All paradoxes are the same one
I want to convince you that every paradox you’ve ever heard is the same one, and you can understand it.
Statistical Paradoxes
Firstly, I’d like to make the argument that many things that are called a paradox aren’t actually paradoxes at all.
This category can be replaced with the phrase “extremely unlikely”. In other words, they are not logical paradoxes, but statistical ones.
For example, the Fermi Paradox states that because there are trillions of stars in our galaxy, there should be so many habitable planets that it is unbelievably unlikely that we have not spotted any signs of alien life.
This, to me, is not a true paradox. It doesn’t break math and logic itself. It’s just something that is expected, a certainty almost, that isn’t true. However, it’d be like saying winning the lottery is a paradox because it’s unlikely.
It’s not a paradox. It’s statistically improbable.
Logical Paradoxes
A logical paradox is something that seems to break the logical system of the universe. It is something that seems incompatible with truth itself.
The most famous example of this is:
Both sentences seem to conflict with each other in a way where no matter how you try to make sense of it, it’s always incorrect. This is a logical paradox. It seems to break down reality. or something.
Self Reference
Yep, a paradox is just an infinite self-reference.
You can’t create a logical paradox without somehow incorporating a recursive loop.
Lets revisit the paradox above and see that all it’s doing is going in an endless loop. The first sentence references the second, which then references the first, which references the second, and so on - into infinity.
We can explain every paradox in 4 steps.
- statement
- negation
- negative statement
- double negation
Paradoxes are mind bending not because of some logical breakdown, but because it’s infinity showing it’s face again and our brains not being able to comprehend it, as usual.
What’s an easy way to create infinity? make a circle. You can loop around forever. This is the fundamental trick of a good paradox.
We can understand 4 though. So next time you hear a paradox, see if you can find the loop.
The Self-Reference Paradox is so fundamental it’s at the root of reality. The The Consciousness Paradox and the Duality Paradox seem to make up experience itself.