logic of the Cantorian followers mind

herc777_at_hotmail.com
Date: 11/22/04 

Date: 22 Nov 2004 13:40:46 -0800

David Petry Subject: Cantor's Theory: Mathematical creationism

Cantor's theory (classical set theory) has the same relationship to
the mathematical sciences as Creationism theory has to the physical
sciences. They are similar in content and similar in origin. Cantor's
theory is essentially a creation myth.

Both Cantor's theory and Creationism theory are founded on the
proposition that we must acknowledge the existence of some abstract
infinite entity lying beyond what we can observe in order to understand
the reality that we do observe.

- - - - - - - - - - - - - - - - - - - - - - - - - -

I cofounded this theory just a couple of days ago. The reason I am
having a problem debunking Cantor is because it is faith based. They
invent an INVISIBLE, imaginary entitiy which is impossible to disprove
no matter what is your substance.

This is the reasoning behind Cantor supporters.

4894389..
4389439..
4378498..
4894894..
..
Diag0 is 4374..
Diag1 is 5485..

Intuitively this is a new sequence, but that is not a *property* of the
number, its merely DEFINED AS DIFFERENT.

P = "Diag1 <> Real1 and Diag1 <> Real2 and Diag1 <> Real3 ..."

P is not a result of the proof, its the *definition* of Diag1 just in
propositional form, but its a poor definition.

What is obviously wrong is that A = "All sequences of digits are
computable, and already present on the list of computable reals".

Although A intuitively disproves P, Cantor followers use R, rebutal to
the argument A

R = "the set 0.1, 0.2, 0.3...0.9, 0.01, 0.02, 0.03... also contains
every sequence of digits, but using strictness analysis it does not
contain any irrationals as all numbers have finite length".

P -> C (Cantors proof, there are uncountable numbers)

A -> !P (All sequences are computable, so Cantors premise of a new
sequence is flawed)

R -> !(A -> !C) (Listing all sequences of digits does not imply you
contain all reals)

They skip over the fact P is disproven, A seems to be debunked just
because sets of rationals that contain all sequences are incomplete.

This is why A still holds:
------------------------------------------------------------
An infinite number of people each toss a coin infinite times, can you
guarantee a new sequence of heads and tails?
------------------------------------------------------------

The answer is clearly no, you cannot come up with something new that
infinite people have done before. Cantor supporters should try to
answer this question.

Herc

Relevant Pages

  • Re: logic of the Cantorian followers mind
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  • Re: logic of the Cantorian followers mind
    ... > the mathematical sciences as Creationism theory has to the physical ... > infinite entity lying beyond what we can observe in order to understand ... I thought you said it was a sequence, ... This is clear by Cantors diagonal argument. ...
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