Re: [lojban] Re: Cake, Pie or Ice Cream?

[Jorge Llambías <jjllambias@gmail.com>]

On Sun, Jan 9, 2011 at 4:08 PM, And Rosta <and.rosta@gmail.com> wrote:
> Jorge Llambías, On 09/01/2011 18:52:
>>
>> If A, B and C are propositions, and "xor" is the usual binary
>> connective, then "A xor B xor C", with either left or right grouping,
>> means "either exactly one or all three of A, B, C". (More generally,
>> adding more "xor"s, any odd number of the propositions.) But probably
>> "... xor ... xor ..." is not meant to be the composition of two binary
>> connectives.
>
> Yes, I know, but hadn't wanted to distract from my main point, which is that
> "xor" is an elaboration of "exactly one from", albeit an elaboration that
> works only for sets with certain cardinalities.

Only for one cardinality: 2.

>> I'm not sure I understand the argument. "ma poi cmima X" and "ma poi
>> me Y", where X is the set of referents of Y, are exactly equivalent.
>> Why is one more basic than the other?
>
> I mean that because logical connectives reduce to quantifiers,

Alternatively: quantifiers reduce to logical connectives.

> the logically
> most basic Lojban form (out of the one with "ce" and the one with "a")
> doesn't use 'logical connectives' but rather uses quantifiers and, where
> necessary, extensionally defined sets (i.e. sets defined by a list of their
> members).

I see what you mean. Maybe I shouldn't have used connectives at all:

  do djica ma poi me ko'a jo'u ko'e jo'u ko'i ...

That doesn't introduce any sets, but it is still an extensional list
with the options.

> My general line of thinking is that when faced with the question "How do you
> say X in Lojban", you should first of all establish the answer to "How do
> you say X in predicate logic".

Yes, predicate logic with plural reference.

(There is a lingering problem with the "ce" version, since as far as I
know it was never established whether "ko'a ce ko'e ce ko'i" is a set
with three members, or one with two members, namely ko'i and the set
{ko'a, ko'e}.)

mu'o mi'e xorxes

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