Le 29-août-07, à 02:59, marc.geddes.domain.name.hidden a écrit :
> I *don't* think that mathematical
> properties are properties of our *descriptions* of the things. I
> think they are properties *of the thing itself*.
I agree with you. If you identify "mathematical theories" with
"descriptions", then the study of the description themselves is
metamathematics or mathematical logic, and that is just a tiny part of
mathematics.
After Godel, even formalists are obliged to take that distinction into
account. We know for sure, today, that arithmetical truth cannot be
described by a complete theory, only tiny parts of it can, and this
despite the fact that we can have a pretty good intuition of what
arithmetical truth is.
Bruno
http://iridia.ulb.ac.be/~marchal/
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to everything-list.domain.name.hidden
To unsubscribe from this group, send email to everything-list-unsubscribe.domain.name.hidden
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en
-~----------~----~----~----~------~----~------~--~---
Received on Wed Aug 29 2007 - 06:48:55 PDT