completeness of arithmetic??
Jul. 15th, 2006 09:01 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
anhinga_anhingaRecently Esenin-Volpin wrote a paper The Completeness of Classical Arithmetic.
The chances that this is correct are not very high, obviously. The discussion of Goedel incompleteness results is on page 43 (Volpin thinks something is wrong with them, and not with his proof). The core of the Volpin's proof is on pages 39-43, if anyone who likes syntactic logical manipulations wants to look at it.
The chances that this is correct are not very high, obviously. The discussion of Goedel incompleteness results is on page 43 (Volpin thinks something is wrong with them, and not with his proof). The core of the Volpin's proof is on pages 39-43, if anyone who likes syntactic logical manipulations wants to look at it.
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Date: 2006-07-16 06:38 am (UTC)no subject
Date: 2006-07-16 03:10 pm (UTC)To explain why they are wrong, or to explain why his result is correct?
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Date: 2006-07-16 05:15 pm (UTC)Now, I remember reading a popular account of Lakatos's work on the history of Euler's theorem V-E+F=2 - it took several tries by brilliant mathematicians to get all the conditions right. So I find it possible, though extremely unlikely, that Goedel and everyone else are wrong - but there should be a simple way of showing it, and this paper isn't.
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Date: 2006-07-16 05:34 pm (UTC)I am not sure, whether a completeness proof itself ought to be simple..
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Date: 2006-07-16 10:50 am (UTC)no subject
Date: 2006-07-16 03:15 pm (UTC)no subject
Date: 2006-07-23 11:33 pm (UTC)no subject
Date: 2006-07-24 02:19 am (UTC)no subject
Date: 2010-06-06 03:10 pm (UTC)