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Re: Matheology � 060
Posted:
Jul 6, 2012 11:42 PM
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Virgil wrote:
> In article
> <8164eb33-af5b-48ac-9e5e-518dc9991d75@w24g2000vby.googlegroups.com>,
> WM <mueckenh@rz.fh-augsburg.de> wrote:
>
>> The cardinal contradiction is simply this: Cantor has a proof that
>> there is no greatest cardinal, and yet there are properties (such as
>> "x = x") which belong to all entities. Hence the cardinal number of
>> entities having a property must be the greatest of cardinal numbers.
>> Hence a contradiction [1, p. 31]
>
> Over a century has passed since Russell wrote that, and that apparent
> contradiction has been resolved
>>
>> An existent class is a class having at least one member. [1, p. 47]
>> {{Surely you are joking Mr. Russell? The class without any member is
>> not among the existent classes?}}
>
> In the century since Russell wrote that, the empty set has been
> discovered.
>
>>
>> Whether it is possible to rescue more of Cantor's work must probably
>> remain doubtful until the fundamental logical notions employed are
>> more thoroughly understood. And whether, in particular, Zermelo's
>> axiom {{of choice}} is true or false {{I am shocked! An axiom could be
>> true or false in your age, Mr. Russell? Mathematicians in fact tried
>> to find truth and meaning in mathematics?}}
Everybody except of course Mückenheim knows that Russell's stance concerning
foundations of mathematics was logicism; and with a little background
knowledge about this philosophy it is quite clear what he means and why he
must be concerned about the truth of that axiom in the above quotation.
Without such background one simply can not understand it. Mückenheim is too
stupid for this subject in any respect. He is even too stupid to imagine
that e.g. Cantor's speech habits might be different from those of today, not
even if he is told so for no less than 8 years. He can just cull quotations
from wherever he finds them and have a kind of feeling whether he likes what
he reads or not. But he can't understand anything, and he can't understand
that he can't understand and so on ad infinitum. Usually idiots stop short
at the second (those who at least know that they don't know much) or third
(those exhibiting the Dunning-Kruger effect) round of this but Mückenheim's
idiocy has infinite deepness and thereby proofs the existence of actual
infinity.
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