From lojban+bncCML0xpmUARDb8crxBBoE27ReWA@googlegroups.com Fri Jul 29 06:43:09 2011 Received: from mail-fx0-f61.google.com ([209.85.161.61]) by chain.digitalkingdom.org with esmtp (Exim 4.72) (envelope-from ) id 1QmnLC-00062i-Fz; Fri, 29 Jul 2011 06:43:08 -0700 Received: by fxd2 with SMTP id 2sf6870761fxd.16 for ; Fri, 29 Jul 2011 06:42:55 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=beta; h=x-beenthere:received-spf:mime-version:in-reply-to:references:date :message-id:subject:from:to:x-original-sender :x-original-authentication-results:reply-to:precedence:mailing-list :list-id:x-google-group-id:list-post:list-help:list-archive:sender :list-subscribe:list-unsubscribe:content-type; bh=D3WxfGiJct75Ov8Zmmu1eHJvsJoE3vXCHv3Rr4BK1SM=; b=GaSfLuX7Mjm7L78uWQgYErEuwb4DdyI7bufGNNTWn+BuKyPoQxo/qrccZZg1HIRmWa 583Bin34TJZ97jQEYKRybfloyZgZTeNseo3wChnAGtTFEvffhesjRqRYhQqNhnAjgE7E oIeTbLXAm/zyxi86IHBAlusTd7oKfQvD1ZPLE= Received: by 10.223.28.193 with SMTP id n1mr644487fac.46.1311946971306; Fri, 29 Jul 2011 06:42:51 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.204.133.90 with SMTP id e26ls4006447bkt.0.gmail; Fri, 29 Jul 2011 06:42:50 -0700 (PDT) Received: by 10.204.37.8 with SMTP id v8mr175297bkd.3.1311946970006; Fri, 29 Jul 2011 06:42:50 -0700 (PDT) Received: by 10.204.37.8 with SMTP id v8mr175296bkd.3.1311946969965; Fri, 29 Jul 2011 06:42:49 -0700 (PDT) Received: from mail-fx0-f52.google.com (mail-fx0-f52.google.com [209.85.161.52]) by gmr-mx.google.com with ESMTPS id k16si927733fah.0.2011.07.29.06.42.49 (version=TLSv1/SSLv3 cipher=OTHER); Fri, 29 Jul 2011 06:42:49 -0700 (PDT) Received-SPF: pass (google.com: domain of blindbravado@gmail.com designates 209.85.161.52 as permitted sender) client-ip=209.85.161.52; Received: by mail-fx0-f52.google.com with SMTP id 18so3384217fxd.11 for ; Fri, 29 Jul 2011 06:42:49 -0700 (PDT) MIME-Version: 1.0 Received: by 10.223.59.17 with SMTP id j17mr1813722fah.120.1311946969684; Fri, 29 Jul 2011 06:42:49 -0700 (PDT) Received: by 10.223.74.194 with HTTP; Fri, 29 Jul 2011 06:42:49 -0700 (PDT) In-Reply-To: <38B81BB6-73B6-485D-9EC1-B9D85046F2B7@yahoo.com> References: <87BB9A86-430F-4F64-9CD4-D8A5BD33B69A@yahoo.com> <1311695892.73678.YahooMailRC@web81305.mail.mud.yahoo.com> <38B81BB6-73B6-485D-9EC1-B9D85046F2B7@yahoo.com> Date: Fri, 29 Jul 2011 09:42:49 -0400 Message-ID: Subject: Re: [lojban] bu'a From: Ian Johnson To: lojban@googlegroups.com X-Original-Sender: blindbravado@gmail.com X-Original-Authentication-Results: gmr-mx.google.com; spf=pass (google.com: domain of blindbravado@gmail.com designates 209.85.161.52 as permitted sender) smtp.mail=blindbravado@gmail.com; dkim=pass (test mode) header.i=@gmail.com Reply-To: lojban@googlegroups.com Precedence: list Mailing-list: list lojban@googlegroups.com; contact lojban+owners@googlegroups.com List-ID: X-Google-Group-Id: 1004133512417 List-Post: , List-Help: , List-Archive: Sender: lojban@googlegroups.com List-Subscribe: , List-Unsubscribe: , Content-Type: multipart/alternative; boundary=0015174028be179c9804a9357571 --0015174028be179c9804a9357571 Content-Type: text/plain; charset=ISO-8859-1 No, my second point doesn't play off of that axiom, which I haven't even heard of. It's a much simpler notion: we're talking about the construction of a hypothetical general purpose human language based on second order predicate logic. It is silly to have a *general purpose* language whose underlying logic is second order without having vocabulary to utilize that underlying logic in a rich fashion. mu'o mi'e latros On Tue, Jul 26, 2011 at 5:00 PM, John E. Clifford wrote: > Yes, making quantifier expressions into sumti makes for problems, since it > makes it seem they have referents rather than ranges (I note in passing that > what you *say her makes it sound like sumti were things rather than > expressions -- and I admit that thanks to JCB, Lojban does talk that way > sometimes). If you ignore their position, however, and just look at their > form (admitting again that having an implicit quantifier makes this somewhat > harder) then you have an operator and a variable it binds an an occurrence > of that variable. In I, you are not allowed to infer "there is a" from "not > not there is a" but the ground for that is in the logic of"not", not of the > quantifier. Yes, the range of second order quantifiers is predicates, but, > barring the oddity of what you say earlier, this just what you *meant > before. > You second point seems to play on Russell's axiom of reducibility, which > says that every higher order sentence (and in Russellthat is a lot more than > just second order) has an equivalent sentence in first order. The > plausibility of this derives from the fact that is true of the pro sties of > predicates that we immediate think of: definition, transitivity, > reflexivity, symmetry, subordination, and