[extropy-chat] Perplexing deduction of the day

[Eliezer Yudkowsky]

Adrian Tymes wrote:
> 
> Didn't we have this thread earlier?  If you see an
> apparent contradiction in logical consequences from
> English (or other "natural") language statements,
> double-check your translations into logic before
> acting on your conclusion or spending further time
> analyzing it, because there is a good chance one of
> those translations is flawed (and thus, any actions
> assuming it was correct might in fact be
> counterproductive, and further analysis of this
> mistake are likely to be a waste of time).

Adrian, I already know why the logic doesn't work.  (Albeit my phrasing is 
somewhat different from yours, having to do with the definition of 
propositional tautology as the absence of a contradictory model, which in 
English would probably translate to the existence of a counterexample among 
possible worlds).  I was just throwing out something silly to amuse the 
mailing list, not complain about the paradox.

Albeit I do wonder whether anyone has tried to describe in more detail what 
humans consider to be "obvious" deductions.  It's not classical logic 
because ~(P->Q)->(P&~Q) does not seem humanly obvious, and it's not 
intuitionistic logic because humans see the Law of the Excluded Middle as 
obvious.  So how does our psychology work, exactly?  Has anyone studied it, 
I wonder?

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