Re: [HM] Landau's Grundlagen and consistency

Martin Davis (martind@cs.berkeley.edu)
Wed, 30 Dec 1998 16:41:41 -0800

At 12:23 PM 12/30/98 -0600, William Tait wrote:

> Stacy Langton writes
>
>> In the "Preface for the Teacher", Landau remarks (p. 9): "I do
>> not, to be sure, prove the consistency of the five Peano axioms
>> (because that can not be done), ...."
>
> and then goes on to give the German:
>>
>> On the other hand, Landau's words "weil man es n"mlich nicht
>> kann" might just mean, "because I don't know how".
>
> and ask
>> So I wonder what Landau had in mind.
>
> I would think that the translation by Steinhardt is simply wrong or
> misleading, and Landau simply meant that one was not able to prove it
> (meaning at that time). Can someone with a better ear for German comment?
>
> Landau's Grundlagen der Analysis was, in my day in graduate school, the
> first introduction into German for those who knew none and had to satisfy
> a requirement in mathematical German. A four page glossary sufficed to
> cruise through it.

There were at least two (German) editions. In the first, Landau gave an
incorrect proof of the existence of functions satisfying the recursion
equations for + and *, and gave quite a mea culpe in the preface to the
second. Any chance this has something to do with the matter?

Martin