so on. It's generally thought not > true by people who still work with this system . And ignored by everyone > else, who are off doing other things, either totally first (like modern set > theory) or managing to do second order without this reliance (though > perfectly happy to use the related sentences as shortcuts where they clarify > and are independently justified). > > Ro bu'a zo'u ganai ge ge da bu'a de gi roda rode rodi zo'u ganai ge da bu'a > de gi de bu'a di gi da bu'a di gi roda rode zo'u ganai da bu'a de gi de > bu'a da gi rada zo'u da bu'a da. ( second order but highly reduced). > > The real gripe is the lack of clear rules for giving characteristic > functions ("predicates" in the confused language that is common here). > Sent from my iPad > > On Jul 26, 2011, at 14:35, Ian Johnson wrote: > > What is hackish about it is the syntax. In {ro bu'a zo'u da bu'a}, {ro > bu'a} is syntactically a sumti, consisting, presumably, of all x1's of > whatever referent the {bu'a} ultimately has (thinking classically; in > intuitionistic logic, what I am saying is not entirely sound), since that's > what it means elsewhere. And yet then the thing that is actually quantified > over is a collection of predicates. It's just an arbitrary decision plopped > into the CLL, changing the type of a variable abruptly. My gripe about it is > irrationally amplified by my irrational mental attempts to statically type > Lojban, but even putting that aside I'd say it's a valid gripe, albeit > irrelevant from a practical standpoint since predicate quantification has > seen no use so far as far as I know, except in my example here > . > > We're also missing second order predicates, or at least things that serve > as convenient required predicates in second order discussions, in general. > Saying something like "{mintu} is the opposite of {drata}", even with > {me'ei} (of selma'o LE, which converts selbri into abstract predicate sumti; > I do NOT think quoted words are suitable as placeholders for abstract > predicates), becomes: > > me'ei mintu cu dukti me'ei drata ....???? > and I ultimately have no way of writing down the dukti3. (I would be > pleased if you could, actually.) The only precise way of saying this (yes, I > admit the English is as imprecise as a statement involving {dukti} with no > dukti3, but I hope you can see the precise meaning that I want to > encapsulate) that I can see is first order to its core: > ro da ro de ro di zo'u go da de di mintu gi da de di to'e drata > > mu'o mi'e latros > On Tue, Jul 26, 2011 at 11:58 AM, John E Clifford < > kali9putra@yahoo.com> wrote: > >> I'm not sure what you take as hackish about it. Simply allows quantifiers >> over predicate variables, which is all that is required. To be sure, it is >> does not seem to allow such quantifiers any place but prenex ('ko'a (cu) suo >> bu'a' don't seem to compute), but the embedded quantifiers are a main source >> of difficulty (pace xorxes) in reconstructing the logic of Lojban, so this >> may not be a flaw. What then is hackish? The pattern of real Logic is >> followed (less a mess of sub- and superscripts that are largely irrelevant >> to Lojban). Yes, Lojban is based on first order, but, then, so is second >> order and Lojban allows that extension (and, in principle, all the other >> orders on up). >> As I said, part of the problem is to figure just what a predicate is in >> Lojban. There are several candidates (sticking to unary predicates for >> simplicity): the things that have the property, the set of things that have >> the property, the characteristic function of that set, and the property, >> which may or may not be what a Montagovian would call a property. Three of >> these have clear expressions in Lojban, but the characteristic function does >> not really, but is the best candidate for the predicate in what follows in >> second order claims. There is talk of the lambda calculus but it is >> unimplemented, so far as I can see (and is second order). >> >> ------------------------------ >> *From:* Ian Johnson < blindbravado@gmail.com> >> *To:* lojban@googlegroups.com >> *Sent:* Tue, July 26, 2011 9:24:10 AM >> *Subject:* Re: [lojban] bu'a >> >> Erm, poor phrasing; I meant that there is no easy way to get between those >> three things. >> >> .u'u .i mu'o mi'e latros >> >> On Tue, Jul 26, 2011 at 10:22 AM, Ian Johnson < >> blindbravado@gmail.com> wrote: >> >>> Quantification over predicates was implemented in a horrifyingly hackish >>> way. This alone is a problem, in my opinion. There is also, at least not in >>> the main body of the language, an easy way to go from predicate-as-function >>> (selbri) to predicate-as-concrete-object (typical sumti) to >>> predicate-as-abstract-object. >>> >>> Lojban is definitely based on FOPL, though, not SOPL, and not a bizarre >>> hybrid of the