Thanks. I guess I agree with the your "quale" and "betting"
descriptions. Finiteness is an existence statement, "there exists an
end". If we are talking about an actual particular group of things, we
need an "observer" to say where the end is, thus declaring it to be
finite. But it is another thing to make an abstraction of (all
instances of) that occurrence (i.e. declaring an end) and call that the
*concept* of "fin"-iteness. It is an abstraction of qualia, like a lot
of math is.
An aside: Some might argue that at that point you can get rid of the
observer (unless it was me!), and then... you didn't need an observer
in the first place...
This thread is somewhat interesting, but it can get circular pretty
fast. (For instance, I was going to say "|||||...." has no end by
definition.) I guess that's the point. But I think the bottom line is
that we agree that finiteness is at the qualia level, but I would say
that we can abstract it. Perhaps it is like Church Thesis?
Bruno Marchal wrote:
> Le 14-juil.-06, à 18:52, Tom Caylor a écrit :
> > Here is where I believe the crux is: "..." means you can continue to
> > add the "I" as many times as you want. Actually, this is equivalent
> > to: "..." means you can continue to add the "I" as many times as you
> > want and you can. It's just a little redundant to say it that way.
> > Now A and B *know*, as well as anyone can even know, what finite means.
> True, but unprovable. With comp you are betting here.
> > All they have to do is perform some experimentation to get the idea
> > that, after a while of adding "I" they eventually get tired and/or
> > loose interest, so they have to *stop*.
> Yes but my friend B, which is an angel, a cousin of the analytical
> second order arithmetic with the omega rule. He is tired after counting
> up to number like |||...|||...|||... ...||||||||.
> > What's so difficult about
> > understanding what stopping is?
> I am not denying we have some intuition of that. Just pointing that
> mathematicians can show we cannot define what finite means through
> first order logic, and then second order logic builds on that
> intuition, so that really "finite" is not a notion we can define in any
> finite way. Nor can we define "NOT finite", that is what "infinite"
> > Even the word "finite" has "fin" in
> > it, i.e. "end". The notion is defined by invariance.
> Relative one. You can imagine something stopping compare to something
> which does not stop.
> > Something
> > similar (invariant) is happening (adding "I" at one step is considered
> > the same action as adding "I" in another step)
> Actually adding | at the end of ||||..... giving |||....| is different
> from adding | at the end of |||.
> > and then the invariance
> > disappears, i.e. the adding of the "I" is no longer happening.
> Yes but when? I know you and me know that. The point is that we cannot
> explain it without admitting at the start that we know that. "that" has
> the type of a quale.
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