[lbo-talk] What's at stake?/AI again

[John Thornton]

>Btw, all
>thinking, algorithmic or not, _can_ be represented as
>the output of a Turing machine, but it turns out that
>this is not a useful or illuminating fact beyond the
>most abstract level of analysis. jks

I don't think so. The definition of what is or isn't computational (i.e. 
algorithmic) is whether it can or can not be done with a Turing machine. 
The Church-Turing Thesis is that Turing machines are formal versions of 
algorithms. No computational procedure is an algorithm unless it can be 
presented as a Turing machine. Church's work shows that any computable 
(i.e. algorithmic) function can be transformed into an expression in the 
lambda-calculus. Church's work is equivalent to Turing's description of a 
LCM. What non-algorithmic function did you have in mind?

John Thornton