The Evolution of Mind and Mathematics: Dehaene Versus Plantinga and Nagel

Today the leading philosopher defending religious belief is Alvin Plantinga.  He is a theistic evolutionist, who argues that theism is not just compatible with, but absolutely necessary for evolutionary science, and indeed for all of science.  As I have indicated in a previous post, I agree with him about the compatibility of theism and evolution, because evolutionary science leaves open the question of whether nature might ultimately depend upon God as First Cause.  But I disagree with his claim that theistic belief is absolutely necessary for evolutionary science.

In his evolutionary argument against naturalism, Plantinga has argued that atheistic naturalism is self-defeating, because if we believe that our minds evolved by natural selection unguided by God's divine mind, then we have no reason to trust our mind's capacity for grasping the truth, and thus we have no reason to trust our belief in atheistic naturalism.  In some previous posts (here and here), I have suggested that Plantinga's argument fails because it assumes a radical Cartesian skepticism that is implausible, by assuming that human beings could be naturally evolved for being in a state of complete and perpetual delusion.

Plantinga has now elaborated his reasoning in a new book--Where the Conflict Really Lies: Science, Religion, and Naturalism (Oxford University Press, 2011).  His general claim in this book is that "there is superficial conflict but deep concord between science and theistic religion, but superficial concord and deep conflict between science and naturalism" (ix).

Thomas Nagel has written a favorable review of this book in The New York Review of Books (September 27, 2012).  (In a previous post, I have written about Nagel's review of David Brooks' The Social Animal.)  This might seem surprising since Nagel is an atheist.  But it's understandable if one has read Nagel's new book--Mind & Cosmos: Why the Materialist Neo-Darwinian Conception of Nature Is Almost Certainly False (Oxford University Press, 2012).  Nagel criticizes what he takes to be the "reductive materialism" of Darwinian naturalism for failing to explain the reality of mind as manifested in human consciousness, cognition, and morality.

I agree with Nagel that a strongly reductionistic science--reducing all phenomena to physics and chemistry--cannot explain mental experience.  But what are the alternatives?  To explain the history of the appearance of mind in the universe, there are, he suggests, at least three alternatives: the historical account must be either causal (law-governed efficient causes), teleological, or intentional.  The causal account will be reductive, if one believes that the most elementary particles of nature are somehow mental, or emergent, if one believes that at some point in the evolution of natural complexity mental capacity arose as an irreducibly complex phenomenon.  In some previous posts, I have argued for the evolutionary emergence of the mind in the brain.  Nagel rejects this without much explanation because it "seems unsatisfactory" or "seems like magic" (55-56).  Although I agree that there might be some natural mystery in the emergence of mind in body, I don't see why we cannot accept this as a natural phenomenon that can be plausibly explained through an evolutionary science of the brain.

What Nagel calls the "intentional" account is the theistic explanation of Plantinga and others (including the proponents of "intelligent design"):  the universe was created by a Divine Mind that created human beings in His image as having minds like His.  According to Plantinga, God has created human beings with a sensus divinitatis--the gift of faith--so that most human beings believe in God's existence without any need for rational proof.  Atheists like Nagel suffer from a form of spiritual blindness.  In his article for the New York Review, Nagel explains: "My instinctively atheistic perspective implies that if I ever found myself flooded with the conviction that what the Nicene Creed says is true, the most likely explanation would be that I was losing my mind, not that I was being granted the gift of faith."

This leaves Nagel with the "teleological" explanation for the place of mind in the universe.  He favors this explanation although he admits that he does not yet understand how to fully develop it.  His idea is that from the very beginning of the universe there was an end or purpose inherent in things that would inevitably lead to the appearance of mind.  It's as though there was a cosmic mind from the beginning guiding the entire history of the cosmos towards the human mind.  He calls this natural teleology, and he insists that there is nothing supernatural or theistic about it.  But what he says about it sounds religious to me.  He writes: "Each of our lives is a part of the lengthy process of the universe gradually waking up and becoming aware of itself" (85).  What does this mean?  The Cosmic Mind was asleep, but then it woke up in our minds? 

If Nagel rejects my belief in the emergent evolution of the mind in the brain because it "seems like magic," then I will reject his belief in the sleeping Cosmic Mind that wakes up because it seems like mysticism.

