Received: from mail-pb0-f58.google.com ([209.85.160.58]:50249) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1Wo05m-0000lu-J3 for lojban-list-archive@lojban.org; Fri, 23 May 2014 17:45:50 -0700 Received: by mail-pb0-f58.google.com with SMTP id jt11sf1441603pbb.13 for ; Fri, 23 May 2014 17:45:36 -0700 (PDT) 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=QRXssmOn/Ex23+X31UAjdbZIoyHc8nAyIXJCii2exbM=; b=UVAlQwxLd3KRCFiobg8TRrf9wPpp8iK8cEwdZfxeH8rzRw62dwMgIopUOhziwP7++S Dpi5TA/kLVZQRGo169+mXO44bDA8t6XRrI9lBcelBwHMwrr2Y1nT/mHBQwTaC6kX2sPE jFNZYBBSTUIEqvTb5ike3KeO08JEB8qbzqF1CJniqpQmJ1FIiCEPfBFG9yEvpIYNE8Lc oPDiv4PWROtyALWtasX0RE5m/QmK9/MG8y9lnbqGiQbKQLCUN6oqaIRmnIh0+DFZpep9 VLgNhDKyqKI1q2TKiekyXTewZVBeAePsC8jjZVOFlZrCEJs1HKVO4akKpx9Ul/C4QBb+ JGFA== X-Received: by 10.50.59.179 with SMTP id a19mr163128igr.10.1400892336549; Fri, 23 May 2014 17:45:36 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.50.29.69 with SMTP id i5ls686408igh.0.gmail; Fri, 23 May 2014 17:45:35 -0700 (PDT) X-Received: by 10.68.134.233 with SMTP id pn9mr3991207pbb.5.1400892335833; Fri, 23 May 2014 17:45:35 -0700 (PDT) Received: from mail-vc0-x235.google.com (mail-vc0-x235.google.com [2607:f8b0:400c:c03::235]) by gmr-mx.google.com with ESMTPS id xn6si282079vdc.2.2014.05.23.17.45.35 for (version=TLSv1 cipher=ECDHE-RSA-RC4-SHA bits=128/128); Fri, 23 May 2014 17:45:35 -0700 (PDT) Received-SPF: pass (google.com: domain of jjllambias@gmail.com designates 2607:f8b0:400c:c03::235 as permitted sender) client-ip=2607:f8b0:400c:c03::235; Received: by mail-vc0-f181.google.com with SMTP id hy4so3695856vcb.12 for ; Fri, 23 May 2014 17:45:35 -0700 (PDT) MIME-Version: 1.0 X-Received: by 10.221.20.199 with SMTP id qp7mr7107095vcb.24.1400892335663; Fri, 23 May 2014 17:45:35 -0700 (PDT) Received: by 10.220.170.73 with HTTP; Fri, 23 May 2014 17:45:35 -0700 (PDT) In-Reply-To: <570dae9f-cda3-42c4-a861-1c7974fe5bfd@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> <4b6b2cb9-51e5-47f6-97a9-2dec16406864@googlegroups.com> <390f1b9f-6edd-42f2-8474-ad1f3610cca3@googlegroups.com> <750f9b01-a747-4b12-80ba-e31b7e7bd20e@googlegroups.com> <570dae9f-cda3-42c4-a861-1c7974fe5bfd@googlegroups.com> Date: Fri, 23 May 2014 21:45:35 -0300 Message-ID: Subject: Re: [lojban] Individuals and xorlo From: =?UTF-8?Q?Jorge_Llamb=C3=ADas?= 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:c03::235 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=001a11339e2e0937c104fa1aaa12 X-Spam-Score: 0.0 (/) X-Spam_score: 0.0 X-Spam_score_int: 0 X-Spam_bar: / --001a11339e2e0937c104fa1aaa12 Content-Type: text/plain; charset=UTF-8 On Mon, May 19, 2014 at 10:04 AM, guskant wrote: > > I have finished English translation of my commentary on gadri from a > logical point of view: > > http://www.lojban.org/tiki/gadri%3A+an+unofficial+commentary+from+a+logical+point+of+view&no_bl=y > Very nice. Here are some comments from me: (1)<< *argument (sumti)*Symbol that refers to a referent, or that another argument can be substituted for. >> Your definition of "sumti" implies that "zi'o" is not a sumti. This is fine, but perhaps it's worth pointing out in a note this odd word, which is also called a "sumti" in a wider, merely syntactic sense, Also things like "no da", "ci lo gerku", "mi .e do" and so on are called "sumti" in our formal grammars, although they only contain sumti by the semantic definition. Two other words that deserve special mention in this context are "ko" and "ma", which can arguably be said to fall under your definition, although they also are illocutionary force indicating devices, which ordinary sumti are not. (2)<< When each of X and Y is an individual, {X jo'u Y} is called *individuals*. >> I think you need to add "and X is not equal to Y" if you want to be more strict. (3)<< A plural constant that is an individual is called *singular constant*. >> I'd rephrase that as: "A plural constant that refers to a single individual is called a singular constant". I think it's