Mathematicians are in deep trouble for 2 reasons

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pam69ur
 
Reply Thu 22 May, 2008 05:31 pm
@VideCorSpoon,
Quote:
Wow... that you have been able to take Ctrl-C, Ctrl-V to such an extent that it is mind boggling. Kudos.

Since you are inextricably familiar with Godel and logic in particular... I'm just curious, can you solve this?

(∃x) (Gx) --> (y) (Gy --> Jy) / (x) (Gx --> Jx)


(There are only eight steps, so its not too much trouble as long as you are familiar with the material. It's kinda like calling your bluff, so lets see what cards you have.)

Do it as the Australian philosopher Colin Leslie Dean would have, may his infinite wisdom grace our lowly existence!!!!



hey all i need to know is that godel tells us he uses system P in his proof and that system has the axiom of reducibility
as the uni of california maths department tell us

Quote:
http://www.math.ucla.edu/~asl/bsl/1302/1302-001.ps.



"The system P of footnote 48a is Godel's
streamlined version of Russell's theory of types built on the natural
numbers as individuals, the system used in [1931]. The last sentence ofthe footnote allstomindtheotherreferencetosettheoryinthatpaper;
KurtGodel[1931,p. 178] wrote of his comprehension axiom IV, foreshadowing
his approach to set theory, "This axiom plays the role of [Russell's]
axiom of reducibility (the comprehension axiom of set theory)."



Quote:
In the proof of Proposition VI the only properties of the system P employed were the following:
1. The class of axioms and the rules of inference (i.e. the relation "immediate consequence of") are recursively definable (as soon as the basic signs are replaced in any fashion by natural numbers).
2. Every recursive relation is definable in the system P (in the sense of Proposition V).
Hence in every formal system that satisfies assumptions 1 and 2 and is ω-consistent, undecidable propositions exist of the form (x) F(x), where F is a recursively defined property of natural numbers, and so too in every extension of such
 
VideCorSpoon
 
Reply Thu 22 May, 2008 06:59 pm
@pam69ur,
The Three Refutations of Pam69ur

First of all, diction and proper syntax is essential to a coherent response.
You say, "hey all i need to know is that godel tells us he uses system P in his proof and that system has the axiom of reducibility as the uni of california maths department tell us" (Pam69ur)

A somewhat proper English composition would say, "Hey, all I need to know is this. Godel tells us he uses System P in his proof and further that that particular system incorporates the axiom of reducibility as the university of California Math department tells us.

That much had to be said. I'm sorry, but for someone who proclaims an intimate understanding of abstract logical ideas, you cannot formulate a proper sentence for the life of you.

Second, you don't know quantifier logic, and I would suspect propositional logic for that matter. That bluff I called and which was justified was ridiculously easy to solve if you knew the foundation on which any of the theories you have quoted. How can you presume to provide your own comment if you cannot even read the basic structure of the argument.

Copying and pasting with VERY spotty logic to say the least is absurd. You know, if you wanted to B.S. a subject, you could have picked something you could at least minimally comprehend in a technical way.

Thirdly, you do not respond to the question and I suspect cannot respond to the question. That much is clear. Also, you support your weak comment by referring to the University of California as a source itself? Even if a university did all of the sudden retain intelligence, you don't even state which university of California it came from.

But maybe you are in earnest. I'll tell you what. I'll give you the rest of the formula, and I'll leave out one citation that can be solved with propositional logic.

1.(∃x) (Gx) --> (y) (Gy --> Jy) / (x) (Gx --> Jx)
2._|__Gu_________Assumed Premises
3._|__(∃x)Gx______Existential Genralization 2
4._|__(y)(Gy-->Jy)__Modus Ponens 1,3
5._|__Gu-->Ju_____Universal Instantiation 4
6._|__Ju__________ [insert citation here] 2,5
7.Gu-->Ju_________Conditional Proof
8.(x)(Gx-->Jx)______Universal Generalization 7

Let the power of the Australian Philosopher Colin Leslie Dean flow through you. Let it fill your soul with courage as Colin Leslie Dean had when he fought twelve grizzly bears with a toothbrush and the sheer actualization of wisdom as Colin Leslie Dean had done when he need only stare at a book for a fraction of a second to get his answers. For Colin Leslie Dean has the power within him to completely reject the periodic table of elements and accept only one element, the element of surprise.
 
pam69ur
 
Reply Thu 22 May, 2008 07:18 pm
@VideCorSpoon,
Quote:
Let the power of the Australian Philosopher Colin Leslie Dean flow through you. Let it fill your soul with courage as Colin Leslie Dean had when he fought twelve grizzly bears with a toothbrush and the sheer actualization of wisdom as Colin Leslie Dean had done when he need only stare at a book for a fraction of a second to get his answers. For Colin Leslie Dean has the power within him to completely reject the periodic table of elements and accept only one element, the element of surprise.


hey i luv deans book
it shows
you dont need a phd in maths to prove one of the greatest maths proofs is rubbish
he shows any moron who can read could see it is rubbish
can you read
or are you blinded by propositional logic

Quote:
In the proof of Proposition VI the only properties of the system P employed were the following:
1. The class of axioms and the rules of inference (i.e. the relation "immediate consequence of") are recursively definable (as soon as the basic signs are replaced in any fashion by natural numbers).
2. Every recursive relation is definable in the system P (in the sense of Proposition V).
Hence in every formal system that satisfies assumptions 1 and 2 and is ω-consistent, undecidable propositions exist of the form (x) F(x), where F is a recursively defined property of natural numbers, and so too in every extension of such


and system P uses the invalid axiom of reducibility
as godel tells you
axiom 1v of system P

Quote:
IV. Every formula derived from the schema
1. (∃u)(v ∀ (u(v) ≡ a))
on substituting for v or u any variables of types n or n + 1 respectively, and for a a formula which does not contain u free. This axiom represents the axiom of reducibility
 
VideCorSpoon
 
Reply Thu 22 May, 2008 07:57 pm
@pam69ur,
So in so many words... you don't know logic and are incapable of answering a single query. Thanks, thats all I needed to know.
 
Aedes
 
Reply Thu 22 May, 2008 08:26 pm
@pam69ur,
pam69ur wrote:
hey i luv deans book
it shows
you dont need a phd in maths to prove one of the greatest maths proofs is rubbish
he shows any moron who can read could see it is rubbish
can you read
or are you blinded by propositional logic
I think enough has been said here. Everyone, including the original poster, has made his point of view abundantly clear. Let's leave it at that, because I don't think any more good is going to come of this.
 
 

 
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