Re: Set Theory Woes

[Logical Language Group <lojbab@ACCESS.DIGEX.NET>]

>>I would not think that left grouping constitutes bounding of the set.
>
>It's not left-grouping alone that bounds the set: it's the binary nature
>of "ce" (as defined on p354) together with left-grouping that bounds the
>set.

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, and
they are not.    The one-liner is a definition, and not a trnaslation,
and you cannot apply it by simple substitution recursively to a text.
The words "the set with" do not recurse.

>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.  Grammatical
constructs in Lojban can go on indefinitely if based on recursive grammatical
constructs.  It is the nature of such recursive rules in the grammar that they
are "the same as" theirnon-recursive form.

But "A" does not have a "ce" in it by itself, so one can make no inferences
about it being a set or not.

In any event, the table definitions ARE brief and more mnemonic than
explanatory.  The examples following that definition include a 3 element
ce-based set, thus clarifying the wording.

>>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.

I can try to make this more clear in the cmavo list definition (which does not
have quite so limited a character length as the one-line-defintiions in the
book).

lojbab
----
lojbab                                                lojbab@access.digex.net
Bob LeChevalier, President, The Logical Language Group, Inc.
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