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Re: Language vs. Library why it matters

  • To: mathgroup at
  • Subject: [mg61600] Re: Language vs. Library why it matters
  • From: Bill Rowe <readnewsciv at>
  • Date: Sun, 23 Oct 2005 05:46:08 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

On 10/22/05 at 12:36 AM, fateman at (Richard J.
Fateman) wrote:

>Bill Rowe wrote:

>>My intent was merely to make the point Godel's results must apply 
>>to Mathematica since they clearly apply to mathematics and
>>Mathematica by design is intended to encompass mathematics.

>Not so.  Mathematica does not prove theorems, generally. Some
>mathsource programs may construct some proofs in some limited
>context, but those don't contradict Godel's result.

Your remarks are confusing. You start by saying "not so" which clearly means you disagree with the statement I made. Then you state Mathematica doesn't prove theorems generally (I agree), a statement that seems to have little to do with my statement. Finally, you state existing mathsource programs do not contradict Godel's results. That would seem to be equivalent to saying Godel's results are applicable to those programs which was the point I was trying to make.

My understanding (perhaps incorrect) of Godel's main result in any suitably complex language (e.g. mathematics), you could form statements consistent with the syntax of that language whose validity could not be decided.

It seems clear to me this must also be true of Mathematica as well as mathematics.
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