Received: from mail-oa0-f60.google.com ([209.85.219.60]:64382) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WHP42-0003IS-D7 for lojban-list-archive@lojban.org; Sat, 22 Feb 2014 18:45:17 -0800 Received: by mail-oa0-f60.google.com with SMTP id j17sf822741oag.25 for ; Sat, 22 Feb 2014 18:45:04 -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=VIAmiejOaPzs+Ot4WwUrGo7o+XTpJnk/A1EX6Jo1O0g=; b=pOScGWaZ+QpDMEYj9h17km6gWURhwh0UMjCOJ1EwqLZrchtqsOX9EPn52j3HguV2mM y6iySPWtWBp4LCVxBMHeyR5j6PxrHmDOmNsayerZnFR+lkYfyvZfbDbwOB0D4iRac3Wy xM29PYNo8pB4I56wJh4LqnkX0N+nmj2H5HOB1XrOjWwYb7ac4x0Wzm512ta+I+eAT9zJ EF6QLxd0XIpcvGk4P440/youzWeRyhlBJCPjGgS6tGWpEDdt5ykVAECTymhhvWnyDG1I zjwwzq1BXqbptETTq8QkIjLIgsLHbRAS16MpMW1nnZ7JtmUaQ4OOzOyEeJRwDl+cN27s DgWw== 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=VIAmiejOaPzs+Ot4WwUrGo7o+XTpJnk/A1EX6Jo1O0g=; b=w8cfF6h9pIjYxwkQIJoPfskuWzGrzDvIuu9ee/AUVTwogd+kxAeIvBwwun4iNlnXaV +wwIxop830E65Nei7vZuxN/VK6xkTs+H5nDP5LOY4EHPeDJL6SVbVuS6A43wNB3P16r7 U0QxLdQfmVvoQDfHUl2ZkKc5PEm8xE9pNlBEpfXDScGTBKFuyxjHVCYacoWtZ/lsNojK BGwsvkw6DfJZA1odDvwSvATzYL8esEnQM0+/MdQNOV/8Y1ygJiWoYbxcLDk1xJ7mJLwB lnMmvpJmOD+zaSUnB4KLpi4RysvopkTAFfNC5my4vRNSgyRXiygrJKFvEp7l1sUTkInX qHLA== X-Received: by 10.50.50.139 with SMTP id c11mr231592igo.14.1393123504065; Sat, 22 Feb 2014 18:45:04 -0800 (PST) X-BeenThere: lojban@googlegroups.com Received: by 10.50.28.18 with SMTP id x18ls1417417igg.25.gmail; Sat, 22 Feb 2014 18:45:03 -0800 (PST) X-Received: by 10.50.82.98 with SMTP id h2mr233800igy.3.1393123503478; Sat, 22 Feb 2014 18:45:03 -0800 (PST) Date: Sat, 22 Feb 2014 18:45:01 -0800 (PST) From: guskant To: lojban@googlegroups.com Message-Id: 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> 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_745_31022760.1393123502028" X-Spam-Score: -0.1 (/) X-Spam_score: -0.1 X-Spam_score_int: 0 X-Spam_bar: / ------=_Part_745_31022760.1393123502028 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Le samedi 22 f=C3=A9vrier 2014 22:40:42 UTC+9, xorxes a =C3=A9crit : > > On Sat, Feb 22, 2014 at 5:02 AM, guskant > > wrote: > >> >>> Because {su'o mei} is neither a sequence of logical elements, nor=20 >> expanded to a sequence of logical elements, a sentence including {su'o m= ei}=20 >> itself cannot be a logical axiom or the equivalent. I call a sentence=20 >> "tautology" only when it is expressed with a sequence of logical element= s=20 >> that is a logical axiom or the equivalent.=20 >> > > But we _are_ defining "su'o mei" (as well as all the other "su'o N mei"= =20 > and "N mei") as logical elements! That's the whole point of what we're=20 > doing, isn't it? Why would you want to give "su'o mei" different meanings= =20 > in differnet contexts? > =20 > "su'o mei" is just the tautological predicate. It has nothing to do with= =20 > whether or not there are individuals. It is true of anything at all. > > {ro'oi da su'o pa mei} alone cannot be expanded to logical elements only,= =20 (D1) (D2) neither, because a predicate {N mei} is not a logical element: {N= =20 mei} is a predicate that reflects natural number theory, not only predicate= =20 logic. They are _distributively_ not tautology. {ro'oi da su'o pa mei}, (D1) and (D2) give _collectively_ a sequence of=20 logical elements: ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de me da and it is not a logical axiom or the equivalent. {ro'oi da su'o pa mei},=20 (D1) and (D2) are _collectively_ not tautology. (D1) and (D2) gives only an order to {su'o N mei} and {N mei}, and they=20 don't give a meaning to the predicate {su'o pa mei}. The starting point {ro'oi da su'o pa mei} gives indeed a meaning to {su'o= =20 pa mei}. =20 > Any of them are fine. (D1-1) is only a "one-shot" definition of a=20 >> particular ko'a in a particular universe of discourse defined by a speak= er.=20 >> It is not for general use. >> > > But what does D1 even mean if you only know what "su'o mei" means when=20 > applied to a particular ko'a? According to D1 > > ko'a su'o re mei :=3D su'o da poi me ko'a su'o de poi me ko'a zo'u ge da= =20 > su'o mei gi nai de me da > > How is that a complete definition of "ko'a su'o re mei", when there is an= =20 > undefined term on the right hand side?=20 > > In all my definitions "ko'a" was intended as a place holder. They=20 > otherwise don't make sense as definitions of the 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.