[FOM] Mathematics and precision

[Henrik Nordmark]

> I cannot imagine anything really precise which cannot be still  
> called a formal system. At least, for the contemporary state of  
> affairs nothing better exists.

I tend to agree that there is nothing better in terms of precision  
than a formal system.

However, I would not want to say that formal systems have a monopoly  
on precision. This would put the threshold of precision way too high.  
Most mathematics gets written in natural languages like Mathematical  
English and NOT in some formal system.

Thus, if one wants to use a threshold precision as a way of defining  
the scope of Mathematics, it seems reasonable to put that threshold  
sufficiently low to include what most mathematicians do in everyday  
life.


And how high should the threshold be?
High enough that we feel confident that in principle what we are  
doing can be formalized even though we may not want to bother doing so.


Henrik Nordmark.


Henrik Nordmark
Institute for Logic, Language and Computation
Universiteit van Amsterdam
www.henriknordmark.com