Chris, (01)
Right. If you are able to find a model, the most
you have demonstrated is consistency. (02)
I like this logic stuff, and I think it's valuable.
But I really can't blame people who say that model
theory is rather pathetic as a meaningful theory
of meaning. (03)
As an example, consider Hao Wang -- former student
of Quine's, former assistant to Kurt Goedel, and
the designer of the first truly efficient theorem
prover in 1959. (It proved the first 378 theorems
of the _Principia Mathematica_ in 7 minutes on an
IBM 704, a machine that was about one-fifth the
speed of the original IBM PC.) But in his book,
_Beyond Analytic Philosophy_, he made some rather
harsh criticisms of his former thesis adviser
and other notables. (Excerpts below.) (04)
Even Wang's old program is beyond the capacity
of most humans to do formal deduction, and if
that were all that was necessary for intelligence,
we'd all be talking to HAL 9000's five years ago.
But we aren't. (05)
John
__________________________________________________ (06)
Wang's original paper about his theorem prover: (07)
http://www.research.ibm.com/journal/rd/041/ibmrd0401B.pdf (08)
Two quotations from the book _Beyond Analytic Philosophy:
Doing Justice to What We Know_, by Hao Wang, MIT Press. (09)
Wang commenting on Quine: (010)
Quine merrily reduces mind to body, physical objects to
(some of) the place-times, place-times to sets of sets
of numbers, and numbers to sets. Hence, we arrive at
a purified ontology which consists of sets only....
I believe I am not alone in feeling uncomfortable about
these reductions. What common and garden consequences
can we draw from such grand reductions? What hitherto
concealed information do we get from them? Rather than
being overwhelmed by the result, one is inclined to
question the significance of the enterprise itself.
(p. 146) (011)
Wang quoted a personal letter from Clarence Irving Lewis, the
founder of the modern systems of modal logic, about the state
of philosophy in 1960: (012)
It is so easy... to get impressive 'results' by replacing
the vaguer concepts which convey real meaning by virtue
of common usage by pseudo precise concepts which are
manipulable by 'exact' methods — the trouble being that
nobody any longer knows whether anything actual or of
practical import is being discussed. (p. 116) (013)
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