Path: news.cambrium.nl!textnews.cambrium.nl!feeder3.cambriumusenet.nl!feed.tweaknews.nl!postnews.google.com!m3g2000yqf.googlegroups.com!not-for-mail From: Marshall Newsgroups: comp.databases.theory,sci.logic,sci.philosophy.tech Subject: Re: Fitch's paradox and OWA Date: Fri, 1 Jan 2010 07:28:30 -0800 (PST) Organization: http://groups.google.com Lines: 40 Message-ID: <3778345b-3bec-4fea-86a5-0fbc7080b183@m3g2000yqf.googlegroups.com> References: <4919dc70-6375-432e-b2aa-2f7c1b3c15ba@n31g2000vbt.googlegroups.com> <793ea30a-d7e3-40f3-b0c4-8a42a80be283@h9g2000yqa.googlegroups.com> <206ead77-34a9-4d58-9210-625564222a4f@m26g2000yqb.googlegroups.com> <841a1d32-bc4d-46a7-8e35-6037d54ff809@h9g2000yqa.googlegroups.com> <8797bda2-6276-40e8-82cd-e2820ee9df51@j24g2000yqa.googlegroups.com> <7Wd%m.554$XU.447@newsfe03.iad> 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 1262359710 8623 127.0.0.1 (1 Jan 2010 15:28:30 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 1 Jan 2010 15:28:30 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: m3g2000yqf.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:158632 comp.databases.theory:38101 On Dec 31 2009, 7:24=A0pm, Nam Nguyen wrote: > Marshall wrote: > > Can you verify that your definition of the naturals meet the definition o= f > formal system model, with say Q is the underlying system at hand, as I di= d > verify M w.r.t to T above? [It's just a pure simple technical question!] I expect so. I haven't gone through the exercise at length, but the whole process seems straightforward enough. I have done certain individual proofs, but not all of them. > > What difficulties do you foresee? > > Ok. this is a much better and more technical question one could entertain= . > > In a nutshell, one of difficulties that formula such as (1) or (1') prese= nts is > that there's no way you could define any model of Q such that a certain e= xpected > set of 2-tuples (i.e. _relation_) can be verified to exist. And if you ca= n't, > you can't tell whether or not you have would conform to the overall defin= ition of a > model of the underlying formal system (say Q in this case). If you don't admit the existence of any possible technique of showing such a thing, it wouldn't be a good use of my time to try to convince you otherwise. Note at least that yours is a minority opinion, here; it's certainly possible to show the necessary relations exist, and have the desired properties, though such ordinary methods as induction. Marshall