Received: from mail-ee0-f59.google.com ([74.125.83.59]:33943) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WHZWd-0007OD-AB for lojban-list-archive@lojban.org; Sun, 23 Feb 2014 05:55:35 -0800 Received: by mail-ee0-f59.google.com with SMTP id d49sf33926eek.14 for ; Sun, 23 Feb 2014 05:55:16 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=20120806; h=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:list-post:list-help:list-archive :sender:list-subscribe:list-unsubscribe:content-type; bh=yTUxdM2XUkTdhztayAOMD1qv8Nj/4hvFZz6F45hxWhg=; b=NCiDnOHRNI/cfofECDFpSeWi+IyWxa656ZXCLt/4FF4PSyl2OxRcYCTlOuQnSeg7tq sLqiCJzGdpWzAeokgmhLz7g7SNiFdzgXWUpqDj/pPsRAGPVtMniUOpg/qW9Z/bTRqfPJ i8WATeAylQKwtcYdGO2dmmhHfWxWTjicE0FmdYv0bvIS/JK1O+3UelVccx+rpjr6tgQ+ 5QLE9fpLUlddEMvP7mKIvuaiVoek0r4OBuS98bzvSS59JCLoN54HeKI17IA+PYYosIj2 KSZuboevXytKeN6Oz68FyDsjmBx7sq9kTXb2DluvqYBe00f3wLkJS9tN3GYKD+f87ZCd 2DYA== X-Received: by 10.180.198.79 with SMTP id ja15mr63792wic.20.1393163715907; Sun, 23 Feb 2014 05:55:15 -0800 (PST) X-BeenThere: lojban@googlegroups.com Received: by 10.180.96.193 with SMTP id du1ls174936wib.28.gmail; Sun, 23 Feb 2014 05:55:15 -0800 (PST) X-Received: by 10.180.72.75 with SMTP id b11mr8367044wiv.3.1393163715255; Sun, 23 Feb 2014 05:55:15 -0800 (PST) Received: from mail-la0-x236.google.com (mail-la0-x236.google.com [2a00:1450:4010:c03::236]) by gmr-mx.google.com with ESMTPS id v3si2404177bkh.2.2014.02.23.05.55.15 for (version=TLSv1 cipher=ECDHE-RSA-RC4-SHA bits=128/128); Sun, 23 Feb 2014 05:55:15 -0800 (PST) Received-SPF: pass (google.com: domain of jjllambias@gmail.com designates 2a00:1450:4010:c03::236 as permitted sender) client-ip=2a00:1450:4010:c03::236; Received: by mail-la0-x236.google.com with SMTP id mc6so884492lab.27 for ; Sun, 23 Feb 2014 05:55:15 -0800 (PST) MIME-Version: 1.0 X-Received: by 10.152.172.103 with SMTP id bb7mr235130lac.49.1393163715046; Sun, 23 Feb 2014 05:55:15 -0800 (PST) Received: by 10.114.181.133 with HTTP; Sun, 23 Feb 2014 05:55:14 -0800 (PST) In-Reply-To: References: <52F26B9E.2090001@gmx.de> <5e023b9a-515c-432b-a389-8f9af4766b51@googlegroups.com> <52F29ED8.1050607@gmx.de> <372dd8f1-1920-4afa-8d11-aa55696982a0@googlegroups.com> <03555bbd-cc44-426f-94ee-65d557f2d301@googlegroups.com> <592497c0-5db5-420e-867f-8df1663eca27@googlegroups.com> <52F65A5C.90605@gmx.de> <348c23bf-6d9f-4a05-bfe7-69b141c03cb7@googlegroups.com> <52F776EE.6070406@gmx.de> <6ffd64d2-2e2c-4b83-8722-b7f262f5837a@googlegroups.com> <52F7A4D5.5070106@gmx.de> <56096dec-1969-420d-b4e5-b8539cbe0cc0@googlegroups.com> <52F8FAA2.9030009@gmx.de> <52FE053C.3000604@gmx.de> <1e6d5917-ad1e-4c5b-abb7-5deb92110b83@googlegroups.com> <68bacba4-a957-481c-ba00-211db2de8dc3@googlegroups.com> <2f4f0766-1f52-46f0-80af-b4de86d9b5bd@googlegroups.com> <618e6524-d7f0-46c9-8d0b-bbee2dd0cd41@googlegroups.com> <36c4c2b2-8f8c-4d44-ac8e-48c02d45a233@googlegroups.com> <4b6b2cb9-51e5-47f6-97a9-2dec16406864@googlegroups.com> Date: Sun, 23 Feb 2014 10:55:14 -0300 Message-ID: Subject: Re: [lojban] Individuals and xorlo From: =?ISO-8859-1?Q?Jorge_Llamb=EDas?= To: lojban@googlegroups.com X-Original-Sender: jjllambias@gmail.com X-Original-Authentication-Results: gmr-mx.google.com; spf=pass (google.com: domain of jjllambias@gmail.com designates 2a00:1450:4010:c03::236 as permitted sender) smtp.mail=jjllambias@gmail.com; dkim=pass header.i=@gmail.com; dmarc=pass (p=NONE dis=NONE) header.from=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=001a113814c459706a04f313345b X-Spam-Score: 0.0 (/) X-Spam_score: 0.0 X-Spam_score_int: 0 X-Spam_bar: / --001a113814c459706a04f313345b Content-Type: text/plain; charset=ISO-8859-1 On Sat, Feb 22, 2014 at 11:45 PM, guskant wrote: > > {ro'oi da su'o pa mei} alone cannot be expanded to logical elements only, > (D1) (D2) neither, because a predicate {N mei} is not a logical element: {N > mei} is a predicate that reflects natural number theory, not only predicate > logic. They are _distributively_ not tautology. > I agree that before "su'o pa mei" is defined, "ro'oi da su'o pa mei" is not a tautology. It is only a tautology once "su'o pa mei" has been introduced as a tautological predicate. In the context I brought it up, I was in the process of defining the "PA mei" series of predicates, and I started by defining "su'o pa mei" such that "ro'oi da su'o pa mei". I did not explicitly write down any definition for "su'o pa mei", but the only definition of "su'o pa mei" that makes "ro'oi da su'o pa mei" true is one that defines it as a tautological predicate. One thing I should have said, and which I took for granted, but I see you didn't from something you say below, is that all the "PA mei" predicates must be non-distributive. We don't want to infer from "ko'a jo'u ko'e re mei" that "ko'a re mei" or "ko'e re mei". That would kill the very meaning of