As I originally heard this, back in the 1970s, the logicians had hats put on their heads, or dots on their foreheads.

I too find the recursive logic unconvincing. Martin Gardner talks about this problem, and goes into greater detail about a similar problem in his book "The Unexpected Hanging" - https://en.wikipedia.org/wiki/Unexpected_hanging_paradox - and there have been further writings but none have actually cracked it, at least for me.