[extropy-chat] Tyranny in place

Eliezer S. Yudkowsky sentience at pobox.com
Tue Oct 3 17:40:01 UTC 2006

spike wrote:
> This is a paradox that we cannot solve with our usual tools.  Logic simply
> fails.

Heinlein had a sympathetic character say, in one of his stories:  "Logic 
is a fine thing, but I have seen a perfectly logical proof that 2 = 1."
(If anyone remembers which story this is from, please let me know.)

Heinlein was probably thinking of this:

x = y = 1
x = y
x^2 = xy
x^2 - y^2 = xy - y^2
(x+y)(x-y) = y(x-y)
x+y = y
2 = 1

Now you could look at that, shrug, and say, like Heinlein, "See, I told 
you logic doesn't always work."

Or, if you felt that math had justly earned a bit more credibility than 
that over the last three thousand years, you might suspect that the flaw 
lay in your use of math, rather than Math Itself.

You might suspect, perhaps, that the proof was not "perfectly logical".

The novice goes astray and says: "The Art failed me."
The expert goes astray and says:  "I failed my Art."

> What happens when a society of religious freedom is confronted by a
> religion that does not allow religious freedom?  Does universal tolerance
> mean we tolerate intolerance?

Does the set of all sets that do not contain themselves, contain itself? 
  Who says there's such a thing as "universal tolerance"?

Eliezer S. Yudkowsky                          http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence

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