Re: [WikiDiscuss] Re: BPFK gismu Section: Parenthetical Remarks in Brivla Definition

On 9/23/06, John E. Clifford <[email protected]> wrote:
>
> Let's see. {lo pavyseljirna} is a simple referring term -- it gets its
> meaning directly from the interpretation in the model.

Yes. For definiteness, let's consider a simple model:

The universe of discourse is a set with three elements:
U={John, unicorns, elephants}.

The theory of the model is the following set of four sentences:
T={"la djan djica lo pavyseljirna", "la djan na djica lo xanto",
"lo pavyseljirna na zasti", "lo xanto cu zasti"}.

> There are two different kinds of interpretations, one that makes
> {lo pavyseljirna} act like a broad scope case and onwe that makes
> it act like a narrow scope case.

An interpretation will assign unicorns as the referent of {lo pavyseljirna},
elephants as the referent of {lo xanto}, and John as the referent of
{la djan}. In this simple model, we don't run into any scope issues.
Each referring term has a single referent in the domain of discourse,
and we have not used quantifiers in the sentences of the theory.

> Which of these are you intending for your model? Or is
> there a third type not yet mentioned? You claim that on your model
> the argument is valid, so it cannot be the model where {lo
> pavyseljirna} acts like a narrow scope, since the argument is invalid
> on that.

Narrow scope of what with respect to what? There are no quantifiers in
the simple sentence {la djan cu djica lo pavyseljirna}.

We can now introduce quantifiers, and an inference rule of Logic tells us
that from {la djan cu djica lo pavyseljirna} it follows that {su'o da zo'u
la djan djica da}. Therefore this is a true sentence of the theory too,
because any sentence that follows logically from true sentences of the
theory will also be a true sentence of the theory.

> So, it must be the other one, broad scope. But, since we
> know that there are models in which the argument is not vlaid, the
> argument is not valid simpliciter. It is, however, valid on ,odels
> that emulate the broad scope quantifier. So you are claiming that,
> contrary to the empirical evidence, the meaning of {mi djica lo
> pavyseljirna} is always the broad scope reading. So, how do we do the
> narrow scope one, which surely turns up from time to time?

In order to distinguish two scope readings we need a model whose theory
contains a sentence with at least two (non-commutative) operators. For
example, we could have a new model with many unicorns as members
of the domain of discourse, instead of the simple model above where
unicorns were a single member of the domain. Then we could distinguish:

    su'o da poi pavyseljirna zo'u mi djica lo du'u mi ponse da

from:

    mi djica lo du'u su'o da poi pavyseljirna zo'u mi ponse da

In a given theory, one of these sentences might be true and the other
might be false.

Any discourse can be seen as a process of model building. Through
their use of language the participants negotiate what things are in the
domain of discourse of the model and what sentences are the true
sentences that conform the theory of the model. In some context, a
simple model where unicorns are a single element of the domain of
discourse might suffice to communicate whatever the participants in
the discourse wish to communicate. In another context, the participants
might wish to build a more detailed model where many unicorns are
each a separate member of the domain of discourse. In this new context,
more complex sentences will be needed to deal with the different scoping
issues that now arise.

mu'o mi'e xorxes


 
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