On 12 Sep 2013, at 11:33, Telmo Menezes wrote:

Time for some philosophy then :)

Here's a paradox that's making me lose sleep:

Probably many of you already know about it.

What mostly bothers me is the epistemological crisis that this
introduces. I cannot find a problem with the reasoning, but it's
clearly false. So I know that I don't know why this reasoning is
false. Now, how can I know if there are other types of reasoning that
I don't even know that I don't know that they are correct?

Smullyan argues, in Forever Undecided, rather convincingly, that it is the Epimenides paradox in disguise, and so it can be said to be solved in the same way (by Tarski theorem and Gödel's theorem), at least for self-referentially correct machine.

I can follow Smullyan here, but I think also that this form of Epimenides, by the use of time, run probably deeper, and that it might lead to deeper explanations. In fact intensional fixed point à-la- Rosser are probably closer to it (we might come back on this, it is technical).




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