[FOM] The Hebrew-English Thesis

[jaN.]

it's an interesting question whether the 'faithful expression' of a piece of
ordinary mathematics into some formal language can be considered as a
translation. if one asks the philosophy of language for advice, the answer
depends on whom do you ask. roughly speaking, the so-called analytic
philosophy tends to conceptualize translation as translation between
artificial languages and concludes (with w. v. o. quine) that translation is
impossible due to the 'indeterminacy of translation'-principle (provided the
artificial languages refer to the 'real' world). in this view there can be
no certitude about the correctness of a translation from ordinary
mathematics to a formal language. on the other hand the so-called
continental philosophy looks at translation as transfer between natural
languages. in this case there is a long tradition of successful translations
based on the familiarity of the according underlying life-forms ( e.g. in
the works of wittgenstein and benjamin).
it obviously plays a crucial role which concept of language one relys to
when it comes to reasoning about the possibility of translating ordinary
mathematics into a formal language (or hebrew into english).
an important argument here is, that one is not entirely free to choose
whatever concept of language one just likes the most. the reason is quit
simple: all artificial languages are based on natural languages in the sense
that whenever one employs the idea of an artificial language one has to
negotiate about it in some natural language. maybe nowadays it is possible
to define one artificial language in another one, but historically natural
languages were the first on the scene.
here is not the place to examine this in detail. i just want to point out
that if one conceptualizes mathematics as a kind of language and plays with
the question whether a certain piece of mathematics is translatable, one
also buys the whole package that belongs to the field of translational
studies.
translation is not formalizable, but never the less there are successful
translations. what makes us able to translate, if we can not explicitly
write down the rules by which we tell whether a translation is successful or
not? in the translational studies this question points in the direction of
anthropology, sociology and history. in which direction does it point in
mathematics?

best regards
jan


concerning mathematics the question could be posed as follows:


2008/1/3, Arnon Avron < aa at tau.ac.il>:
>
> 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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