From: Geoffrey Norman Watson 
Date: Thu, 14 Nov 1996 13:12:08 +1000
Organization: Computer Science Dept, University of Queensland

On 14 Nov 1996, Anders N Weinstein wrote:

> 
> The real answer is that you would have to assume your own consistency
> as a premise in the reasoning process by which you come to add G to
> your stock of truths about numbers in the course of your reading.  And
> that leap of faith means engaging in some kind of reasoning not
> embraced by any formal system.
> 

But suppose we *were* the embodiment of such an algorithm:

If we accept that the logic of our formal system is the "classical" one
then we have some *empirical* evidence to support the premise of consistency,
since no one has yet proved that ~(2+2=4).  And presumably, our "faith" in
empirical evidence would be justified by the algorithm that we embody ...

Of course our formal system could be inconsistent, but with a logic that 
could tolerate local inconsistencies, this would be enough to escape the
problem of Goedel's theorem but also preserve the consistency of arithmetic.
However such systems are usually judged counter-intuitive.

BTW Alan Turing did much of his work on such formal systems, is it true to
say that his views on intelligent machines WERE referring to the "machines-
as-embodiments-of-formal-algorithms" approach?

--------------------------------------------------------------------------