The identification of syntactic derivability with extensional complexity classes conflates proof-theoretic and model-theoretic notions, a distinction Kreisel's 'unwinding' program treats as non-trivial.

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Conflates(in argumentation and logic): Treats two different things as if they're the same thing, or mixes them up in a way that causes confusion.
Extensional complexity classes(in mathematical logic and computer science): Groups or categories of problems organized by how hard they are to solve in terms of computational resources (like time or memory), based on what sets or objects they actually deal with.
Georg Kreisel(as a key figure in philosophy of mathematics): A 20th-century mathematician and logician who studied how informal mathematical reasoning relates to formal logical systems, and argued that intuitive understanding cannot be completely separated from formal proof.
Proof-theoretic(as used in logic): Relating to how we prove statements are true using formal logical rules and methods, rather than thinking about what statements mean in the world.

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