[FOM] Hamkins's multiverse and ultrafinitism

[Timothy Y. Chow]

MK wrote:

> It is a mistake to use the term "ultra-finitist flavor" in reference to
> Hamkins' position.
>
> If anything his position can be more appropriately described as 
> "ultra-infinitest". Namely, our usual concept of familiar integer ends 
> up (more or less inevitably, depending on to what extent one is 
> committed to the multiverse scheme) incorporating ideal entities that 
> behave like infinite ones from the viewpoint of a more "economical" 
> universe, and so on ad infinitum.

Thanks, this helps a little, although I'm still puzzled about some things.

There is an old joke about a little child who was asked to spell "banana." 
"I can do that," was the reply, "except that I don't know when to stop."

So if I understand correctly, the vagueness of "finite" is *not* that we 
are worried that we can't "count that high," but we don't have a clear 
conception of "when to stop"?

It still strikes me as difficult to construct a convincing heuristic 
argument for this point of view.  In particular, what it means is that 
what we think of as the standard natural numbers actually include 
nonstandard numbers, from someone else's point of view.  But how can we 
picture this "someone else"?  This "someone else" thinks that some of our 
good ol' finite natural numbers aren't really finite.  Doesn't that mean 
that that "someone else" is a closet ultrafinitist (at least in our eyes)?

Tim