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I am lying!

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jknilinux:
So, how would you solve it? It seems to imply an innate problem with modus ponens* itself.

(modus ponens is a fancy way of saying "if p then q", "p", therefore "q".)

abyaly:
The paradox only arises in logical systems that allow the construction of that type of statement. So if you're working in a system that doesn't, then there is no problem.
Moonfisher suggested an example of one such: a language with no words referring to elements of the language itself. So it wouldn't have the word "sentence", "proposition" or anything along those lines, preventing the construction of self-referential statements.

The problem isn't with modus ponens, but rather that casual languages are not designed to be logically consistent. Their purpose is strictly communication.
This is why more logic reliant issues like mathematical proofs are generally not delivered in casual language.

d-EVO:
does my sig have anything to do with the beginning of this thread

easiest way to solve is to say:
 (this sentence is false) is false and forget about it.


--- Quote ---the green cloud tastes sad is ilogical
--- End quote ---

did you know that some people can taste sound and hear colour.
no jokes. the visual , taste and orditary parts of the brain are all  wired together in those people

jknilinux:
It can't be false, by definition of falsehood

btw, logic allows curry's paradox to be constructed.

Numsgil:

--- Quote from: jknilinux ---It can't be false, by definition of falsehood

btw, logic allows curry's paradox to be constructed.
--- End quote ---

Think more that it's nonsense.  Not every proof possibly constructed using logic is a valid proof.  That's all it means.  It doesn't mean that all proofs are suspect, just that a proof is only as good as the set of axioms upon which it's built.  To build a self contradicting proof, you have to start with an invalid axiom, which nullifies your whole proof before you get started.

"This sentence is false" is an invalid axiom.  If you expand it out to something like:

1.  2 is false.
2.  1 is false.

Then you have two invalid axioms.  In neither case is any logic actually applied, you're just starting with nonsense and so the trip to impossible is pretty short.  If your starting axioms are all solid, anything you derive from them is at least as solid as the axioms.  If one of your starting axioms is weak, all subsequent work with them is just as weak.

Now, if you can construct a self contradicting proof from self consistent axioms, I'll be impressed.

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