Received: from mail-qc0-f185.google.com ([209.85.216.185]:46482) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WGeUc-0002m1-Ru for lojban-list-archive@lojban.org; Thu, 20 Feb 2014 17:01:36 -0800 Received: by mail-qc0-f185.google.com with SMTP id m20sf643622qcx.12 for ; Thu, 20 Feb 2014 17:01:24 -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=p/tqudpft1pzb7rUPpkUxwGGc8d6JBTSYfzkubF5sno=; b=McZiJpcHIKcsBpQjwrD/aU8xH569dhw8zxek51pBtsy/LTXompZFwfkLwaiUL0YYz7 yAEcqNAVdE2ihwHCD3mbdUcoW6OcYLmKcTUm3R1I4DF75QzS8IUHfkdb7CmqIq5hYYDA tqe1zML3jv+nAUaGCTG81mPKa/PAiliUbqeQO4e9G9gJiwLVqONj3umnLMZ79Mb86SLS YANkC0mDUzOcs9RRFODoAsUwEyBaWKsQfrDEyJg+CErkwlhdyK8WYANs+JkpaBNrN6Jj RGgNZv6RDRsesQgJ42QyS1AQ62zgGzMqbk88B2s1nYGk7YvMKviwlTfY1XurZFPRHYJE 7Wog== 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=p/tqudpft1pzb7rUPpkUxwGGc8d6JBTSYfzkubF5sno=; b=yuZYOoo/SPRGKmQLBwTOhykVJzVLn+N+2peK8OGoj2kOvmw0bYWO7R0s9YF6Mx8S52 7jismXBVUvNyF2AHtWNduhSA6Fu91SEfXhLua5THgS2a6602p+QHhyeiBWPmcvU3uDSL R2/oljXlzqRg6cSkEp3oWgFVmcmidnd3vj9JVfHOWEagfni1IO6H/fvY13cFRB9Znvvb j4DkWG2+jLiv+9HV1SFArIgFJLOckdC7EkH3BTvCEaTNTTQUD3Ph/NmlNeu57WdHN1h2 705/K4fIOS/iDiDIhrtUIjBtOerj2eIM+DKKfxz1sv3+we5BCZqohcRaqvEXfYe8RV8C YDvQ== X-Received: by 10.50.112.101 with SMTP id ip5mr29826igb.1.1392944484475; Thu, 20 Feb 2014 17:01:24 -0800 (PST) X-BeenThere: lojban@googlegroups.com Received: by 10.50.43.193 with SMTP id y1ls261580igl.3.gmail; Thu, 20 Feb 2014 17:01:23 -0800 (PST) X-Received: by 10.50.79.232 with SMTP id m8mr30380igx.12.1392944483734; Thu, 20 Feb 2014 17:01:23 -0800 (PST) Date: Thu, 20 Feb 2014 17:01:21 -0800 (PST) From: guskant To: lojban@googlegroups.com Message-Id: <36c4c2b2-8f8c-4d44-ac8e-48c02d45a233@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> 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_154_19185502.1392944481403" X-Spam-Score: -0.1 (/) X-Spam_score: -0.1 X-Spam_score_int: 0 X-Spam_bar: / ------=_Part_154_19185502.1392944481403 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable 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: > >> >> 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= =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 >> >> >> 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. > =20 > 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. =20 > > Once {ko'a su'o pa mei} is defined in some way, (D2) and (D3) are valid= =20 >> for an integer N>=3D1. (D2) is expanded as follows: >> [...] >> Then {ko'a N mei} implies also=20 >> ro'oi de poi me ko'a zo'u de me ko'a >> > =20 > "ro'oi de poi me ko'a zo'u de me ko'a" is true independently of whether= =20 > "ko'a N mei" is true or not. It's just a case of the general "ro'oi de po= i=20 > broda zo'u de broda".=20 > =20 > >> 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 >> > > Yes, and since "su'o pa mei" is a tautology, that reduces to: > > ko'a pa mei=20 > =3D 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= =20 > else would a one-some be if not an individual?) > =20 > Because "ro'oi da su'o pa mei" is based on a non-logical axiom, it cannot= =20 be called "tautology" in normal meaning. With this axiom, {ko'a pa mei}=20 says that "ko'a" is an individual, of course. =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}.=20 >> > > I don't think that can happen if "ko'a pa mei" is true. > =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. =20 > > 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 k= o'a=20 >> zo'u de me da >> > > Since that is also a tautology ("ko'a" itself will instantiate "su'oi da= =20 > poi me ko'a"), it works, but it's more complicated that it needs to be. W= e=20 > 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=20 > tautological predicate. =20 > > The complicated form of (D1-1) is intended to add a non-logical part {ije= =20 da me de} in order to say explicitly the case that ko'a is an individual. =20 > =20 > >> (D1-1) says nothing related the number one, but it reflects a property o= f=20 >> one-some of non-individual: any non-individual sumti can be one-some. On= ce=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 coun= ted=20 >> to be an integer, and it is meaningful: at least, an order of cardinalit= y=20 >> is given to the pair of B and C. >> > > If by "one-some" you mean "pa mei", then only indiciduals can satisfy it.= =20 > If you mean "su'o pa mei", then yes, anything satisfies it, it's a=20 > tautology. Or am I missing something? > =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, they= =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. =20 > > 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 bot= h=20 >> atomist and non-atomist. >> Actually, an outer fractional quantifier {piPA sumti} =3Dca'e {lo piPA s= i'e=20 >> be pa me sumti} is available to atomists only. >> > > I assume "lo piPA broda" will have some such meaning , but it's a=20 > different system. And it relies on a previous definition of "si'e", which= =20 > we don't have from basics like the ones we're discussing here for "mei". > > I agree. I just want to suggest it on my personal gadri page for symmetry= =20 of definitions of quantifiers. =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_154_19185502.1392944481403 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable


