[FOM] mathematics as formal

Vaughan Pratt pratt at cs.stanford.edu
Sun Mar 23 02:10:06 EDT 2008

Vladimir Sazonov wrote:
> My definition: 
>   Mathematics is nothing else as taking and exploring the form of 
>   human thought seriously and consistently.

I can't accept this as I don't see how it distinguishes an Archimedes, 
Euler, Gauss, or Erdos from those who debate logical positivism, 
freewill, formalism, etc.  I don't consider the latter mathematicians 
unless they bring mathematical tools to bear effectively on their subject.

I also have trouble with "human".  Aliens might not be DNA-based, but it 
seems to me that they'd more likely to arrive at the concept of prime 
number than of logical positivism once they get past mere street smarts. 
  Mathematics is surely the least specifically human of all thought 
processes, with physics, chemistry, etc. close behind.

I do however appreciate our shared goal of defining mathematics. 
Applied to myself as much as to anyone, "better to have defined and lost 
than never to have defined at all."

> What I tried to defend above can be called the formalist view on 
> mathematics (or formal nature of mathematics). This is the old 
> brand arisen in the previous century but requiring a fresh description 
> (and rehabilitation).

Indeed.  You have correctly discerned that I am not a formalist.

Vaughan Pratt

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