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I am lying!

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jknilinux:
Hi everyone,

This is a problem I've been working on a bit recently, and I'm starting to give up.
Has anyone here ever heard of the liar paradox? Basically, it states:

This sentence is false.

The problem is; is it true or is it false? And this isn't just a word problem- it's a problem with logic itself. Godel proved arithmetic must be incomplete or inconsistent using an arithmetic version of this. Unfortunately, there is a predicate-logic based version of this too:

P: "P is false"

The statement P can not fit into either the set of all true things or the set of all false things... Does this mean logic is incomplete or inconsistent as well?

Post any solutions, like modifications to logic, new truth values, or anything else you come up with to solve it here.



EDIT:
Just found another interesting paradox:

P: "P => Q"

If it's false, then the conditional evaluates to true, so what P means is true, so P is true. If P is true, then what P means must be true, which is that P implies Q, so since P is true and P => Q, then Q is true...

But what is Q? Well, Q is anything! God exists, God does not exist, you don't exist, you are an invisible pink unicorn... anything.

Anyway, if you don't understand the logic behind the liar or my new invented one, let me know.

Peter:
Hmm, this reminds me of botsareus.....

Well, to keep it short what is your logic. I know the liar paradox.
As in,
The next sentance is wrong. The earlier sentance is right.

The rest just seems random-rambling. I lost you when you started at P: "P is false"

Jez:
Isn't that like where you have the options I, O, or I and O? Quantum computers or something.

I mean you have a statement and you have an answer to a statement and because it is not working the model can be considered to be wrong or the way of looking at the model can be considered to be wrong.

And the statement exits, it makes sense, I don't see why the statement is wrong.
Its only when I try to apply the rules of logic, as I know them, to the statement that I run into problems.

So maybe the rules of logic are not sufficient to deal with the problem and they need expanding.

Or maybe the logic is ok and you just need to look at it through 4 dimensional space. Although you might consider it only a two dimensional question.

I suggest you change the rules until the statement works...

Peter:
Jez, are you checking out what changed. There is a new F3. A plan for a new complex behaviour league, and eric seems to be away for a few weeks(not sure why)

Numsgil:
All it basically means is that not everything that can be expressed is possible.  Language is so descriptive that it can be used to describe things which cannot be true.

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