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On 9/27/06, John E. Clifford <clifford-j@hidden.email> wrote:
And "Theory" is just the sentences held to be true? This is, of course, a different sense of theory from the usual one, so part of our problem may be merely teminological.
"The term 'theory' also has a precise technical usage in mathematics, particularly in mathematical logic and model theory. A theory in this sense is a set of statements in a formal language, which is closed upon application of certain procedures called rules of inference." That's basically the sense I was using. Did you have some other sense of "model" in mind than the one used in model theory?
But I suspect there is more to it than that. You really do hold that any referring expression (in a fairly narrow sense apparently -- in Lojban, descriptions and what are tied to them somehow by identification) whereever it appears in a sentence has to have a referent, even if the purport of the whole sentence is that it has no referent.
I take (practically) any Lojban sumti without outer quantifiers to be a
referring expression, yes. Examples: {la djan}, {le mlatu}, {lo gerku},
{lo nu mi klama}, {lo ka ce'u bajra}, {li pa}, {di'u}, {la'e di'u}, {zo valsi},
{lu mi klama le zarci li'u}, {do}, {ti}, {ko'a}, etc.
The very few exceptions would be {ce'u}, {ke'a}, {zi'o} and perhaps one or
two others I'm forgetting, but no more than that. The bound variables {da},
{de}, {di} are also not referring terms, although I'm sometimes tempted
to include them as well with the referring terms when not bound
*explicitly* by a quantifier.
I'm not sure how the purport of a sentence could be that one of the
referring expressions used (as opposed to mentioned) in the sentence
have no referent.
> Model_0: Does not contain p in its theory. > Model_1: Includes p and turns out to be inconsistent, so the model is ditched. > Model_2: Includes the theory of Model_0 plus ~p. The examination of Model_1 > was helpful to determine that Model_0 could be expanded to Model_2. "Had to be expanded" is perhaps more to the point. A situation ultimately must contain all the logically entailled + claims. But that is not entirely relevant here.
p could be a new proposed axiom rather than just a theorem of the theory. If it was logically entailed by the truths of Model_0, it was as you say, already in Model_0. When it comes to ordinary discourse, seen as a process of model building, most new sentences will be incorporated as new axioms since what already follows from already extant axioms are usually trivialities that noone would bother uttering.
The question is ow how to get the other reading. but your present positions seems to be that there is no orther reading, which flies in the face of everyboy's linguistic experience.
My position is that for a given model, there is only one reading for the
sentence, and furthermore that it is not always necessary to build a
model where the distinction is of interest. I of course do not argue that
it is never necessary to build a model where the two readings have to
be distinct. Clearly {su'o da poi pavyseljirna zo'u mi djica lo du'u mi
ponse da} and {mi djica lo du'u su'o da poi pavyseljirna zo'u mi ponse
da} are not interchangeable in a model where {su'o re da pavyseljirna}
is true.
> None of the relevant articles in the Stanford Encyclopedia site seem to > be aware of there being such a consensus. Do any othem talk about this approach or offer alternatives. I would be especially interested in the latter, since I have not come across any such theories.
This is from the "nonexisting objects" article: << Meinong was concerned about the problem of intentional states which are not directed at anything existent. The starting point of this problem is the so-called "principle of intentionality", which says that mental phenomena are characterized by an "intentional directedness" towards an object. For instance, to love is always to love something, to imagine is always to imagine something, and so forth. In other words, every intentional act is "about" something. The problem is that sometimes people imagine, desire or fear something that does not exist. Some people fear the devil, although the devil doesn't exist. Many people hope for peace in the Middle East. But there is no peace in the Middle East. Ponce the Leon searched for the fountain of youth, even though it doesn't exist. It is easy to imagine a golden mountain, even if no such thing exists. Cases like these seem to be clear counterexamples to the principle of intentionality. However, many philosophers found this principle too appealing to be given up completely. While some came to the conclusion that intentionality is not a real relation and therefore does not require the existence of an object (see, for instance, Brentano 1874, Searle 1983), Meinong offered another solution: there is indeed an object for every mental state whatsoever —if not an existent then at least a nonexistent one.[3] The problem of intentionality may still count as one of the most important motivations for thinking there are nonexistent objects. But there are other motivations as well.
> <http://plato.stanford.edu/entries/nonexistent-objects/> I don't think this is an ontological issue. We are not in any case (except a strict real world model) concerned with what exists, only with what the variables range over, what is.
If the fact that unicorns are nonexistent is not problematic, why do you have such a hard time admitting them into the domain of discourse?
And even that is not
about reality in any sense but merely about how a particular theory
fits together to produce certain results. It turns out that, to get a
sentence like {mi djica lo pavyseljirna} (narrow reading), we don't
need to have unicorns in our domain. Indeed, having them there
complicates matters slightly. So, what is the best derivation of the
narrow scope want for Lojban and how might we best indicate that,
differentiating it from the broad scope case?
When there is a single thing in the model that is the referent of
{lo pavyseljirna}, there is no distinction between narrow and wide
scope. One can claim that someone wants it or that someone doesn't
want it, but it makes no sense to distinguish "a particular one of them
is such that the person wants it" from "the person wants just any one
of them".
When more than one thing of a kind is at stake, the distinction is
certainly there, and I of course agree with you that the way to make
it is to put the {su'o} quantifier either inside or outside the scope of
some other operator. Our disagreement is not about that. Our
disagreement is about whether or not we can have a model where
a single thing is the referent of an expression with that single thing
having a generic or type interpretation.
mu'o mi'e xorxes