Compositionality is a property that a semantics for some language has, if the meaning of any of its complex expressions (relative to the semantics) is uniquely determined by the meaning of the expressions' parts and their mode of composition.
Some logicians such as Kit Fine argue that the standard semantics for first-order logic is not compositional. I've always been puzzled by this claim among other things because there is no uncontroversial meaning concept associated with first-order formulas.
Actually I've never come across a formal proof of this claim. By a formal proof I mean a proof carried out in the now standard algebraic framework for compositionality provided by Wilfrid Hodges (Journal of Logic, Language and Information 10 (2001)). So is there any formal proof out there?