two. >>> >>> mu'o mi'e latros >>> >>> On Sun, Jul 24, 2011 at 2:51 PM, John E. Clifford < >>> kali9putra@yahoo.com> wrote: >>> >>>> Lojban isn't clearly of one order or the other, since it treats sets and >>>> properties and the like on a par with tree and dogs. There is no particular >>>> problem in grammar or vocabulary to treating properties of predicates and >>>> quantification over them. There are some arguments about the correct way to >>>> express a predicate as an argument, but that seems to revolve around just >>>> what a predicate is in Lojban ontology. All the answers yield grammatical >>>> and intelligible results, though sometimes different ones. None of them >>>> seem particularly stilted, but I haven't seen enough cases to get a feel for >>>> that. >>>> >>>> Sent from my iPad >>>> >>>> On Jul 24, 2011, at 14:13, Ian Johnson < >>>> blindbravado@gmail.com> wrote: >>>> >>>> I think bu'a/bu'e/bu'i would be much much much more useful if Lojban >>>> were a second order language, because then we could talk about the existence >>>> of predicates with desired properties in a non-stilted fashion. As a first >>>> order language, though, with second order mechanisms requiring stilted >>>> language, I don't think bu'a/bu'e/bu'i are especially useful. >>>> >>>> mu'o mi'e latros >>>> >>>> On Sun, Jul 24, 2011 at 12:01 PM, tijlan < >>>> jbotijlan@gmail.com> wrote: >>>> >>>>> What is your view on the bu'a series? Potentially useful? Totally >>>>> pointless? I've never used it myself, but I could be missing some >>>>> important aspect of Lojban as a logical language. >>>>> >>>>> mu'o mi'e tijlan >>>>> >>>>> -- >>>>> You received this message because you are subscribed to the Google >>>>> Groups "lojban" group. >>>>> To post to this group, send email to >>>>> lojban@googlegroups.com. >>>>> To unsubscribe from this group, send email to >>>>> >>>>> lojban+unsubscribe@googlegroups.com. >>>>> For more options, visit this group at >>>>> >>>>> http://groups.google.com/group/lojban?hl=en. >>>>> >>>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "lojban" group. >>>> To post to this group, send email to >>>> lojban@googlegroups.com. >>>> To unsubscribe from this group, send email to >>>> >>>> lojban+unsubscribe@googlegroups.com. >>>> For more options, visit this group at >>>> >>>> http://groups.google.com/group/lojban?hl=en. >>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "lojban" group. >>>> To post to this group, send email to >>>> lojban@googlegroups.com. >>>> To unsubscribe from this group, send email to >>>> >>>> lojban+unsubscribe@googlegroups.com. >>>> For more options, visit this group at >>>> >>>> http://groups.google.com/group/lojban?hl=en. >>>> >>> >>> >> -- >> You received this message because you are subscribed to the Google Groups >> "lojban" group. >> To post to this group, send email to >> lojban@googlegroups.com. >> To unsubscribe from this group, send email to >> >> lojban+unsubscribe@googlegroups.com. >> For more options, visit this group at >> >> http://groups.google.com/group/lojban?hl=en. >> >> -- >> You received this message because you are subscribed to the Google Groups >> "lojban" group. >> To post to this group, send email to >> lojban@googlegroups.com. >> To unsubscribe from this group, send email to >> >> lojban+unsubscribe@googlegroups.com. >> For more options, visit this group at >> >> http://groups.google.com/group/lojban?hl=en. >> > > -- > You received this message because you are subscribed to the Google Groups > "lojban" group. > To post to this group, send email to lojban@googlegroups.com. > To unsubscribe from this group, send email to > lojban+unsubscribe@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/lojban?hl=en. > > -- > You received this message because you are subscribed to the Google Groups > "lojban" group. > To post to this group, send email to lojban@googlegroups.com. > To unsubscribe from this group, send email to > lojban+unsubscribe@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/lojban?hl=en. > -- You received this message because you are subscribed to the Google Groups "lojban" group. To post to this group, send email to lojban@googlegroups.com. To unsubscribe from this group, send email to lojban+unsubscribe@googlegroups.com. For more options, visit this group at http://groups.google.com/group/lojban?hl=en. --0015174028be179c9804a9357571 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable No, my second point doesn't play off of that axiom, which I haven't= even heard of. It's a much simpler notion: we're talking about the= construction of a hypothetical general purpose human language based on sec= ond order predicate logic. It is silly to have a *general purpose* language= whose underlying logic is second order without having vocabulary to utiliz= e that underlying logic in a rich fashion.

