Saussure conceptualised a language as a set of semantic concepts (signifié) and patterns analogous to tokens1 (significant). Each semantic meaning is given via its relations to other concepts, rather than as an intrinsic feature of that concept per se or via the external object denoted. Those relations are defined via the morphology and other grammatical operations.
More formally, we can define a language as a set of semantics S, and a set of relational orderings R1,…, Rn. There exists a permutation, f:S→S, such that every relation and ordering is preserved:
Ri(x1,…,xk) < - > Ri(f(x1),…,f(xk)) for i = (1,…,n)
Hence each word is given a unique meaning once we consider its relations to other words or concepts. In other words, f(.) is an automorphism, and all languages are sets linked via relation-preserving automorphisms.
Crucially, this automorphism preserves invariance in meaning. If there exists an automorphism linking elements a to b in S, then a corresponds to b in a manner such that they're semantically equivalent. In general, if you replace all the elements of a group with different objects, yet preserve the same permutations and functional operations, then such a group is isomorphic. Languages are no different. Indeed, Tarski's definition of truth uses this intuition over isomorphisms mapping between different formal structures2.
In general, I'm inclined to agree with the structuralist approach emphasised by the likes of Levi-Strauss (albeit the set of relations is broader than binary!). However Derrida and the deconstructivists are simply wrong when they claim this implies that all semantic meaning is arbitrary, and a function of social power structures and the like. The fact that languages are defined via an automorphic structure means that semantic meaning is invariant, including to social fads and privilege. Of course, correspondance to truth and objective reality is debatable, but the deconstructivists are likely wrong there.
Letters/sounds, words, etc
Note that “formal systems need not be isomorphic”, yet all languages are automorphic. If a mathematician could verify that Astra's theorem is true, then I think this structuralist approach could resolve the Brouwer vs Hilbert controversy; something I've been thinking about for a while.