worth keeping the distinction between the words or symbols, (constants and variables) and the referents of those symbols (things, people, trees, mountains, numbers, and so on). A constant can be singular or plural, and it can refer to an individual, but the constant is not the individual. The individual is the person, the tree or the house that the constant refers to. So if "X" is a singular constant, then X is an indifidual. (4)<< No matter whether each of X and Y is plural or singular, {X jo'u Y} is not a singular constant. >> Unless X=Y and X is an individual. But linguistically that would be odd indeed. "jo'u" should not be generally used to join something with itself, although theoretically it can be. (5)<< ro da ro'oi da poi ro'oi de poi ke'a xi pa me ke'a xi re zo'u ke'a xi re me de su'o da su'oi da poi ro'oi de poi ke'a xi pa me ke'a xi re zo'u ke'a xi re me de >> When "poi" is used to restrict the domain for da/de/di, it is not necessary to use "ke'a", and indeed it's more clear to not use "ke'a". "ke'a" is needed when there is no explicit variable bound by the quantifier, but here your definitions are much more clear as: ro da ro'oi da poi ro'oi de poi de me da zo'u da me de su'o da su'oi da poi ro'oi de poi de me da zo'u da me de (6)<< For example, a plural constant {A jo'u B} can be in a domain of a bound plural variable, but it cannot be in a domain of a bound singular variable because it is not an individual. >> Constants are not in the domain of variables, it's their referents that are in the domain. And plural and singular quantifiers can share the same domain. I think what you want to say is that a variable bound by a singular quantifier cannot take more than one individual value at a time. (7)<< *lo* (LE)It is prefixed to selbri, and forms a plural constant that refers to what satisfies x1, the first place of the selbri. If a quantifier follows {lo}, the quantifier represents the sum of all the referents of the plural constant. In the case that a quantifier follows {lo}, a sumti may follow it, and the quantifier represents the sum of all the referents of the sumti. >> I think "number", "count" or "quantity" would be better than "sum" there. To take an extreme example: "lo ci namcu" has three referents, three numbers. But "ci" is not (necessarily) the sum of the three numbers. The three numbers could be 1, 2 and 3. Their sum is 6, while their number is 3. That nitpick aside, the second part is at least unclear. In "lo ci ko'a", "ci" is the number of referents of "lo ci ko'a", but "ko'a" could have more than three referents. If you want to express that three is the number of referents of the inner sumti as well you need "lo ro ci ko'a". "lo ci lo mu gerku" has three referents, but the inner sumti has five. (8)<< An empty set is {lo selcmi be no da}, and an expression {lo no broda} is officially meaningless (see Section 3.1[image: Edit Plugin:alink]. This implies that an empty set cannot be expressed with {lo'i/le'i/la'i}. >> Arguably, lots of things can be described as "lo selcmi be no da", not just the empty set. A spoon, for example, or anything else that is not a set, will satisfy "ke'a selcmi no da". "lo selcmi be no da" works well as a description of the empty set in a universe of discourse in which there are only sets. (But then that is really the only universe of discourse in which one should mention sets at all, in my opinion.) There's another problem with the "lo'i" definition. Can "lo selcmi be lo broda" be any set that has lo broda among its members, or is it the one and only set that has lo broda as its sole members? "cmima" only says that x1 is/are among the members of x2, does "selcmi" say that its x2 are all the members of its x1? Open question. mu'o mi'e xorxes -- 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 email 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/d/optout. --001a11339e2e0937c104fa1aaa12 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable

