I said: The Godelian paradox seems to be a feature of any Language that is strong enough to be dependent on evaluation across a finite or infinite iteration via a theoretical representation. That means that the valuation of a sentence may need to be based on more information that might be represented using a virtual meta-language.
I meant: The Godelian paradox seems to be a feature of any Language that is strong enough to be dependent on evaluation across a finite or infinite iteration via a theoretical representation. That means that the valuation of a sentence may need to be based on more information than can be analyzed in a single step. That information could be represented with what would effectively be a virtual meta-language. Jim Bromer On Sun, Aug 24, 2014 at 8:29 PM, Jim Bromer <[email protected]> wrote: > I don't completely understand the paper but the underlying belief that if > you use weighted reasoning or probability reasoning then the problem of > 'understanding' can be resolved by methods of increasing the accuracy of > successive approximations seems a little presumptuous to me. The reliance > of methods which are based on this kind of premise may be the foundation of > some of the applied science for technicians but it is not a > secure foundation for research science or even for engineering. > > While I think their idea is interesting (if I understand it as far as I > have gotten) I don't think that you can deny Godelian paradoxes just by > defining an algorithm which is designed to avoid them. Even assuming that > their use of the Oracle approximator is a stub for unknown processes which > could be used to examine a sentence in the induction process, the denial > that the strings that are being produced by the algorithm has to constitute > a logical Language is a little weak. And if the examination of successive > approximations is based on a poor theoretical analysis then paradoxes be > insipidly inducted into the system. > > When I was first told about paradoxes I am sure the concept went right > over my head. I believe I eventually discovered paradoxes in general rules > of how I was supposed to behave or in trying to find good ways to respond > to situations. Because of the importance of being able to use a language to > consider the nature of paradoxes, any foundational AGI mathematical system > has to be able to deal with paradoxes that can be analyzed even it they > can't be valued as True or False. How could a Language (with a fancy L) be > considered as a good theoretical underpinning for an AGI project if it > cannot hold paradoxes? The Godelian paradox seems to be a feature of any > Language that is strong enough to be dependent on evaluation across > a finite or infinite iteration via a theoretical representation. That > means that the valuation of a sentence may need to be based on more > information that might be represented using a virtual meta-language. And > the typical nature of a logic statement is that its evaluation may require > more than a single simple evaluation step. A logical sentence may be > partially evaluated but the evaluation of the entire sentence will usually > need to take more than one step. > > I think Logical Positivism faded away because the languages of > the Positivists were not strong enough to be used to analyze logical > statements other than those that were already evaluated. I suspect that > you might not be technically able to use a truly Positivist Language to > study logical statements because some logical statements can be paradoxical. > > It is important to be able to work with apparent paradoxes in order to > discover how the paradoxes might be resolved. While their Oracle would be > able to tell you that a resolution was more likely after taking successive > analytical steps, that does not always (or usually) hold for practical > methods of study. > > I am making what is probably my last effort to find an effective solution > to Boolean Satisfiability not because I think that Logic would be > sufficient for an AGI language of thought but because I think that a > polynomial time solution would provide a great deal of leverage for a > program capable of 'thought' to work with. > > > Jim Bromer > > > On Thu, Aug 21, 2014 at 1:02 PM, Ben Goertzel via AGI <[email protected]> > wrote: > >> >> This time some of the MIRI (Singularity Institute) guys have discovered a >> fairly cool mathematical nugget, that relates a bit to OpenCog... >> >> http://intelligence.org/files/DefinabilityTruthDraft.pdf >> >> What they show here is basically that some paradoxes of "reflection" in >> logical systems go away if one considers only statements with (open) >> interval truth values, rather than single-point truth values... >> >> This has direct implications for PLN, which uses imprecise (i.e. >> interval) truth values.... It shows that, in a sense, PLN can be >> reflective without spawning nasty Godel paradoxes.... It shows that one >> can define "truth within PLN" within PLN, without running into >> Godelian/Tarskian limitations.... Kinda cool... >> >> -- Ben >> >> -- >> Ben Goertzel, PhD >> http://goertzel.org >> >> "In an insane world, the sane man must appear to be insane". -- Capt. >> James T. Kirk >> >> "Emancipate yourself from mental slavery / None but ourselves can free >> our minds" -- Robert Nesta Marley >> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> >> <https://www.listbox.com/member/archive/rss/303/24379807-f5817f28> | >> Modify >> <https://www.listbox.com/member/?&;> >> Your Subscription <http://www.listbox.com> >> > > ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
