From: Ben Goertzel (firstname.lastname@example.org)
Date: Sun Oct 24 2004 - 09:32:55 MDT
> 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.
-- Ben G
> Do you think you've come far enough, whether through your years of
> philosophizing on mind, or your more recent AGI research, to describe the
> difference? If you don't know, would you say that the difference is the
> sort of thing on which we can only say words in the philosophy of mind
> until we get significantly more empirical input? Or do you think
> it ought
> to be possible to work out a mathematical and rigorous and definite
> description of the difference between philosophical understanding and
> rigorous understanding? Obviously if you can give an exact
> description of
> the difference between philosophical understanding and rigorous
> understanding, it will be of great help in moving past philosophy...
> Eliezer S. Yudkowsky http://intelligence.org/
> Research Fellow, Singularity Institute for Artificial Intelligence
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