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Re: [lojban] Individuals and xorlo






On Sun, May 25, 2014 at 6:08 AM, guskant <gusni.kantu@gmail.com> wrote:

Le samedi 24 mai 2014 09:45:37 UTC+9, xorxes a écrit :

"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.)


{lo selcmi be no da} is a standard definition of "empty set" of set theory.

Yes, but in set theory there are only sets in the universe of discourse. In set theory with ur-elements, the ur-elements don't have members, so they are "lo selcmi be no da", "things with no members", but I don't think they are called empty sets. As far as I'm aware there is only one empty set in set theory, not any number of them.
 
In other words, {zo'e noi roda naku zo'u ke'a selcmi da}. We can think of a universe of discourse in which a spoon satisfies {ke'a selcmi no da}, but it means that the spoon is regarded as an empty set in that universe of discourse. An empty set is indeed a kind of set, {lo selcmi}. If we wanted to imply that a spoon is not a set, we could rather say that a spoon satisfies {ke'a selcmi zi'o}, in which the meaning of {selcmi} was changed by {zi'o}.

I think it's the other way around. If we want a general word for "set" then "selcmi be zi'o" is better than plain "selcmi", which means "thing with members" rather than the (slightly) more general "set". 
 
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.

You created a Lojban entry of {selcmi} in jbovlaste:
It might have been modified by someone else, and is now defined as follows:
{x1 selcmi x2} =ca'e {x1 se cmima ro lo me x2 me'u e no lo na me x2} 
That is to say, the meaning of {selcmi} is different from {se cmima}, and {lo selcmi be lo broda} is the one and only set that has lo broda as its sole members.

Ah, yes, I had forgotten about it. 

However, I would prefer that the meaning of {selcmi} is the same as {se cmima}, and that {A cmima A ce B} is implied by {A ce B selcmi A}.

That's implied with either definition. I think you mean the converse: (A cmima A ce B) implies (A ce B selcmi A). In other words, "selcmi" would mean "contains" rather than "is the set of". 

In that case, {lo selcmi be lo broda} can be any set that has lo broda among its members. I am willing to add a comment on it, but I'm not sure if I should obey the definition of jbovlaste, or rather keep it as an open question.

Lujvo definitions in jbovlaste are not official, so you can feel free to enter a competing definition. (The original idea was that people would vote for the one they preferred, although that aspect of jbovlaste never really took off.)

mu'o mi'e xorxes 

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