What would the rule be about using a negative as a positive? What would that type of word or phrase be called?
Example: "Let's see if we can't find a solution." or "I wonder if we couldn't make a reservation."
A friend suggested "autoantonym" but I can't see it as appropriate, as the negative use is gramatically incorrect, yet idiomatically correct.

Anyone? Anyone?
What would the rule be about using a negative as a positive? What would that type of word or phrase be called?

Sarcasm.
Example: "Let's see if we can't find a solution." or "I wonder if we couldn't make a reservation." A friend suggested "autoantonym" but I can't see it as appropriate, as the negative use is gramatically incorrect, yet idiomatically correct.

I can't see anything ungrammatical about it.
Stewart.

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What would the rule be about using a negative as a positive? What would that type of word or phrase ... friend suggested "autoantonym" but I can't see it as appropriate, as the negative use is gramatically incorrect, yet idiomatically correct.

Using a negative sort of takes off the pressure of asking for the positive, making a request more tentative, and hence more polite, eg "I don't suppose you know...", though the combination of the softener "I wonder if..." with the negative in your second example sounds a bit odd to my (BrE) ear. Unless that's one hell of a restaurant.

Adrian Smith