This is a lot of ground to cover to get to what is, in my opinion, a very bizarre conclusion which is epistemologically extremely lugubrious: that all structures expressible mathematically also exist and we are (obviously) a subset of those structures.
Frankly, this doesn't even feel like any kind of knowledge to me. Its operationally meaningless! In any case, I think the author has the cart before the horse: numbers (and other sorts of mathematics) do not pre-exist reality. Numbers are abstractions of regularities we see in nature.
Mathematics is nothing but the observation of regularities in certain sorts of elaborate rituals involving making markings on paper. Many of those rituals are inspired by and correlated with regularities which exist in the world, but its difficult to me to see any reason to believe that they have an independent existence.
Frankly, this doesn't even feel like any kind of knowledge to me. Its operationally meaningless! In any case, I think the author has the cart before the horse: numbers (and other sorts of mathematics) do not pre-exist reality. Numbers are abstractions of regularities we see in nature.
Mathematics is nothing but the observation of regularities in certain sorts of elaborate rituals involving making markings on paper. Many of those rituals are inspired by and correlated with regularities which exist in the world, but its difficult to me to see any reason to believe that they have an independent existence.