Mathematics, Metaphysics and Evolution (guest post by Aaron Sloman)

Topics discussed on the last day of the FramePhys/Gothenburg conference on Metaphysical Explanation in Science, linking mathematics, science, biological evolution and metaphysics led Aaron Sloman to write some comments available online here:

Inspired by a combination of Immanuel Kant’s philosophy of mathematics and Al Wilson’s notion of grounding as metaphysical causation, Sloman draws attention to the extraordinary metaphysical creativity of biological evolution (the most creative mechanism known to us) repeatedly “discovering” and instantiatiating new metaphysical types of ever increasing complexity and generative power, building on (still unidentified) generative features of fundamental physics that made everything else possible, including increasingly complex and varied forms and uses of information (mostly via chemistry).

He suggests that key features of evolution constitute a process in which pre-existing parametrisable mathematical structures of ever increasing complexity and generative power, are systematically “discovered”, combined and used in creating new (parametrised) instances that when combined with appropriate parameters produce instances of newly discovered metaphysical types, including not only new physical structures and processes but also increasingly complex and powerful new types of information, and information processing mechanisms. This creative, productive, grounding, can be construed as exemplifying Wilson’s characterisation of Grounding as Metaphysical Causation [G=MC].

The details of this process, and its products provide deep challenges for both neuroscience and current AI, neither of which explains the ability of animal brains to discover and use powerful mathematical theories, e.g. concerning topology and geometry. Sloman also links this to Alan Turing’s suggestion (1938) that digital computers cannot replicate human mathematical intuition, only mathematical ingenuity.

— Aaron Sloman

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