Transcendental undecidability, and the identity of thought and being

This talk examines the significance of the theory of computation for the perennial philosophical problem of the identity of thought and being. I give an accessible overview of the history and main results of computability theory, and then discuss the Church-Turing thesis and its generalisations. I then consider our epistemic states in possible worlds where we are, or are not, computationally equivalent to nature, and therefore under what circumstances we might break through the Turing barrier. The main argument is that deciding our computational equivalence to nature is transcendentally undecidable, and therefore will we never halt on this decision problem. In consequence, the identity of thought and being is a purely "scholastic matter" (Marx's 2nd thesis on Feuerbach) and we have no rational reason to suppose that any persistent unintelligibility in nature cannot, one day, yield its secrets.

We cannot know we know; and we cannot know we cannot know.