On Thu, Sep 12, 2013 at 5:56 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
> 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).
Thanks Bruno! I really have to find some time to read Forever
Undecided, and hope you can come back to the intensional fixed point.
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