Re: The Law of the Excluded Middle again (long)

On Fri, 07 Dec 2007 19:57:49 EST, "T.H. Ray"
<thray123@xxxxxxx> wrote:

On Fri, 07 Dec 2007 19:09:41 EST, "T.H. Ray"
<thray123@xxxxxxx> wrote:

On Thu, 06 Dec 2007 17:32:08 EST, "T.H. Ray"
<thray123@xxxxxxx> wrote:

[I wrote:]

On Thu, 06 Dec 2007 09:33:58 EST, "T.H. Ray"

<thray123@xxxxxxx> wrote:

Perhaps you are aiming at the constructive
result
that
all real functions are continuous.

I don't understand how I could be "aiming"
at
such
a
thing
(which I also don't understand at all).

See, e.g., Weyl, 1987,The Continuum;

(I have the book, but haven't got around to
reading
it yet.)

Chapter 1, pp 5-50, Dover 1994.

I was going to post something about this, in a
message to another
thread, but I can't find the theorem in my copy
of
the book (same
edition, Dover 1994). I've looked twice.
Sorry
if I
should have
looked a third time!
--

Exposition on continuous functions starts on page
80.

I know that (the book has an index, and I didn't
just
search up
to the indicated page 50!); but where is the
theorem
that every
real-valued function of a real variable is
continuous? (I could
read the whole thing, but that would take time,
and I
would of
course prefer to read the book as a whole, at my
leisure; also,
you presumably already know the location of the
reference.)
--

The Continuum is exposition, not a book of theorems.

If that's all you want,

Stop projecting. You mentioned the theorem,
suggesting that
it might be what I was interested in. I disclaimed
interest
in it, also saying that I could not understand the
idea. In
response, you gave a reference. It was entirely
natural for
me to assume that it was a reference to the theorem
that you
had erroneously suggested I was interested in, in an
article
following up an article of mine to whose content you
did not
actually respond. This entire conversation is quoted
above.
Need I comment further?

use the Wikipedia reference:

http://en.wikipedia.org/wiki/Continuous_function

OK, thanks, I will. I hope it isn't another wild
goose chase.

I was trying to get you to appreciate Weyl's
construction
of the argument, and that you have to read to
conclusion
(p. 86) "In the realm of _continuous_ functions,
_differentiation_ and _integration_ serve as
function-
generating processes just as they do in contemporary
analysis; no change in the foundations is
necessary."

You go on with questions about what constructive
method is good for--and I keep showing you how
analytic
concepts of system and process precede the
construction.
And then you want to see the formalism, as if it
will
somehow impart magical meaning a posteriori? My
point is
apparently lost.

You apparently expect me to swallow and digest an
entire
constructivist philosophy in one gulp! Moreover you
address
me disrespectfully. In both respects, this is poor
pedagogy.

In saying that, I am not saying I have nothing to
learn. I
have much to learn. But I am not likely to learn
much from
you, if the conversation continues in this fashion.
--

You are absolutely right. I surrender.

Tom


Angus Rodgers
(twirlip@ eats spam; reply to angusrod@)
Contains mild peril
.

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