Re: Calculus XOR Probability

stephen@xxxxxxxxxx wrote:

Han.deBruijn@xxxxxxxxxxxxxx wrote:

stephen@xxxxxxxxxx wrote:

Why should anyone hesitate to recognize that 'infinite' and 'finite'
are very different things?

If it comes to non-mathematics, physics for example, then the 'finite'
_becomes_ 'infinite' only by increasing the former. Meaning that there
is _no_ essential difference between the two.

But that is not what it means to mathematicians. If you
are going to discuss things with mathematicians, you should
either use mathematical definitions, or make it clear that
you are using a different definition.

I _am_ making clear that we are using a different notion, which is not
(yet) the same as a different "definition".

In mathematics there is an essential difference between finite
and infinite, which is why mathematicians are not all hesitant
to recognize that finite and infinite are very different things.

Yes, that's quite clear, after all those years.

'Infinite' in physics is
a way of expressing that something is finite, but very large.

But that is not what 'infinite' means in mathematics.
Why you stubbornly refuse to recognize that fact is
quite puzzling. It seems rather childish to insist
everyone use the physicists definition of 'infinite',
assuming of course that is actually the physicists definition.

I _know_ what 'infinite' means in mathematics. I am _not_
stubbornly refusing to recognize that fact. I do _not_ insist
that everyone uses the physicists definition of 'infinite',
which nevertheless is the "definition" in _all_ other sciences
as well.

I'm only making clear, time after time, that the mathematical
definition of 'infinity' is at odds with any scientific content.
If that is OK with you, then why bother? If you find that kind
of disturbing, then better start to think about it.

Who was talking about physics? Was your question about probability theory supposed to by a physics question?

Probability Theory _plays_ a role in physics. Hence my concern.

Anyway, if you want to use "infinite" which literally means
"not finite" to mean "finite, but very large", then go ahead.
Just do not be so foolish to assume that is what everyone
else means by the word, or that is what everyone else should
mean by the word.

It's the other way around. This is as silly as trying to forbid the use
of the word "ring" in Lords of the Ring, because mathematics claims the
word for itself. Same for common speech words like "measure" and "ideal"
and "infinity". A far more sensible program would be to figure out where
the mathematical definition of infinity leads to "jumps from the finite
to the infinite" which cannot possibly have any counterpart in empirical
science. There are two possibilities. Either start mathematics all over
again, from i.e. constructive principles. Either accept mathematics as
it is and develop kind of 'AfterMath' to protect science from infinities
that cannot arise from the finite. The pleasant news is that many of the
infinities in mathematics are "good" infinities in science as well. That
makes i.e. calculus so highly useful.

Han de Bruijn

.

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