[hexhex]

The author puts Gödel's Incompleteness and the Continuum hypothesis on the same level, which is misleading. The continuum hypothesis is unprovable in our current mathematical foundation ZFC, but there are extensions to ZFC that either make the continuum hypothesis true or false.

Incompleteness is a property of every sufficiently complex formal system and thus poses a general constraint in logic.

That a particular learning problem is not provable in ZFC is not that surprising. Connections between learning and Incompleteness are way more interesting (and there is a lot of pseudo-research going on, "proving" that humans are not simulatable by computer etc.)