[FOM] Foundational Issues: Friedman/Carneiro

[Timothy Y. Chow]

Mario Carneiro wrote:

> I think we have a difference of understanding of the word "exists" here. 
> When I say "the natural numbers exist", I mean no more or less than "? 
> N, (0 in N /\ ? n in N, n+1 in N) is a theorem in the theory of 
> interest". That's a finite statement about a finite string, with a 
> finite proof (assuming I am not making a false claim). It's all well and 
> good if you want to think there is some world out there where you can 
> meet the actual natural numbers, but it literally has no bearing on the 
> statement. I suppose you could call this "anti-platonism", although that 
> makes it sound as if I assert the *non*existence of platonic objects, 
> when instead my position is closer to "who cares".

Just for clarification, do you believe that there is "some world out there 
where you can meet actual finite strings"?

Only a diehard skeptic would deny that there is a world out there where we 
can meet ink attached to paper, or fluorescent pixels on a screen, or talc 
clinging to slate, but that of course is not the same as meeting a "finite 
string."  A string, on the face of it, is a platonic object.  Is your 
position on the existence of strings close to "who cares"?

Tim