Re: Does a potential infinity actually exist?

On Aug 30, 4:26 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:
mike3 wrote:
On Aug 23, 5:04 pm, david petry <david_lawrence_pe...@xxxxxxxxx>
wrote:

On Aug 23, 9:39 am, aatu.koskensi...@xxxxxxxxx wrote:

MoeBlee wrote:

If you would either give 'potential infinity' as a primitive and
axioms with it or 'potential infinity' defined from primitives, then
there might be something of specific mathematical interest there.

It would appear that Moeblee didn't understand anything I wrote. I'm
arguing that when we acknowledge that infinity only has a potential
existence, then we see that infinity is merely a figure of speech, and
anything that can be said using the word "infinity" could also be said
without it. The best I could do is present rules for transforming
sentences using "infinity" into sentences not using it, but the
example I gave in the article gives the main idea.

You need an axiom to define it.

What _axioms_ does "Potential Infinity"(TM) satisfy? Or how
can you derive it from some accepted set of axioms?

The "need" for axioms is a _peculiarity_ which originally stems from
Euclidian geometry. It's a great invention, but it's _not_ a panacea
for everything. There is a school in mathematics, called constructivism,
the founder whereof, L.E.J. Brouwer, has said that axiomatics and logic
are accompanying the _act_ (i.e. construction) of mathematical entities,
but are by no means the foundations they can be based upon.

How can you manipulate "potential infinity"?

Constructively, that is: not by means of an axiom system.


So do you think the original poster's "potential infinity"
thing is a good idea?


.

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