Received: from mail-ve0-f186.google.com ([209.85.128.186]:55806) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WGLab-0008AI-NQ for lojban-list-archive@lojban.org; Wed, 19 Feb 2014 20:50:34 -0800 Received: by mail-ve0-f186.google.com with SMTP id c14sf342616vea.23 for ; Wed, 19 Feb 2014 20:50:19 -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=gDz/KCNjAPYOHG+/eOQWaUu7Pfcweo8mWrBbJ1fD08s=; b=R5kaPuFUy9igmBuqx65uS7VDyK1FR99VtZIP+Z+eTbh3IKcXqJm+ugWM/lwhCtYm+M DxWzEqptAyvXZ7/nGcRjb4Vi2ld43cExTn2qMRgOZ3cTleGTqB2BHRZ2dHBtgGSwIUMS W3xaMkwsUDVInM2QjePex7UApAKf82TGWt6hhEP6nMOI5ayzbBAlqzS9C3sG3a1P84e3 BJVLSmiVQn3fdcdbbUTutMZwbcEUDODn4zSl36c8LFpBJ+P4YFCUjViusw031fxTbuom OnaHJJSpU/7ZeKU0UIJNX8CLyqQnjsQ3vQk/x95r+1/ONvzQxJ7HtvpMJxg8a/ly06F9 h5cw== 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=gDz/KCNjAPYOHG+/eOQWaUu7Pfcweo8mWrBbJ1fD08s=; b=nOU9drkSoU3y7tpCXwcP8il/8AUKJsnOT83th65hy0yxAAIxhKexLbME5QsJCeYIIO mCcT/vtRGPqmmNFpFq0rAKL8GNyzGXH+nr2oysg3NK0ZvYV5Tn3x3os0Rw7mbOSOzBLm Bsx3RF8VxjH9yyLgJ0SeaM3VkS36e91cxwNYQ1oYZiw2WRg+3Fa6sygF60AahNRehTOD fpSKsI0miXtDXln16/AbV+aP9pyoxel8YBPDWvCp0k21UYWpJMA4z3KSziMxxD38dQry yJC+m1c1OT4o/kXGCaVkHQK4YxciMwTDVRhMCFvCiMsbnb9/U1/PLPRifl/N1K6xvF7X VGXA== X-Received: by 10.50.217.201 with SMTP id pa9mr123008igc.13.1392871819283; Wed, 19 Feb 2014 20:50:19 -0800 (PST) X-BeenThere: lojban@googlegroups.com Received: by 10.50.29.70 with SMTP id i6ls2985799igh.7.canary; Wed, 19 Feb 2014 20:50:18 -0800 (PST) X-Received: by 10.50.122.10 with SMTP id lo10mr123340igb.11.1392871818500; Wed, 19 Feb 2014 20:50:18 -0800 (PST) Date: Wed, 19 Feb 2014 20:50:16 -0800 (PST) From: guskant To: lojban@googlegroups.com Message-Id: <618e6524-d7f0-46c9-8d0b-bbee2dd0cd41@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> 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_848_4192485.1392871817064" X-Spam-Score: -0.1 (/) X-Spam_score: -0.1 X-Spam_score_int: 0 X-Spam_bar: / ------=_Part_848_4192485.1392871817064 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Le mercredi 19 f=C3=A9vrier 2014 05:38:50 UTC+9, xorxes a =C3=A9crit : > > > > > On Tue, Feb 18, 2014 at 10:13 AM, guskant > > wrote: > >> >> Le mardi 18 f=C3=A9vrier 2014 07:41:04 UTC+9, xorxes a =C3=A9crit : >> >>> >>> lo PA broda :=3D zo'e noi ke'a PA mei gi'e broda >>> >> >> >> I prefer that definition to the current one because the system of=20 >> counting is clearer than {zilkancu}, though atomicity is still not requi= red=20 >> for {PA mei}. >> > > Atomicity is not strictly required for the definition, but it's kind of= =20 > implicit. If atomicity is false, then "su'o N mei" is always true. They a= re=20 > just a series of tautological predicates. And "N mei" is always false for= =20 > any finite N, a series of contradictory predicates. So we _can_ define "P= A=20 > mei" in the absence of atomicity, but actually using those predicates for= =20 > anything meaningful requires atomicity. In the absence of atoms, anything= =20 > at all satisfies su'o N mei and consequently nothing at all satisfies N m= ei. > > If we really need atomicity for {lo PA broda}, we could add a condition o= f=20 >> individual for {lo pa broda}: >> {lo pa broda} =3Dca'e {zo'e noi ro'oi da poi ke'a xi pa me ke'a xi re zo= 'u=20 >> ke'a xi re me da gi'e broda} >> >> However, I think atomicity is not necessary for a definition of inner=20 >> quantifier.