“I don’t think the brain came in the Darwinian manner. In fact, it is disprovable. Simple mechanism can’t yield the brain. I think the basic elements of the universe are simple. Life force is a primitive element of the universe and it obeys certain laws of action. These laws are not simple, and they are not mechanical.”
~Kurt Gödel, [6.2.12]
Gödel’s incompleteness theorem is a devastating proof which demonstrates that in any system of logic there will always be unresolvable problems – problems which cannot in principle be logically resolved. The implications of this proof have yet to be completely absorbed by the philosophical community (and with good reason, since it is huge). One such implication might be that ‘artificial intelligence’ is not possible, or, less subtly, that, in the words of Gödel: “materialism is false.” Intelligence as we experience it requires an access to truths which are, strictly speaking, trans-logical and which we apprehend by intuition. However, intuition is a rational apprehension of truths immediately by the mind (meaning non-mediately, and thus not with the aid of any other ideas). Intuition has classically been associated with rationalist and theistic models of the mind, and intuitive apprehension has often been identified as the result of man’s mind having an intimate relation to the mind of God. Thus Nicholas Malebranche could say “God is the place where thinking happens in the same way that space is the place where motion happens” [paraphrase].
Alan Turing attempted to make Gödel’s incompleteness theorem more obvious by way of exemplifying it, and the machine he used to do this was the computer, a logic computer. Turing suggested that computers will always be left with some problems which cannot be resolved. Turing himself seems to have been an advocate of the view that man was essentially a machine or computer, and thus found no difficulty in suggesting that the project of creating/constructing artificial intelligence was not doomed. However, Gödel, at least, was not an advocate of that view, and did intend to show that the human mind had a way of transcending logic or ‘reaching’ beyond the confines of any logical system.
Gödel was a rationalist, and believed that in intuition man had access to something which was strictly beyond the confines of ‘logic’.
“The brain is a computing machine connected with a spirit.” [6.1.19]
“Consciousness is connected with one unity. A machine is composed of parts.” [6.1.21]
This may imply that Gödel’s incompleteness theorem is the best argument for rationalism that there has ever been. Not surprisingly, other than the incompleteness theorem, Gödel left us with one other very fascinating contribution: a persuasive Ontological argument for the existence of God. As one of the foremost logicians in the history of philosophy, his contributions pack a punch in favour of Theism and Rationalism.
[All quotes taken from here all of which are taken from – Hao Wang’s supplemental biography of Gödel, A Logical Journey, MIT Press, 1996]