Eric, looks 'real' good. Thx for the link. - g Sent from my iPhone
> On Dec 29, 2015, at 9:19 AM, David Eric Smith <[email protected]> wrote: > > Right. > > I thought the point was that you can have propositions that are "true" in the > sense of being consistent within the system, but not provable by > constructions defined within the system. > > But all this, too relies heavily on what you consider to constitute truth > value for propositions (some acceptance criterion more liberal than strict > constructivism). > > Also, the incompleteness theorems are a particular property of the indexing > of the integers, and their maps to proofs. I believe there are no > counterpart problems within the reals, because the cardinality mismatch is > not the same. A book on this that I have liked is Torkel Franzen's > relatively short and pleasant survey: > http://www.amazon.com/G%C3%B6dels-Theorem-Incomplete-Guide-Abuse/dp/1568812388 > > If there are any here who don't like non-constructive notions of truth, there > is recent work to find out how much of mathematics can be built only from > constructive arguments (I think I have this right). Perhaps we have > discussed it before on this list (getting old and dotty), but a wikipedia > summary is here: > https://en.wikipedia.org/wiki/Univalent_foundations > and the group's webpage is here > https://www.math.ias.edu/sp/univalent/goals > > All best, > > Eric > > >> On Dec 28, 2015, at 1:33 PM, Grant Holland wrote: >> >> Oh yes, it need not be neither. It just can't be both! >> >> Grant >> >> Sent from my iPhone >> >>> On Dec 28, 2015, at 3:29 PM, Grant Holland <[email protected]> >>> wrote: >>> >>> Glen, Eric, >>> >>> If "reality" is complete, must not then (assuming that it is at least as >>> complex as arithmetic), aka Godel, it be also inconsistent? >>> >>> Grant >>> >>> Sent from my iPhone >>> >>>>> On Dec 28, 2015, at 11:23 AM, glen <[email protected]> wrote: >>>>> >>>>> On 12/28/2015 06:30 AM, David Eric Smith wrote: >>>>> A language that is not even internally consistent presumably has no hope >>>>> of having an empirically valid semantics, since evidently the universe >>>>> "is" something, and there is no semantic notion of ambiguity of its >>>>> "being/not-being" some definite thing, structurally analogous to an >>>>> inconsistent language's being able to arrive at a contradiction by taking >>>>> two paths to answer a single proposition. >>>> >>>> It's not clear to me that the presumption is trustworthy. Isn't it >>>> possible that what is (reality) does not obey some of the structure we >>>> rely on for asserting consistency (or completeness)? In other words, >>>> perhaps reality is inconsistent. Hence, the only language that will be >>>> valid, will be an inconsistent language. Of course, that doesn't imply >>>> that just any old inconsistency will be tolerated. Perhaps reality is >>>> only inconsistent in very particular ways and any language that we expect >>>> to validate must be 1) inconsistent in all those real ways and 2) in only >>>> those real ways. >>>> >>>> Further of course, inconsistency is a bit like paradox in that, once you >>>> identify an inconsistency very precisely, you may be able to define a new >>>> language that eliminates it. ... which brings us beyond the (mere) points >>>> of higher order logics and iterative constructions, to the core idea of >>>> context-sensitive construction. There is no Grand Unifying Anything >>>> except the imperative to approach Grand Unified Things. >>>> >>>> And this targets Patrick's argument against the idealists (e.g. >>>> libertarians and marxists). The only reliable ideal is the creation and >>>> commitment to ideals. Each particular ideal is (will be) eventually >>>> destroyed. But for whatever reason, we seem to always create and commit >>>> ourselves to ideals. Old people tend to surrender over time and build >>>> huge hairballs of bandaged ideals all glued together with spit and bailing >>>> wire. Any serious conversation with an old person is an attempt to >>>> navigate the topology of their iteratively constructed, stigmergic, >>>> hairball of broken ideals ... and if that old person is open-minded, such >>>> conversations lead to new kinks and tortuous folds ... which is why old >>>> people make the best story tellers. >>>> >>>> But I can't help wondering why music is dominated by the young. [sigh] >>>> >>>> -- >>>> -- >>>> ⊥ glen ⊥ >>>> >>>> ============================================================ >>>> FRIAM Applied Complexity Group listserv >>>> Meets Fridays 9a-11:30 at cafe at St. John's College >>>> to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> >> ============================================================ >> FRIAM Applied Complexity Group listserv >> Meets Fridays 9a-11:30 at cafe at St. John's College >> to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
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