=20 >> > > I agree it's not necessary for the definition, but the use of a finite=20 > inner quantifier presupposes individuals. > > I don't yet understand how the definitions on {PA mei} could suggest=20 implicit atomicity. The definitions on the topic are: (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=20 ge da su'o N-1 mei gi de na me da (I interpret here {su'oi da su'oi de zo'u de na me da} =3D {su'oi da su'oi = de=20 naku zo'u de me da} in accordance with your suggestion=20 http://www.lojban.org/tiki/scope+of+na , not {naku su'oi da su'oi de zo'u= =20 de me da} of CLL.) (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 Actually, (D2) fails on N=3D1: ko'a pa mei=20 =3D ko'a su'o pa mei gi'e nai su'o re mei=20 =3D ge=20 su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u=20 ge da su'o no mei gi de naku me da -----(S1) gi=20 naku su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u=20 ge da su'o pa mei gi de naku me da -----(S2) Consider (S1): because {su'oi da no mei} is false, (S1) actually says only= =20 {su'oi da poi me ko'a zo'u ge da su'o pa mei gi de naku me da}. It=20 contradicts (S2). For precise definitions on {PA mei}, we need therefore an explicit=20 definition of {ko'a su'o pa mei} besides (D1). Once {ko'a su'o pa mei} is defined in some way, (D2) and (D3) are valid for= =20 an integer N>=3D1. (D2) is expanded as follows: (D2) ko'a N mei=20 =3D ko'a su'o N mei gi'e nai su'o N+1 mei=20 =3D ge ko'a su'o N mei -----(S1) gi naku ko'a su'o N+1 mei -----(S2) (S2) =3D naku su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u=20 ge da su'o N mei=20 gi de naku me da =3D ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u naku ge da su'o N mei=20 gi de naku me da =3D ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u ganai da su'o N mei=20 gi de me da Therefore, ko'a N mei=20 =3D ge (S1) gi (S2)=20 =3D ge ko'a su'o N mei gi ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u ganai da su'o N mei=20 gi de me da Then {ko'a N mei} implies also=20 ro'oi de poi me ko'a zo'u de me ko'a When N=3D1,=20 ko'a pa mei=20 =3D 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=20 gi de me da=20 In every derivation from (D1) and (D2), {ko'a} may have {ko'e} such that=20 {ko'e me ko'a ijenai ko'a me ko'e}. There seems to be no reason for {ko'a}= =20 beeing an individual {ro'oi da me ko'a zo'u ko'a me da} or individuals. If= =20 atomicity is implied, that should be caused by the expression {ko'a su'o pa= =20 mei}, which is not yet defined. As a reasonable definition for {ko'a su'o pa mei}, I would suggest as=20 follows: (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 When a condition {ije da me de} is also satisfied with (D1-1), {ko'a} is an= =20 individual. Otherwise, {ko'a} of (D1-1) is individuals or non-individual. (D1-1) says nothing related the number one, but it reflects a property of= =20 one-some of non-individual: any non-individual sumti can be one-some. Once= =20 non-individual B such that {B me ko'a} is fixed as one-some {B pa mei}, and= =20 if C such that {C me ko'a} satisfies conditions (D1) and (D2), C is counted= =20 to be an integer, and it is meaningful: at least, an order of cardinality= =20 is given to the pair of B and C. It may be off topic, but if there were a definition for inner fractional=20 quantifier=20 {lo piPA broda} =3Dca'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= =20 atomist and non-atomist. Actually, an outer fractional quantifier {piPA sumti} =3Dca'e {lo piPA si'e= =20 be pa me sumti} is available to atomists only. --=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_848_4192485.1392871817064 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable


