In the last chapter of "Galileo's Finger," Professor Peter Atkins invites us to consider the view that mathematics is a product of the mind, but also a reflection of the underlying structure of the universe. Mathematics is hard-wired into the brain, because we are the products of a logically self-consistent universe. Thus mathematics maps so neatly onto the universe because our internal logic is an expression of the deeper structure.
On the deep structuralist view, the universe is, in a sense, mathematics, but does this imply that mathematical objects such as triangles and squares exist anywhere outside our heads? No, we may safely assume that mathematical objects are abstract. Atkins' deep structuralism does not require that mathematical objects exist in any concrete way. The universe operates mathematically. Or to put it another way, mathematical consistency is a property of our universe (any universe that survives its own birth must be self-consistent). And our brains have evolved by means of natural selection to be able to operate in a mathematically-structured universe. Qualifier: Atkins is careful to caution us that the model he has tentatively put forth is speculative. He reminds us that speculation must be tested and either borne out or falsified by evidence.
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