[FOM] The Natural Language Thesis and Formalization

[andre rodin]

Joao Marcos asked Arnon Avron:

> 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.
 
It seems that Joao Markos as well as many other participants of this
discussion (including the Formalisation thread) equate translational
*equivalence* with the translatability as such. But this is obviously wrong
- as far as the term *equivalence* is taken in anything like its usual
sense. To get equivalence classes of linguistic expressions belonging to
different languages A,B through translations between A,B one has to assume
that these translations are *reversible*, i.e. are isomorphisms.
Translations between natural languages are usually *not* reversible as an
experiment involving backward translation of a sufficiently long phrase may
easily demonstrate. To check this translate this message into any other
language you know and then ask someone else who writes in the two languages
to translate your translation back into English.

(One may try to save the idea that translations provide equivalences arguing
that the original expression and its backward translation from some other
language are still equivalent up to certain paraphrase. But then once again
one needs to justify the claim that paraphrases are generally reversible and
hence determine the desired equivalence relation. I think that they are
generally not. The existence of reversible paraphrase is a far stronger
requirement than the existence of *some* paraphrase.)


Thus the possibility of translation between languages doesn't, generally,
imply their translational equivalence. Conversely, the lack of translational
equivalence doesn't mean that there is something (some meaning) that can be
expressed in one language but not in another one.

This has a bearing on the issue of formalisation. Formalisation viewed as a
translation of mathematical reasonings into a fixed formal language is
non-reversible because a given formal theory may have multiple
interpretations. The claim that all these interpretations are nevertheless
"essentially equivalent" is a strong epistemic claim which doesn't follow
from (and in my own view is not supported by) Formalisation Thesis. The
problem about the Thesis itself is that it leaves completely unclear what
counts as a faithful translation. Nevertheless, I think that the Thesis can
be reasonably "made true". What about its possible bearing on FOM? Rather
surprisingly this latter issue has been so far only very little discussed.

Andrei