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> > Gödel’s theorem, you may recall, shows that certain claims in mathematics are true but cannot be proven This is not correct to begin with. Incompleteness i

> > Gödel’s theorem, you may recall, shows that certain claims in mathematics are true but cannot be proven This is not correct to begin with. Incompleteness in this setting means that a formal system is either unprovable or indeed inconsistent (ie. wrong). A "known unknown" is just an oxymoron. > that the consistency of sufficiently-complex systems cannot be proved that sounds more like it. EDIT: I have to read up on it again and again ... the consistency of sufficiently-complex systems cannot be proved within that system.

dvt 10y ago
> that sounds more like it. EDIT: I have to read up on it again and again ... the consistency of sufficiently-complex systems cannot be proved within that system. Nope. Godel's Incompleteness Theorems (GIT) are metalogical[1]. They leak to any (sufficiently-complex) formal system. You can't logic them away by going up a level of abstraction. Let's say you have a (sufficiently-complex) system A which is susceptible to GIT. You can describe A in terms of a meta-system B. By definition, B will also be susceptible to GIT. You can describe B in terms of C, and so on, but every meta-system that follows will still be susceptible to GIT. [1] http://www.mbph.de/Logic/Para/Metalogic.pdf http://www.mbph.de/Logic/Para/Metalogic.pdf