[FOM] Feasible and Utterable Numbers

[Charles Silver]

On Aug 5, 2006, at 4:45 PM, V.Sazonov at csc.liv.ac.uk wrote:
> "Natural" is good (and can be subjective and depending on time), but I
> consider that the main criterion for any idea to be mathematical is
> "adequately formalisable".
>
> For me the question is: can we ever treat feasibility in a
> mathematically rigorous way or it is non-formalisable at all and
> nothing except useless speculations is possible? The answer is: it is
> formalisable, but somewhat unusually. The formalisation could/ 
> should be
> probably improved to be more natural. Anyway, it is better to have  
> some
> (adequate) formalisation than nothing at all.

	I believe I understood your various distinctions, and of course I  
know the difference between modifying the logical versus the non- 
logical features of your theory.   Since there are many unusual  
characteristics and variants, I am led to an extremely primitive  
question: What makes your theory a theory of some "concept"?   This  
relates to the question of "naturalness".    For example, I could  
make up some non-logical axioms and declare that certain inference  
rules are off limits, but that would not make the resultant theory a  
theory of anything.   So, could you please explain--I know this is a  
decidedly primitive question--why "feasibility" is a real concept,  
and also why it seems to resist formalization?
	Also, according to my intuitions (which may be bad), it seems to me  
that a feasible number should not have a sharp cut-off.   That is, I  
think there should be numbers in between those accepted by most  
people as feasible and much larger numbers considered non-feasible,  
with a lot of numbers in between.   Call these numbers the Betweens.   
But then, the question would arise why the largest number in the  
Betweens is not really non-feasible, and why the least number in the  
Betweens should not be considered feasible.

	(Incidentally, I am not trying to suggest that "fuzzy logic" or  
"fuzzy set theory" or fuzzy anything should be employed.)

Charlie Silver