=20 For a place holder, {ke'a} and {ce'u} are suitable, because they are free= =20 variables: such usage is not described in CLL, but it is useful at least in= =20 the current discussion. When {ce'u} appears more than two times in a sequence of words, different= =20 sumti can be substituted for them, while only a common sumti can be=20 substituted for {ke'a}s. For the current purpose, using {ke'a} is better. Using {ke'a}, our definitions are described as follows: (D1-7) ko'a su'o pa mei (D1) ke'a su'o N mei :=3D su'oi da poi me ke'a ku'o su'oi de poi me ke'a zo= 'u=20 ge da su'o N-1 mei gi de na me da (D2) ke'a N mei :=3D ke'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 When (D1) and (D2) are applied to a particular sumti, ke'a are replaced=20 with it. As for (D3), ke'a is in noi-clause, and it is already fixed to=20 zo'e, and is not replaced with another sumti, of course.=20 Because (D1-7) defines only for {ko'a}, (D1) (D2) (D3) are valid only for= =20 sumti that involves a referent of {ko'a} such as {ko'e noi ko'a me ke'a},= =20 {ko'i no'u ko'a jo'u ko'o} etc. (D1) (D2) (D3) are not used for other sumti= =20 unless (D1-7) is applied to one of the referents that is involved by the=20 sumti. =20 > =20 > >> Even with (D1-1b), "mi jo'u do su'o pa mei" is true. >> >> (D1-1b) is also a "one-shot" definition defined by a speaker on a=20 >> particular ko'a that is an individual, and is not applied generally.=20 >> It gives a meaning to {su'o pa mei} with a particular ko'a. >> >> For example, suppose a speaker applies (D1-1b) to {mi}: >> (D1-1b) mi su'o pa mei :=3D su'oi da poi me mi ku'o ro'oi de poi me mi z= o'u=20 >> de me da ije da me de >> Then {mi jo'u do} satisfies (D1) of N=3D2: >> mi jo'u do su'o re mei >> >> From (D1),=20 >> ganai ko'a su'o N mei gi ko'a su'o N-1 mei >> is always true.=20 >> > >> (proof: >> > > I didn't check your proof in detail, but it seems to me you must be be=20 > relying on D1-1, not just on D1. Otherwise both "su'o N mei" and "su'o N-= 1=20 > mei" are undefined. With D1-1b in effect, the statement is false. From "m= i=20 > jo'u do su'o re mei" we cannot conclude "mi jo'u do su'o pa mei" if "D1-1= b"=20 > applies to "mi jo'u do". > I used only (D1) and logical axioms including transitivity of {me}. Any=20 mention of {su'o pa mei} is not necessary for the proof. =20 > =20 > >> Therefore=20 >> mi jo'u do su'o pa mei >> is also true. >> > > As long as D1-1b applies only to "mi", and D1-1 applies to "mi jo'u do",= =20 > yes. But why would you use different definitions of "su'o mei" in the sam= e=20 > context? > If you need {su'o mei} for other sumti that does not involve {mi} in the=20 same context, you must use (D1-7) or (D1-1b) to that sumti. For {ko'a noi= =20 naku mi me ke'a}, {ko'a su'o mei} is not defined otherwise. =20 > > > For example, suppose that a speaker regards {lo nanba} is=20 > non-individual: > >> ro'oi da poi me lo nanba ku'o su'oi de poi me lo nanba zo'u de me da=20 >> ijenai da me de >> >> That is, the speaker regards a half of {lo nanba} is also {me lo nanba}.= =20 >> > > Yes. > =20 > >> Even though there is no individual {lo nanba}, an expression {N mei} is= =20 >> 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=20 convenience. 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= =20 lo nanba xi re/ci cu me lo nanba xi pa}, the first sentence is true, and=20 the second and the third are false. That is to say, if {(D1-7) lo nanba cu su'o pa mei} is defined, and if all= =20 the appearances of {lo nanba} have a common referent, the first sentence is= =20 true, and the second and the third are false. =20 =20 > =20 > >> The speaker arbitrarily fix a referent to be {lo pa nanba}. If another= =20 >> {lo nanba xi re} is given, {lo pa nanba jo'u lo nanba xi re} is {lo re= =20 >> nanba}. >> > > If "lo pa nanba" satisfies D1-1 and D1 and it also satisfies "ro'oi da po= i=20 > me lo pa nanba ku'o su'oi de poi me lo pa nanba zo'u de me da ijenai da m= e=20 > de", then it cannot satisfy D2.=20 > > (D1) is meaningless for N=3D1, because (D1)+(D2) for N=3D1 produces=20 contradiction. The meaning of {su'o pa mei} is defined by the starting point {ro'oi da=20 su'o pa mei} XOR (D1-7), not by (D1). (D1) is meaningful only for N>=3D2, in both procedures of starting with=20 {ro'oi da su'o pa mei} and of using (D1-7). When=20 (D1-7) lo nanba cu su'o pa mei is defined, (D1-7), (D1) for N=3D2, (D2) and (D3) produce a meaningful {lo = pa=20 nanba}. (D1) for N=3D1 is not used here. When another {ko'e noi nanba} is given, (D1) can be used for saying {lo=20 nanba (ku) jo'u ko'e noi nanba cu su'o re mei}. Please note that the=20 referent of the first {lo nanba} is different from ko'e. =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_745_31022760.1393123502028 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable


Le samedi 22 f=C3=A9vrier 2014 22:40:42 UTC+9, xor= xes a =C3=A9crit :
On Sat, Feb 22, 2014 at 5:02 AM, guskant &= lt;gusni...@gmail.com> wrote:

Because {su'o mei} is neither a sequence of logical elements, no= r expanded to a sequence of logical elements, a sentence including {su'o me= i} itself cannot be a logical axiom or the equivalent. I call a sentence "t= autology" only when it is expressed with a sequence of logical elements tha= t is a logical axiom or the equivalent. 

But we _are_ defining "su'o mei" (as= well as all the other "su'o N mei" and "N mei") as logical elements! That'= s the whole point of what we're doing, isn't it? Why would you want to give= "su'o mei" different meanings in differnet contexts?
 
"su'o mei" is just the tautological predicate. It= has nothing to do with whether or not there are individuals. It is true of= anything at all.



{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 log= ical element: {N mei} is a predicate that reflects natural number theory, n= ot only predicate logic. They are _distributively_ not tautology.

{ro'oi da su'o pa mei}, (D1) and (D2) give _collectively_ a= sequence of logical elements:
ro'oi da poi me ko'a ro'oi de poi = me ko'a zo'u de me da
and it is not a logical axiom or the equiva= lent. {ro'oi da su'o pa mei}, (D1) and (D2) are _collectively_ not tautolog= y.

(D1) and (D2) gives only an order to {su'o N me= i} and {N mei}, and they don't give a meaning to the predicate {su'o pa mei= }.
The starting point {ro'oi da su'o pa mei} gives indeed a meani= ng to {su'o pa mei}.


 
Any of them are fine. (D1-1) is only a "on= e-shot" definition of a particular ko'a in a particular universe of discour= se defined by a speaker. It is not for general use.

But what does D1 even mean if you only kno= w what "su'o mei" means when applied to a particular ko'a? According to D1<= /div>

ko'a su'o re mei :=3D su'o da poi me ko'a su'o de = poi me ko'a zo'u ge da su'o mei gi nai de me da

How is that a complete definition of "ko'a su'o re mei"= , when there is an undefined term on the right hand side? 
<= div class=3D"gmail_quote">

In all my definitions "ko'a" was intended as a place holder. They othe= rwise don't make sense as definitions of the predicates.
<= /div>


It seems that using "k= o'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 n= ot 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.

