[FOM] Non-constructiveness.

Lucas Wiman wiman at uiuc.edu
Fri Jul 4 13:22:17 EDT 2003

>> This is the sense in which it is non-constructive:  an existence 
>> theorem, even in the "large finite" arena can fail to really give you 
>> the object of which it speaks.
>> - Lucas Wiman
> In that case I think my objection shrinks to one of objecting to the 
> vocabulary. We're no longer talking about constuctiveness but rather of 
> feasibility (a very difficult subject on which I have nothing to say). 
> If we're seriously worried about feasibility then all sorts of things 
> that are constructively unproblematic will fail - e.g. 'every number is 
> prime or composite'.

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.

- Lucas Wiman

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