Received: from mail-ob0-f184.google.com ([209.85.214.184]:62280) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WGbPQ-0001HZ-Nq for lojban-list-archive@lojban.org; Thu, 20 Feb 2014 13:44:07 -0800 Received: by mail-ob0-f184.google.com with SMTP id wo20sf604515obc.1 for ; Thu, 20 Feb 2014 13:43:49 -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=7PeFWroN0UoCfJ9sjb7LEm04cjsqO9QhZJBM4tzr3To=; b=SftrelrmEwAzJubKOVFf0euicXsMWj3u8R3tHWNerX7KRcPvxE0cltzZkIS4qqMdXP QT1msr4F4i2S/p1H7VqVAFdXb56uYenV/K7NrJQ5gyNT5abRn70PFfBasXV1LdxhaiVp HMLcSeriaJ6mN4HosVCC9AooKQARo+a7khi5ksio1cqg0VQ5qte4ftPizd4432qpVtAD dU4XfkbgsAtVpUngEXXONTiOkEr3y/8VTiNjb28bxPhDRWt3EgVVLMcy1N3yCUifM+LC 0X776eYuh6+W5KqZ+89qZauyvuFVPd0AYiZYkjA1A9TJgdoDE5MT3q9Z+UEofp5rfeQW JpFQ== X-Received: by 10.50.20.161 with SMTP id o1mr18260ige.10.1392932629793; Thu, 20 Feb 2014 13:43:49 -0800 (PST) X-BeenThere: lojban@googlegroups.com Received: by 10.50.138.66 with SMTP id qo2ls177157igb.43.canary; Thu, 20 Feb 2014 13:43:48 -0800 (PST) X-Received: by 10.68.197.73 with SMTP id is9mr1884291pbc.0.1392932628662; Thu, 20 Feb 2014 13:43:48 -0800 (PST) Received: from mail-ve0-x234.google.com (mail-ve0-x234.google.com [2607:f8b0:400c:c01::234]) by gmr-mx.google.com with ESMTPS id kf5si901753vdb.3.2014.02.20.13.43.48 for (version=TLSv1 cipher=ECDHE-RSA-RC4-SHA bits=128/128); Thu, 20 Feb 2014 13:43:48 -0800 (PST) Received-SPF: pass (google.com: domain of jjllambias@gmail.com designates 2607:f8b0:400c:c01::234 as permitted sender) client-ip=2607:f8b0:400c:c01::234; Received: by mail-ve0-x234.google.com with SMTP id cz12so1216197veb.39 for ; Thu, 20 Feb 2014 13:43:48 -0800 (PST) MIME-Version: 1.0 X-Received: by 10.221.20.199 with SMTP id qp7mr2476960vcb.24.1392932628496; Thu, 20 Feb 2014 13:43:48 -0800 (PST) Received: by 10.221.72.74 with HTTP; Thu, 20 Feb 2014 13:43:48 -0800 (PST) In-Reply-To: <618e6524-d7f0-46c9-8d0b-bbee2dd0cd41@googlegroups.com> 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> Date: Thu, 20 Feb 2014 18:43:48 -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 2607:f8b0:400c:c01::234 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=001a11339e2e84873004f2dd667b X-Spam-Score: 0.0 (/) X-Spam_score: 0.0 X-Spam_score_int: 0 X-Spam_bar: / --001a11339e2e84873004f2dd667b Content-Type: text/plain; charset=ISO-8859-1 On Thu, Feb 20, 2014 at 1:50 AM, guskant wrote: > > I don't yet understand how the definitions on {PA mei} could suggest > implicit atomicity. > > The definitions on the topic are: > > (D1) ko'a su'o N mei := su'oi da poi me ko'a ku'o su'oi de poi me ko'a > zo'u ge da su'o N-1 mei gi de na me da > (D2) ko'a N mei := ko'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 > > > For precise definitions on {PA mei}, we need therefore an explicit > definition of {ko'a su'o pa mei} besides (D1). > That's why I started by saying "ro'oi da su'o pa mei", which is to say that "su'o pa mei" is a tautological predicate, always true of anything. Once {ko'a su'o pa mei} is defined in some way, (D2) and (D3) are valid for > an integer N>=1. (D2) is expanded as follows: > [...] > Then {ko'a N mei} implies also > ro'oi de poi me ko'a zo'u de me ko'a > "ro'oi de poi me ko'a zo'u de me ko'a" is true independently of whether "ko'a N mei" is true or not. It's just a case of the general "ro'oi de poi broda zo'u de broda". > When N=1, > ko'a pa mei > = ge ko'a su'o pa mei > gi ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u > ganai da su'o pa mei > gi de me da > Yes, and since "su'o pa mei" is a tautology, that reduces to: ko'a pa mei = ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da which says that "ko'a" is an individual. (Which is to be expected, what else would a one-some be if not an individual?) In every derivation from (D1) and (D2), {ko'a} may have {ko'e} such that > {ko'e me ko'a ijenai ko'a me ko'e}. > I don't think that can happen if "ko'a pa mei" is true. As a reasonable definition for {ko'a su'o pa mei}, I would suggest as > follows: > > (D1-1) ko'a su'o pa mei := su'oi da poi me ko'a ku'o ro'oi de poi me ko'a > zo'u de me da > Since that is also a tautology ("ko'a" itself will instantiate "su'oi da poi me ko'a"), it works, but it's more complicated that it needs to be. We can just as well define it as: ko'a su'o pa mei := ko'a me ko'a or: ko'a su'o pa mei := ko'a du ko'a or any other tautology. Or just state that "su'o pa mei" is the tautological predicate. > (D1-1) says nothing related the number one, but it reflects a property of > one-some of non-individual: any non-individual sumti can be one-some. Once > non-individual B such that {B me ko'a} is fixed as one-some {B pa mei}, and > if C such that {C me ko'a} satisfies conditions (D1) and (D2), C is counted > to be an integer, and it is meaningful: at least, an order of cardinality > is given to the pair of B and C. > If by "one-some" you mean "pa mei", then only indiciduals can satisfy it. If you mean "su'o pa mei", then yes, anything satisfies it, it's a tautology. Or am I missing something? It may be off topic, but if there were a definition for inner fractional > quantifier > {lo piPA broda} =ca'e {zo'e noi ke'a piPA si'e be lo pa broda} > then the language would be richer; this definition would be avaiable both > atomist and non-atomist. > Actually, an outer fractional quantifier {piPA sumti} =ca'e {lo piPA si'e > be pa me sumti} is available to atomists only. > I assume "lo piPA broda" will have some such meaning , but it's a different system. And it relies on a previous definition of "si'e", which we don't have from basics like the ones we're discussing here for "mei". 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. --001a11339e2e84873004f2dd667b Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable



