"I paid you back yesterday, if you remember"

I take this example from a footnote in Austin's "Ifs and Cans" ( p. 213 Phil Papers 3rd Ed ). Austin credits it to Peter Geach and describes it as another "excellent' example to illustrate the difference between "the conditional if and the if of doubt or hesitation". I don't disagree that the if clause does not state a sufficient condition for the apodosis, but let's see if we understand exactly what going on with this usage.

Austin suggests as a paraphrase the question "I paid you back yesterday, don't you recall?" That is possible, I suppose, but I can't hear someone asking a question in that idiom. If a person genuinely wants to ask a question, he will say "Do you/do you not recall that I paid you back yesterday?"

"I paid you back yesterday, if you remember", first of all, asserts that I paid you back. Your recalling at this time that I did so is obviously no condition of that having happened in the past. The utterance also suggest to the listener, politely, that he take some time and recall what happened. Less, or perhaps much less polite, would be the suggestion "You will remember that I paid you back yesterday." That directive, I suppose we'd call it, comes close to be a command or a demand, in a situation where giving commands or making demands is not appropriate. We prefer an idiom which does not demand the listener remember something, but suggests that if he think about it, you will perhaps remember that I paid you.

That is the paraphrase I would offer. "I paid you back yesterday. If you will take a minute to reflect, perhaps you will remember that I did so." But I don't ordinary speakers need a paraphrase. They understand quite well what the speaker is doing and saying.

I don't like Austin's description of this usage as an if of doubt or hesitation. The speaker is signaling no doubt or hesitation. He is making a polite suggestion or request rather than a demand. But should look at some similar usages to confirm this.