Arthur James Balfour was the British Prime Minister from 1902-05 and the namesake of the Balfour Declaration. However, this isn't the dangerous idea I'm referring to. He was also a philosopher who wrote several books which all contain, to some extent, the argument that influenced C. S. Lewis's Argument from Reason (AFR). This is the idea that physicalism, materialism, naturalism are all self-defeating because when applied to the mind they remove any claim for our beliefs and belief-forming capabilities to be veridical -- and this would obviously include beliefs in physicalism, materialism, and naturalism. Lewis's version of the argument has recently been defended by Victor Reppert in C. S. Lewis's Dangerous Idea, and has been given a more rigorously analytical form in Alvin Plantinga's Evolutionary Argument against Naturalism.
I just finished Balfour's first book A Defence of Philosophic Doubt, published in 1879. It's interesting because it contains the earliest version of the AFR that I've been able to discover, namely, chapter 13, "The Evolution of Belief." In fact, this chapter is a re-working of an essay he published in the Fortnightly Review in 1877. I think future accounts of this argument will need to delve into Balfour's version to see how it influenced C. S. Lewis and others.
Balfour's other books spend more time on the AFR and, like Defence, they're all in the public domain. There's The Foundations of Belief, Theism and Humanism, and Theism and Thought, the latter two being two series of Gifford Lectures (which I wrote about here). There's also a critique of Balfour's philosophy in the public domain, Mr. Balfour's Apologetics Critically Examined by W. B. Columbine. At any rate, while Balfour's writings are very dry, I think they have some value and need to be taken seriously.
(cross-posted at Quodlibeta)