The Scrambling Theorem unscrambled: A response to commentaries

Abstract

If we assume that conscious experiences exist and can be represented by sets, then conscious experiences are not identical to functional relations, no matter what mathematical structure one chooses to model such relations. This is the content of the Scrambling Theorem. The proof is trivial: any mathematical structure on one set of conscious experiences can be transported, intact, to any other scrambled set of the same conscious experiences. We thus conclude that reductive functionalism is provably false. The imaginative commentary by Hardin and Hardin distinguishes two versions of reductive functionalism. The ‘‘black box’’ version restricts functional descriptions to behaviors of the whole organism, ignoring inner states. The second version, call it ‘‘glass box,’’ extends functional descriptions to include inner states. The question raised by Hardin and Hardin is whether the Scrambling Theorem disproves black box, but not glass box, functionalism. The short answer is that the Scrambling Theorem disproves both. Glass box functionalism, when finally made precise, must posit mathematical structures that model the function of inner states. All such structures are subject to the Scrambling Theorem. This short answer holds no matter how finely one individuates inner states. They might be neural systems, individual neurons or, at the finest level, every subatomic particle in the brain. One can debate whether the subatomic level is too fine; some argue that the functional descriptions relevant to consciousness are at a coarser level, say the level of individual neurons or neural systems. The outcome of this argument is, for present purposes, irrelevant. The point here is that even if the relevant functional descriptions extend to the quantum state of every subatomic particle of the brain, the Scrambling Theorem, and its disproof of reductive functionalism, still holds. Even if Jack and Jill are functionally equivalent down to their subatomic particles, the conscious experiences of Jack could, in principle, be completely scrambled relative to those of Jill. The only version of reductive functionalism that can escape the purview of the Scrambling Theorem is one that refuses to specify the relevant functional relations with mathematical precision. But such refusal precludes doing science. Mausfeld and Andres nicely summarize the meaning of the Scrambling Theorem in their quote and discussion of Weyl: due to the ‘‘insurmountable boundary’’ of isomorphism, science cannot capture the essence of its objects. This holds for electrons no less than for conscious experiences. The wave equation of the free electron is not an electron and does not create an electron; no physicist thinks otherwise. Functional descriptions of the