Re: paths through binary trees in ZF

In article
<abafab30-b21b-4875-bbba-3a5a454b1baa@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 5 Apr., 06:12, "cbr...@xxxxxxxxxxxxxxxxx"
<cbr...@xxxxxxxxxxxxxxxxx> wrote:
On Mar 30, 9:31 am, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:





On 28 Mrz., 09:48, ah...@xxxxxxxxxxxxxxxxxxx (David Libert) wrote:

  This article is inspired by the current thread

[1]    The complete infinite binary tree has only countably many
infinite paths
       sci.logic
       184 articles
     
 http://groups.google.com/group/sci.logic/browse_thread/thread/393003b..
.

  In  [1],  WM  claims to prove that the usual  binary tree  (finite
depth nodes under 1 root)  has
only countably many infinite branches through it,  thereby showing  ZF
inconsistent since it also
proves there are continuum many such branches.

  I myself believe ZF is consistent.  (Bah!  ZF?  I think ZFC + high
large cardinals are consistent.)

Hi, David,
I have not (yet?) understood your proof. But I did not try hard,
because I do not deny that there may be proofs showing the set of
paths beeing uncountable. My problem is that I am not able to explain
how a countable set of points of distinction (nodes), where every
point distinguishes exactly one more path, is able to distinguish an
uncountable set of paths.
Therefore I feel Weyl's and Brower's position comforting, according to
which logic fails for infinite sets.

That's probably the most intellectually honest posting I've seen from
you.

You don't really understand David's proof,

You have missed the central point. And so you believe that you can use
my statement for your unintellectual and inhonest ramblings: There is
no need to follow David's proof - may it be correct or not. The
problem is not that there are (or may be) proofs showing the set of
paths uncountable. The problem is that there are proofs showing the
contrary too. I have given three of these proofs in the parallel
thread. The only counter arguments are unmathematical nonsense.

Not according to those more competent than WM to judge.
According to them, each of what WM claims as proofs contains logical
fallacies, such as assuming its conclusion.

However, you approach is to
find comfort by contemplating various philosophical statements of some
famous mathematicians from long ago.

Not so long that they would not have known what they talked about.

Mathematics does not progress by bowing to past authorities, but by
finding sufficiently formal arguments to convince.
The opinions of the most eminent of the mathematical giants of the past
are of no account if they run counter to formal arguments.

There are no new developments that would contradict them. Except for
some present fools of matheology who have adapted the position that
the cartesian product of the countable set of finite alphabets is
uncountable.

Since "matheology" is entirely WM's invention, he is the only fool
inhabiting it.

Such an incoherent nonsense is required to spread the word.

WM's incoherent nonsense is spreading the word about WM.
It may eventually get back to that place where he tries to corrupt the
young.
.

Relevant Pages

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    (sci.logic)
  • Re: paths through binary trees in ZF
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    (sci.logic)
  • Re: paths through binary trees in ZF
    ... only countably many infinite branches through it,  thereby showing  ZF ... because I do not deny that there may be proofs showing the set of ... In fact, in any complete infinite binary tree, each node "distinguishes" ...
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