Path: news.cambrium.nl!textnews.cambrium.nl!feeder3.cambriumusenet.nl!feed.tweaknews.nl!postnews.google.com!m25g2000yqc.googlegroups.com!not-for-mail From: Marshall Newsgroups: comp.databases.theory,sci.logic,sci.philosophy.tech Subject: Re: Fitch's paradox and OWA Date: Thu, 31 Dec 2009 16:39:50 -0800 (PST) Organization: http://groups.google.com Lines: 40 Message-ID: <37b01b4f-e2cc-4369-bb8b-e7d105de0e25@m25g2000yqc.googlegroups.com> References: <4919dc70-6375-432e-b2aa-2f7c1b3c15ba@n31g2000vbt.googlegroups.com> <793ea30a-d7e3-40f3-b0c4-8a42a80be283@h9g2000yqa.googlegroups.com> <17e8ec70-caf8-4177-8e04-da413070d540@e27g2000yqd.googlegroups.com> NNTP-Posting-Host: 24.4.91.50 Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: posting.google.com 1262306390 25125 127.0.0.1 (1 Jan 2010 00:39:50 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 1 Jan 2010 00:39:50 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: m25g2000yqc.googlegroups.com; posting-host=24.4.91.50; posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA User-Agent: G2/1.0 X-HTTP-UserAgent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.9.1.6) Gecko/20091201 Firefox/3.5.6,gzip(gfe),gzip(gfe) Xref: news.cambrium.nl sci.logic:158580 comp.databases.theory:38086 On Dec 31, 4:18=A0pm, Nam Nguyen wrote: > Marshall wrote: > > On Dec 31, 3:40 pm, Nam Nguyen wrote: > >> Barb Knox wrote: > > >>> They are true or false in any *particular* model. =A0Since we apparen= tly > >>> cannot formally pin down arithmetic to have just one particular model > >>> (the Standard one) then there will always be some arithmetic statemen= ts, > >>> the undecidable ones, which are true in some models and false in othe= rs. =A0 > >> Agree. The question - and the heart of my argument - is whether or not= there > >> exists a formula F such that it's impossible to know/assert a truth va= lue > >> in the collection K of _all_ arithmetic models: K =3D {the standard on= e, the > >> non-standard ones}? I've argued that there exist such statements. > > > Why would the existence of such statements imply that there > > are truth values other than true or false? > > Because a) FOL truth is no longer absolute: it has to be relativized to s= ome > models; and yet b) what one constructs and _label_ as a model might indee= d > be impossible to be technically verified as a model. How could a statemen= t be > true or false if in the first place it can't be true-able or false-able? > > I think I've asked/raised this question a few times but have yet to hear > a response to it! There is simply no issue here to respond to. Everything you've said here is either false or else it's the same as the conclusion you're trying to establish. Marshall