Thing of the Day #96: Recursive Metaphysics

Today’s letter:

Dear Thing of the Day,

Is the world made of math?

- Joey

It’s actually much weirder than that Joey.

Here’s a paradox from The Road to Reality by mathematical physicist Roger Penrose:

All physical laws are described by equations, but not all equations are physical laws. Therefore physics is a proper subset of mathematics

Mathematics is just chains of precise formalised thoughts, but not all thoughts are mathematical. Therefore mathematics is a subset of thoughts

All thoughts are computed via physical brains or computers, but not all physical processes result in thoughts. Therefore thoughts are a proper subset of physics

So:

• Physics is a proper subset of the mathematics

• Mathematics is a proper subset of thoughts

• Thoughts are a proper subset of physics

Which is logically impossible.