I love paradoxes. When I first found out about them, it was interesting to think that some statements are not true, nor false. They are somewhere else, like imaginary numbers. The classic paradox, is, of course:
This statement is false.
This way this paradox works is this: if the statement is true, then, do to what it states, it must be false. But, if it is false, then what it states cannot be true, and therefore, it is not false, but true. This self-controdiction extends to infinity, thus making it a paradox, neither true nor false.
So I thought that there were really three states of truth for statements: True, false, and paradoxical. That seemed to make sense: one weird, half in half, neither true nor false state. Just three states. However, I soon proved myself wrong when I discovered this little gem (of which I have titled this thread):
This statement is false if it is not a paradox.
So, what of it? It cannot be paradoxical, as if it was, then it would not be false and therefore not a paradox. In other words, it's being paradoxical prevents it from being paradoxical, just as the original paradox's being true prevented it from being true.
So this must be a new bread of paradox, for it cannot be a paradox due to what it states. It is, however, also neither true, nor false, so it must be something else. Due to the way it uses a paradox for self contradiction, I'd like to think of it as a "Multi-Layered Paradox", a paradox within a paradox. In this way, I shall term it, "Duel-Paradox". So that means that there are, at least, four states of truth for statements.
But if there are "Duel-Paradoxes", why not not "Tri-Paradoxes"? What about:
This statement is false if it is not a paradox or duel-paradox.
Would that not, then, prevent itself from being a duel-paradox for, if it is a duel-paradox, does it not preventing the original paradox, and thus, not being paradoxical, or having self-paradoxical contradiction, be false? And, if it is false, does it not create a paradox, thus creating a duel-paradox, thus creating a tri-paradox?
Of course, I could go on for ever, adding more clauses and parts to the statement, extending it forever. So wouldn't that mean that there are actually an infinite number of possibilities for the truth of any given statement, with higher and higher classes of paradox? I certainly hope so. It would be exiting indeed. Of course, I do not enjoy being wrong, so if there is a flaw in my logic, please point it out to me so I can correct my thinking.
I thank any who read all of this, and doubly so anyone who provides thoughtful feedback.
Yes, I'd imagine that a duel-paradox would be the ultimate AI destroyer. Even if it is paradox proof, it will manage to infiltrate it's logic units. ^^
This way this paradox works is this: if the statement is true, then, do to what it states, it must be false. But, if it is false, then what it states cannot be true, and therefore, it is not false, but true. This self-controdiction extends to infinity, thus making it a paradox, neither true nor false.
So I thought that there were really three states of truth for statements: True, false, and paradoxical. That seemed to make sense: one weird, half in half, neither true nor false state. Just three states. However, I soon proved myself wrong when I discovered this little gem (of which I have titled this thread):
So, what of it? It cannot be paradoxical, as if it was, then it would not be false and therefore not a paradox. In other words, it's being paradoxical prevents it from being paradoxical, just as the original paradox's being true prevented it from being true.
So this must be a new bread of paradox, for it cannot be a paradox due to what it states. It is, however, also neither true, nor false, so it must be something else. Due to the way it uses a paradox for self contradiction, I'd like to think of it as a "Multi-Layered Paradox", a paradox within a paradox. In this way, I shall term it, "Duel-Paradox". So that means that there are, at least, four states of truth for statements.
But if there are "Duel-Paradoxes", why not not "Tri-Paradoxes"? What about:
Would that not, then, prevent itself from being a duel-paradox for, if it is a duel-paradox, does it not preventing the original paradox, and thus, not being paradoxical, or having self-paradoxical contradiction, be false? And, if it is false, does it not create a paradox, thus creating a duel-paradox, thus creating a tri-paradox?
Of course, I could go on for ever, adding more clauses and parts to the statement, extending it forever. So wouldn't that mean that there are actually an infinite number of possibilities for the truth of any given statement, with higher and higher classes of paradox? I certainly hope so. It would be exiting indeed. Of course, I do not enjoy being wrong, so if there is a flaw in my logic, please point it out to me so I can correct my thinking.
I thank any who read all of this, and doubly so anyone who provides thoughtful feedback.
Yes, I'd imagine that a duel-paradox would be the ultimate AI destroyer. Even if it is paradox proof, it will manage to infiltrate it's logic units. ^^