On Thursday, September 12, 2013 11:56:12 AM UTC-4, Bruno Marchal 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: > > http://en.wikipedia.org/wiki/Unexpected_hanging_paradox > > > > 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,
It's the symbol grounding problem too. From a purely quantitative perspective, a truth can only satisfy some condition. The expectation of truth being true is not a condition of arithmetic truth, it is a boundary condition that belongs to sense. Computers cannot lie intentionally, they can only report a local truth which is misinterpreted as being false in some sense that is not local to the computation. For the same reason, computers cannot intend to tell the truth either. As in the Chinese Room - the output of a program is not known by the program to be true, it simply is a report of the truth of some internal process. The interesting part is that besides being true locally, the computer's report is also true arithmetically, which is to say that it is true two ways (or senses): 1) the most specific/proprietary sense which is unique, private, instantaneous and local 2) the most universal/generic sense which is promiscuous, public, eternal, and omni-local The computer's report is, however not true in any sense in between, i.e. in any sense which relates specifically to real experienced events in space time. Real events in spacetime (which occur orthogonally through mass-energy, or rather mass-energy is the orthogonal cross section of events) are: 3) semi-unique, semi-private, semi-spatiotemporal, semi-local, semi-specific, semi-universal. Thanks, Craig > 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). > > Best, > > Bruno > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