these predicates. > It seems that using "ko'a" as a place holder causes a problem. > I use {ko'a} as a plural constant, not as a place holder. > For a place holder, {ke'a} and {ce'u} are suitable, because they are free > variables: such usage is not described in CLL, but it is useful at least in > the current discussion. > > When {ce'u} appears more than two times in a sequence of words, different > sumti can be substituted for them, while only a common sumti can be > substituted for {ke'a}s. For the current purpose, using {ke'a} is better. > When using the language, yes. We don't need free variables for ordinary use of the language. But when talking about the language, as we are doing here, using ko'a, ko'e, ko'i, ... is more convenient. We may need to use more than one free variable. (The next step is defining the restricted series of numerical predicates, with two places, "ko'a PA mei ko'e", and using subscripts for the different places in addition to the numbers in the predicate just adds a lot of confusion.) Also, sometimes we need the free variable to appear within a relative clause. I have always used ko'a, ko'e, ... as the place holders when writing definitions for brivla. I haven't found anything else more convenient. Some people prefer to write their definitions with "ka", "ce'u" and subscripts, but I find them unnecessarily cumbersome. Using {ke'a}, our definitions are described as follows: > (D1-7) ko'a su'o pa mei > (D1) ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a > zo'u ge da su'o N-1 mei gi de na me da > (D2) ke'a N mei := ke'a su'o N mei gi'e nai su'o N+1 mei > (D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda > > When (D1) and (D2) are applied to a particular sumti, ke'a are replaced > with it. As for (D3), ke'a is in noi-clause, and it is already fixed to > zo'e, and is not replaced with another sumti, of course. > > Because (D1-7) defines only for {ko'a}, (D1) (D2) (D3) are valid only for > sumti that involves a referent of {ko'a} such as {ko'e noi ko'a me ke'a}, > {ko'i no'u ko'a jo'u ko'o} etc. (D1) (D2) (D3) are not used for other sumti > unless (D1-7) is applied to one of the referents that is involved by the > sumti. > If D1-7 defines only for ko'a, then it is not necessarily valid for ro'oi da poi me ko'a. You need "ro'oi da poi me ko'a cu su'o mei" if you want it to be valid for anything among ko'a. But that won't make it valid for ko'a jo'u ko'o if something in ko'o is not in ko'a. I used only (D1) and logical axioms including transitivity of {me}. Any > mention of {su'o pa mei} is not necessary for the proof. > Then there must be something wrong in the proof. You just cannot prove "ganai ko'a su'o N mei gi ko'a su'o N-1 mei" for N=2 from just D1, because D1 does not define "su'o pa mei". You may have forgotten the restriction on N somewhere in the proof. > For example, suppose that a speaker regards {lo nanba} is >> non-individual: >> >>> ro'oi da poi me lo nanba ku'o su'oi de poi me lo nanba zo'u de me da >>> ijenai da me de >>> >>> That is, the speaker regards a half of {lo nanba} is also {me lo nanba}. >>> >> >> Yes. >> >> >>> Even though there is no individual {lo nanba}, an expression {N mei} is >>> available with (D1-7) (D1) (D2) (D3). >>> >> >> No: >> >> "lo nanba cu su'o pa mei" is true >> "lo nanba cu su'o re mei" is true >> "lo nanba cu su'o ci mei" is true >> > > I call them {lo nanba xi re} and {lo nanba xi ci} respectively for > convenience. > But it's the same "lo nanba"! lo nanba cu su'o pa mei gi'e su'o re mei gi'e su'o ci mei gi'e ..." is true. > If > (D1-7) lo nanba xi pa cu su'o pa mei > is defined, and if {naku ge lo nanba xi pa cu me lo nanba xi re/ci gi naku > lo nanba xi re/ci cu me lo nanba xi pa}, the first sentence is true, and > the second and the third are false. > I don't see how that makes the second and third false. > That is to say, if {(D1-7) lo nanba cu su'o pa mei} is defined, and if all > the appearances of {lo nanba} have a common referent, the first sentence is > true, and the second and the third are false. > No. Your starting point was that every part of lo nanba has a proper part, so for lo nanba, and for every one of its parts, "su'o N mei" is true for every natural N, and for "lo nanba", and for every one of its parts, "N mei" is false for every natural N. . mu'o mi'e xorxes -- You received this message because you are subscribed to the Google Groups "lojban" group. To unsubscribe from this group and stop receiving emails from it, send an email to lojban+unsubscribe@googlegroups.com. To post to this group, send email to lojban@googlegroups.com. Visit this group at http://groups.google.com/group/lojban. For more options, visit https://groups.google.com/groups/opt_out. --001a113814c459706a04f313345b Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable



