From nobody@digitalkingdom.org Fri Jul 14 08:44:33 2006 Received: with ECARTIS (v1.0.0; list lojban-list); Fri, 14 Jul 2006 08:44:33 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G1Ppu-0008Ux-En for lojban-list-real@lojban.org; Fri, 14 Jul 2006 08:44:14 -0700 Received: from web81313.mail.mud.yahoo.com ([68.142.199.39]) by chain.digitalkingdom.org with smtp (Exim 4.62) (envelope-from ) id 1G1Ppt-0008Un-GB for lojban-list@lojban.org; Fri, 14 Jul 2006 08:44:14 -0700 Received: (qmail 80744 invoked by uid 60001); 14 Jul 2006 15:44:12 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=sbcglobal.net; h=Message-ID:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding; b=yjBiUymrrvsUl3f02o8PIncvFhgqDq71A/HV7eXNMJjdRfXQgSprEtvMqFo1IEVQXrsW7Umwgukxh7CgxOL7JpmJfhlMkGA5r4oWGrgH3M41++ZQ+pFVurqwbSl3bkzA+rfmjs1FrH13bikS6THzRxIAJUxkqswLEynCI0pcvgk= ; Message-ID: <20060714154412.80742.qmail@web81313.mail.mud.yahoo.com> Received: from [70.230.169.179] by web81313.mail.mud.yahoo.com via HTTP; Fri, 14 Jul 2006 08:44:12 PDT Date: Fri, 14 Jul 2006 08:44:12 -0700 (PDT) From: John E Clifford Subject: [lojban] Re: A (rather long) discussion of {all} To: lojban-list@lojban.org In-Reply-To: <925d17560607131846jb3d95d1wf9559cf162677db5@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Spam-Score: -0.6 (/) X-archive-position: 12196 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: clifford-j@sbcglobal.net Precedence: bulk Reply-to: lojban-list@lojban.org X-list: lojban-list --- Jorge Llamb�as wrote: > On 7/13/06, John E Clifford wrote: > > > > > A is an assignment iff A is a function from variables to concepts > > A(c/x) is an assignment just like A except that it assigns the concept c to variable x instead > of > > A(x). > > (I assume assignment A and relation A are different things, it might > be a good idea to use different letters.) Yeah; this thing went through at least three versions so somethings didn't get caught up from one version to the next. Will fix. thanks. > Question: Given an assignment A, is the assignment A(c/x) also given, > or are they independent functions? Yes, that is, given A and c and x, A(c/x) is defined. > > If a is a term, R(a) = I(a) if a is a name, R(a) = A(a) if a is a variable, R(a) is a concept > c > > such that F is true for A(c/x), if a = txF > > So R is a function from terms to concepts. Is it called something? Well, the usual expressions is "reference" but that doesn't seem appropriate here. > We don't know what "F is true" means at this point, not sure if this > could lead to circularity. These definitions are all collapsed forms of recursive definitions (I was trying to keep this as uncomplicated as possible -- but when you simplify one place it always makes a probelm sowhere else). So txF is a term of a degree higher than F is a formula and truth for F is defined then before R for txF is defined. > > Where P is a predicate and a a term, Pa is d-true for I and A iff for every individual i > included > > in R(a) and for every concept c s.t. I(c) = i, I(P)(c) = 1 > > That would be "every individual i included in I(R(a))", I think. Yes, R(a) is just a concept, not a set. Deeper thanks, as that was a real problem, not just an infelicity. > > A Pluralist model > ... > > C is a relation between concepts and items in D, such that for every d in D, there is at least > > once c such that c is related by C only to d (C/d) > > What's (C/d) ? A specific c such that cCd. > The restriction for every d doesn't seem to have an equivalent in the > singularist model. I'm not sure it is needed (I'm not sure it is needed here, come to that, but it was a quick solution to a problem I saw -- there may be others). It would require something like that there be a concept for set, which is less plausible somehow. the point where this comes up may need some reworking, which is why this kite is up. > > And interpretation I is a function which assigns > ... > > To A the function from pairs of concepts into {0,1} such that I(A)(R(a)R(b)) = 1 iff > > for every thing d such that R(a)Cd holds, R(b)Cd holds > > Couldn't A be defined more generaly for any c1,c2 like for the singularist > model, instead of just for R(a)R(b)? Yes, but it was stuck in here looking toward a definition of truth. To unsubscribe from this list, send mail to lojban-list-request@lojban.org with the subject unsubscribe, or go to http://www.lojban.org/lsg2/, or if you're really stuck, send mail to secretary@lojban.org for help.