Return-Path: <@segate.sunet.se:LOJBAN%CUVMB.BITNET@BITMAIL.LSOFT.COM> Received: from segate.sunet.se by xiron.pc.helsinki.fi with smtp (Linux Smail3.1.28.1 #1) id m0syN4q-0000ZSC; Thu, 28 Sep 95 19:48 EET Message-Id: Received: from listmail.sunet.se by segate.sunet.se (LSMTP for OpenVMS v0.1a) with SMTP id 6EADD914 ; Thu, 28 Sep 1995 18:33:56 +0200 Date: Thu, 28 Sep 1995 13:21:19 EDT Reply-To: jorge@PHYAST.PITT.EDU Sender: Lojban list From: jorge@PHYAST.PITT.EDU Subject: Re: quantifiers and existence X-To: lojban@cuvmb.cc.columbia.edu To: Veijo Vilva Content-Length: 2361 Lines: 65 djer: > I think what pc means here is that something of the form: > > E(x)[A(x)broda(x)]. has a scope that asserts the second x exists. I don't think pc would accept that as a well formed expression. You can't quantify the same variable twice. (You can use the same variable in two independent expressions, but that's a different story.) > pc has said that "re broda" means the standard Russell expression > which I take to be: > > ExEy[(x\=y & Az(z=x v z=y)) & broda(x) & broda(y)]. This is not quite right. {re broda} is an argument, it is not a claim. Russell's expression corresponds to a full bridi. It would apply to {reda broda}. But you are still missing something there. Az(z=x v z=y) should be replaced by Az(broda(z) -> (z=x v z=y)). Otherwise, you are claiming that there are only two things in the universe. > What does it mean now to say "lo re broda"? {lo re broda} is not constructed from {re broda}. Remember that {re broda} is only a shorthand for {re lo ro broda}. (Or maybe it is something else, as pc proposes, but in any case it is not the inside part of {lo re broda}. In {lo re broda}, the "re broda" part cannot stand alone. > lo by itself claims existence > for the broda it modifies. No, the article only says that we are talking about individuals. The existence comes from its default quantifier. {lo broda} stands for {su'o lo ro broda}, but you can override the default by giving another explicit quantifier. {lo re broda} means {su'o lo re broda} = "at least one of the two broda that there are in all". It claims nothing by itself because it is a sumti, not a bridi. > lo is also a determiner. "Determiner" is very ambiguous, but the key difference between {lo} and {le} is that {lo} is indeterminate or nonspecific and {le} is determinate or specific. {lo} does not tell you _which_ broda you are talking about. {le} does. > Now what does "pa lo re broda" mean? "Exactly one of the two broda that there are in all." > In exploring this we find that the > lo has yet another function. It separates the pa and re from merging > into one number, pare, or 12. But there is no difference between > > "pa ti lo ci broda" and > "pa ti ci broda". Both of those expressions are two sumti: {pa ti} and {lo ci broda} or {ci broda} respectively. {pa ti} means "one of these". The second part is a separate sumti. Jorge