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Re: five reasons why mathematics ends in meaninglessness
Posted:
May 13, 2011 11:41 AM
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On May 11, 6:23 pm, Jim Burns <burns...@osu.edu> wrote:
> On 5/11/2011 12:45 PM, Transfer Principle wrote:
> > It's not until one is learning analysis, not arithmetic -- when one
> > learns to view the reals as D-cuts or classes of C-sequences rather
> > than infinite decimals -- when the distinction between finite and
> > infinite decimal becomes less important.
> However, unless you can find some other distinction beyond
> what you have pointed out here, you have also conceded my
> point that byron's distinction between infinite and finite
> decimal expansions doesn't have any useful purpose in a
> discussion of the Nature of Truth.
Apparently, according to byron, if a real number has _both_ a
finite and an infinite expansion, then this would imply that
the finite equals the infinite -- and hence "finite" and
"infinite" are _meaningless_ concepts.
Of course, in classical analysis, a real number can have more
than one decimal expansion without problems. But that doesn't
exclude the possibility of a system in which every real has
only one such expansion, or at the very least, one where a
real with a finite expansion can't have an infinite expansion.
> Let me present a tri-lemma for you, TP:
> "byron is a [snip label]" is
> (1) a retail truth, and disagreements about his
> crankhood should be settled by discussions of things
> immediate to our perceptions, like what he has written,
> (2) a wholesale truth, and disagreements about his
> [label] are very deep and philosophically interesting,
> or (3) a third category of truth, which you will honor
> us by now describing:
I would say that (2) is the closest to how I feel.
Certain posters use labels to describe other posters. I
disagree with the use of such labels, because I don't
believe that the posters always merit such labels. I
consider such labels to be overused.
I'd probably wouldn't be complaining about the labels had
they not been used on sci.math so often. But, in my
opinion, they are overused.
Oh, and by the way, some posters have been criticizing me
for always snipping out the overused words. But I mainly
do so in response to earlier criticisms that I _myself_
use the words more often than my opponents. To counter
such criticism, I've decided that I don't want the words
to appear in any post listed under my username, not even
when I directly quote another poster who uses the word.
> Surely, if "what they write" is not the reason they
> are called [labels]
Of course "what they write" is the reason for the labels,
since all we know about other posters on Usenet is what
they write in their posts. There's _something_ in byron's
posts that lead to the labels, and I want to address the
content of the posts that causes the labels.
> (I can't help pointing out that you recognized what is
> probably the most important characteristic of [label]
> when you expressed that skepticism: it is close to
> unheard of for [the labeled] to change their behavior,
> especially because of any argument. On the other hand,
> your project of finding reasonable non-standard analysis
> that mimics the ideas of [label] assumes that you /will/
> be able to alter the behavior of non-[label] that way.)
It's difficult to change the behavior of _anyone_, label
or no. But what I want to do is _try_, no matter how hard
it may be, to convince users of the labels that the
posters they so label don't merit the labels.
Of course, I'll never completely _eliminate_ the use of
such labels, but I'll consider myself successful if I can
at least _reduce_ their use in any small way.
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