Pat and Chris, (01)
JFS>>> A Tarski-style model is a set of entities and a set of
>>> relations among those entities. Those entities and relations are
>>> *approximate* representations of aspects of the world according to
>>> some ontology. (02)
CM>> Sure. Every model leaves out information that is found in the
>> piece of the world that the model represents. (03)
PH> Represents? Ouch. If there is a 'represents' relationship between
> models and reality, then all our axiomatic ontologies must be given
> a two-stage semantics, in which model theory describes the first
> stage of interpretation, yielding a new kind of 'representation'
> which then needs another, presumably different, semantic theory to
> relate it to actuality. (04)
Welcome to reality. As George Box said and I quoted in my previous
note, "All models are wrong, but some are useful." (05)
PH> Not only has this project never been undertaken to completion,
> I don't think its needed. (06)
That is why 20th century analytic philosophy has trivialized the
subject to the point where the total number of bookshelves devoted
to philosophy in a large Barnes & Noble store is equal to the
number devoted to Sudoku puzzles. (07)
CM> ... it might look like Pat and I disagree about this, but I
> don't think we do. I believe that all Pat is saying is that
> Tarski-style models can be constructed out of real world objects
> and (extensions of) real world relations in such a way that, as
> far as they go, they directly represent reality as it is; they
> don't just contain "formal surrogates" of real world objects or
> the like (as I recall John putting it once). (08)
I'll agree that this statement is more acceptable than Pat's way
of stating it. But it is still an apology for the status quo. (09)
CM> But, given that a Tarski-style model (in contemporary model
> theory) is *literally* an n-tuple of a certain sort, I think
> Pat would agree that they are not *literally* parts of (physical)
> reality but rather structurally very accurate representations
> of reality. (010)
I certainly won't accept the phrase 'very accurate'. Just consider
your examples of "people, tables, and cabbages". How are you going
to form n-tuples of such things when you can't even state clear
criteria for identifying individuals of those types? And those are
the simplest "real world" examples you can find. Everything else
is immensely more difficult. (011)
Whenever I raise issues like this, people try to hush me up with
complaints like "You're confusing ontology, epistemology, and logic."
But that distinction, which might be acceptable if you're writing an
academic paper, doesn't help anyone design programs that understand
language or guide robots down a highway or across a field. (012)
PH> I will just note that almost all writers on formal semantics
> (including Quine, Russell and Carnap, and indeed every written
> authority I have ever consulted on the topic) disagrees with you. (013)
If you add Frege to that list, you have a quartet of brilliant
logicians and philosophers who have helped us all hone our
logical skills. But their attitudes toward language, logic,
and their interrelationships have polished formal semantics to
an elegant system that ignores problems instead of solving them. (014)
The alternative I would suggest is what I mentioned in my
previous note to another thread (copy below). I believe that
philosophers would have made far more useful contributions to
linguistics and AI if they had given equal attention to those
other three. As it is, the failures of many formal approaches
have caused many people to reject logic itself as irrelevant. (015)
John
______________________________________________________________________ (016)
RF>> I don't think this indicates an "End of Theory" so much as
>> "the birth of the theory that there can be lots more theories
>> buried in a set of data than we've ever imagined we needed to
>> look for before." (017)
My only quarrel with that statement is over the word 'birth'.
Some logicians I admire (among them, Peirce, Whitehead, and the
later Wittgenstein) have said or implied something similar. In
fact they would agree that the number of possible theories and
even theories that are reasonably accurate for useful applications
is either infinite or far beyond our practical ability to count. (018)
At the end of this note are some of my favorite quotations from
Whitehead, Peirce, and Robert Frost. If you do a global change
of Frost's word 'poem' to 'theory', you would get a statement
that Peirce, Whitehead, and Wittgenstein would have agreed with. (019)
Actually, they would have agreed with Robert Frost's original
with the word 'poetry' in it. That attitude should be contrasted
with Rudolf Carnap, whose favorite phrase for denouncing some
idea was "That's poetry!" (020)
John
___________________________________________________________________ (021)
Alfred North Whitehead: (022)
Human knowledge is a process of approximation. In the focus of
experience, there is comparative clarity. But the discrimination
of this clarity leads into the penumbral background. There are
always questions left over. The problem is to discriminate exactly
what we know vaguely. (023)
Charles Sanders Peirce: (024)
It is easy to speak with precision upon a general theme. Only,
one must commonly surrender all ambition to be certain. It is
equally easy to be certain. One has only to be sufficiently vague.
It is not so difficult to be pretty precise and fairly certain at
once about a very narrow subject. (025)
Robert Frost: (026)
I've often said that every poem solves something for me in life.
I go so far as to say that every poem is a momentary stay against
the confusion of the world.... We rise out of disorder into order.
And the poems I make are little bits of order. (027)
Alfred North Whitehead: (028)
We must be systematic, but we should keep our systems open. (029)
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