Suppose there are n (physically, including neurally) healthy mature humans on earth. Let Q1, ..., Qn be their non-mental qualitative profiles: complete descriptions of their non-mental life in qualitative terms. Let Hi be the hypothesis that everything with profile Qi is conscious. Now, consider the hypotheses:
M: All healthy mature humans have a mental life.
N: Exactly one healthy mature human has a mental life.
Z: No healthy mature human has a mental life.
Assume our background information contains the that there are at least two healthy mature humans. Given that background, the hypotheses are mutually exclusive. Now add that there are n healthy mature humans on earth, where n is in the billions, and that they have profiles Q1, ..., Qn, which are all different. What’s a reasonable thing to think now? Well, N is no more likely than M or Z. Conservatively, let’s just suppose they are all equally likely, and hence all have probability 1/3. Furthermore, if N is true, exactly one Hi is true. Moreover all the Hi are just about on par given N, so P(Hi|N)≈1/n for all i, and hence P(Hi&N) is at most about 1/(3n). On the other hand, P(Hi|Z)=0 and P(Hi|M)=1.
Now suppose I learn that Qm is my profile. Then I learn that Hm is true. That rules out the all-zombie hypothesis Z, and most of the Hi&N conjunctions. What is compatible with my data are two mutually exclusive hypotheses: Hm&N as well as M. It’s easy to check (e.g., with Bayes’ theorem) that my posterior probability for Hm&N will then be approximately at most 1/(n + 1). Thus, the probability that there is another mind is bigger than 0.999999999.
Whether we can argue for M in this way depends on how the priors for M compare to the priors of hypotheses in between M and N, such as the hypothesis that all but seven healthy mature humans have consciousness.
