Now, I want to raise some worries and problems for substance dualism. (Remembering our methodology, these will come in two categories: epistemological and metaphysical.)
One way that a substance dualist might try to solve this problem is with the "Argument from Analogy". But, as we saw, that argument seems pretty weak.
So, in the end, it looks like substance dualism can never solve the problem of other minds.
Thus, for many philosophers this is a reason to reject substance dualism. They feel that we clearly do have knowledge, or at least reasonable, justified belief, about other minds. If that isn't possible given substance dualism, then we should reject substance dualism.
The first is a very general worry about the mind being an immaterial, non-physical substance. This seems spooky and metaphysically suspect. (The reason Ryle calls it the "ghost" expresses just this worry. We don't believe in ghosts and spookstuff.)
The second worry is a bit more specific (and actually approaches an argument against dualism). Given Descartes' view, how can there be any interaction between mind and body?
We ordinarily think that mental phenomena cause various physical phenomena, and vice versa. For example, my desire for another sip of coffee [mental state] causes me to reach out and take another sip [physical behavior]. In the other direction, hitting my thumb with a hammer [physical] causes me to feel intense pain [mental]. But given Descartes view that the mind is completely non-physical (it's entirely "outside of the physical world" so to speak) how can there be any interaction between mind and body?
Again, this seems to many to be sufficient reason to reject substance dualism.