[FOM] Non-constructiveness.

[richman]

>===== Original Message From Lucas Wiman <wiman at uiuc.edu> =====

>It's not quite this, as mathematicians are more than willing to say
>that there is a constructive method for telling whether a number is
>prime, even very large numbers on which the algorithm couldn't
>possibly be run.  The desire is not an epistemic requirement, but
>rather an important psychological one.  It might be compared to the
>desire in science for good explanations of phenomena over just a
>empirical description of the phenomena.  A "try them all" approach
>to an existence proof doesn't really "explain" why the object
>exists, since it gives no other properties of the object.

I probably missed something here, but isn't the standard algorithm for telling 
whether a number is prime, or factoring it if it is composite, one of these 
"try them all" approaches? It doesn't explain anything. An article was 
recently brought to my attention wherein the author refers to this algorithm 
as "highly nonconstructive".

--Fred