Mark,
I've been a long-term "math-head", but I sympathize
with your point to a considerable extent:
MPL> As a matter of personal preference, I could do
> with fewer math-heads in linguistics.
There are quite a few people with both linguistics
degrees and other kinds of degrees who try to pursue
elegant formalisms at the expense of preserving the
phenomena.
In fact, some of the worst offenders are those who do
*not* have math or comp. sci. degrees. They suffer
from a certain degree of math envy and overcompensate
by becoming "more formal than thou". One could accuse
Chomsky of that fault, but there are many, many others.
There are also people with a solid background in logic,
such as Montague, who have tried to force their view
of logic onto language. Although I believe the formal
semanticists have made some interesting contributions,
I also believe that lexical semantics has made far more
useful contributions to NLP as well as theoretical
linguistics. Barbara P. has also been softening her
views on that issue. (See the quotation below.)
And I would add one further advantage of having a good
background in math: self defense. It gives you enough
self confidence to see through the some of the empty
formalism. (See the poem by Henry Kautz below.)
John Sowa
____________________________________________________________
Source: http://people.umass.edu/partee/RGGU_2005/RGGU054.pdf
In Montague’s formal semantics the simple predicates of the
language of intensional logic (IL), like love, like, kiss,
see, etc., are regarded as symbols (similar to the “labels”
of [predicate calculus]) which could have many possible
interpretations in many different models, their “real meanings”
being regarded as their interpretations in the “intended model”.
Formal semantics does not pretend to give a complete characterization
of this “intended model”, neither in terms of the model structure
representing the “worlds” nor in terms of the assignments of
interpretations to the lexical constants. The present formalizations
of model-theoretic semantics are undoubtedly still rather primitive
compared to what is needed to capture many important semantic
properties of natural languages, including for example spatial
and other perceptual representations which play an important role
in many aspects of linguistic structure. The logical structure
of language is a real and important part of natural language
and we have fairly well-developed tools for describing it. There
are other approaches to semantics that are concerned with other
aspects of natural language, perhaps even cognitively “deeper”
in some sense, but which we presently lack the tools to adequately
formalize. It is to be hoped that these different approaches can
be seen as complementary and not necessarily antagonistic.
____________________________________________________________
If your thesis is utterly vacuous,
Use first-order predicate calculus.
With sufficient formality,
The sheerest banality
Will be hailed by all as miraculous.
If your thesis is quite indefensible,
Reach for semantics intensional.
Over Montague grammar,
Your committee will stammer,
Not admitting it's incomprehensible!
by Henry Kautz
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