Re: Does a potential infinity actually exist?

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.

Intuitionistic analysis and intuitionistic mathematics in general will
probably not be to Petry's liking, though, highly abstract and
infinitary as they are.

That is true. I argue that the ultimate purpose of mathematics is to
provide tools that help us understand the world we live in (i.e. it
should be of practical use to physicists, engineers, computer
scientists, etc.), and also that we should make liberal use of
Ockham's razor and KISS (keep it simple). It baffles me that
mathematicians, including most intuitionists, won't grudgingly
acknowledge that those are worthy ideals.



.

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