Received: from mail-pb0-f55.google.com ([209.85.160.55]:46371) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WGjsi-0004Bk-VC for lojban-list-archive@lojban.org; Thu, 20 Feb 2014 22:46:51 -0800 Received: by mail-pb0-f55.google.com with SMTP id up15sf738391pbc.0 for ; Thu, 20 Feb 2014 22:46:38 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=20120806; h=date:from:to:message-id:in-reply-to:references:subject:mime-version :x-original-sender:reply-to:precedence:mailing-list:list-id :list-post:list-help:list-archive:sender:list-subscribe :list-unsubscribe:content-type; bh=EgYmllLuE5uO3Jcu29EJRNTrXDUDGofOJerF/j175Ss=; b=sSa+9To9l91784+u+cCZFIQOzzj+lzEvzXJ1nkYRZ/JW7goEhPbbLZaIAkmbpHtwpO Fd1D7nqKSVykjzxK94W3UQ0lJzmkO4mOtUwm0J8g5ce0PdNwPXbQ/kodBgiYbAQEG04d +2+jyqC6SfuaD0ziS8Q1kzreNQRzmIL2ou+d39rAdjf6j+DCNO58L0Suc0uedn1U0EBl gkHnKNf7uy1U3qR4J8kidmc7Gvo4BPuk8qTbCvwoY1hfkwbFhA4tyNtMAAnx2Kc0s85Z 7HbzCpH6KR9zljr/3DTHkv1vX22zpNrd/8vGlx4J6tIUhubIyarkuB3dUl287BzlDtTy fEVg== DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=date:from:to:message-id:in-reply-to:references:subject:mime-version :x-original-sender:reply-to:precedence:mailing-list:list-id :list-post:list-help:list-archive:sender:list-subscribe :list-unsubscribe:content-type; bh=EgYmllLuE5uO3Jcu29EJRNTrXDUDGofOJerF/j175Ss=; b=l+W/2GGg5xpw7Mkm3v/L75jW5i9GwlsDe0YV43Vc6zPhwDmRw2/z52mbuCPY+voWIm rEte6UDhaax3MqPr2ze6Y5yNTYd/h3WR2TQRHrn23cD9OBGN5zCvkNnDY4aXGAYbmSXt /qHcQrA6J55U8UqUAfFeAKlA5v8zWxXAHZWL1EvC36wOGFMNiQMJdo2b6gQ1/Autb68k cw/BZrr5c6+PPr5kFDg9sVE5LM3YyDw1xpLa9mH4ZPuW9yyMkOTbJ3KNlKZiWf38/MbM fBgZ5cX98CCXoFM8ocifVIKjZjXgTF4mI6hZ8KRQbYH4FnE1r4HCA4taG89Jw3h1TC2C SxQQ== X-Received: by 10.50.50.242 with SMTP id f18mr48825igo.17.1392965198832; Thu, 20 Feb 2014 22:46:38 -0800 (PST) X-BeenThere: lojban@googlegroups.com Received: by 10.50.43.193 with SMTP id y1ls407814igl.3.gmail; Thu, 20 Feb 2014 22:46:38 -0800 (PST) X-Received: by 10.50.59.179 with SMTP id a19mr50035igr.10.1392965198250; Thu, 20 Feb 2014 22:46:38 -0800 (PST) Date: Thu, 20 Feb 2014 22:46:36 -0800 (PST) From: guskant To: lojban@googlegroups.com Message-Id: <4b6b2cb9-51e5-47f6-97a9-2dec16406864@googlegroups.com> 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> Subject: Re: [lojban] Individuals and xorlo MIME-Version: 1.0 X-Original-Sender: gusni.kantu@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="----=_Part_416_31214356.1392965196888" X-Spam-Score: -0.1 (/) X-Spam_score: -0.1 X-Spam_score_int: 0 X-Spam_bar: / ------=_Part_416_31214356.1392965196888 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Le vendredi 21 f=C3=A9vrier 2014 10:51:11 UTC+9, xorxes a =C3=A9crit : > > > > > On Thu, Feb 20, 2014 at 10:01 PM, guskant > > wrote: > >> >> Le vendredi 21 f=C3=A9vrier 2014 06:43:48 UTC+9, xorxes a =C3=A9crit : >> >>> >>> On Thu, Feb 20, 2014 at 1:50 AM, guskant wrote: >>> >>>> >>>> >>>> For precise definitions on {PA mei}, we need therefore an explicit=20 >>>> 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= =20 >>> 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= =20 >> logical axiom should be given. That's why an explicit definition for {ko= 'a=20 >> su'o pa mei} is necessary especially for the case that ko'a is an=20 >> individual. >> > > No, I'm defining "su'o pa mei" as the tautological predicate, a predicate= =20 > true of anything. I'm doing exactly the same thing you do with D1-1 > > (D1-1) is not the same. (D1-1) says only that there is a largest referent= =20 of what is {me ko'a}. It is a tautology, and says nothing particular. The= =20 difference from {ro'oi da su'o pa mei} is that the speaker fixes {ko'a} to= =20 be {su'o pa mei}: once {ko'a} is fixed, the other thing that is {me ko'a}= =20 is not called {su'o pa mei}. (D1-1) says nothing, but a kind of dummy to=20 make (D1) (D2) (D3) be meaningful also to non-individual. When another condition {ije da me de} is added to (D1-1), (D1-1) is not a= =20 tautology, and {ko'a} is an individual (not only {ko'a su'o pa mei} but=20 also {ko'a pa mei}, though): then the conditions are equivalent to {ro'oi= =20 da su'o pa mei}, which makes {ko'a su'o pa mei} always true. As long as talking about among theory, (D1-1)+{ije da me de} is not a=20 logical axiom or equivalent, though it is necessary for comforming to=20 mereology with atoms. =20 > =20 > >> You are right under the condition that "ro'oi da su'o pa mei" is true.= =20 >> However, it is a non-logical axiom or the equivalent. I discussed that (= D1)=20 >> (D2) (D3) without any non-logical axioms are meaningful even in the=20 >> case that ko'a is non-individual in the point that they give an order of= =20 >> cardinality. >> > > Definitions D1 are not a valid set of definitions without a starting=20 > point. "su'o re mei" is undefined if "su'o pa mei" is not defined first,= =20 > and then "su'o ci mei" is also undefined, and so on. > > That is the reason why I added (D1-1), a dummy definition for {ko'a su'o pa= =20 mei}, so that (D1) is meaningful without {ro'oi da su'o pa mei}. =20 > =20 > >> I mean "pa mei" by "one-some". As I mentioned above, In order to say {pa= =20 >> mei} is an individual, a non-logical part {ije da me de} is necessary to= be=20 >> added to (D1-1). This addition is equivalent to a non-logical axiom "ro'= oi=20 >> da su'o pa mei", but explicitly mentions the condition for ko'a being an= =20 >> individual. Because (D1) (D2) (D3) give only an order of cardinality, th= ey=20 >> alone can be used both cases of individuals and non-individual. Starting= =20 >> with a non-logical axiom "ro'oi da su'o pa mei" is available only to the= =20 >> case that ko'a is an individual or individuals, but (D1) (D2) (D3)=20 >> themselves are more generally available without non-logical axioms. >> > > I'm sorry, I don't follow you now. Are these the definitions we are=20 > 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=20 > 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= =20 > 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=20 > (D3) lo PA broda :=3D zo'e noi ke'a PA mei gi'e broda > > ? > > Yes, and please note that (D1-1) is not equivatent to {ro'oi da su'o pa=20 mei}.=20 =20 > 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 me= i=20 > 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 > > The result requires {ro'oi da su'o pa mei}. As I discussed above, (D1-1) is= =20 a kind of dummy to say {ko'a su'o pa mei} for a particular ko'a. With=20 (D1-1), once ko'a is said to be {su'o pa mei}, {ro'oi da su'o pa mei} is=20 not true, and we don't get the same result. =20 > which is pretty much what an individual is. If there are no individuals i= n=20 > the world, "ko'a pa mei" is false, because whatever ko'a refers to, it=20 > won't satisfy that anything Y among it will be among anything X among it.= =20 > Only individuals satisfy that. I'm not sure what you say has to be added.= =20 > In a world without individuals, "pa mei" is false of everything (and so a= re=20 > all of the "N mei" with finite N) , and in such a world not just "su'o pa= =20 > mei", but every "su'o N mei" are tautologies. In such a world all these= =20 > numeric predicates are pretty useless. That's why by using any of these= =20 > predicates we invoke a world with individuals. That doesn't mean we can't= =20 > have a universe of discourse without individuals, it just means that in= =20 > such a universe of discourse we won't be using the numeric predicates,=20 > because they all reduce to tautologies and contradictions. > > With a dummy defintion (D1-1), "PA mei" is not meaningless even for=20 non-individual. Set {B su'o pa mei} according to (D1-1). Suppose {C na me B}. From a=20 property of {jo'u}, {B me B jo'u C} and {C me B jo'u C}. Then {B jo'u C=20 su'o re mei} according to (D1). A non-atomist speaker must fix a referent of sumti to be {su'o pa mei}. For= =20 enjoying atomicity, just add a condition {ije da me de} to (D1-1), then it= =20 becomes clear that {ko'a} is an individual. Starting with {ro'oi da su'o pa mei} is useful, but excludes non-individual= =20 from expressions {lo PA broda}. (D1-1) makes (D1) (D2) (D3) available also= =20 to non-individual. =20 --=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. ------=_Part_416_31214356.1392965196888 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable


Le vendredi 21 f=C3=A9vrier 2014 10:51:11 UTC+9, x= orxes a =C3=A9crit :



On Thu, Feb 20, 201= 4 at 10:01 PM, guskant <gusni...@gmail.com> wrote:










That is the reason why I added (D1-1), a dummy definition for {ko'a s= u'o pa mei}, so that (D1) is meaningful without {ro'oi da su'o pa mei}.


 
 
I mean "pa mei"= by "one-some". As I mentioned above, In order to say {pa mei} is an indivi= dual, 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'oi da su'o pa mei",= but explicitly mentions the condition for ko'a being an individual. Becaus= e (D1) (D2) (D3) give only an order of cardinality, they alone can be used = both cases of individuals and non-individual. Starting with a non-logical a= xiom "ro'oi da su'o pa mei" is available only to the case that ko'a is an i= ndividual or individuals, but (D1) (D2) (D3) themselves are more generally = available without non-logical axioms.

I'm sorry, I don't follow you now. A= re 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

<= div>?



Yes, and please note that (D1-1) is not equivatent to {ro'= oi da su'o pa mei}. 


 
Do you agree that with just those def= initions:

ko'a pa mei
=3D ko'a su'o pa m= ei 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'o= i 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
=


The result requires {ro'oi da su'o pa mei}. As I discussed above, (D1-1) i= s a kind of dummy to say {ko'a su'o pa mei} for a particular ko'a. With (D1= -1), once ko'a is said to be {su'o pa mei}, {ro'oi da su'o pa mei} is not t= rue, and we don't get the same result.


<= div> 
which is pretty much wha= t 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 finit= e N) , and in such a world not just "su'o pa mei", but every "su'o N mei" a= re tautologies. In such a world all these numeric predicates are pretty use= less. That's why by using any of these predicates we invoke a world with in= dividuals. 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 c= ontradictions.


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