Le vendredi 21 f=C3=A9vrier 2014 06:43:48 UTC+9, x= orxes a =C3=A9crit :



On Thu, Feb 20, 201= 4 at 1:50 AM, guskant <gusni...@gmail.com> wrote:

I don't yet unde= rstand 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 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>

For precise definitions on {PA mei}, we n= eed 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 tautologic= al predicate, always true of anything.
 


Yes, and in order to say "ro'oi da su'o pa mei", an axiom that is n= ot 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 ind= ividual.


 

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:
[...]
Then {ko'a N mei} implies also 
ro'oi d= e 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 whet= her "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". 
 
Whe= n N=3D1, 
ko'a pa mei 
=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 = ;
gi de me da <= /div>

Yes, and since "su'o pa m= ei" is a tautology, that reduces to:

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

which says that "ko'a" is an individu= al. (Which is to be expected, what else would a one-some be if not an indiv= idual?)
 

<= br>
Because "ro'oi da su'o pa mei" is based on a non-logical axio= m, it cannot be called "tautology" in normal meaning. With this axiom, {ko'= a pa mei} says that "ko'a" is an individual, of course.


 

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

<= /div>
I don't think that can happen if "ko'a pa mei" is true.
 


You are right under the condition that "ro'oi da su'o pa mei" is tr= ue. 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 ca= se that ko'a is non-individual in the point that they give an order of= cardinality.


 

As a r= easonable 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 me ko'a ku'o = ro'oi de poi me ko'a zo'u de me da

<= /div>
Since that is also a tautology ("ko'a" itself will instantiate "s= u'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 :=3D ko'a me ko'a

=
or:

ko'a su'o pa mei :=3D ko'a du ko'a
<= div>
or any other tautology. Or just state that "su'o pa mei"= is the tautological predicate.  



The complicated form of (D1-1) is intended to add a non-logical part = {ije da me de} in order to say explicitly the case that ko'a is an individu= al.


 
 
<= /div>
(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 mei},= and if C such that {C me ko'a} satisfies conditions (D1) and (D2), C is co= unted to be an integer, and it is meaningful: at least, an order of cardina= lity 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?
 


I mean "pa mei" by "one-some". As I mentioned above, In order to sa= y {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'oi da su'o pa mei", but explicitly mentions the condition for ko'a bein= g an individual. Because (D1) (D2) (D3) give only an order of cardinality, = they alone can be used both cases of individuals and non-individual. Starti= ng 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) themsel= ves are more generally available without non-logical axioms.

=

 

It may be off topic, but if there were a definition for inner fraction= al quantifier 
{lo piPA broda} =3Dca'e {zo'e noi ke'a piPA s= i'e be lo pa broda}
then the language would be richer; this defin= ition 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 me= aning , 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".



I agree. I just want to suggest it on my personal gadri page for symm= etry of definitions of quantifiers.
 

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