On Tuesday 15 January 2008 11:57, Pat Hayes wrote:
> At 10:26 AM -0800 1/15/08, Randall R Schulz wrote:
> >...
> >
> >Is it not impossible in FOL to finitely axiomatize finiteness? (Does
> >that count as a paradox??)
>
> Its impossible to axiomatize finiteness (in the sense of a sentence
> having only finite models) in FOL, true. (01)
> No, that does not count as a paradox. (02)
That was meant as humor... (03)
> It is possible to axiomatize finiteness (in the same
> technical sense) in logics of higher order. (04)
Yes, of course. I only meant to refer to first-order logic. (05)
> ...
> Pat (06)
Randall Schulz (07)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (08)
|