Reducing reductionism to irrationality

Francis Crick is best known as the co-discover with James Watson of the structure of DNA and of the hypothesis of the genetic code. This was the beginning of a whole new field of science, molecular biology. Given this scientific success perhaps it is not surprising that Crick was a passionate reductionist. Later in Crick's career he turned to neuroscience and wrote a popular book, The Astonishing Hypothesis: the scientific search for the soul. In it he makes the classic reductionist claim (p. 3):

"You, your joys and your sorrows, your memories and your ambitions, your sense of personal identity and free will, are in fact no more than the behaviour of a vast assembly of nerve cells and their associated molecules"

In response John Polkinghorne writes that Crick's agenda is 

ultimately suicidal. If Crick’s thesis is true we could never know it. For, not only does it relegate our experiences of beauty, moral obligation, and religious encounter to the epiphenomenal scrap-heap. It also destroys rationality. Thought is replaced by electro-chemical neural events. Two such events cannot confront each other in rational discourse. They are neither right nor wrong. They simply happen… The very assertions of the reductionist himself are nothing but blips in the neural network of his brain. The world of rational discourse dissolves into the absurd chatter of firing synapses. Quite frankly, that cannot be right and one of us believes it to be so.

John Polkinghorne, One World, p. 92.

I thank Lewis Jones for bringing these quotations to my attention. They are discussed in more detail by John Lennox, in God's Undertaker: Has science buried God?
On a lighter note, these issues are also discussed here.