[FOM] Model theory and foundations

[Ayan Mahalanobis]

Stephen G Simpson wrote:

> > I am increasingly of the opinion that nonstandard analysis is one
> > of the big foundational discoveries of the 20th century.
>
>I like nonstandard analysis a lot, but I don't see it as measuring up
>to the epochal work of Goedel and Turing.  In particular, one can't
>use nonstandard analysis as the basis of an exposition of mathematics
>from the ground up.  Part of the difficulty is that, in a precise
>sense, one can't give an example of an infinitesimal.  
>  
>
I don't know much about non-standard analysis. I will dare ask a 
question here in hope that at the end I might end up wiser. Why is the 
non-existence of infinitesimals an issue? I have tried to understand the 
concept of continuity in classical mathematics and it seems to me that 
the use of epsilon-delta is highly conceptual. So what is wrong with 
conceptual infinitesimals?

Ayan