On Thu, Feb 20, 2014 at 1:50 AM, guskant <gusni.kantu@gmail.co= m> wrote:

I don't yet = understand how the definitions on {PA mei} could suggest implicit atomicity= .

The definitions on the topic are:

<= div>(D1) ko'a su'o N mei :=3D su'oi da poi me ko'a ku'o= su'oi de poi me ko'a zo'u ge da su'o N-1 mei gi de na me d= a
(D2) ko'a N mei =A0:=3D ko'a su'o N mei gi'e nai su= 9;o N+1 mei=A0
(D3) lo PA broda :=3D zo'e noi ke'a PA= mei gi'e broda


For precise def= initions on {PA mei}, we need therefore an explicit definition of {ko'a= su'o pa mei} besides (D1).

That's why I started by sa= ying "ro'oi da su'o pa mei", which is to say that "s= u'o pa mei" is a tautological predicate, always true of anything.<= /div>
=A0

On= ce {ko'a su'o pa mei} is defined in some way, (D2) and (D3) are val= id for an integer N>=3D1. (D2) is expanded as follows:
[...]
Then {ko'a N mei} implies also=A0
ro'= ;oi de poi me ko'a zo'u de me ko'a
=A0
"ro'oi de poi me ko'a zo'u de me ko&#= 39;a" is true independently of whether "ko'a N mei" is t= rue or not. It's just a case of the general "ro'oi de poi brod= a zo'u de broda".=A0
=A0
When N= =3D1,=A0
ko'a pa mei=A0
=3D ge ko'a su'o pa mei
gi ro'oi da poi me ko'a ku'o ro'oi de poi m= e ko'a zo'u
ganai da su'o pa mei= =A0
gi de me da=A0

Yes, and since "su= 9;o pa mei" is a tautology, that reduces to:

ko'a pa mei=A0
=3D ro'oi da poi me ko'a ku'o ro'oi= de poi me ko'a zo'u de me da

which says t= hat "ko'a" is an individual. (Which is to be expected, what e= lse would a one-some be if not an individual?)
=A0

=
In every derivation from (D1) and (D2), {ko'a} may have {ko'e} such= that {ko'e me ko'a ijenai ko'a me ko'e}.

I don't think that can happen if &quo= t;ko'a pa mei" is true.
=A0

As= a reasonable definition for {ko'a su'o pa mei}, I would suggest as= follows:

(D1-1) ko'a su'o pa mei :=3D su'oi da poi m= e ko'a ku'o ro'oi de poi me ko'a zo'u de me da

Since that is also a tautology (&= quot;ko'a" itself will instantiate "su'oi da poi me ko= 9;a"), it works, but it's more complicated that it needs to be. We= can just as well define it as:

ko'a su'o pa mei :=3D ko'a me ko'a

or:

ko'a su'o pa mei = :=3D ko'a du ko'a

or any other tautology. = Or just state that "su'o pa mei" is the tautological predicat= e. =A0

=A0
(D1-1) says nothing related the number one, but it reflects a property= of one-some of non-individual: any non-individual sumti can be one-some. O= nce non-individual B such that {B me ko'a} is fixed as one-some {B pa m= ei}, and if C such that {C me ko'a} satisfies conditions (D1) and (D2),= C is counted to be an integer, and it is meaningful: at least, an order of= cardinality is given to the pair of B and C.

If by "one-some" you= mean "pa mei", then only indiciduals can satisfy it. If you mean= "su'o pa mei", then yes, anything satisfies it, it's a t= autology. Or am I missing something?
=A0

It may be off topic, but if there were a definition for inner fraction= al quantifier=A0
{lo piPA broda} =3Dca'e {zo'e noi ke'= ;a piPA si'e be lo pa broda}
then the language would be riche= r; this definition would be avaiable both atomist and non-atomist.
Actually, an outer fractional quantifier {piPA sumti} =3Dca'e {lo = piPA si'e be pa me sumti} is available to atomists only.

I assume "lo piPA broda" will= have some such meaning , but it's a different system. And it relies on= a previous definition of "si'e", which we don't have fro= m basics like the ones we're discussing here for "mei".

mu'o mi'e xorxes

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