Using {ke'a}, our definitions are d= escribed as follows:
(D1-7) ko'a su'o pa mei
(D1) ke'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 s= u'o N-1 mei gi de na me da
(D2) ke'a N mei  :=3D ke'a su'o N= mei gi'e nai su'o N+1 mei 
(D3) lo PA broda :=3D zo'e noi k= e'a PA mei gi'e broda

When (D1) and (D2) are appli= ed to a particular sumti, ke'a are replaced with it. As for (D3), ke'a is i= n noi-clause, and it is already fixed to zo'e, and is not replaced wit= h another sumti, of course. 

Because (D1-7) d= efines only for {ko'a}, (D1) (D2) (D3) are valid only for sumti that involv= es 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.

 
 
Even with (D1-1b), "mi jo'u do su'o pa mei" is true.<= /div>

(D1-1b) is also a "one-shot" definition defined by= a speaker on a particular ko'a that is an individual, and is not applied g= enerally. 
It gives a meaning to {su'o pa mei} with a particular ko'a.
=
For example, suppose a speaker applies (D1-1b) to {mi}:
(D1-1b) mi su'o pa mei :=3D su'oi da poi me mi ku'o ro'oi de poi me m= i zo'u de me da ije da me de
Then {mi jo'u do} satisfies (D1) of N=3D2:
mi jo'u do s= u'o re mei

From (D1), 
ganai ko'a s= u'o N mei gi ko'a su'o N-1 mei
is always true. 

(p= roof:

I didn't check your proof in detail,= but it seems to me you must be be relying on D1-1, not just on D1. Otherwi= se both "su'o N mei" and "su'o N-1 mei" are undefined. With D1-1b in effect= , the statement is false. From "mi jo'u do su'o re mei" we cannot conclude = "mi jo'u do su'o pa mei" if "D1-1b" applies to "mi jo'u do".


I used only (D1) a= nd logical axioms including transitivity of {me}. Any mention of {su'o pa m= ei} is not necessary for the proof.


 
=
 
Therefore 
mi jo'u do su'o pa mei
is also true.

As long as D1-1b applies only to "mi", and D1-1 = applies to "mi jo'u do", yes. But why would you use different definitions o= f "su'o mei" in the same context?
=

If you need {su'o mei} for other sumti that d= oes not involve {mi} in the same context, you must use (D1-7) or (D1-1b) to= that sumti. For {ko'a noi naku mi me ke'a}, {ko'a su'o mei} is not defined= otherwise.


 


    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 nanb= a zo'u de me da ijenai da me de

That is, the speak= er regards a half of {lo nanba} is also {me lo nanba}. 

Yes.
 
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 nanba cu su'o ci mei" = is true


<= div>
I call them {lo nanba xi re} and {lo nanba xi ci} respec= tively for convenience.
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 nanb= a xi re/ci gi naku lo nanba xi re/ci cu me lo nanba xi pa}, the first sente= nce is true, and the second and the third are false.

That is to say, if {(D1-7) lo nanba cu su'o pa mei} is defined, and if a= ll the appearances of {lo nanba} have a common referent, the first sentence= is true, and the second and the third are false.
 
 
 
The speaker arbitra= rily fix a referent to be {lo pa nanba}. If another {lo nanba xi re} is giv= en, {lo pa nanba jo'u lo nanba xi re} is {lo re nanba}.

If "lo pa nanba" satisfies D1-1 and = D1 and it also satisfies "ro'oi da poi me lo pa nanba ku'o su'oi de poi me = lo pa nanba zo'u de me da ijenai da me de", then it cannot satisfy D2. = ;



(D1) is meaningless for N=3D1, because (D1)+(D2) for N=3D1 produces c= ontradiction.
The meaning of {su'o pa mei} is defined by the star= ting point {ro'oi da su'o pa mei} XOR (D1-7), not by (D1).
(= D1) is meaningful only for N>=3D2, in both procedures of starting with {= ro'oi da su'o pa mei} and of using (D1-7).

W= hen 
(D1-7) lo nanba cu su'o pa mei
is defined, (D= 1-7), (D1) for N=3D2, (D2) and (D3) produce a meaningful {lo pa nanba}. (D1= ) for N=3D1 is not used here.

When another {ko'e n= oi nanba} is given, (D1) can be used for saying {lo nanba (ku) jo'u ko= 'e noi nanba cu su'o re mei}. Please note that the referent of the first {l= o nanba} is different from ko'e.

 
<= /div>

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