This sentence is neither true nor a paradox.

So what is it?

false

If it is false, then it must either be true or a paradox.

false

It is a paradox.

If it is a paradox, then it must be false.

hrm

Ok, right, I agree.

No, I disagree. If it is a paradox it is false, if it is false it is true or a paradox. If it is true or a paradox that makes it false.

Thus this is a paradox.

But you just said if it is a paradox, then it must be false.

Is it both false and a paradox at the same time?

Being false and a paradox at the same time sounds like a paradox to me.

I suppose, being false and being a paradox are not mutually exclusive might be a good supporting statement.

Its a paradox and its false

That is the same conclusion I came to. It was not quite what I was expecting.

Oh. Detmer just said that.

If you say it's not a paradox, and it is, then it is a lie and therefore false, while being a paradox at the same time.

I realize I'm basically restating what Detmer said, but this is also to help me clear it up in my own head.

EDIT: Oh, good, I'm not the only late responder.

If its a paradox, then the part about the sentence not being true is true, which means its false, etc. etc.

Did you devise this on your own? A quick google search does not turn up this question.

I am going to bed now but I will probably lay in bed thinking about it for a while ;)

I did come up with it on my own, but it is so incredibly simple that I would be foolish to claim to be the first to have come up with it on their own.

Its Confused!

I never assume I am the first to think of anything, but I consider a thought to be effectively novel if I came up with it on my own.

I've been reading the book by Ernest Nagel and James Newman about Gödel's Proof, and my facebook status last weekend was "If I was an evil math teacher, I would put "This sentence is a lie." on a true-false test."

I "finished" the book today, but I will need to reread the 2nd to last chapter of the book a bunch of times to better understand it. I followed most of the book pretty easily, but the 2nd to last chapter of the book where they actually discuss his proof is something I could not comprehend my first time through.

But the book has had me thinking about the idea of consistency, which is why I tried tonight to come up with a statement that if it was a paradox implied it was not a paradox.

Get a life

We're playing a text-based game based mostly on mathematics and perfect timing. I think "get a life" is wasted on us.

rofl

This is why I've stuck around for 14 yrs,

Not many communites have this type of material on a regular basis.

After thinking about it some more, and talking with my dad (who has a phd in math), we concluded that this really depended on how one defines a paradox. The definition my dad and I were most comfortable with is that a statement p is a paradox means "p iff p". Or in less mathematical terms, a statement is a paradox if the statement implies its negation and the negation implies the statement. Additionally, a statement being a paradox is not enough to indicate that a statement is either true or not true, or is false or not false.

Since this definition does not indicate that a paradox cannot also be true at the same time, or cannot also be false at the same time, then it is possible that a statement could meet one of those criteria.

The sentence "This sentence is neither true nor a paradox. " is therefore both false and a paradox.
Similarly, the sentence "This sentence is either false or is a paradox." is therefore both true and a paradox.

This sentence is neither true nor a paradox
is equivalent to
(This sentence is not true) and (this sentence is not a paradox)
This sentence is not true = paradox, thus
This sentence is a paradox and this sentence is not a paradox
:D

Which... is a paradox in itself... I really should stay out of threads I don't understand, I have no excuse.

for the record and after a long drawn out conversation with gnome, my answer is "paradox". it cannot be both a paradox and false at the same time, and being a paradox doesn't imply falsity either.

i can't be bothered to explain myself again. damn j00 gnome for eating up my sleep.

this has nothing to do with mathematics.