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Comment by gizmo686 | Hacker News Reader

Is this article meant to be a joke?

He goes from the statement "For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent." To "all basic claims are more or less false." If we could actually prove that all claims were false, we would be in violation of the Incompletness theorum.

Not to mention the absurtidy of his conclusion. Proving a statement for a set of values you thought of is far more likely to be wrong than proving it with formal mathamatics.

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> Gödel's 1931 Second Incompleteness Theorem insists that it is strictly forbidden to ever claim the truth of any scientific or mathematical statement

That is grossly wrong interpretation of the theorem. I stopped reading the article right there.

It gets even worse. I can't tell if this guy is pulling my leg, or if he's just a crank.

Why don't you write a program to show that a particular statement in my article would be wrong?

Your article constains no assert statement, therefore, according to itself, it is false.

I like your attempt. At least, it is meaningful. Only the domain of statements about facts can be verified with facts. The domain of statements about statements cannot. You have indeed correctly underlined that the rules governing scientific statements -- statements about statements -- cannot be scientific themselves.

>Not to mention the absurtidy of his conclusion. Proving a statement for a set of values you thought of is far more likely to be wrong than proving it with formal mathamatics.

This, if the program did fail all that's been proven is that that particular delta-epsilon function, the defeatEpsilon here, doesn't work. In order to prove that the function doesn't converge you have to prove there is no function which can satisfy the conditions.

(Luckily there are some theorems which make it so one only have to prove that two different sequences of the function converge to different values. But that's getting into Real Analysis which is a whole semester worth of explanations.)

> This, if the program did fail all that's been proven is that that particular delta-epsilon function, the defeatEpsilon here, doesn't work.

It would prove that such epsilon exists. That counterexample should be enough to reject the claim itself.

It only disproves that the particular delta-epsilon function works though. That just proves that the proof writer wasn't clever enough to find a working d-e, not that there isn't a d-e.

Well, if there is such d-e, the person challenging the reduction should be able to supply it. Since it just a number, he should be able to supply that number to the program and trigger a failure.

Our inability to disprove a statement does not mean that the statement is true.

If the program fails, it only proves that the chosen defeatEpsilon proof does not work. In order to prove that that their is no defeatEpsilon, you would need to run you program against every function of the Real->Real. If your delta epsilon did work, you would need to test in for every delta>0.

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