Emerald paradox tiers

Emerald paradox tiers is a way to categorize paradoxes, created by user:tommyaweosme.

Tier 1 paradox

A tier 1 paradox would be the following statement:

This statement is false

Let us use a method for figuring out the tier of a paradox.

First, we assume the statement is true. That means that it is true that the statement is false.

So, let us assume it is false. That means it is false that the statement is false, meaning it is true.

Therefore, if it can neither be true nor false, it is a tier 1 paradox.

Tier 2 paradox

But what about a statement like this?

This statement is false OR a tier 1 paradox.

OR represents the OR gate, which only outputs false if both inputs are false.

If it is true, then it is neither false nor a tier 1 paradox (as it is true), so it returns false.

That means it must be false, but it is false, so it returns true.

That means it must be a tier 1 paradox, but that means it is a tier 1 paradox, so that would make it true, and therefore no longer a tier 1 paradox.

Thus, the only thing we can conclude is that it is a tier 2 paradox.

Tier 3 paradox

A tier 3 paradox is neither a tier 1 nor a paradox 2 paradox.

This statement is false OR a tier 1 paradox OR a tier 2 paradox.

This statement forces itself to be a tier 3 paradox.

What about this statement?

This statement is false OR a tier 1 paradox OR a tier 2 paradox OR a tier 3 paradox.

This is still a tier 3 paradox. Any statement that is not true, false, a tier 1 paradox, nor a tier 2 paradox, has to be a tier 3 paradox. Attempting to make it impossible to be a tier 3 paradox is invalid.

Esolangs that use this concept

None yet.