On Sat, Feb 22, 2014 at 11:45 PM, guskant <gusni.kantu@gmail.c= om> wrote:

{ro'oi da su'= o pa mei} alone cannot be expanded to logical elements only, (D1) (D2) neit= her, because a predicate {N mei} is not a logical element: {N mei} is a pre= dicate that reflects natural number theory, not only predicate logic. They = are _distributively_ not tautology.

I agree that before "su'o p= a mei" is defined, "ro'oi da su'o pa mei" is not a t= autology. It is only a tautology once "su'o pa mei" has been = introduced as a tautological predicate. In the context I brought it up, I w= as in the process of defining the "PA mei" series of predicates, = and I started by defining "su'o pa mei" such that "ro= 9;oi da su'o pa mei". I did not explicitly write down any definiti= on for "su'o pa mei", but the only definition of "su'= ;o pa mei" that makes "ro'oi da su'o pa mei" true is= one that defines it as a tautological predicate.=A0

One thing I should have said, and which I took for gran= ted, but I see you didn't from something you say below, is that all the= "PA mei" predicates must be non-distributive. We don't want = to infer from "ko'a jo'u ko'e re mei" that "ko&#= 39;a re mei" or "ko'e re mei". That would kill the very = meaning of these predicates.

=A0
It seem= s that using "ko'a" as a place holder causes a problem.
I use {ko'a} as a plural constant, not as a place holder.=A0
=
For a place holder, {ke'a} and {ce'u} are suitable, because th= ey are free variables: such usage is not described in CLL, but it is useful= at least in the current discussion.

When {ce'u} appears more than two times in a sequen= ce of words, different sumti can be substituted for them, while only a comm= on sumti can be substituted for {ke'a}s. For the current purpose, using= {ke'a} is better.