mu'o mi'e latros

On Tue, Jul = 26, 2011 at 5:00 PM, John E. Clifford <kali9putra@yahoo.com> wrote:
Yes, making quantifier expressions into sumti= makes for problems, since it makes it seem they have referents rather than= ranges (I note in passing that what you *say her makes it sound like sumti= were things rather than expressions -- and I admit that thanks to JCB, Loj= ban does talk that way sometimes). If you ignore their position, however, a= nd just look at their form (admitting again that having an implicit quantif= ier makes this somewhat harder) then you have an operator and a variable it= binds an an occurrence of that variable. =A0In I, you are not allowed to i= nfer "there is a" from "not not there is a" but the gro= und for that is in the logic of"not", not of the quantifier. =A0Y= es, the range of second order quantifiers is predicates, but, barring the o= ddity of what you say earlier, this just what you *meant before. =A0
You second point seems to play on Russell's axiom of reducibility,= which says that every higher order sentence (and in Russellthat is a lot m= ore than just second order) has an equivalent sentence in first order. The = plausibility of this derives from the fact that is true of the pro sties of= predicates that we immediate think of: definition, transitivity, reflexivi= ty, symmetry, subordination, and so on. =A0It's generally thought not t= rue by people who still work with this system . =A0And ignored by everyone = else, who are off doing other things, either totally first (like modern set= theory) or managing to do second order without this reliance (though perfe= ctly happy to use the related sentences as shortcuts where they clarify and= are independently justified).

Ro bu'a zo'u ganai ge ge da bu'a de gi roda= rode rodi zo'u ganai ge da bu'a de gi de bu'a di gi da bu'= a di =A0gi roda rode zo'u ganai da bu'a de gi de bu'a da gi rad= a zo'u da bu'a da. =A0( second order but highly reduced).

The real gripe is the lack of clear rules for giving ch= aracteristic functions ("predicates" in the confused language tha= t is common here).
Sent from my iPad

On = Jul 26, 2011, at 14:35, Ian Johnson <blindbravado@gmail.com> wrote:

What is hackish about it is the syntax. In {ro bu'a zo'u da bu'= ;a}, {ro bu'a} is syntactically a sumti, consisting, presumably, of all= x1's of whatever referent the {bu'a} ultimately has (thinking clas= sically; in intuitionistic logic, what I am saying is not entirely sound), = since that's what it means elsewhere. And yet then the thing that is ac= tually quantified over is a collection of predicates. It's just an arbi= trary decision plopped into the CLL, changing the type of a variable abrupt= ly. My gripe about it is irrationally amplified by my irrational mental att= empts to statically type Lojban, but even putting that aside I'd say it= 's a valid gripe, albeit irrelevant from a practical standpoint since p= redicate quantification has seen no use so far as far as I know, except in = my example here.

