From nobody@digitalkingdom.org Mon Jul 17 08:46:33 2006 Received: with ECARTIS (v1.0.0; list lojban-list); Mon, 17 Jul 2006 08:46:33 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G2VIR-0006FX-3X for lojban-list-real@lojban.org; Mon, 17 Jul 2006 08:46:12 -0700 Received: from web81315.mail.mud.yahoo.com ([68.142.199.41]) by chain.digitalkingdom.org with smtp (Exim 4.62) (envelope-from ) id 1G2VII-0006FO-Tu for lojban-list@lojban.org; Mon, 17 Jul 2006 08:46:07 -0700 Received: (qmail 12033 invoked by uid 60001); 17 Jul 2006 15:46:01 -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=WwxMEtbiwisRKZ0A3eIo7ZBiXoc8W9VpZ8XndvJGXR6JfalgL4RH3BZYoWys4C1+bi8+1Jc2LCBni9+rvRmODuEzB01BZ2kTr6nGfMTRhFr52WzggdR3rMtZ4OioU3F8L2iGTXmQSM9+ke5suh0tdd1QF9ZVJ3aANia610ns5Z8= ; Message-ID: <20060717154601.12031.qmail@web81315.mail.mud.yahoo.com> Received: from [70.237.227.139] by web81315.mail.mud.yahoo.com via HTTP; Mon, 17 Jul 2006 08:46:01 PDT Date: Mon, 17 Jul 2006 08:46:01 -0700 (PDT) From: John E Clifford Subject: [lojban] Re: A (rather long) discussion of {all} To: lojban-list@lojban.org In-Reply-To: <20060717120549.46481.qmail@web81304.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Spam-Score: -0.7 (/) X-archive-position: 12230 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 Correction and expansion --- John E Clifford wrote: > Trying again in a more straightforward way: > > Singularist: > > Domain D > Masses M: all subsets of D with two or more members > > Interpretation I > assigns to each name a member of D u M > assigns to each predicate a set included in D u M > assigns to Y the relation between D u M and M that hold just in case the first relatum is > a member of or included in the second relatum. > > Assignment A assigns to each variable a member of D u M > If A is an assignment, A(d/x) is an assignment just like A except for assigning d from > D u M to variable x in place of A(x) > > R is a function from terms a to members of D u M, such that > If a is a name, R(a) = I(a) > If a is a variable, R(a) = A(a) > If a = txF, R(a) is some member d of D u M such that F is true for I and A(d/x) > > A formula Pa is d-true for I and A iff either I(a) e D and I(a) e I(P) or I(a) e M and for > every d e I(a) d e I(P). > > A formula Pa is c-true for I and A iff I(a) e I(P). > > A formula Pa is true for I and A iff it is either c-true or d-true > > A formula ~F is true for I and A iff F is not true for I and A > > A formula &FG is true for I and A iff both F and G are true for I and A > > A formula ExF is true for I and A iff for some d e D u M, F is true for I and A(d/x) > > > Pluralist: > > Domain D > > I is a relation whose first relatum is A name and whose second relatum is a member of d A predicate and whose second relatum is an n-place function over D into {0,1} Y and whose second relatum is an n+m-place function over D into {0,1} Such that each name is related to at least one member of D, each predicate is related to exactly one n-place function, for every n between 1 and the size of D, Y is related to exactly one function fnm for each n, m between 1 and the size of D, such that I(Y)(nm) (d1…dn e1…em) = 1 iff each di is identical to one of the es. Since the array of functions for each predicate is unique as is the function for each number, we can refer to the n-place function of a given predicate P as I(P)(n). For convenience, we will abbreviate “d1 … dn such that each di aIdi” as I(a). In the sequence d1 … dn it is understood that 1) no two items are identical and 2) the order of the items is not significant (the value of a function for d1…dn in order is the same as the value for any permutation of that order). In the definition of I(Y) above , the ds and the es are separate sequences to which the above restrictions apply: a permutation of the whole conjoined sequence that involved es and d being interdigitated would not necessarily yield the same value and an e may be identical with a d, just not another e. We say “d1…dn numbers n” > > A is a relation between variable and members of D > A(d1…dn/x) is a relation just like A except that x is related to each of d1… dn rather than > to > the things it is related to by A > > We use A(x) analogously to I(a) > > In the same vein we can define > R(a) = I(a) if a is a name > R(a) = A(a) if a is a variable > R(a) is some d1…dn such that F is true for I and A(d1…dn/x) if a = txF > > Pa is d-true for I and A iff for every d in R(a) I(P)(1)(d) = 1 > Pa is c-true for I and A iff R(a) numbers n and I(P)(n)(R(a)) = 1 > > F is true for I and A iff > F = Pa and Pa is d-true for I and A or Pa is c-true for I and A. > F = Yab and R(a) numbers n and R(b) numbers m and I(Y)(nm) (R(a)R(b)) =1 > F = ~G and G is not true for I and A > F = &GH and both G and H are true for I and A > F = ExG and, for some d1…dn from D, G is true for I and A(d1…dn/x) > > > > 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. > > 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.