FOM: rigor and intuition

Vladimir Sazonov V.Sazonov at
Wed Feb 13 12:17:36 EST 2002

charles silver wrote:
> Vladimir Sazonov writes:
> ----- > > In response to the quote from Kit Fine that
> > > > > when there is a clash between intuition and rigour,
> > > > > when one's sense of rigour prevents one from saying
> > > > > what, from an intuitive point of view, it seems that one can say,
> > > > > then it is rigour and not intuition that should give way.
>  .....
> Vladimir Sazonov:
> > But always remembering that mathematical
> > intuition cannot exist in a pure form, only with and due to
> > formalisms. Otherwise it is not a mathematical intuition.

Let me give some addition here to be little bit more precise. 

Mathematical intuition can be started from anything, 
but it becomes a true mathematical one only after formalization. 
Of course, we can presentiment it in some our first vague ideas. 
(But we could mistake in this presentiment.) 

Essentially I see nothing in my understanding what would contradict 
to this message of Charles Silver (which I omit here almost completely). 

I also think that Kit Fine was not very precise by saying 

> > > > > then it is rigor and not intuition that should give way.

According to the message of of Charles Silver, Kit Fine did not 
neglect rigor, he just found some appropriate formalism for, 
firstly, vague idea of "arbitrary object". (Unfortunately, 
I myself did not read his book and cannot say anything more.) 

Charles Silver [continuation; cf. the original letter]:

>     I don't want to be seen as constantly defending Kit Fine, but I do
> believe Fine clearly has a point here that's being neglected, and I think
> it's a rather important point--also one that's in line with Martin Davis's
> comments about Robinson's formalization of infinitesimals.   Suppose a
> person has an intuition--a mathematical intuition--that flies in the face of
> available formalism.   Take the quotation I cited, where Kit Fine has an
> "intuition" in favor of "arbitrary objects," but he knows that the available
> formalism does not support this intuition.  What does he do?   


Vladimir Sazonov                        V.Sazonov at 
Department of Computer Science          tel: (+44) 0151 794-6792
University of Liverpool                 fax: (+44) 0151 794 3715
Liverpool L69 7ZF, U.K.

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