Le mercredi 19 f=C3=A9vrier 2014 05:38:50 UTC+9, x= orxes a =C3=A9crit :



On Tue, Feb 18, 201= 4 at 10:13 AM, guskant <gusni...@gmail.com> wrote:

Le mardi 18 f=C3=A9vrie= r 2014 07:41:04 UTC+9, xorxes a =C3=A9crit :

lo PA = broda :=3D zo'e noi ke'a PA mei gi'e broda


I prefer that definition= to the current one because the system of counting is clearer than {zilkanc= u}, though atomicity is still not required for {PA mei}.

Atomicity is not strictly required f= or the definition, but it's kind of implicit. If atomicity is false, then "= su'o N mei" is always true. They are just a series of tautological predicat= es. And "N mei" is always false for any finite N, a series of contradictory= predicates. So we _can_ define "PA mei" in the absence of atomicity, but a= ctually using those predicates for anything meaningful requires atomicity. = In the absence of atoms, anything at all satisfies su'o N mei and consequen= tly nothing at all satisfies N mei.

If we r= eally need atomicity for {lo PA broda}, we could add a condition of individ= ual for {lo pa broda}:
{lo pa broda} =3Dca'e {zo'e noi ro'oi da poi ke'a xi pa me ke'a xi re = zo'u ke'a xi re me da gi'e broda}

However, I think= atomicity is not necessary for a definition of inner quantifier. 

I agree it's not necessary for the d= efinition, but the use of a finite inner quantifier presupposes individuals= .



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 me= i :=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 m= ei gi de na me da

(I interpret here {su'oi da su'o= i de zo'u de na me da} =3D {su'oi da su'oi de naku zo'u de me da} in accord= ance with your suggestion http://www.lojban.org/tiki/scope+of+na , not {nak= u su'oi da su'oi de zo'u de me da} of CLL.)

(D2) k= o'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>Actually, (D2) fails on N=3D1:
ko'a pa mei 
=3D ko'a su'= o pa mei gi'e nai su'o re mei 
=3D ge 
su'oi da poi me ko'a ku'o = su'oi de poi me ko'a zo'u 
ge da su'o no mei gi de naku me da -----(S1= )
gi 
naku su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u 
g= e da su'o pa mei gi de naku me da -----(S2)

Consid= er (S1): because {su'oi da no mei} is false, (S1) actually says only {su'oi= da poi me ko'a zo'u ge da su'o pa mei gi de naku me da}. It contradicts (S= 2).

For precise definitions on {PA mei}, we need t= herefore an explicit definition of {ko'a su'o pa mei} besides (D1).

Once {ko'a su'o pa mei} is defined in some way, (D2) and = (D3) are valid for an integer N>=3D1. (D2) is expanded as follows:
=

(D2) ko'a N mei 
=3D ko'a su'o N mei gi'e nai su'o= N+1 mei 
=3D ge ko'a su'o N mei -----(S1)
gi naku ko'a su'o N+1 mei -= ----(S2)

(S2)
=3D naku su'oi da poi me ko'a ku'o su'oi de po= i me ko'a zo'u 
ge da su'o N mei 
gi de naku me da
=3D ro'oi da p= oi me ko'a ku'o ro'oi de poi me ko'a zo'u
naku ge da su'o N mei 
=
gi de= naku me da
=3D ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u
ganai d= a su'o N mei 
gi de me da

Therefore,
ko'a N mei 
=3D ge (S1) gi (S2) 
=3D ge ko'a su'o N mei
gi ro'o= i da poi me ko'a ku'o ro'oi de poi me ko'a zo'u
ganai da su'o N mei 
g= i de me da

Then {ko'a N mei} implies also 
ro'oi de poi me ko'a zo'u de me ko'a

When = N=3D1, 
ko'a pa mei 
=3D ge ko'a su'o pa mei
= gi ro'oi d= a 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 

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}. T= here seems to be no reason for {ko'a} beeing an individual {ro'oi da me ko'= a zo'u ko'a me da} or individuals. If atomicity is implied, that should be = caused by the expression {ko'a su'o pa mei}, which is not yet defined.

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

(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
=
When a condition {ije da me de} is also satisfied with (D1-1= ), {ko'a} is an individual.
Otherwise, {ko'a} of (D1-1) is indivi= duals or non-individual.

(D1-1) says nothing relat= ed 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.


It may be off topic, but if= there were a definition for inner fractional quantifier 
{l= o piPA broda} =3Dca'e {zo'e noi ke'a piPA si'e be lo pa broda}
th= en the language would be richer; this definition would be avaiable both ato= mist and non-atomist.
Actually, an outer fractional quantifier {p= iPA sumti} =3Dca'e {lo piPA si'e be pa me sumti} is available to atomists o= nly.


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