Their minds are not real minds, or are not anything like my mind, or their minds are just in my mind.
No, this is not an insane ramble. This is a philosophy argument; and a physically possible one. This argument has no realistic hypothesis or physical evidence to statistically confirm or deny it. Really, all I do – and perhaps you too – know is that you exist because you’re sentient right now (“I think therefore I am”, i.e. Rene DeScarte style).
So logically, it’s fair to have at least a bit of a problem about what you believe about other minds. Yeah? For instance, you can’t prove if I’m telling you this to make you believe I’m truly an extrinsic human mind (but I may just be an alien or a robot), or that I’m the one certain proof that at least one mind exists out there you can believe in. Talk about a theory of mind with a problem of other minds.
Personally, I prefer to just believe all apparent human minds are 100% legitimate minds; minds like mine. However, I can’t argue against any doubters.
Good luck out there mind problem solvers!