, effectively, only sensitive to a notion of “representing as same”. “Cicero”,”Cicero” represent as same, but “Cicero”,”Tully” do not represent as same. This is the relational semantic difference Fine uses to explain the difference in semantic value between “Cicero = Cicero” and “Cicero = Tully”. Consequently, “Cicero”,”Tully” and “Cicero”,”Marcus” have the same semantic value (in Fine’s terminology, both pairs share an uncoordinated content, and are negatively coordinated, whereas the pair “Cicero”,”Cicero” has the same uncoordinated content, but is positively coordinated). Consequently, we can generate a puzzle using Compositionality Proper (the principle of compositionality Fine accepts). Again, the puzzle also requires Semantic Difference and Referential Link, so again, the puzzle can be resolved either by the same maneuver as used by the Fregean or through the maneuver used by the Referentialist. Making such a move in this case, however, undermines the motivation for rejecting the stronger version of Compositionality in the first place.
So, to really address Frege’s puzzle, it appears that one has to either reject Semantic Difference (i.e. adopt the Referentialist position), or reject Referential Link (i.e. adopt the Fregean position).
In fairness to Fine, he discusses the case I am calling “Too Few Occurrences”, but there is a dilemma for understanding his discussion: Either the material addressing it in chapter 3 is intended to consistently extend the account presented in chapter 2, in which case, the objections above still present a problem for the case, or it is a revision of the view. If the view from chapter three forward is an outright revision of the view presented in chapter 2, then, the real work is being done by Fine’s discourse-level semantic treatment (which assigns something like a semantic values collectively to entire discourses — sets of sentences), then there is no need for fine to reject compositionality for intrinsic semantic values; the chapter 2 mechanisms are idle in the broader solution to Frege’s puzzle. At any rate, the chapter 2 view itself is insufficient for resolving Frege’s puzzle.
I have a draft of a paper that presents all of this more clearly, which I may post after tidying it up a bit.