No, I don’t mean that kind of zombie; you’d know it if they were. No special philosophical training is required to detect Hollywood zombies; they are easily recognized by their facial expressions, gait, and characteristic behavior patterns. The philosopher’s zombie, in contrast, is indistinguishable on grounds of physical appearance alone, and a dualist might want to argue that no material distinctions can be made between the zombies in your department and the rest of your colleagues. What makes a zombie a legitimate object of philosophical inquiry is its (his? hers? eir?) absence of consciousness. And today’s question is whether mathematical research requires consciousness, or whether it could just as well be left to zombies. If I were a philosopher of mind I’d consider it my professional duty to spend at least an hour every week imagining that my colleagues are all zombies, totally lacking in conscious experience, and introspecting about what, if anything, would be different about my professional and personal relations to them. (And writing up the notes of my introspection for publication.) No such duty weighs upon me as a mathematician, but I still recommend the exercise for the light it sheds on the question of mechanization of mathematics. My colleagues may or may not think their colleagues are zombies, but those who profess a belief in a future in which the field is dominated by artificial intelligence are telling us that we may as well be, for all the difference it makes to mathematics. I was led to this train of thought by reading Andrew Smart’s Beyond Zero and One, subtitled Machines, Psychedelics, and Consciousness. Chapter 7 of MWA is largely inspired by the notion that mathematics is neither invented nor discovered but is rather an altered state of consciousness, and to this end sought (without much success) to catalogue examples of mathematicians working creatively under the influence of mind-altering drugs. Elsewhere I have described mathematics as a consensual hallucination, following the expression originally due to William Gibson. But it had not occurred to me before reading Smart’s book to explore the more basic question of whether mathematics and consciousness necessarily have anything to do with one another. Smart is writing about artificial intelligence, and about when, if ever, consciousness will be attributed to computers. His argument, which I think is original, is that altered states of consciousness are not merely coding errors but are inseparable from the very possibility of consciousness. Thus he proposes to replace the Turing test for AI consciousness with a Turing-acid test, in which an AI would be tested for the ability to hallucinate as well as to display the normal attributes of consciousness. Colleagues who favor mechanization of mathematics should reflect upon this comment from Chapter 8 of Smart’s book:
…in order for a machine to have human consciousness and its own intuitions, the computer might also have to develop human-like biases and errors, even though these are the things we wish to eliminate by using robots to reason perfectly.
Since the expressed motivation for mechanization is precisely to eliminate the errors of human reasoning, it follows, if Smart is right, that the ideal mechanical mathematician will be unconscious. Smart follows John Searle in his own account of the objectivity of mathematics:
Mathematics, like language, is observer-relative: its mode of existence is ontologically subjective in that it depends on conscious agents for its existence. But mathematics has epistemically objective truths.
If you accept this characterization of mathematics, then you have to agree that talk of zombie mathematicians is a category mistake, and that the machines that some of our colleagues expect to replace us on the near side of the singularity will necessarily be epistemically indistinguishable from human beings; in particular they will be conscious. Thus we may be tempted to read the dialogue between Tim Gowers and C, the AI helper in his essay entitled Rough Structure and Classification as an account of an hallucination; but which of the two characters is hallucinating?
(Image from Night of the Living Dead, public domain)
Update: You may want to refer to this site for additional information on the title question.