I have this idea that impredicative systems create little universes that exist separate from the larger universe, including recursive universes, impenetrable universes et al. But then that leads me to self-enveloping universes.
"This moment contains all moments" -- CS Lewis On Apr 22, 2013 4:33 AM, "Chris Warburton" <[email protected]> wrote: > John Carlson <[email protected]> writes: > > > If there truly is a universal language, is it a systems language? A > logic > > language can describe hardware. What about things like pointers? Have > > they come up with self-referential logic? > > On Apr 20, 2013 11:18 PM, "John Carlson" <[email protected]> wrote: > > Self-referential logics are known as "impredicative"[1], but surely any > Universal programming language is a Universal language? > > Having a Universal language only guarantees that we can represent every > (computable) thing; it tells us nothing about how difficult it is to > construct them[1]. > > Plus we can only ever construct models of things; no system can describe > pointers completely (for example), since we can write Goedel sentences > which involve pointers; a trivial example would be the halting problem > for pointer-manipulating programs. > > [1] http://en.wikipedia.org/wiki/Impredicativity > [2] http://en.wikipedia.org/wiki/Turing_tarpit > > Regards, > Chris > _______________________________________________ > fonc mailing list > [email protected] > http://vpri.org/mailman/listinfo/fonc >
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