Consider the case of mathematics.  How do we explain what physicist Eugene Wigner called "the unreasonable effectiveness of mathematics in the natural sciences"?  How do we explain the amazingly precise fit between the mathematical abstractions developed in the human mind and the natural regularities of the external world, which makes natural science possible? 

Plantinga explains this as an example of the "deep concord" between theism and science (284-91).  He quotes Paul Dirac: "God is a mathematician of a very high order, and He used advanced mathematics in constructing the universe."  We cannot trust our mathematical knowledge of the world, Plantinga argues, unless we believe that God is a mathematician who created the world mathematically and created our minds to grasp its mathematical order.

Nagel's alternative explanation would manifest his Platonic idealism: the whole universe is somehow ruled by an impersonal Cosmic Mind that is mathematical, which "wakes up" in the mind of the human mathematician.

The Darwinian view that I embrace is open to Plantinga's theistic explanation as conceivable: it is possible that the Divine Mathematician created the world so that the human mind would arise from a natural evolutionary process with a capacity for mentally grasping the mathematical order in the world.  But even if one is skeptical of such beliefs, because one lacks the gift of faith (the sensus divinitatis), one can still explain mathematics as a purely natural product of the emergent evolution of the mind in the brain.

A good elaboration of this position is Stanislas Dehaene's The Number Sense: How the Mind Creates Mathematics (Oxford University Press, 1997).  Dehaene is a mathematician who became interested in the evolution of mathematics as a product of both genetic evolution and cultural evolution.  In particular, he set out to explain the evolution of the "number sense."  Summarizing his reasoning, he writes:

That the human baby is born with innate mechanisms for individuating objects and for extracting the numerosity of small sets.

That this "number sense" is also present in animals, and hence that it is independent of language and has a long evolutionary history.

 That in children, numerical estimation, comparison, counting, simple addition and subtraction all emerge spontaneously without much explicit instruction.

That the inferior parietal region of both cerebral hemispheres hosts neuronal circuits dedicated to the mental manipulation of numerical quantities.

Intuition about numbers is thus anchored deep in our brain.  Number appears as one of the fundamental dimensions according to which our nervous system parses the external world.  Just as we cannot avoid seeing objects in color (an attribute entirely made up by circuits in our occipital cortex, including area V4) and at definite locations in space (a representation reconstructed by occipitoparietal neuronal pathways), in the same way numerical quantities are imposed on us effortlessly through the specialized circuits of our inferior parietal lobe.  The structure of our brain defines the categories according to which we apprehend the world through mathematics. (244-45)
 

According to Wigner, "the miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."  And according to Johannes Kepler, "the principal object of all research on the external world should be to uncover its order and rational harmony which were set by God and which he revealed to us in the language of mathematics." 

By contrast, Dehaene denies that there is any need to see a miracle in the correspondence between mathematics and nature if one explains this as the outcome of natural evolution.  Even nonhuman animals show a number sense that has evolved to help them survive and reproduce because it helps them to track the regularities in the natural world.  The same is true for human beings, except that human beings have a unique capacity for symbolic abstraction that allows them to develop mathematical symbolism far beyond the capacity of other animals.  The cultural evolution of mathematical symbolism in human history is an evolutionary process of trial and error in which some mathematical systems are more effective than others, and some of those mathematical ideas turn out to be useful for understanding the natural world.

To which Plantinga responds:

     Of course it is always possible to maintain that these mathematical powers are a sort of spandrel, of no adaptive use in themselves, but an inevitable accompaniment of other powers that do promote reproductive fitness.  The ability to see that 7 gazelles will provide more meat than 2 gazelles is of indisputable adaptive utility; one could argue that these more advanced cognitive powers are inevitably connected with that elementary ability, in such a way that you can't have the one without having the other.

     Well, perhaps; but it sounds pretty flimsy, and the easy and universal availability of such explanations makes them wholly implausible.  (287)

On the contrary, such explanations seem very plausible to me, especially when one realizes that the correspondence between mathematics and nature is not exact but only an approximation.  The discovery by Pythagoras that irrational quantities were required to express the incommensurability of the diagonal of a square was deeply disturbing to the ancient Greeks.  But this is not surprising if one sees that mathematics has evolved in the mind as only an approximation of the order in nature.  Similarly, while Kepler thought that the elliptic trajectory of planets in the solar system manifested the mathematical genius of God, the fact that these trajectories are only rough approximations to ellipses might make us doubt the exactness of God's mathematics.