Re: [lojban] Attempting to bring the ro debate to a resolution

[John Cowan <jcowan@reutershealth.com>]

And Rosta scripsit:

> The position supported by everybody except pc (= me, xorxes, Jordan,
> Adam, Nick + probably xod & Robin -- everybody who's participated,
> & probably the remainder of Lojbanists too) is this:
> 
> A. ro broda cu brode = ro da poi broda cu brode
> B. ro da poi broda cu broda = ro da ga na broda gi brode
> C. ro broda cu brode = ro da ga na broda gi brode
> 
> The position supported by pc is that C is definitely invalid, while
> either one of A and B may be declared valid, with the other one
> declared invalid (though his preference is for A to be valid and
> B to be invalid).

Well, I must break consensus on this.  The position here labeled pc's is
definitely mine as well.  (I take it, however, that all of ABC are true
if there are a non-zero number of brodas.)  In fact, I will strengthen
it by saying that A is true by definition, and B and C are false.

To me, (1) the unconditional form "Each globnik is spatulous" (ro
[da poi] broda cu brode) entails that there are globniks, whereas
(2) the conditional form "For each thing, if it is a globnik, then it
is spatulous" (ro da ganai broda gi brode) does not.  Consequently,
since there are no globniks, "Each globnik is spatulous" is trivially
false, whereas "For each thing, if it is a globnik, it is spatulous"
is vacuously true.

Is there a (pc-less, John-less) consensus about the truth values of (1)
and (2)?  It would seem to be consistent with the consensus to reject
either of them.

> Each position is partially but not fully consistent with CLL (which 
> itself is not internally consistent).

I still don't understand where the inconsistency is.

> The debate about whether the universal quantifier and/or ro is 
> importing is pretty much a red-herring, because it boils down to
> a question of the effect of an empty universe on truth values.

I agree.

-- 
One art / There is                      John Cowan <jcowan@reutershealth.com>
No less / No more                       http://www.reutershealth.com
All things / To do                      http://www.ccil.org/~cowan
With sparks / Galore                     -- Douglas Hofstadter