[FOM] Infinity and the "Noble Lie"

[Calvin Ostrum]

On 1/6/06, Karlis Podnieks <Karlis.Podnieks at mii.lu.lv> wrote:

> [Quoting "Option three"]
> "Are you prepared to say that the question of the "truth" of an
> arithmetical statement proved using the axiom of infinity is also
> ridiculous?"

> Couldn't be the invention of the axiom of infinity simply an act of
> fantasy? One is iterating the successor function, and, watching the process,
> asks the question: how long could this last without changes?

I don't understand.  Which option are you taking, or are you
suggesting that there is another option that was not listed?

Your question seems to apply to the committments one
makes in Peano Arithemetic just as much as it does to the
committment one makes in accepting the axiom of infinity, so
can we presume you are taking option one of the three options?