Are impredicative statements and axiom reducibility invalid

[das]

simple yes or no

 

ramsey say the axiom of reducibility

Such an axiom has no place in mathematics

 

and anything which cannot be

proved without using it cannot be regarded as proved at all

 

 

is he right or wrong

russell wittgenstien and others say the axiom id invalid

are they right or wrong

 

 

Poncicare Russell and philosophers say impredicative statements are invalid

 

'Whatever involves all of a collection must not be one of the collection.'

Put otherwise, if to define a collection of objects one must use the total

collection itself, then the definition is meaningless. This explanation

given by Russell in 1905 was accepted by Poincare' in 1906, who coined the

term impredicative definition, (Kline's "Mathematics: The Loss of

Certainty"

 

are they right or wrong

[Mr Skeptic]

Mathematicians are never "right" and "wrong" in the same sense as scientists. Mathematicians do not need to conform to the real world, only to the logical world. They may take as axioms whatever they wish, so long as they are not contradictory. Hence, to show that a set of axioms is wrong, you must show that they lead to a contradiction -- not that they don't conform to the real world.

[das]

Mathematicians are never "right" and "wrong" in the same sense as scientists. Mathematicians do not need to conform to the real world, only to the logical world. They may take as axioms whatever they wish, so long as they are not contradictory. Hence, to show that a set of axioms is wrong, you must show that they lead to a contradiction -- not that they don't conform to the real world.

 

i asked for a simple yes or no-is that so hard

are those mathematician right or wrong when they say ar IMPREDICATIVE STATEMENTS ARE INVLAID

IS A YES OR NO SO HARD

[insane_alien]

a yes or no answer is hard when the answer is neither yes nor no.

 

not everything exists in a boolean state.

[das]

a yes or no answer is hard when the answer is neither yes nor no.

is ramsey right when he says axiom of reducibility has no place in mathematics

 

a yes or no answer is hard when the answer is neither yes nor no.

 

are ponicare russell and philosophers right in saying impredicative statements are invalid

[Mr Skeptic]

Impredicative statements that do not lead to a contradiction are perfectly valid. Since it is unlikely that all impredicative statements lead to a contradiction, I would say that it is likely that some impredicative statements are valid.

 

The axiom of reducibility is perfectly valid if it does not lead to a contradiction.

 

You ask hard questions. Some yes or no questions remain unsolved for thousands of years, and some are unsolvable.

[das]

Impredicative statements that do not lead to a contradiction are perfectly valid. Since it is unlikely that all impredicative statements lead to a contradiction, I would say that it is likely that some impredicative statements are valid.

 

The axiom of reducibility is perfectly valid if it does not lead to a contradiction.

 

simple question

is ramsey et al right in saying AR is invalid

are ponicare russell etal right in saying impredicative statements are invalid

they are either right or wrong -which is it-simple question

[Mr Skeptic]

If it is so simple, why don't you answer it yourself?

[das]

If it is so simple, why don't you answer it yourself?

why are you reluctant to say ramsey russell ponicare and philosophers are wrong

[Mr Skeptic]

why are you reluctant to say ramsey russell ponicare and philosophers are wrong

 

Because I can't prove it.

[das]

Because I can't prove it.

 

then are they right

[insane_alien]

then are they right

 

but you can't prove that either.

[das]

then why do you argue dean is wrong when he says godels theorems are invalid because he uses invalid axioms and statements based on the testimony of ramsey russell ponicare and philosophers

[uncool]

So long as a series of axioms aren't self-contradictory, they can't automatically be considered wrong. The reason we don't say Godel was wrong is the same reason as the reason we don't say Ramsey was wrong.

 

Once again, find the contradiction in the proof - find the line where the proof goes wrong - and people will believe you. Not before, not after.

=Uncool-

[das]

So long as a series of axioms aren't self-contradictory, they can't automatically be considered wrong. The reason we don't say Godel was wrong is the same reason as the reason we don't say Ramsey was wrong.

 

if you cant say ramsey is right or wrong

you cant say dean is wrong when he uses ramsey to show godel s invalid

[Reaper]

You guys are such horrible philosophers.

 

Godel's theorem is a mathematical statement, which has so far been proven to be consistent.

 

It does NOT say that "you can't prove anything"; rather, Godel's first theorem says that it is possible to construct a true statement that is consistent, but not provable in theory. By theory, I mean axioms.

 

What that basically means is that in any branch in mathematics, there lies statements that are true, or false, but cannot be proven with basic axioms or with first order logic.

 

You can read more about it right here:

 

http://en.wikipedia.org/wiki/Incompleteness_theorem

 

or

 

http://www.miskatonic.org/godel.html

 

===================================

 

The theorems themselves have not been proven false. Also, there are actual practical applications for them, such as in computer programming.

[das]

You guys are such horrible philosophers.

 

godel uses impredicative statements which philosophers say are invalid thus as dean points out godels theorems are invalid

 

it is no uses giving us the standard view as dean overthrows it

if you cant say ramsey is right or wrong

you cant say dean is wrong when he uses ramsey to show godel s invalid

[the tree]

Why are you desperate for Gödel to be right or wrong?

 

His theorem leads correctly from the given axioms, which are fine since they don't lead to contradiction, that is all.

[bascule]

His theorem leads correctly from the given axioms, which are fine since they don't lead to contradiction, that is all.

 

Exactly.

 

das, post a proof in the form of predicate calculus which follows from Godel's theorems which leads to a contradiction

 

Seriously, put up or SHUT THE F*CK UP

 

Admins, can you please ban this bullshit-spouting linkspamming troll?

[ecoli]

done and done