Is synonymy transitive?

 One might think that this is obviously true: Two expressions are synonyms if they have the same content and having the same content is a transitive relation. This is a direct corollary from a more general principle that if we define a relation by an identity (or in general, we have a relation that is equivalent to some identity), the relation will inherent from the relevant identity its structural features, including transitivity. In other words, for every R if there is an F that R(x,y) =def F(x)=F(y) then R is transitive. This applies not only to the definition of synonym as sameness of meaning, but also to the definition of synonym as substitution salva veritate:

φ is cognitively synonym to ψ if and only if, for all allowed sentential  contexts χ[. . .], we have χ[φ] iff χ[ψ].

Here, the double conditional in the final equation hides also an identity (of truth value). This can be made explicit thus:

φ is cognitively synonym to ψ if and only if, for all allowed sentential  contexts χ[. . .], I(χ[φ])=I(χ[ψ]).

Thus if we want to argue that synonymy is not transitive, we must define it in a different way (Quinean concerns about metaphysical parsimony may also serve as motivation for not using identity (which is about objects) for defining any relation) (Goodman 1949, Mates 1952, Churchland 1993). For example, if we define synonymy as something like mutual obvious entailment (Bjerring and Schwarz 2017), we can get a non-transitive sense of synonymy.

But, of course, it is hard to challenge the strong link between synonymy and sameness of meaning or substitution salva veritate. Thus, the defender of the non-transitivity of synonymy would do well by providing non-transitive analogues of these two notions.

For sameness of meaning, the obvious alternative is to talk of similarity of meaning. For substitution salva veritate, there is not such an obvious alternative. But there are paths worth exploring: one can change again identity for similarity, so that instead of substitution without change in truth value, it would have to be something like substitution with only a slight change in truth value. But is one is a bivalentist, there is no such thing as similarity among truth values. Thus, one can work within a fuzzy logic and define synonymy thus:

φ is cognitively synonym to ψ if and only if, for all allowed sentential  contexts χ[. . .], |I(χ[φ]) - I(χ[ψ])| < d, for a small enough d.

The second strategy would be to change from truth to other semantic value or attitude, which would give us something very similar to mutual obvious entailment.

My comments on the sixth and last session of Francesco Berto's Cáedra Gaos on hyperintensionality.