Does the too many thinkers problem present a counter-argument to John Locke's account of personal identity, if we apply it to his conceptions of Man and Person?
If so, how might Locke answer this objection? Does he think that only the person (and not the man) can think, so there is no problem?
EDIT: The problem doesn't need to be focused on Person vs Man, could it be a problem for Locke's conception of a Person vs Soul or Biological Body?
The way to answer such objections is to make them formal in the language of computation, as we can do nowadays. The dualistic conceptions of the mind are like the split between hardware and software. Given a program running on a computer, say Microsoft Windows, which has a bug. You can ask
Does the computer running the program have the bug? Or does the program have the bug?
If you believe the "too many thinkers" argument, there is a "too many algorithms" problem here: if the entity which produced the bug is the program, then the computer running by itself produces the bug without any "algorithm", just by physics, while the abstract program algorithm produced the bug abstractly. But then, shouldn't only one of the two produce the bug?
It is always this way when you have an abstract high level description of a physical system, like the computer and the software. The software is manifested in the computer in a way that we completely understand (at least, I hope you completely understand), and there is no paradox at all.
So for human beings, identifying mind and soul with software and the brain with the computational hardware running this software, it is possible to conceptually separate the software from the hardware without any paradox that doesn't have a parallel (and an obvious resolution) in the case of the computer.
The reason is not because the brain is analogous to a computer, and the soul to the software, but because the brain is a computer and the soul is the software. This point of view required 20th century developments, and was obviously unavailable to Locke. But it gives a formal meaning to dualism and to psycho-physical parallelism, and it gives the dualism debate an obvious resolution.
Note that it doesn't really resolve the dualism debate--- you can still consider the program as separate from the computer, living in a Platonic realm, or consider the program as identified with its particular instantiation, and you might believe that these are separate ideas. But in terms of logical positivism, they predict the same behaviors, and so there is no logical positivist reasoning that can separate which of these is true. In the case of the computer, we use software/hardware dualistic language all the time, without confusion.
