Equating formal containment results with claims about relative 'power' conflates mathematical provability with the underlying computational reality, a category error Hartmanis and Stearns warned against.

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Category error(as used in logic and philosophy of language): A logical mistake where you apply a rule or concept to something it doesn't actually fit, like using a math formula on a poem.
Computational reality(in philosophy of computer science): The actual constraints and nature of what computers can and cannot do, independent of how we write the rules.
Formal containment results(in computational theory and mathematical logic): Mathematical proofs showing that one system of logic or computation can fit inside another system—like proving that all the problems solvable by one type of computer can also be solved by another type.
Hartmanis and Stearns(as founders of computational complexity theory): Two computer scientists who developed an important framework for understanding how much computational effort (time or memory) different types of problems require to solve.

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