Re: Why does Cantor a target for cranks?

From: "galathaea" <galath...@xxxxxxxxx>
Wildberger's hyperbole of speech notwithstanding, his
argument is not particularly cranky.
I'm looking at that now. It looks rather cranky to me, but also
rather interesting and insightful, a mix of the two.
why the obsession with the label "crank"?

I'm not obsessed with that label. I was just responding to the
other poster's use. Ask whoever started this thread ("Andrew
Usher") or that previous poster who mentionned Wildberger just
before I responded ("T.H. Ray"), or the person who first cited
"Wildberger's rant" ("Proginoskes").

is he a crank?

I prefer E-prime:
<http://www.nobeliefs.com/eprime.htm>
<http://en.wikipedia.org/wiki/E-Prime>
! Does he act cranky much/most of the time?
! Does he act super-cranky or just mildly cranky?
A: Mildly cranky some of the time.

it seems the only legitimate characterisation as a mathematician
at least is: "is this person _consistent_"?

What about if the mathematician intrudes personal morality into
what was supposed to be a math treatise? Isn't that a fault?

people like james harris are regularly inconsistent

I don't actually know if he's inconsistent because he never makes
it clear which ring he's using for talk about divisibility, and he
presents such a large sequence of large math formulas that I just
don't have time/energy to check even a small fraction of them to
see what they mean.

allowed to run forever. So we don't exclude infinite sets, but we
include them only as a way of talking about specific unbounded data
output from algorithms.
but where does this meaning come from?
and why is it necessary?

From the formalist point of view, a set of axioms for a theory, and
derivations from those axioms, it's not needed. But from a
constructionist point of view, starting from something totally
elementary and then using that to construct the topic of interest,
it does make a difference where you start from. Set theory, or
computing processes, are different starting points, hence construct
different versions of the target theory. Both constructions are
isomorphic in the end, but the different starting points make a
difference to a constructionist who accepts one method of
construction but rejects another. I rather like constructing
algorithms and then talking about the output they generate, whereas
I rather dislike oracles that answer impossible-to-decide
questions, or anything based on the Axiom of Choice.

what use is it to speak of a unfulfillable collection process?

You mean the potency of *all* the output that an algorithm can ever
generate if allowed to run an unlimited time? So long as there's no
arbitrary choice involved, so running the process longer merely
accumulates more elements to the set, never discards old elements
due to change in choice, it seems to me easier to collect *all*
potential output into a single theory rather than special-case each
finite set.

Actually my original example of "systemic ambiguity" dealt with
... and to be consistent in sticking with
a particular category throughout a derivation/proof/problem instead
of switching definitions midway.
that is the whole origin of symbology
the abstraction on inputs

So apparently you like the way I described my idea of "systemic
ambiguity"?

So while I'm
basically a "computationalist", I'm not a "finitist". Still the
finitist viewpoint of Wildberger is interesting and enlightening.
doesn't computationalism at least bring you to constructivism?

Yes, most definitely. My computationist view is a flavor of the
constructivist view. I prefer constructions of my topics of study,
rather than handwaves that we can pretend the stuff exists even if
it doesn't. I make very few extensions to pure constructionism, one
being potential completions of sequential deterministic algorithms.
But I definitely don't accept as "definitely existing" a real
number generated by an infinite sequence of arbitrary/random
choices. An oracle that answers halting or hanging problems is used
only rarely when needed to talking about hypothetical stuff that we
can't be sure really exists.

Mathematics as a secret cult?
Yeah, that's rather cranky.
again this obsession with crankdom...

Nope, just that one tiny part out of his entire Web page that I
considered definitely cranky. The previous poster spotted that
item, and one other, and I agreed about this but disagreed about
the other. So at a rough estimate, he rated two percent of the Web
page as cranky and I downrated it to only one percent. (Assuming a
total of about 100 claims in the Web page, which I estimate is
approximately correct.) I complained a lot more about his treatment
of long division of polynomials and taking the limit using only one
of the possible metrics, yet I didn't call any of that "cranky",
just mistaken or incomplete or misleading (not in so many words,
but that was my tone of critique).

wildberger gave very clear reasons
why he used the term "secret societies"
they can be debated openly without labeling the author

And his "reasons" are totally bogus. He had cause to refer to them
as very poor education, and moderately poor foundations logic, but
the word "secret" was utter bull***, i.e. cranky talk.
There's nothing secret about graduate-school math curriculum.

i personally believe his evaluation is pretty spot-on

Please justify why you think graduate-school math currculum is secret.

repetition of mantras

I don't repeat mantras. I think for myself, and often take a path
less traveled by, and sometimes take what to me is a brand new path
I am not aware anybody before me ever took.

inability to question foundations

I question the foundations to the extreme of inventing alternate
foundatations to replace the ones I don't like. For example, I
invented "sub-countable" myself when I was in college circa 1966,
and I invented the potency of everrunning algorithms just a day or
two ago as a clarification of my longstanding constructionist
viewpoint, and I'm not aware of anyone else who ever came up with
either idea in quite the form I'm using it. I also invented nested
intervals as an alternative to Dedekind cuts, although I expect
many others have come up with the same exact construction of the
reals, and it's only a small derivation from ideas I read prior to
my "invention". But still I bucked the Dedekind and Cauchy major
parties, like bucking both Democrats and Republicans, in making my
choice/preference.

in many professional mathematicians...

Oh, you're not complaining about me? Never mind.
.

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