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

Jorge Llambías, On 09/01/2011 18:52:

On Sun, Jan 9, 2011 at 3:31 PM, And Rosta<and.rosta@gmail.com>  wrote:

Jorge Llambías, On 09/01/2011 14:44:


You don't spell out the solution. Presumably it was something like:

   do djica ma poi cmima ... ce ... ce ... ce ...

But you don't really need to use sets, you could also say:

   do djica ma poi me ... .a ... .a ... .a ...


Symmetrical connectives reduce logically to quantification over sets.
"A or B (or C)" = "at least one from {A,B(,C)}"
"A and B (and C)" = "each one from {A,B(,C)}"


Yes.


"A xor B (xor C)" = "exactly one from {A,B(,C)}"


Not really. At least it's not very clear what you mean by "A xor B (xor C)"

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.




alternatival OR is:

"A alt-or B (alt-or C)" = "which one(s) from {A,B(,C)}"
and for the alternatival exclusive OR:
"A alt-xor B (alt-xor C)" = "which one from {A,B(,C)}"

So I'd argue that "do djica ma poi cmima ... ce ... ce ... ce ..." is
logically the most basic.


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, 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).

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".

--And.

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