[FOM] Fictionalism About Mathematics

[Aatu Koskensilta]

Quoting charlie <silver_1 at mindspring.com>:

> 	   I personally reject the essential Hersh line that math is like a  
> game of baseball with referees making the decision of what's right  
> and what's wrong.   Mathematical referees would be, according to  
> him, a body of  experts who stamp their imprimaturs on theorems.    
> One reason I think that's wrong is that experts can be proven wrong  
> long after a theorem has been previously endorsed.   Hersh could  
> still maintain his view, arguing that new referees can always be  
> later added to the referee group.  This may be a good account of  
> what we accept as mathematical theorems, but not as mathematical  
> truth, since I believe we all agree--don't we?--that a long-lasting  
> mathematical theorem can nevertheless be wrong no matter how many  
> experts for how long a time have endorsed it (even when higher  
> mathematics is based on an earlier error).  Thus, to me,  
> mathematical truth is out there beyond our fictions.

   This, naturally, is one of the very useful fictions we find in  
mathematics. In the story we tell about mathematics we meet an  
idealized notion of proof, an essential part of which is that only  
true things can be proven. And of course we accept that we're  
fallible, so that we can think something a proof even if it in  
(fictional) fact is not, and there are many (fictional) connections  
between mathematical theorems, methods of proof, concepts, that  
sometimes allow us to recognize our mistakes. In our less fictional  
moments, as we reflect on our practice of mathematics, we must in all  
honesty admit there's nothing more to such things than we put there,  
nothing beyond our decisions in this case and that, constrained by  
general (fictional) stipulations and principles, as decided by us and  
emerging from the stories we tell. The appeal of these mathematical  
fictions is such that we're soon drawn into it again, forgetting all  
about these reflective reflections, and arguing in earnest about  
correctness of proofs and other mathematical matters as if they were  
factual questions. And so it goes.

-- 
Aatu Koskensilta (aatu.koskensilta at uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus