David Corfield diagnosis

Reflecting on Friedman's Dynamics of Reason, perhaps we should see as linked

• The analytic tradition failing to grasp properly mathematics, and its relation to physics, deterring people from conducting the most appropriate Friedmanian meta-scientific work. Deterring philosophers, at least. What stopped people realising that mathematics concerns ideas of space, symmetry, quantity, extension, classification, etc.? Between logic and physics

• Its failure to take category theory seriously as a radical change of point of view. This is partly due to the idea that if something can be rewritten in an existing language, e.g., set theory, then it’s not new. Of late we see many ways in which higher category theory is revealing itself as a revolution.

• The failure to see the proper value of type theory. What to attribute this to? Satisfaction with untyped logic, perhaps due to its role in ZFC?

• Friedman telling a slightly ‘thin’ story of the mathematics involved, not seeing maths as multi-layered, involving a similar overturning of principles to physics. This lets us see category theory and then higher category theory as revolution. Instead, Dynamics of Reason points to things like quantum logic as revolution. (Note Coecke’s The logic of quantum mechanics - Take II, perhaps the very idea of symmetric monoidal categories is revolution enough.)

• Maths and physics failing to talk (1930s-1970s). “I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce”, Freeman Dyson, Missed Opportunities, 1972. Joint work since then Donaldson, Floer, some often category theoretic, mirror symmetry, string duality,KK-cascades (Kontsevich, Witten, Atiyah, etc.)

  • “The marriage between gauge theory and the geometry of fiber bundles from the sometime warring tribes of physics and mathematics is now over thirty years old. The marriage brokers were none other than Chern and Simons. The 1978 paper by Wu and Yang can be regarded as the announcement of this union. It has led to many wonderful offspring.” (K. Marathe, Topics in Physical Mathematics, 2010, p. xi).
  • “The love affair between math and physics has turned from a fling into a serious, committed relationship.” (Jeff Harvey, Strings 2011).
  • Mina Aganagic, String Theory and Math: Why This Marriage May Last, (arXiv:1508.06642)
  • The Unreasonable Effectiveness of Physics in the Mathematical Sciences

• The idea of gruppenpest. (Continues with the $n$-gruppenpest.)

• Quantum mechanics not being philosophically grounded by meta-scientific work. But Heisenberg 1958.

• Weyl and von Neumann changing their minds on mathematical foundations

• Ernst Cassirer and Albert Lautman being ignored.

See Between logic and physics.