Re: Set Theory Woes

[Ashley Yakeley <AshleyB@HALCYON.COM>]

At 1997-12-26 04:09, Logical Language Group wrote:

>If you are referring to the one line definition in the table, then you are
>reading mathematical precision into English ambiguity. The one line
>definitions do NOT say that they are exclusively binary operators,

Yes it does: it says all cmavo in selma'o JOI have clear defintions as
sumti connectives; and it then gives those definitions as unambigously
binary.

In particular, the _Complete Lojban Language_ says "A ce B" is the set
with elements A and B, but fails to mention what is allowable A and B. It
doesn't work for e.g. either A or B is "C ce D".

> and they are not.

I agree, but the CLL should really say it explicitly.

>>The only solution is to define "A ce B ce C ce D..." as a special form
>>where the "ce"s cannot be considered separately.
>
>Nothing ever says that they are considered separately.

The CLL gives only a binary definition.

>In any event, the table definitions ARE brief and more mnemonic than
>explanatory.

True in fact, but the CLL claims they are 'clear definitions as sumti
connectives'.

>The examples following that definition include a 3 element
>ce-based set, thus clarifying the wording.

This needs to be put in the definition.

>>>If you want to formally get into mathematical set spectification, then you
>>>need to goi fully into Mex, where you have parenthesis to set bounds on the
>>>set definition.
>>
>>Fine, but this kind of mathematical set specification may turn up in
>>ordinary Lojban utterances.
>
>True, but it still needs to be used with the grammar of Mex to acieve
>mathematical constructs in the regular grammar.  "ce" operating outside of
>the MEX section of the grammar does not form a mathematical object, but a
>linguistic one.

A set is a set, just as the number three is the number three. The same
mathematical rules apply no matter what context they're in.

For instance, "lu'i ti joi ta" is the set {this, that} (two things the
speaker is pointing at). It's just as much a "mathematical" set as a
"linguistic" one. The "mathematical" operations 'number of members',
'union', 'intersection' etc. all apply the same way.


--
Ashley Yakeley, Seattle WA
http://www.halcyon.com/ashleyb/