There are two ideas that seem to come up in tandem often in philosophical theorizing, reflexivity and iteration. The liar paradox if reflexive, while theories of truth that try to deal with it via a hierarchy of truth, with some distinguished class of truths being ‘grounded’, are iterative. Common knowledge is iterative, i.e. all agents know X, they know that they all know it, etc. This is iteration of mutual knowledge. The canonical interpretation of Grice’s theory of implicature posits an iterative hierarchy of communicative intentions. An agent intends for an audenience A to recognize X, intends for A to recognize that intention, etc. Bach put forward an interpretation of Grice’s theory that dispenses with the iterative hierarchy and replaces it with an reflexive intention. The reflexive communicative intention is satisfied by its recognition. I will have to go back to Grice’s articles to see how this squares with what he said, but it is appealing. We can dispense with an infinite hierarchy and replace it with an intention that refers to to itself. Does this create a paradox? The reflexive paradoxes (e.g. the liar) are brought about by conditions that are mutually contradictory. The sentence’s being true implies its falsity, and the converse.. Or, in the case of Russel’s paradox, a set’s containing itself implies that it does not contain itself, and the converse. What happens if we move this to intentionality? If I intend that my intention is satisfied only by its non-recognition, then I would be in trouble. However, it is does not seem like this could be a communicative intention, since at the very least those must be recognized to be satisfied. It looks like Bach’s interpretation is safe from that.

As an aside, both Recanati and Bach provide differing interpretations of Grice that take their views on language to very different places. It would be worthwhile to read through both of their writings and work out exactly how their views differ and how these differences play out in their ideas on, say, pragmatics.