We're also missing second order predicates, or at least thing= s that serve as convenient=A0required=A0predicates in se= cond order discussions, in general. Saying something like "{mintu} is = the opposite of {drata}", even with {me'ei} (of selma'o LE, wh= ich converts selbri into abstract predicate sumti; I do NOT think quoted wo= rds are suitable as placeholders for abstract predicates), becomes:<= /div>
me'ei mintu cu dukti me'ei drata ....????
and I ultimately have = no way of writing down the dukti3. (I would be pleased if you could, actual= ly.) The only precise way of saying this (yes, I admit the English is as im= precise as a statement involving {dukti} with no dukti3, but I hope you can= see the precise meaning that I want to encapsulate) that I can see is firs= t order to its core:
ro da ro de ro di zo'u go da de di mintu gi da de di to'e drata
=
mu'o mi'e latros
On Tue, Jul 26, = 2011 at 11:58 AM, John E Clifford <kali9putra@yahoo.com> wrote:
I'm not sure what you take as h= ackish about it.=A0 Simply allows quantifiers over predicate variables, whi= ch is all that is required.=A0 To be sure, it is does not seem to allow suc= h quantifiers any place but prenex ('ko'a (cu) suo bu'a' do= n't seem to compute), but the embedded quantifiers are a main source of= difficulty (pace xorxes) in reconstructing the logic of Lojban, so this ma= y not be a flaw.=A0 What then is hackish?=A0 The pattern of real Logic is f= ollowed (less a mess of sub- and superscripts that are largely irrelevant t= o Lojban).=A0 Yes, Lojban is based on first order, but, then, so is second = order and Lojban allows that extension (and, in principle, all the other or= ders on up).
As I said, part of the problem is to figure just what a predicate is i= n Lojban.=A0 There are several candidates (sticking to unary predicates for simplicity)= : the things that have the property, the set of things that have the proper= ty, the characteristic function of that set, and the property, which may or= may not be what a Montagovian would call a property.=A0 Three of these hav= e clear expressions in Lojban, but the characteristic function does not rea= lly, but is the best candidate for the predicate in what follows in second = order claims. There is talk of the lambda calculus but it is unimplemented,= so far as I can see (and is second order).

= From: Ian Johnson <blindbravado@gmail.com> To: lojban@googlegroups.c= om
Sent: Tue, July 26= , 2011 9:24:10 AM
Subject: Re: [lojban] bu'= ;a

Erm, poor phrasing; I meant that there is no easy way to get between those = three things.

.u'u .i mu'o mi'e latros

On Tue, Jul 26, 2011 at 10:22 AM, Ian Johnson <blindbravado@gmail.com> wrote:
Quantification over predicates was implement= ed in a horrifyingly hackish way. This alone is a problem, in my opinion. T= here is also, at least not in the main body of the language, an easy way to= go from predicate-as-function (selbri) to predicate-as-concrete-object (ty= pical sumti) to predicate-as-abstract-object.

Lojban is definitely based on FOPL, though, not SOPL, and not a bizarre= hybrid of the two.

mu'o mi'e latros

On Sun, Jul 24, 2011 at 2:51 PM= , John E. Clifford <kali9putra@yahoo.com> wrote:
Lojban isn't clearly of one or= der or the other, since it treats sets and properties and the like on a par= with tree and dogs. =A0There is no particular problem in grammar or vocabu= lary to treating properties of predicates and quantification over them. =A0= There are some arguments about the correct way to express a predicate as an= argument, but that seems to revolve around just what a predicate is in Loj= ban ontology. =A0All the answers yield grammatical and intelligible results= , though sometimes different ones. =A0None of them seem particularly stilte= d, but I haven't seen enough cases to get a feel for that.

Sent from my iPad

On Jul 24, 20= 11, at 14:13, Ian Johnson <blindbravado@gmail.com> wrote:

=
I think bu'a/bu'e/bu'i would be much much much more useful= if Lojban were a second order language, because then we could talk about t= he existence of predicates with desired properties in a non-stilted fashion= . As=A0a first order language, though, with second order mechanisms requiri= ng stilted language, I don't think bu'a/bu'e/bu'i are espec= ially useful.
=A0
mu'o mi'e latros
=A0
On Sun, Jul 24, 2011 at 12:01 PM, tijlan <jbotijlan@gmail.com> wrote:
What is your view on the bu'a ser= ies? Potentially useful? Totally
pointless? I've never used it mysel= f, but I could be missing some
important aspect of Lojban as a logical language.

mu'o mi'e = tijlan

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