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[Posted to the FOM mailing list, January 6, 2006.]

[FOM] Infinity and the "Noble Lie"

Karlis Podnieks Karlis.Podnieks at
Fri Jan 6 09:08:10 EST 2006

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
University of Latvia
Institute of Mathematics and Computer Science

My personal page - click here.