On 24 Mar 2015, at 01:50, meekerdb wrote:
On 3/23/2015 5:02 PM, LizR wrote:
On 24 March 2015 at 08:02, meekerdb <[email protected]> wrote:
That every number has a unique successor for one.
"Let's call the first number that doesn't have a unique successor
n..."
That's one possible form of ultrafinitism, but not the only one.
Let's see you derive a contradiction from that (without implicitly
assuming infinities). Most forms of finitism don't assume a biggest
number.
http://www.jeanpaulvanbendegem.be/strict%20finitism.pdf
Excellent text. No problem at all. Almost an argument for using RA
even when wanting to play with RA and ZF. RA *is* strict finitism. PA
is still finitism. and if infinitist ZF can help, why not interviewing
her, but all have the same G+G* theology. Except the base strictly
finitist.
Some aspect of the theology would disappear, if we use such ontology
to forbid interviewing the many infinitist believers existing in the
strictly finitist realm, though.
Computationalism is a finitism. And RA is a strict finitism. It can
have a biggest number. I show this in more detail later perhaps. The
existence of a biggest number does not contradict the axiom:
0 ≠ s(x)
s(x) = s(y) -> x = y
x = 0 v Ey(x = s(y))
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf
Nice points, but less serious, contain errors.
Bruno
Brent
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