Eliezer writes: “But in any case, Godel’s Theorem surely does not show that natural numbers don’t exist. It says you’ll have trouble proving certain theorems. The observed universe is like the natural numbers, not like a theorem about them.”
I think whether Godels Theorem applies or not depends on how we define “understanding reality”. A lot of people would interprete it as not only being able to theoretically predict the state of the universe at any given time (ignoring the pratical issues of course!), but being able to determine stuff like what can exist. Answering these types of questions requires much more complicated logic and could quite possibly be non-computatable.
Eliezer writes: “But in any case, Godel’s Theorem surely does not show that natural numbers don’t exist. It says you’ll have trouble proving certain theorems. The observed universe is like the natural numbers, not like a theorem about them.”
I think whether Godels Theorem applies or not depends on how we define “understanding reality”. A lot of people would interprete it as not only being able to theoretically predict the state of the universe at any given time (ignoring the pratical issues of course!), but being able to determine stuff like what can exist. Answering these types of questions requires much more complicated logic and could quite possibly be non-computatable.