From: Eliezer Yudkowsky (sentience@pobox.com)
Date: Sun Oct 24 2004 - 10:56:44 MDT
Ben Goertzel wrote:
>>What exactly would you say is the difference between "philosophical"
>>understanding and "mathematical and rigorous and definite" understanding?
>
> Eliezer, here is the difference.
>
> When you have a mathematically rigorous argument about some topic, then the
> following holds: When you explain your assumptions and arguments to ANY
> properly educated, non-insane listener, they then will accept that your
> conclusions follow from your assumptions, with close to 100% confidence.
>
> Note that this is a cultural definition. A more formal definition would
> require that an argument, in order to be mathematically rigorous, would have
> to be spelled out to the level of Mizar or some other formal system. But
> this is not pragmatic, so in practice we rely on the common intuition of the
> mathematically and scientifically educated community to recognize when an
> argument is rigorous and could, in principle, be reduced to the Mizar level
> if one were to take the time. In an odd case where you felt you had a
> rigorous argument but couldn't get 100% agreement from the community, then
> you could undergo the pain of reducing your argument to the Mizar level, in
> which case everyone would then accept your argument.
>
> Philosophical arguments, on the other hand, have enough ambiguities and
> holes in them that even when you explain your assumptions and arguments to a
> properly educated, non-insane listener, they may not fully agree that your
> conclusions follow from your assumptions.
Would you characterize the definition you've just given as "philosophical"
or "rigorous"? And do you think you could give a rigorous definition, if
required?
-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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