A Mathematician’s Defense of Functionalism

Mind and Function

A central question in philosophy of mind is what constitutes the basis for conscious experience. One branch of modern philosophy—functionalism—claims that any system which functionally replicates human thought and behavior would also replicate human consciousness. Other philosophers suggest that functional equivalence to the human mind is insufficient for producing consciousness, that conscious experience transcends the ability to produce thought or behavior.

I wrote this essay just as I was moving from advanced math into brain and behavior. It’s a mathematician’s defense of functionalism against the arguments of John Searle, the Chinese Room thought experiment, et al.:

Functionalism, the idea that mental states are characterized by their function, formally arose in the mid 20th century in response to earlier attempts at demystifying the mind(Levin, 2009). Many felt that behaviorism had failed to describe the mind at an appropriate conceptual level, or that attempts such as identity theory were overly restrictive upon the conditions of mental states(Levin, 2009). Functionalists declared that the particular physical processes underlying mental activity in an entity were inconsequential; what mattered was the functional role a state played in that entity’s existence.

…In this paper, I don’t try to prove that functionalism is true. Opponents of functionalism will always be able to find harbor in the the ineffable, the empirically unobservable. I only wish to show that functionalism is valid, that it’s plausible, that it’s potentially consistent with our experience of the world.

…We can formalize this notion a bit more by appealing to the mathematical formulation of isomorphism. Let G and H be sets, and the function f be a one-to-one mapping between them. Let ★ be the function from G to G that we wish to preserve. Then f is an isomorphism with respect to ★ iff f[★(a)]=★'[f(a)] for all a in G<read entire paper>

For some good introductory point/counterpoint on the topic of functionalism, read John Searle’s Mind: A brief introduction and Daniel Dennett’s Conciousness Explained.