Pat, (01)
>...The Tarskian model-theory view of
>the 'universe of discourse' D as being a set,
>does not imply that the things in that set have
>to be... real... Real,
>unreal, imaginary, Platonic, abstract or physical
>things can all be things in sets. (02)
Absolutely. (03)
But this thread started when I said some people object to model
theory as being too abstract, and you said nothing prevents the
things in D from being actual real things such as people or horses. (04)
I agree with you fully on that. (05)
But my purpose was to note explicitly that a logical theory can be
about BOTH the real world and a Tarski model, without requiring one
to believe that the "things" in the Tarski model correspond directly
to anything real. (06)
In my attitude example, I can regard the sentence, "Aunt Jane has a
positive attitude" to be about the real world without accepting the
claim that there are actual physical or mental "things" that
correspond in any direct way to attitudes. I use the shorthand
"positive attitude" because it conveys to the listener a
good-enough-for-purpose approximation of what I mean. But I don't
really believe Aunt Jane "has" some sort of "attitude-thing." (07)
There is, however, an "attitude-thing" in the Tarski model, and it is
associated with an "Aunt-Jane-thing" in the Tarski model. Pat
pointed out that there is nothing stopping the "Aunt-Jane-thing" in
the Tarski model from being my actual in-the-flesh aunt. However, if
I don't believe there really are attitudes, then the "attitude-thing"
in the Tarski model is not a real thing in the world. (08)
Now let's go back to the question of what my sentence is really about. (09)
The sentence is about a Tarski model that has an "Aunt-Jane-thing" in
it (perhaps my actual Aunt Jane), and the "Aunt-Jane-thing" has an
associated "attitude-thing," and the "attitude-thing" has the
property of being positive. Because the sentence is about this Tarski
model, I can apply reasoning engines to it, and derive conclusions
about the life expectancy of the "Aunt-Jane-thing" in the Tarski
model. (010)
The sentence is ALSO about how a very real person -- my mother's
sister -- thinks, feels, and acts in relation to the world around
her and the events that occur in her life. The sentence can be about
Aunt Jane and her mode of being without requiring me to believe the
world contains anything that corresponds in any direct way to those
pesky "attitude-things" in my Tarski model. (011)
Although I don't buy the assertion that there is a real "attitude"
that is "possessed" by my Aunt Jane, I do believe that the modeling
fiction of pretending she "has" an "attitude" corresponds in a rough
sort of way to reality, in the sense that pretending it is true and
applying my reasoning engine to the logical theory gives pretty
accurate predictions about Aunt Jane's life expectancy. (012)
That's why mathematics works. It is why most of the time (although
not yesterday in Minnesota, unfortunately) we can expect the bridges
not to collapse. (013)
>So the
>distinction you are drawing here between a set of
>attitudes and a set of real physical things,
>while no doubt important for judging the utility
>or accuracy of an ontology, has nothing at all to
>do with model-theoretic semantics, which applies
>to both of these cases in exactly the same way. (014)
I wasn't making a point about model-theoretic semantics per se. I
was amplifying of my previous point that a sentence can be about
both a Tarski model and the real world. I simply wanted to note that
a sentence can be (usefully!!) about the real world without requiring
one to believe that the set theoretic machinery of Tarski
interpretations is an accurate reflection of how the world actually
is. (015)
>...The 'universe of discourse' D... is something like
>the universe that one would have to accept as
>real if one were to take the assertions made in
>the language at face value, as themselves
>veridical. (016)
Right. (017)
One can construct theories about D and make effective use of them to
do things like saving the lives of cancer patients, while also
regarding them as modeling fictions that are not veridical images of
the actual world. (018)
>If my language talks of attitudes,
>then taken at face value it does indeed require
>that the world it describes contains things
>called 'attitudes'. If the real world cannot
>contain such things, then my language is false of
>it; but it might be true of some possible but
>non-actual world. (019)
If it's a consistent sentence in a logical theory, then it IS true of
some possible world. The possible worlds of which it is true need not
be veridical reflections of the real in order for the theory to be
useful. (020)
Kathy (021)
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