Disclaimer: I have absolutely no background in philosophy or logic.
I've just randomly read the short story "What the Tortoise said to Achilles" by Lewis Carrol. As far as I have understood this, Achilles tries to force the tortoise to accept a simple conclusion, but fails because the tortoise leads him into an infinite regression.
But I couldn't stop thinking about the following: Couldn't Achilles force the turtle to accept the statement with the help of self reference? Like, by writing
(C) If A and B and C are true, Z must be true.
Something in my gut tells me this is not possible, but I can't figure out why. Why would this solution not work?