ZFC is is proven to be inconsistent

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pam69ur
 
Reply Fri 13 Jun, 2008 07:19 pm
Nocture asked in a thread

Quote:
If you want to argue that ZFC, or any other formal language is inconsistent then I am all ears


the australian philosopher colin ****** dean points out that
the skolem paradox shows ZFC is inconsistent

Skolem's paradox - Wikipedia, the free encyclopedia

Quote:
set theory which only contains a countable number of objects. However, it must contain the aforementioned uncountable sets, which appears to be a contradiction


note it say set theory ie ZFC is has a contradiction-which means it is inconsistent

mathematicians at the time agreed it was an antinomy-contradiction
even Abraham Fraenkel) said so

Skolem's paradox - Wikipedia, the free encyclopedia

Quote:
Neither have the books yet been closed on the antinomy, nor has agreement on its significance and possible solution yet been reached." - (Abraham Fraenkel)

now you will all just say only APPEARS

this only appears is based on skolem attempted solution of the paradox
mathematicians don not accept his solution as it guts set theory

Peter Suber, "The Lwenheim-Skolem Theorem"

Quote:
For many, this view guts set theory, arithmetic, and analysis. It is also clearly incompatible with mathematical Platonism which holds that the real numbers exist, and are really uncountable, independently of what can be proved about them.


YOU MUST NOTE THAT THE WIKI ENTRY HAS BEEN CHANGED TO NOT SHOW THAT SKOLEM PARADOX IS AN INCONSISTENCY IN zfc
THE ARTICLE I SAW HAD MANY QUOTES FROM SUBERS ARTICLE SHOWING THIS BUT ALL HAS BEEN DELETED

THE EDITORS SAYS
Talk:Skolem's paradox - Wikipedia, the free encyclopedia

Quote:
I am a mathematician but not an expert in the subfield of math logic. However I find the edits promoting the work of one "Peter Suber" extremely suspicious. He appears to be an expert in legal and philosophical matters, but as far as I can see has no credentials in mathematical logic. I am reverting his edits until he presents proof that his course notes are authoritative.--98.224.223.201 (talk) 19:06, 19 May 2008 (UTC)


subers course nores are from Philosophy Department, Earlham College
http://www.earlham.edu/~peters/courses/logsys/low-skol.htm

this deletion is a prime example of ideas that dont sit well will orthodoxy being censored




NOW


even skolem said his attempted solution destroyed set theory

Skolem's paradox - Wikipedia, the free encyclopedia

Quote:
I believed that it was so clear that axiomatization in terms of sets was not a satisfactory ultimate foundation of mathematics that mathematicians would, for the most part, not be very much concerned with it. But in recent times I have seen to my surprise that so many mathematicians think that these axioms of set theory provide the ideal foundation for mathematics; therefore it seemed to me that the time had come for a critique



suber notes

Quote:
Insofar as this is a paradox it is called Skolem's paradox. It is at least a paradox in the ancient sense: an astonishing and implausible result


further


Quote:
One reading of LST holds that it proves that the cardinality of the real numbers is the same as the cardinality of the rationals, namely, countable. (The two kinds of number could still differ in other ways, just as the naturals and rationals do despite their equal cardinality.) On this reading, the Skolem paradox would create a serious contradiction, for we have Cantor's proof, whose premises and reasoning are at least as strong as those for LST, that the set of reals has a greater cardinality than the set of rationals.



Quote:
If the intended model of a first-order theory has a cardinality of http://www.earlham.edu/%7Epeters/writing/aleph.gif1, then we have to put up with its "shadow" model with a cardinality of http://www.earlham.edu/%7Epeters/writing/aleph.gif0. But it could be worse. These are only two cardinalities. The range of the ambiguity from this point of view is narrow. Let us say that degree of non-categoricity is 2, since there are only 2 different cardinalities involved.
But it is worse. A variation of LST called the "downward" LST proves that if a first-order theory has a model of any transfinite cardinality, x, then it also has a model of every transfinite cardinal y, when y > x. Since there are infinitely many infinite cardinalities, this means there are first-order theories with arbitrarily many LST shadow models. The degree of non-categoricity can be any countable number.
There is one more blow. A variation of LST called the "upward" LST proves that if a first-order theory has a model of any infinite cardinality, then it has models of any arbitrary infinite cardinality, hence every infinite cardinality. The degree of non-categoricity can be any infinite number.
A variation of upward LST has been proved for first-order theories with identity: if such a theory has a "normal" model of any infinite cardinality, then it has normal models of any, hence every, infinite cardinality.
 
Professer Frost
 
Reply Fri 13 Jun, 2008 10:03 pm
@pam69ur,
Dear Pam69ur,
Perhaps you should introduce people to the basics of Colin Dean's philosophy before you start making assumptions. Then perhaps we could all have an interesting talk about the basis in (non-Aristotelian) logic for his overall world picture. That would certainly be much more edifying than debating what is essentially (I think) a minor point in that picture and serves merely to illustrate more important points.
Thank you for your attention,
Professor Frost
 
pam69ur
 
Reply Sat 14 Jun, 2008 05:38 am
@Professer Frost,
Quote:
Dear Pam69ur,
Perhaps you should introduce people to the basics of Colin Dean's philosophy before you start making assumptions. Then perhaps we could all have an interesting talk about the basis in (non-Aristotelian) logic for his overall world picture. That would certainly be much more edifying than debating what is essentially (I think) a minor point in that picture and serves merely to illustrate more important points.
Thank you for your attention,
Professor Frost


what do you mean Professor Frost have I got the views of dean wrong if I have please let me and the forum know what deans views are then
i am always ready to be corrected i welcome you enlightenment on this subject

you say i debate minor points of deans view and not the major ones
please inform me where i am mistaken:confused:
 
Professer Frost
 
Reply Sat 14 Jun, 2008 12:32 pm
@pam69ur,
I'm guessing (and if this guess is wrong I'll silence myself) that Dean is using this particular mathematical problem to illustrate his point about all views arrived at via Aristotelian logic being meaningless, and if so wouldn't it be better to talk about his basic idea of contentless thought ?
Your friend,
The confused Professor Frost
Edit: I see Pam69ur has been banned so have no fears about this two-star discussion continuing. Go some place else people, there's nothing to see here.
 
Justin
 
Reply Mon 16 Jun, 2008 12:23 pm
@Professer Frost,
Pam69ur was banned for several reasons. 1 is talking in the third person. He is Colin Dean. Second is spamming the forum by starting threads with Colin Dean keywords and that's all he talks about and was asked politely not to start new threads but continued.

I'm not exactly sure of the objective of this individual but based on searches on the Internet, he is trying to build himself as a respected philosophy by spamming forums on the Internet. Never really claiming ownership for his ideas or his work but speaking in the third person.
 
Professer Frost
 
Reply Mon 16 Jun, 2008 12:27 pm
@Justin,
How can you be certain he is Dean?
 
Justin
 
Reply Mon 16 Jun, 2008 12:32 pm
@Professer Frost,
Not exactly certain but in our PM exchange he never denied my assertion. Based on his IP address, he claimed he was in Canada when in fact he was logging into the forum from Australia. So, I believe he is Dean. Either way, he is banned.
 
Professer Frost
 
Reply Mon 16 Jun, 2008 12:52 pm
@Professer Frost,
 
 

 
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