When using the language, yes. We don= 't need free variables for ordinary use of the language. But when talki= ng about the language, as we are doing here, using ko'a, ko'e, ko&#= 39;i, ... is more convenient. We may need to use more than one free variabl= e. (The next step is defining the restricted series of numerical predicates= , with two places, =A0"ko'a PA mei ko'e", and using subsc= ripts for the different places in addition to the numbers in the predicate = just adds a lot of confusion.) =A0Also, sometimes we need the free variable= to appear within a relative clause. I have always used ko'a, ko'e,= ... as the place holders when writing definitions for brivla. I haven'= t found anything else more convenient. Some people prefer to write their de= finitions with "ka", "ce'u" and subscripts, but I f= ind them unnecessarily cumbersome.
=A0

Using {= ke'a}, our definitions are described as follows:
(D1-7) ko'a su'o pa mei
(D1) k= e'a su'o N mei :=3D su'oi da poi me ke'a ku'o su'oi= de poi me ke'a zo'u ge da su'o N-1 mei gi de na me da
(D2) ke'a N mei =A0:=3D ke'a su'o N mei gi'e nai su'o N= +1 mei=A0
(D3) lo PA broda :=3D zo'e noi ke&#= 39;a PA mei gi'e broda

When (D1) and (D2= ) are applied to a particular sumti, ke'a are replaced with it. As for = (D3), ke'a is in noi-clause, and it is already fixed to zo'e, and i= s not=A0replaced with another sumti, of course.=A0

Because (D1-7) defines only for {ko'a}, (D1) (D2) (= D3) are valid only for sumti that involves a referent of {ko'a} such as= {ko'e noi ko'a me ke'a}, {ko'i no'u ko'a jo'u = ko'o} etc. (D1) (D2) (D3) are not used for other sumti unless (D1-7) is= applied to one of the referents that is involved by the sumti.

If D1-7 defines only for ko'a, t= hen it is not necessarily valid for ro'oi da poi me ko'a. You need = "ro'oi da poi me ko'a cu su'o mei" if you want it to = be valid for anything among ko'a. But that won't make it valid for = ko'a jo'u ko'o if something in ko'o is not in ko'a.=A0<= /div>

I use= d only (D1) and logical axioms including transitivity of {me}. Any mention = of {su'o pa mei} is not necessary for the proof.=A0

Then there must be somet= hing wrong in the proof. =A0You just cannot prove "ganai ko'a su'o N mei gi k= o'a su'o N-1 mei" for N=3D2 from just D1, because D1 does not = define "su'o pa mei". You may have forgotten the restriction = on N somewhere in the proof.

=A0
=A0 =A0 Fo= r example, suppose that a speaker regards {lo nanba} is non-individual:
ro'oi da poi me lo nanba ku'o su'oi de po= i me lo nanba zo'u de me da ijenai da me de

Th= at is, the speaker regards a half of {lo nanba} is also {me lo nanba}.=A0

Yes.
=A0
Even though there is no individual {lo nanba}, an exp= ression {N mei} is available with (D1-7) (D1) (D2) (D3).

No:

"lo nanba cu su= 'o pa mei" is true
"lo nanba cu su'o re mei" is true
"lo nan= ba cu su'o ci mei" is true

I call them {lo nanba xi re} and {lo nanba xi ci} re= spectively for convenience.

But it's the same "lo nanba= "!=A0

lo nanba cu su'o pa mei gi'e su= 'o re mei gi'e su'o ci mei gi'e ..." is true.
=A0
If
(D1-7) lo nanb= a xi pa cu su'o pa mei
is defined, and if {naku ge lo nanba xi pa cu me lo nanba xi re/ci gi = naku lo nanba xi re/ci cu me lo nanba xi pa}, the first sentence is true, a= nd the second and the third are false.

I don't see how that makes the second and third false.
=
=A0
That is to say, if {(D1-7) lo nanba cu su&= #39;o pa mei} is defined, and if all the appearances of {lo nanba} have a c= ommon referent, the first sentence is true, and the second and the third ar= e false.

No. Your starting point was that eve= ry part of lo nanba has a proper part, so for lo nanba, and for every one o= f its parts, "su'o N mei" is true for every natural N, and fo= r "lo nanba", and for every one of its parts, "N mei" i= s false for every natural N.
.
mu'o mi'e xorxes

<= /div>

--
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