[FOM] The natural numbers as marks on paper

Thomas Forster T.Forster at dpmms.cam.ac.uk
Thu Feb 23 04:04:07 EST 2006

I think this is an important idea.  I even have it on my "topics for
theses i'd be willing to supervise" page linked to my home page.  Keyword
here is "lazy evaluation".  If there is a philosophical/CS literature on 
this i'd be grateful for references.


On Thu, 23 Feb 2006, Eray Ozkural wrote:

> On 2/22/06, Martin Davis <martin at eipye.com> wrote:
> > Alas, one person's marks on papers are another's abstract object smelling
> > foully of Platonism. As Weaver perfectly well knows, a sheet of paper holds
> > only finitely many marks. An example of an outstanding mathematician who
> > finds the marks-on-paper no help is Jack Schwartz who has written on the
> > matter on FOM and elsewhere.
> As I indicated on my post about this problem, I think all matters are
> easily resolved if one thinks of marks as computer programs. A finite
> program can easily denote an "infinite" structure such as the list of
> all natural numbers. This does not seem to be Platonist in the least
> bit.

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