[FOM] The Hebrew-English Thesis

[catarina dutilh]

Dear Arnon,
 
Well, I'm happy that I could be of service by calling your attention to something that is considered a very important issue in the philosophy of language, which is known as the problem of indeterminancy of translation (it applies to Hebrew-English or any other pair of languages). Quine, whose logical skills are, I believe, beyond any doubt, is usually thought to have been the one who started the whole discussion. If you want to read more about it and enlighten yourself a little further, you can start with
 
http://en.wikipedia.org/wiki/Indeterminacy_of_translation
 
But, as I believe this is a topic out of the scope of FOM, if you want to discuss this topic any further, I suggest that this be done off-list.
 
Regards,
 
Catarina

----- Original Message ----
From: Arnon Avron <aa at tau.ac.il>
To: Foundations of Mathematics <fom at cs.nyu.edu>
Cc: Arnon Avron <aa at tau.ac.il>
Sent: Thursday, January 3, 2008 6:48:58 PM
Subject: [FOM] The Hebrew-English Thesis

The discussions concerning the "formalization thesis" 
have a lot of aspects. At this posting  I want to comment 
just about one of them: the "faithfulness" issue.

Well, as you all know the world was created using Hebrew
(if you do not believe, read again the first chapter of the 
bible, and recall that what most of you read is an attempt
for a faithful translation from the original text in Hebrew
into your favourite language).  Therefore there is no question 
that the language of mathematics (=the language of nature) is Hebrew. 
Fortunately for me, this was the language in which I did mathematics 
when I was younger. Unfortunately for me, in recent years I 
publish most of my mathematical work in English. This did not worry 
me at all until this week, because I was certain about
the validity of the following Hebrew-English (HE) thesis:

Every peace of ordinary mathematics written in Hebrew can be
faithfully translated into English.

However, after what I read this week I realized that I was
wrong. Take for example what catarina dutilh wrote
on Mon, Dec 31, 2007: 

"As to whether FT does or does not hold, this is basically an
*empirical* question, a matter of rolling up sleeves and moving 
on to formalizing theorems of mathematics (which is, of course, 
something that is already happening). But again, the hardest part 
seems to me to be the precise account of the relation of 
'faithful expression' between a theorem of ordinary mathematics 
and a statement in some formal language. 
>From all the discussions on this so far, I gather that it is
sufficiently clear to everyone that there is no formal method to 
perform such a translation, that it is essentially a conceptual matter."

This argument shows me that the HE thesis might be wrong.
In fact:
  As to whether HE does or does not hold, this is basically an
*empirical* question, a matter of rolling up sleeves and moving
on to translate theorems written in mathematics (i.e. Hebrew)
into Englishg (which is, of course, something that is already 
happening). But again, the hardest part
seems to me to be the precise account of the relation of
'faithful expression' between a theorem of ordinary mathematics
written in Hebrew and a statement in English.
>From all the discussions on this so far, I gather that it is
sufficiently clear to everyone that there is no formal method to
perform such a translation, that it is essentially a conceptual matter.

Arnon Avron



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