Isn't his second point incompatible with the first one? In the second, he implies that human minds might be Turing machines due to no one proving otherwise. Bu

Isn't his second point incompatible with the first one? In the second, he implies that human minds might be Turing machines due to no one proving otherwise. But if human minds were Turing machines, then they are certainly axiomatic systems since Turing machines are axiomatic systems. This contradicts his initial point which concludes that not all of our sources of knowledge are axiomatic in nature.