Can Any Formal System Prove Its Own Consistency?

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Since an inconsistent system can prove its own consistency...

Say a proof for the consistency of a formal system (proved within the formal system) is known. There are two possible cases: 1. the formal system is consistent and it can be and has been proven to be, or 2. the formal system is inconsistent (i.e. contains a contradiction), thus anything is provable, hence the proof of its consistency. Is there a way to determine whether 1 or 2 is the case?

Answer:

Gödel's Incompleteness Theorem says that if a system is consistent, recursively axiomatised and...

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supernaturalgospel at Mathoverflow Mark as irrelevant Undo

Other solutions

Does the Gold medal 1st ranking system create long term problems for athletes and sports in the Olympics?

Even though the IOC isn't supposed to officially rank countries by medals starting in 1992 they have unofficially started posting the gold only system first. In other words country A wins 6 gold medals and country B wins 5 Gold and 25 Silver it doesn...

Answer:

I use the gold=3 etc. system. Here are my results for the 2008 Olympics CHN: 223 pts. USA: 220 pts....

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What is the purpose of an economy? What economic system best serves this purpose? Prove it?

Is it to make everyone as happy as possible without conflict? Or what what is the purpose of an economy? And what system of economy will best accomplish this purpose? Prove it. DEFINITIONS (src: Chambers Dictionary 12ed) state capitalism n. = Control...

Answer:

Economics is the strategy in which goods are distributed amongst a population. Socialism is most effective...

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Does economic theory prove that the free market system is best? Why?

No, economic theory proves nothing about what system is best. It simply gives ways to look at systems, and what the advantages and disadvantages of various systems will likely be. Normative decisions about what is best can only follow from one’s value...

Answer:

It's B.The best means only in terms of efficiency. It is correct that the other system will be a miscalculation...

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Anjaree at Yahoo! Answers Mark as irrelevant Undo

I need some one to prove that the solar system exists?

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Answer:

Take her out at night and point her head in the general direction of the sky - our solar system and...

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Doesn't this prove that the UK's 'First Past the Post' voting system is a joke?

Northern Irish election results 2010: Sinn Féin - 25.5% of the vote - 5 seats. DUP - 25% of the vote - 8 seats. And they wonder why Catholics in Northern Ireland feel the voting system isn't fair to them... When will the UK grow up and adopt a...

Answer:

Whilst I certainly believe our system needs an overhaul and PR seems to offer a fairer system, I have...

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Beans on Toast at Yahoo! Answers Mark as irrelevant Undo

Doesn't this prove that the UK's 'First Past the Post' voting system is a joke?

Northern Irish election results 2010: Sinn Féin - 25.5% of the vote - 5 seats. DUP - 25% of the vote - 8 seats. And they wonder why Catholics in Northern Ireland feel the voting system isn't fair to them... When will the UK grow up and adopt a...

Answer:

Completely agree - even more unfair when you consider that the Republic of Ireland has a single transferable...

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Beans on Toast at Yahoo! Answers Mark as irrelevant Undo

Prove wheter a discrete-time system is LTI (linear time-invariant)?

This is an assignment question which make me so puzzled. This question says, For the following discrete-time systems with input x(n) and output y(n), prove whether it is LTI. Show your working. y[n] = | cos ( 2π x(n) ) | Please help, many thanks!

Answer:

1) Test for linearity: The summation of the output for two different inputs should be the same as the...

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priereca at Yahoo! Answers Mark as irrelevant Undo

What should i do if i cant get my job back after i prove that i had no drugs in my system?

so today i got a random drug test supposedly failed it but have been clean for a while already it was one of those instant test results cup when i got home tested myself and i passed it .After that i went to go get a lab test so i can prove that i am...

Answer:

You have no right to demand your job back. If they choose to rehire you, great. If not, they have that...

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roger at Yahoo! Answers Mark as irrelevant Undo

Some people's questions look a little too promotional to our system? Ask.com asked to prove I am a person.

I gave an answer to a question but after pressing submit ask.com told me to type in the verification code to prove I'm not a computer. I typed in the code but it still doesn't work, it keeps on re-appearing. I typed with a space, the correct letters...

Answer:

It happened to me as well, but after I just quit it, I noticed that the question I was trying to answer...

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