Subject: [lojban] standard logic

From: Adam Raizen <[email-masked]>
Date: Fri, 08 Nov 2002 13:15:58 +0200

la pycyn cusku di'e

>Strictly spaking, of course, what pc favors is taking {ro broda cu brode} , 
>with standard Lojban importing {ro} as basic and introducing the 
>non-importing form as
>{ro da zo'u ganai da broda gi da brode}, as it normally is in Logic.

and

>The fact that your {ro} gives truth in the empty universe shows that it is 
>not the universal quantifier of standard logic, all of whose quantified 
>sentences are false in the empty universe.

I think you need to distinguish between logic and Logic. Lojban is
first and foremost the language of Logic, which is the theoretical
framework which logicians use to develop logic, which is how logicians
actually implement Logic. As has been noted, there are many different
ways to choose your quantifiers, and many of them allow all the
possibilities in one way or another. Lojban can potentially choose any
of them, as long as what it chooses is self-consistent, and still be
the language of Logic.

Anyway, as I have already noted, it is possible in standard logic to
have universal quantification give truth in the empty universe. Also,
in modern standard logic, statements of the form "All P are S" are
almost always automatically rewritten to the form "Ax(Px->Sx)", and
very little is done with restricted quantification (and thus Lojban can
certainly do the same). Plus, as you surely know, there are many, many
logicians, and they are not inclined to agree on everything, so I think
that it is highly disingenuous of you to claim that logic does it only
one way, and all other ways are incompatible with Lojban calling itself
[Ll]ogical.

mu'o mi'e .adam.