

all 9 comments

[–]JoriQ 2 points3 points  (2 children)

Yes, it fails because it is self referential. Language and even logic of seems, does not handle self - reference very well.

There is a famous proof of Santa Claus that is similar.

"If this sentence is true, then Santa Claus exists" - Curry's paradox

[–]GOD_Over_Djinn 0 points1 point  (1 child)


A sentence's truth value can't depend on its own truth value. It's not so hard to see why that should be true.

[–]JoriQ 0 points1 point  (0 children)

Well, it's not quite that simple. There has been a lot of debate for centuries about what the implications of these types of sentences are.

[–]AssassinAzn 2 points3 points  (0 children)

I believe this is similar to Russell's paradox. Whenever self-reference is not properly/consistently axiomatized, it is possible to run into these situations.

[–]redxaxder 2 points3 points  (0 children)

I think your problem is Curry's paradox in disguise.

[–]LeepySham 1 point2 points  (0 children)

It does come with (2) being self-referential. I suppose this is somewhat similar to Russel's paradox, if you say that the statements are actually sets. The set for a given statement is empty if the statement is false, and non-empty if it is true. Pretend that these are the only two sets in existence:

(1) = the empty set if DrSeaFood is a billionaire, and if DrSeaFood is not a billionaire, then a non-empty set, with (1) as one of its elements. In other words, (1) contains itself if and only if DrSeaFood is not a billionaire.

(2) = the set of all sets that do not contain itself. If any given set is empty, then it must be an element of (2), since it doesn't contain itself. Thus, if either (1) or (2) are empty, then (2) is non-empty. This is analogous to the formulation in the OP.

(2) is either empty or non-empty. Assume it is empty. But then it must contain itself, and thus must be non-empty. So (2) is non-empty.

That means it must contain either (1) or (2), as we said these are the only two sets that we are considering. It can't contain itself, because that would immediately lead to a contradiction. So it has to contain (1).

Therefore, (1) must not contain itself, making DrSeaFood a billionaire. Congrats. You broke naive set theory and made some money doing it.

This formulation is a bit more confusing, but as you can see, it's pretty similar to Russel's paradox.

[–]RoflCopter4 0 points1 point  (2 children)

Genuine question, can something in math be obviously untrue if it's truth violates laws of reality? If I replace statement 1 with "2 does not equal 1" then we can see that both statements make no sense. Is this not proof enough that the logic is unsound?

[–]AssassinAzn 0 points1 point  (0 children)

How do you define this "logic?" That is the basis for much math research as shown by the Principia Mathematica. "Logic" as you and most of the world knows it is something inherent and commonly understood. In the mathematical sense, logic must be axiomatized correctly in order to produce meaningful results.

[–]BasedMathGod -1 points0 points  (0 children)

lol "laws of reality"