[FOM] The Natural Language Thesis

[Joao Marcos]

In http://cs.nyu.edu/pipermail/fom/2008-January/012439.html Arnon Avron wrote:
>
> The discussions concerning the "Formalization Thesis" reveal that
> many of us still hold a sort of "natural language thesis" (NLT).
> [...]

Do you have a specific reason or example hidden up your sleeve to
doubt the translational equivalence between natural languages?  If so,
it would be nice to hear about that from you.

Of course, ancient Hebrew would have difficulties expressing many
things now easily expressed by modern dialects of Ben-Yehudah's
Hebrew, but I somehow found it disturbing the idea that some theorems
could *not* be expressed, maybe awkwardly, using ancient Hebrew
"augmented with a number of expressions accepted by Modern Hebrew".

To be sure, I find it appealing to subscribe to your thesis about both
formal languages and natural languages being both used to express
mathematical facts and model valid reasoning (to put it in a slogan,
"all reasonable languages are intended to model reasoning"), and I do
concede that formal languages fare much better in that respect.
NEVERTHELESS, the comparison you suggested involving ancient and
modern Hebrew made me suspicious that maybe you would admit that there
are many theorems yet-to-be-proven that cannot be formulated in ANY of
the presently known natural languages, or maybe even by ANY of the
presently studied formal languages of logic and mathematics...  Do you
believe that to be the case?  Do you think that to be the case perhaps
on what concerns "geometrical reasoning"?

The "Natural Language Thesis", as you put it, following Shapiro and
much of the philosophically inspired Anglo-Saxon approaches to logic,
seems similar to the thesis that mathematics is aimed primarily at
modeling facts from physics, that mathematics is made to fit physics,
and that mathematics should necessarily be seen as a counterpart of
physics.  That might have made sense to a lot of French mathematicians
in the XIX Century, but it might strike many practicing mathematicians
nowadays like an impoverished reductionist viewpoint...  Or does it?

If one checks the literature on "formalizations of natural language",
some (mostly exclusively-English-speaking?) authors surely seem to
think that some natural languages are "more natural" than others.
Some people seem to think the same about formal languages, whatever
that might mean.  Maybe someone should promote a congress on the
"unusual effectiveness of logic in linguistics and communication"...

JM

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