Re: A little knowledge is a dangerous thing - THE HALTING PROOF


Bhupinder Singh Anand wrote:

> A closer look at the arguments will show that,
> formally, the possibility that there is always a
> non-algorithmic, but effective, way, of assigning
> a natural number to any given real number cannot
> be ruled out.

That is flatly ridiculous. It is ruled out immediately
by the BRUTE FACT that there IS NO formal definition of
"effective"! The CLOSEST THING to a formal definition of
"effective" is "algorithmic", i.e., TM-computable.
The Church-Turing thesis is that this closeness is absolute,
that, no PRIOR formal definition of "effective" being
extant, we are FREE TO STIPULATE the formal definition of both
"effective" AND "algorithmic" as "TM-computable".

.