[FOM] Infinity and the "Noble Lie"

[Karlis Podnieks]

From: <joeshipman at aol.com>
Sent: Thursday, January 05, 2006 9:37 AM
"...
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? Of course, if
"applying successor function" would mean adding a U235 atom, then the
conditions of the process will change sometime...  Thus, in the
physical world, it always depends on the implementation, how long the
iteration process can last. And thus, an iteration process that lasts
without changes and never stops, can be only an invention, an act of fantasy
(some people call this act "idealization").

In a similar way, in 17th century, people invented the "uniform movement"
that also did not exist in the physical world, but, nevertheless, could 
serve as a basis
for much better modeling principles (Newton's Laws) than the obvious 
Aristotle's
principle "any movement stops, if one does not apply force".

The same kind of process leads to creatures populating Disneyland.

Of course, all that is trivial, but do we need a more complicated
("nobler"?) philosophy here?

Karlis.Podnieks at mii.lu.lv
www.ltn.lv/~podnieks
University of Latvia
Institute of Mathematics and Computer Science