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Re: Language vs. Library why it matters


On 10/19/05 at 2:16 AM, hattons at globalsymmetry.com (Steven T.
Hatton) wrote:

>I'm not sure Gödel's (anti-)proof is the core reason that
>Mathematica is difficult to understand, though it certainly plays
>into the whole picture.  

I would agree Godel's theorem's do not explain the steep learning curve for Mathematica. I believe the steep learning curve for Mathematica is due to the richness of the tool set made available. 

>In particular, Gödel's results tells us any sufficiently powerful
>language necessarily leads to the possibility of formulating
>selfcontradictory statements.  I'm not aware of Mathematica producing
>any such selfcontradictions.

But Godel's theorems were statements about mathematics. And Mathematica is clearly intended to encompass mathematics, to allow the user to do any valid mathematics. Consequently, Mathematica must either inherit any inconsistencies existing in mathematics or restrict the user from performing certain mathematics. 
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