[FOM] f.o.m. documentary 2

[Margaret MacDougall]

Hello Michael

When you say, within the context of referring to ZFC, that "the 
paradoxes are STILL not properly handled within the foundations", what 
exactly are you getting at here?  Also, in what sense(s) to you believe 
that category theory has "outgrown" ZFC? Further explanation would be 
welcome.

Many thanks

Margaret


  On 14/02/2012 20:37, Michael Lee Finney wrote:
> I would like to point out that in addition to the areas that Harvey
> mentioned, that there are a number of logicians who feel that
>
> 1. That classical logic is at least partially incorrect or that it is
> insufficient,
>
> 2. Classical foundations such as ZFC or even naive set theory are
> either incorrect or insufficient.
>
> For those who believe either or both of the above, the foundation
> tasks of the '30s are not done yet. We have simply had a haitus while
> the general field has progressed making new attempts possible.
>
> I personally think that this is one of the most important areas in
> foundational logic that needs to be addressed.
>
> I see ZFC as a bunch of band-aids applied to solve a problem. They
> sort of work, but are very restrictive. One example is category theory
> which has outgrown ZFC. Another is that the paradoxes are STILL not
> properly handled within the foundations. And, of course, it is now
> clear that the regularity axiom is completely unnecessary and does not
> add anything useful.
>
> This is usually an area to which most working mathematicans and even
> most logicians are indifferent, but it is vital and there are a number
> of logicans working in this area.
>
>
> Michael Lee Finney
>
>
> HF>  Continuing the discussion surrounding my plans for the f.o.m.
> HF>  documentary
>
> HF>  CAN EVERY MATHEMATICAL QUESTION BE ANSWERED?
>
> HF>  THE DECLINE OF FOUNDATIONS OF MATHEMATICS.
>
> HF>  The spectacular Golden Age of f.o.m. in the 1930s was followed by a
> HF>  period of more than 2 decades of much more specialized f.o.m.
> HF>  activity, where the results were no longer of general intellectual
> HF>  interest - with some arguable exceptions.
>
> .........
> HF>  The intention is that the documentary series become the place of
> HF>  record for a clear and creative presentation of state of the art
> HF>  f.o.m. for at least professional - and aspiring professional -
> HF>  intellectuals. How deeply it penetrates into the general literate (and
> HF>  illiterate!) culture remains to be seen. The science videos I think
> HF>  have penetrated to a reasonable extent into (at least) the general
> HF>  literate culture. I have the same hopes for this f.o.m. documentary
> HF>  series.
>
> HF>  Harvey Friedman
>
>
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
>



-- 
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.