February 18, 2021

The True & False Paradox

Consider the following statement:

My name is Rick.

If I say this statement is not false, is must be true, because not false = true. And yes, I’m Rick.

Another statement:

I’m older than 18.

If I say that statement is not true, it must be false, because not true = false. And again, it works. I’m 17.

Easy, right?

Now, consider this statement:

This statement is false.

We can apply the logic above to draw the following conclusion:

  • If the statement were true, we would have a contradiction, hence it is not true. Therefore, it must be false.

  • If the statement were false, we would also have a contradiction, hence it is not false. Therefore, it must be true.

Using the exact same, easy not logic, we get two different answers. This shouldn’t be possible. Because the statement is neither true nor false, we can’t say not true or not false.

But why can we apply that exact same logic to “I’m older than 18”? Perhaps that statement is also not true nor false. We simply don’t know. Maybe I’m $i$ (the imaginary number) years old.

Final question: Does this have anything to do with Schrödinger’s cat thought experiment?

If you know the answer to this mind breaking thought, please let me know.

Thanks for reading

I hope this post was useful to you. If you have any questions or comments, feel free to reach out on Twitter or email me directly at rick_wierenga [at] icloud [dot] com.