From nobody@digitalkingdom.org Mon Jul 17 16:29:09 2006 Received: with ECARTIS (v1.0.0; list lojban-list); Mon, 17 Jul 2006 16:29:09 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G2cW9-0002AV-BL for lojban-list-real@lojban.org; Mon, 17 Jul 2006 16:28:49 -0700 Received: from web81315.mail.mud.yahoo.com ([68.142.199.41]) by chain.digitalkingdom.org with smtp (Exim 4.62) (envelope-from ) id 1G2cW8-0002AN-8W for lojban-list@lojban.org; Mon, 17 Jul 2006 16:28:49 -0700 Received: (qmail 98391 invoked by uid 60001); 17 Jul 2006 23:28:47 -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=ibnUP2MADzGeuOd6lx5e6OXh68bicC2fGid3ebweEKmFFqAIvDCICXLb6bOBCXjXmSsEti6+f27ZLJPKDn4g7mb+pshEqplHtZJAmMU63H1Tui7DpApUCg5iU0ZSweDZg6a463w8K3Or7XmJ6c3VyQsm75B3CK0Ul9B9mOutJ9U= ; Message-ID: <20060717232847.98389.qmail@web81315.mail.mud.yahoo.com> Received: from [70.237.227.139] by web81315.mail.mud.yahoo.com via HTTP; Mon, 17 Jul 2006 16:28:47 PDT Date: Mon, 17 Jul 2006 16:28:47 -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: 12238 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 And more --- 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 ei is identical to one of the ds. > > Since the array of functions for each predicate is unique as is the function for each number, we > casn 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). > > 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 Where R is a relation between terms and things in the domain such that If a is a name then iff aRd, aId If a is a variable then iff aRd, aAd If a is txF, for some formula F and variable x, then there are d1,…dn such that F is true for I and A(d2…dn/x) and aRd iff d=di (1 less than or equal i less than or equal n) > 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) [All this probably needs reference to R as well as I and A.] > > 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.