Re: how to list all of the real numbers

On Aug 9, 4:12 pm, lwal...@xxxxxxxxx wrote:
On Aug 9, 1:28 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

On Aug 8, 1:16 pm, lwal...@xxxxxxxxx wrote:

On Aug 6, 12:23 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

Who are all these mathematicians who do all this non-hesitating
'crank'-calling just on the basis of one choosing to eschew choice and/
or infinity?

Yesterday, a nonstandard mathematician initiated a thread here on
this newsgroup entitled "Another Inconvenient Truth." The OP
states that he denies the Axiom of Infinity because he believes
that no infinite sets exist in the real world. Then today, Mike
Kelly wrote that the Axiom of Infinity "is _useful_. That is
indeed an inconvenient truth for cranks," strongly implying that
the OP and all other finitists are cranks. Therefore, to answer
your question, Mike Kelly is one such mathematician who calls
anyone who eschews Infinity a crank.

I don't know the specifics of that context, and I don't know all of
Mike Kelly's views on such matters, but what you quoted by Mike Kelly
does not in itself "strongly imply" he holds that anyone who eschews
infinity is a crank. Whether trenchantly or not, he said cranks don't
reconcile themselves to the usefulness of the axiom of infinity; he
didn't say that anyone who eschews infinity is a crank.

I see what you mean, but still, I've never seen a thread on this
newsgroup initiated by a finitist in which the word "crank" didn't
eventually appear.

I've not seen every thread, but most of the people I read who rail
against infinite sets are cranks. Notice that I'm not claiming that
anyone opposes that there exist infinite sets is a crank; but rather
that most of those who do happen to post in that vein are cranks.

And what is a "finitist"? I think some people regard Hilbert's view as
a form of finitism; and I surely don't regard Hilbert as a crank.
Abraham Robinson views the notion of infinite sets as meaningless; and
I surely don't regard Robinson as a crank.

Most basically, I am not aware that there is any kind of consensus
among working mathematicians and students of mathematics in math and
logic threads that a person who proposes dropping the axiom of
infinity or adopting its negation is thereby, merely on that basis, a
crank.

MoeBlee

.

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