The discovery or invention of a mathematics so in tune with reality also amazes Nagel. (Many evolutionary epistemologists are not surprised that brains, which evolve from nature, are thus in tune with nature.) Even neuroscientists cannot yet explain how mind emerges from the electronic circuitry of the brain. (That “they can’t explain that” posits some as yet unknown explanation. It is one thing to say this explanation is supernatural and by definition such explanations are outside the purview of science. It is another to say that further explanation is needed, and no scientist would disagree with that.)

To fully explain mind, Nagel argues, requires another scientific revolution. Such a revolution posits mind as fundamental and a universe primed “to generate beings capable of comprehending it.” This would require directional, possibly even purposeful evolution, and would expand on the model of random mutations and environmental selection. “Above all,” Nagel writes, “I would like to extend the boundaries of what is not regarded as unthinkable, in light of how little we really understand about the world.” (Again few scientists would disagree. Thus Nagel’s views are not as revolutionary as they appear.)

In addition, notes Johnson, the biologist Stuart Kauffman also suggests that Darwinian theory must be expanded to explain the emergence of intelligent creatures like ourselves. (There is nothing surprising about this. My article on “Piaget’s Biology” in The Cambridge Companion to Piaget (Cambridge Companions to Philosophy)notes multiple biologists who argue similarly.) And David Chalmers, an important philosopher of mind, has seriously considered panpsychism–the idea that rudimentary consciousness pervades everything in the universe. (However, Chalmers does not say that panpsychism and the physicalism underlying contemporary biology conflict, although he does say, in this interview, that panpsychism “is a radical form of physicalism precisely because it introduces mental properties as fundamental.” So Chalmer’s views are not as revolutionary as they appear. It seems to me that panpsychism might even be expected given the evolution of higher intelligence from lower ones. It also seems, on briefest reflection, that this does not mean mind is more fundamental than matter, but rather that it is an emergent property in evolution. My basic point is that the reference to panpsychism doesn’t clearly challenge scientific orthodoxy.)

Johnson also notes that the renowned physicist Max Tegmark argues that mathematics is an irreducible part of nature–perhaps the most fundamental part. Johnson marvels at mathematics’ effectiveness in describing reality. (Piaget wrote extensively about how children’s reflective abstractions largely explain how the mind evolves, as well as the correspondence of mathematics and reality. And there are Platonic, evolutionary and other explanations of this correspondence.) Tegmark argues the universe is a mathematical structure from which matter, energy, space, and time emerge. Other mathematicians note that most mathematics doesn’t describe reality at all. But for Johnson, Tegmark provides another example of a challenge to scientific orthodoxy.

Johnson’s conclusion from all this is mixed. On the one hand, we’ve come a long way in understanding our universe in the 5,000 years or so of civilization. On the other hand, from the vantage point of 5,000 years hence, our science today will be primitive. So Johnson is not sure of the extent to which challenges to the orthodoxy are substantive.

My conclusion is that Johnson is correct about the former claim—we have come a long way since the dawn of civilization, but I’m not sure about his latter claim—that today’s science will be primitive in retrospect. In some ways this is true, but in others, it may not be. There is a good chance that evolutionary, quantum, relativity, gravitational, and atomic theories will survive almost intact. Why? Because while revolutionary disruptions occasionally happen in science, as Kuhn suggested, more often change is slow. Change is mostly gradual, evolutionary change, not radical, revolutionary change. Newton’s theory of gravity is not wrong—it works fine at speeds much slower than light—although Einstein’s theory of gravity is more complete.  The ancient atomists were correct that atoms are small indeed even though they didn’t have a modern atomic theory. And Euclidean geometry is not invalid because of non-Euclidean geometry–parallel lines still don’t meet in Euclidean space! In the far future, we may find out we knew a lot more than we thought we knew.

As for new ideas that challenge scientific orthodoxy I think Carl Sagan said it best: “It pays to keep an open mind, but not so open your brains fall out.”