Subject: Re: [lojban] RECORD:Quantifiers

From: [email-masked]
Date: Fri, 15 Mar 2002 16:49:41 EST

In a message dated 3/15/2002 2:54:32 PM Central Standard Time, 
[email-masked] writes:

> I basically agree, but one could add a fifth form,
> {Q da poi broda zo'u da broda}. You probably include it
> in the second form. Also, taking the third as basic is
> somewhat arbitrary. It is also possible to start from the
> {poi}-form and define {ro da} as {ro da poi ke'a du ke'a}.
> (This is basically what the reference I quoted last time
> does.) But this is just an additional comment, no real
> disagreement here.
> 

The third is just that of standard logic, as used even in the book you cited, 
so not exactly arbitrary. I would, in fact, take {Q da poi broda zo'u} as a 
case of {Q da poi broda}. You could go the other way, but it makes thes 
entences a lot longer (and whether self-identity is enough for logical 
existence is problematic -- see Quine and various responses)

<My system simply does not have this presupposition. In many cases
the set of broda has to be non-empty by conversational implicature,
but that's all. The reason for this is that it simplifies things
enormously, and nothing is lost as far as I can tell.>

You mean A-E-I+ O+? For {lo broda}, we don't in fact have a presupposition, 
since none emptiness is part of the structure. This transfers to {da poi} by 
identities. 
As the present system stands, except for one extra step in translation into 
ultimate forms, the moves are a simple as can be. But the outward effect (if 
you leave the {ni'u} off) is the same.

<I suspect these rules work for Q=ro and Q=su'o, but not for
Q=no and Q=me'iro. Example:

no da poi broda cu brode
-> no da zo'u ge broda gi brode

And that would be it according to the rules. But you would
need to prefix {ge da broda gi} to give it existential import.
Maybe by "ultimate form" you mean ro/su'o forms, right?
In that case, you would go to:

-> ro da zo'u ganai da broda ginai da brode

and then yes, the rules tell you to add {ganai da broda gi}.
So perhaps it should be made explicit that "ultimate forms"
must be in terms of the positive quantifiers.>

Thank you, I missed that point. Yes, standard logic has only positive 
quantifiers, so it is assumed that all negations have been moved to smallest 
scope.

<. For unmarked Qs in the {Q (da poi) broda} format, all of the usual
>negation moves hold: ro = no... naku = naku mei'ro = naku su'o ... su'o 
>and
>so on for all the regular quantifiers of the Aristotelian set (A = ro, E =
>no, I = su'o, O = me'iro). With negative quantifiers {Q ni'u} the 
>quantifier
>inside a negation will be non-negative and, conversely an unmarked 
>quantifier
>in side a negation will result in a negative quantifer. These latter 
>factors
>are only relevant when and where negative quantifirs are used.

This is true in my system as well.

In my system, the complicated rules can be recovered by
marking the universals as {roma'u} and {noma'u}.>

I don't see how making quantifiers longer helps any here, though the 
statement of the rules could be simplified a bit. The "moving a negation 
across changes quantity, quality and import" seems too short, however.