Kit Fine's Denial of Compositionality

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.