= On Mon, May 19, 2014 at 10:04 AM, guskant <gusni.kantu@gmail.com&g= t; wrote:

I have finished English translation of my=C2=A0commentary on gadri from a = logical point of view:

Very nice. Here are some comments fr= om me:


(1)<<
argument (sumti)
Symbol that = refers to a referent, or that another argument can be substituted for.
>>

Your definition of "sumti= " implies that "zi'o" is not a sumti. This is fine, but = perhaps it's worth pointing out in a note this odd word, which is also = called a "sumti" in a wider, merely syntactic sense, =C2=A0Also t= hings like "no da", "ci lo gerku", "mi .e do"= and so on are called "sumti" in our formal grammars, although th= ey only contain sumti by the semantic definition. Two other words that dese= rve special mention in this context are "ko" and "ma", = which can arguably be said to fall under your definition, although they als= o are illocutionary force indicating devices, which ordinary sumti are not.= =C2=A0

(2)<<
When e= ach of X and Y is an individual, {X jo'u Y} is called=C2=A0individuals.=C2= =A0
>>

I think you need to add "= and X is not equal to Y" if you want to be more strict.
=C2= =A0
(3)<<
A plural constant that is an individual is = called=C2=A0singular constant.

>>

I'd r= ephrase that as: "A plural constant that refers to a single individual= is called a singular constant". I think it's worth keeping the di= stinction between the words or symbols, (constants and variables) and the r= eferents of those symbols (things, people, trees, mountains, numbers, and s= o on). A constant can be singular or plural, and it can refer to an individ= ual, but the constant is not the individual. The individual is the person, = the tree or the house that the constant refers to. So if "X" is a= singular constant, then X is an indifidual.=C2=A0

(4)<<

No matter wh= ether each of X and Y is plural or singular, {X jo'u Y} is not a singul= ar constant.=C2=A0

>>

Unless X=3DY an= d X is an individual. But linguistically that would be odd indeed. "jo= 'u" should not be generally used to join something with itself, al= though theoretically it can be.


(5)<<

ro da =C2=A0=C2=A0 ro'oi da poi ro'oi de poi ke'a xi pa me ke&#= 39;a xi re zo'u ke'a xi re me de

su'= o da =C2=A0=C2=A0 su'oi da poi ro'oi de poi ke'a xi pa me ke= 9;a xi re zo'u ke'a xi re me de

>>

When "poi" is used to = restrict the domain for da/de/di, it is not necessary to use "ke'a= ", and indeed it's more clear to not use "ke'a". &qu= ot;ke'a" is needed when there is no explicit variable bound by the= quantifier, but here your definitions are much more clear as:

ro da =C2=A0=C2=A0 ro'oi da poi ro'oi de poi de= me da zo'u da me de

su'o da =C2=A0=C2=A0 = su'oi da poi ro'oi de poi de me da zo'u da me de
=
(6)<<
For example, a plural constant {A jo'u = B} can be in a domain of a bound plural variable, but it cannot be in a dom= ain of a bound singular variable because it is not an individual.
>>

Constants are not in the domai= n of variables, it's their referents that are in the domain. And plural= and singular quantifiers can share the same domain. I think what you want = to say is that a variable bound by a singular quantifier cannot take more t= han one individual value at a time.

(7)<<
= lo=C2=A0(LE)
It is prefixed to selbri, and forms a plural constant that refers to what s= atisfies x1, the first place of the selbri. If a quantifier follows {lo}, t= he quantifier represents the sum of all the referents of the plural constan= t. In the case that a quantifier follows {lo}, a sumti may follow it, and t= he quantifier represents the sum of all the referents of the sumti.
>>

I think "number", &q= uot;count" or "quantity" would be better than "sum"= ; there. To take an extreme example: "lo ci namcu" has three refe= rents, three numbers. But "ci" is not (necessarily) the sum of th= e three numbers. The three numbers could be 1, 2 and 3. Their sum is 6, whi= le their number is 3.

That nitpick aside, the second part is at least unclear= . In "lo ci ko'a", "ci" is the number of referents = of "lo ci ko'a", but "ko'a" could have more tha= n three referents. If you want to express that three is the number of refer= ents of the inner sumti as well you need "lo ro ci ko'a". &qu= ot;lo ci lo mu gerku" has three referents, but the inner sumti has fiv= e.

=C2=A0(8)<<
= An empty set is {lo selcmi be no da}, and an expression {lo no broda} is of= ficially meaningless (see=C2=A0Sectio= n 3.1. This implies that an empty = set cannot be expressed with {lo'i/le'i/la'i}.
>>

Arguably, lots of things= can be described as "lo selcmi be no da", not just the empty set= . =C2=A0A spoon, for example, or anything else that is not a set, will sati= sfy "ke'a selcmi no da". "lo selcmi be no da" works= well as a description of the empty set in a universe of discourse in which= there are only sets. (But then that is really the only universe of discour= se in which one should mention sets at all, in my opinion.)

There's another problem with the "lo'= i" definition. Can "lo selcmi be lo broda" be any set that h= as lo broda among its members, or is it the one and only set that has lo br= oda as its sole members? "cmima" only says that x1 is/are among t= he members of x2, does "selcmi" say that its x2 are all the membe= rs of its x1? Open question.

mu'o= mi'e xorxes


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