[OmegaHN]

Eh, this doesn't really explain Godel's 2nd Incompleteness theorem; it only describes it in a roundabout way. The entire piece could be shortened down to: in math, all false statements are possible (i.e. their impossibility cannot be proved), and it doesn't go into any reasoning behind it.

I'm not sure about Godel's 2nd, but his 1st theorem can be described and explained with one simple sentence: this statement cannot be proven. If it is proven, then a false statement is proven. If it cannot be proven, then the proving system is flawed.

[NHQ]

I like George Boolos' explanation because it plays with my paradoxic sensebrain, with something like poetry. Why not call it a poem?

But I like your explanations too.

However, I think that the Goedel card is counter-played well by the Schrodinger one. "This statement cannot be proven" is only a false statement because you inspect it with your system. It might otherwise be completely true.

[cwzwarich]

> However, I think that the Goedel card is counter-played well by the Schrodinger one. "This statement cannot be proven" is only a false statement because you inspect it with your system. It might otherwise be completely true.

Gödel doesn't actually rely on any argument regarding the meaning of the statement "this statement cannot be proven"; he merely uses it as inspiration for an analogous entirely formal construction.

[md224]

Ah, but "true" and "proven true" are two different things!

I'm sensing an epistemology thread developing...

[NHQ]

Not so fast!

I am taking issue with the so-called "falsity" of the "this statement is false". If you imagine that statement, and imagine that what you imagine is probable in the extreme, outside of your imagination, free, and unmolested by your probings, then "this statement is false" is always, only, incidental.

And don't come back saying saying "false" and "proven false" are different. I can compare strings!

[md224]

That's the thing though... I interpreted it as being a true statement, but one that cannot be "proven" to be true. I merely possess the strong belief that it is true.

Is your argument that the statement could possibly be false? Otherwise we're already in agreement... Nobody is suggesting the statement is false (I think).

Edit: to clarify, the statement in question is "this statement cannot be proven," not "this statement is false."

[NHQ]

You are right about the statement in question. I got mixed up, but I think the principal of "same difference" applies :D

He says, "If it [the statement] is proven, then a false statement is proven." (Proven true or false?)

I am not interpreting the statement "this statement cannot be proven" as true, as you do, or false.

What I argue is that one's interpretation has an effect, without which the statement is neither true nor false, but, as I claim, incidental. We can imagine the statement, but what we imagine is not the statement, even if it looks and smells like it.

Thus, the Schrodinger Card trumps the Goedel. The trick here is that I am standing outside of "the system", not permitting myself to enter paradox land. If you so much as look at me, I'll get sucked in.