FOM: Ontology of Mathematics

[V. Sazonov]

Jan Mycielski <Sat, 24 Jun 2000 15:09:36 -0600 (MDT)>
presented his views on 

>             ONTOLOGY OF MATHEMATICS (J. SHIPMAN'S INQUIRY)

and wrote 

>         I believe that this is so simple and so compelling, 

I have a feeling of some understanding and agreement with this 
idea of Ontology of Mathematics (or, more precisely, ZFC?). 
But it is presented too briefly (even if it is so "simple"). 
Once Professor Mycielski already wrote on this. Now he repeats 
almost in the same words. It is evidently not enough. I do not 
know how about other participants of FOM, but it seems it would 
be good if we will ask Jan Mycielski to write, please, all of 
this with more details, as in a scientific paper (not only as 
an abstract of a paper as in his posting). I believe that this 
will be extremely useful, even necessary, for further discussions 
in FOM. We have in FOM a lot of misunderstanding on the nature of 
mathematical objects as well as on some terminology in f.o.m. 
Any clearly presented picture will be very helpful. The following 
only confirms that the need of such a paper is urgent. 
(We are waiting almost 100 years!) 

>         The above ontology is briefly mentioned by Hibert in 1904, however
> at that time he does not have yet his epsilon symbols. He introduced the
> latter no later than in 1924, but in a paper of 1925 he does not mention
> his ontology of 1904. (My readings are from van Heijenoort and a book
> (thesis) by Leisenring.) I have not seen anywhere a clear (as above) 
> definition of this ontology, 

I am not sure that this is so clear to all of us (in particular, to me). 
Therefore my request above which I ask other FOMers to support. 

> but I have read a lot of confusing and
> confused (I believe) papers and books. It looks to me as if everybody
> forgot about Hilbert's 1904 paper, and although his epsilons are
> remembered, their fundamental significance (as tools for describing the
> structures which are really present in human imaginatioins) is never
> recalled. Am I right about this silence?


Vladimir Sazonov