Received: from mail-ob0-f183.google.com ([209.85.214.183]:36150) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WGfGp-00030F-A0 for lojban-list-archive@lojban.org; Thu, 20 Feb 2014 17:51:30 -0800 Received: by mail-ob0-f183.google.com with SMTP id wm4sf677403obc.10 for ; Thu, 20 Feb 2014 17:51:13 -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=F3Hu6Us1ec0PYbdp+W1X7lUxotNzibQuxoSqOv1Tk38=; b=EPIKrR1nXKm1iLuSPwY1S76gM7edJQC1i7Ozng0HsIJNUtIlLwQvWixysAV1Pk1MTW cImsBHoVlWx9RwbQaWCGibEQyQ++Nw+/jxEDM8sh9VE1Z4uIXNBjInDkXRKPRqlxLBHd vjCMt3c9C3sGSfrupb1awby8/jyytmdhBs3MiRc8WME7SrRyutqN+8IMoyxA9bIdrx69 tm1lsg+mET+N9ACE/SxbzeMHGYdnSKALwV8rqwSlViNCe530yExPnouRQYWIiMy6lt6A eLVPlvclS3kCjfBHsUgNd9Q3RlMNVI9V9GyYzjCdV3Hv/f0L0XLDvEkFSm79WGWe76vo dvvA== X-Received: by 10.50.47.74 with SMTP id b10mr49832ign.1.1392947472880; Thu, 20 Feb 2014 17:51:12 -0800 (PST) X-BeenThere: lojban@googlegroups.com Received: by 10.50.29.70 with SMTP id i6ls258985igh.7.canary; Thu, 20 Feb 2014 17:51:12 -0800 (PST) X-Received: by 10.67.21.145 with SMTP id hk17mr2202596pad.35.1392947472330; Thu, 20 Feb 2014 17:51:12 -0800 (PST) Received: from mail-ve0-x22a.google.com (mail-ve0-x22a.google.com [2607:f8b0:400c:c01::22a]) by gmr-mx.google.com with ESMTPS id hh7si1003627vdb.1.2014.02.20.17.51.12 for (version=TLSv1 cipher=ECDHE-RSA-RC4-SHA bits=128/128); Thu, 20 Feb 2014 17:51:12 -0800 (PST) Received-SPF: pass (google.com: domain of jjllambias@gmail.com designates 2607:f8b0:400c:c01::22a as permitted sender) client-ip=2607:f8b0:400c:c01::22a; Received: by mail-ve0-x22a.google.com with SMTP id oz11so2683966veb.29 for ; Thu, 20 Feb 2014 17:51:12 -0800 (PST) MIME-Version: 1.0 X-Received: by 10.221.39.138 with SMTP id tm10mr3091192vcb.7.1392947472172; Thu, 20 Feb 2014 17:51:12 -0800 (PST) Received: by 10.221.72.74 with HTTP; Thu, 20 Feb 2014 17:51:11 -0800 (PST) In-Reply-To: <36c4c2b2-8f8c-4d44-ac8e-48c02d45a233@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> <36c4c2b2-8f8c-4d44-ac8e-48c02d45a233@googlegroups.com> Date: Thu, 20 Feb 2014 22:51:11 -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::22a 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=001a1133953a450d5104f2e0db84 X-Spam-Score: 0.0 (/) X-Spam_score: 0.0 X-Spam_score_int: 0 X-Spam_bar: / --001a1133953a450d5104f2e0db84 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable On Thu, Feb 20, 2014 at 10:01 PM, guskant wrote: > > Le vendredi 21 f=E9vrier 2014 06:43:48 UTC+9, xorxes a =E9crit : > >> >> On Thu, Feb 20, 2014 at 1:50 AM, guskant wrote: >> >>> >>> >>> 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 >> > > Yes, and in order to say "ro'oi da su'o pa mei", an axiom that is not an > logical axiom should be given. That's why an explicit definition for {ko'= a > su'o pa mei} is necessary especially for the case that ko'a is an > individual. > No, I'm defining "su'o pa mei" as the tautological predicate, a predicate true of anything. I'm doing exactly the same thing you do with D1-1 > You are right under the condition that "ro'oi da su'o pa mei" is true. > However, it is a non-logical axiom or the equivalent. I discussed that (D= 1) > (D2) (D3) without any non-logical axioms are meaningful even in the > case that ko'a is non-individual in the point that they give an order of > cardinality. > Definitions D1 are not a valid set of definitions without a starting point. "su'o re mei" is undefined if "su'o pa mei" is not defined first, and then "su'o ci mei" is also undefined, and so on. > I mean "pa mei" by "one-some". As I mentioned above, In order to say {pa > mei} is an individual, a non-logical part {ije da me de} is necessary to = be > added to (D1-1). This addition is equivalent to a non-logical axiom "ro'o= i > da su'o pa mei", but explicitly mentions the condition for ko'a being an > individual. Because (D1) (D2) (D3) give only an order of cardinality, the= y > alone can be used both cases of individuals and non-individual. Starting > with a non-logical axiom "ro'oi da su'o pa mei" is available only to the > case that ko'a is an individual or individuals, but (D1) (D2) (D3) > themselves are more generally available without non-logical axioms. > I'm sorry, I don't follow you now. Are these the definitions we are discussing: (D1-1) ko'a su'o pa mei :=3D su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da (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 da (D2) ko'a N mei :=3D ko'a su'o N mei gi'e nai su'o N+1 mei (D3) lo PA broda :=3D zo'e noi ke'a PA mei gi'e broda ? Do you agree that with just those definitions: ko'a pa mei =3D ko'a su'o pa mei gi'e nai su'o re mei =3D na ku ko'a su'o re mei =3D na ku su'oi da poi me ko'a su'oi de poi me ko'a zo'u ge da su'o pa mei = gi de na me da =3D ro'oi da poi me ko'a ro'oi de poi me ko'a na ku zo'u na ku de me da =3D ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de me da which is pretty much what an individual is. If there are no individuals in the world, "ko'a pa mei" is false, because whatever ko'a refers to, it won't satisfy that anything Y among it will be among anything X among it. Only individuals satisfy that. I'm not sure what you say has to be added. In a world without individuals, "pa mei" is false of everything (and so are all of the "N mei" with finite N) , and in such a world not just "su'o pa mei", but every "su'o N mei" are tautologies. In such a world all these numeric predicates are pretty useless. That's why by using any of these predicates we invoke a world with individuals. That doesn't mean we can't have a universe of discourse without individuals, it just means that in such a universe of discourse we won't be using the numeric predicates, because they all reduce to tautologies and contradictions. mu'o mi'e xorxes --=20 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 e= mail 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. --001a1133953a450d5104f2e0db84 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable



On Thu, Feb 20, 2014 at 10:01 PM, guskant <gusni.kantu@gmail.c= om> wrote:


=A0
=
You are right under the condition that "ro'oi da su'o pa = mei" is true. However, it is a non-logical axiom or the equivalent. I = discussed that (D1) (D2) (D3) without any non-logical axioms are meaningful= even in the case=A0that ko'a is non-individual in the point that they = give an order of cardinality.

Definitions D1 are not a valid set o= f definitions without a starting point. "su'o re mei" is unde= fined if "su'o pa mei" is not defined first, and then "s= u'o ci mei" is also undefined, and so on.

=A0
I mean = "pa mei" by "one-some". As I mentioned above, In order = to say {pa mei} is an individual, a non-logical part {ije da me de} is nece= ssary to be added to (D1-1). This addition is equivalent to a non-logical a= xiom "ro'oi da su'o pa mei", but explicitly mentions the = condition for ko'a being an individual. Because (D1) (D2) (D3) give onl= y an order of cardinality, they alone can be used both cases of individuals= and non-individual. Starting with a non-logical axiom "ro'oi da s= u'o pa mei" is available only to the case that ko'a is an indi= vidual or individuals, but (D1) (D2) (D3) themselves are more generally ava= ilable without non-logical axioms.

I'm sorry, I don't follow yo= u now. Are these the definitions we are discussing:

(D1-1) ko'a su'o pa mei :=3D su'oi da poi me ko'a ku'= o ro'oi de poi me ko'a zo'u de me da
(D2) ko'a N mei =A0:=3D ko'a su'o N mei gi'e nai su'= o N+1 mei=A0
(D3) lo PA broda :=3D zo'e noi ke'a PA mei gi'e broda



=3D na ku ko'a su'o re mei
=3D na ku su'oi da po= i me ko'a su'oi de poi me ko'a zo'u ge da su'o pa mei g= i de na me da
=3D ro'oi da poi me ko'a ro'oi de poi m= e ko'a na ku zo'u na ku =A0de me da
=3D ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u= de me da

which is pretty much what an individual = is. If there are no individuals in the world, "ko'a pa mei" i= s false, because whatever ko'a refers to, it won't satisfy that any= thing Y among it will be among anything X among it. Only individuals satisf= y that. I'm not sure what you say has to be added. In a world without i= ndividuals, "pa mei" is false of everything (and so are all of th= e "N mei" with finite N) , and in such a world not just "su&= #39;o pa mei", but every "su'o N mei" are tautologies. I= n such a world all these numeric predicates are pretty useless. That's = why by using any of these predicates we invoke a world with individuals. Th= at doesn't mean we can't have a universe of discourse without indiv= iduals, it just means that in such a universe of discourse we won't be = using the numeric predicates, because they all reduce to tautologies and co= ntradictions.

mu'o mi'e xorxes=A0

<= /div>

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