Frege’s judgment stroke

Are the conditions required to assert something conventions? Can they be formalized? Donald Davidson on whether convention is foundational to communication:

But Frege was surely right when he said, “There is no word or sign in language whose function is simply to assert something.” Frege, as we know, set out to rectify matters by inventing such a sign, the turnstile ⊢’ [sometimes called Frege’s ‘judgment stroke’ or ‘assertion sign’]. And here Frege was operating on the basis of a sound principle: if there is a conventional feature of language, it can be made manifest in the symbolism. However, before Frege invented the assertion sign he ought to have asked himself why no such sign existed before. Imagine this: the actor is acting a scene in which there is supposed to be a fire. (Albee’s Tiny Alice, for example.) It is his role to imitate as persuasively as he can a man who is trying to warn others of a fire. “Fire!” he screams. And perhaps he adds, at the behest of the author, “I mean it! Look at the smoke!” etc. And now a real fire breaks out, and the actor tries vainly to warn the real audience. “Fire!” he screams, “I mean it! Look at the smoke!” etc. If only he had Frege’s assertion sign.

It should be obvious that the assertion sign would do no good, for the actor would have used it in the first place, when he was only acting. Similar reasoning should convince us that it is no help to say that the stage, or the proscenium arch, creates a conventional setting that negates the convention of assertion. For if that were so, the acting convention could be put into symbols also; and of course no actor or director would use it. The plight of the actor is always with us. There is no known, agreed upon, publically recognizable convention for making assertions. Or, for that matter, giving orders, asking questions, or making promises. These are all things we do, often successfully, and our success depends in part on our having made public our intention to do them. But it was not thanks to a convention that we succeeded.¹

1. Davidson, Donald. (1984). Communication and convention. Synthese 59 (1), 3-17. [↩]