Saying “I don’t know”, does sound like as good an answer as any to a question made by those with no intent on modifying their actions according to the answers they provide for their questions.
But, assuming that’s not the case, perhaps there are preliminary questions that may as well be asked first. For example, “Is it possible that others lack something in their decision making process that I don’t lack?” Long story short, would there be much chance of any sort of beneficial results among one who asked that question and answered yes?
Well, I agree that you can never prove that other minds exist through deductive methods.
You might be able to improve it through inductive methods, but this would require some kind of identity relationship between brain states and mental states.
I kind of like the Heideggerian line that belief in other minds is a basic presupposition of the kind of beings we are and the kind of world we live in. It’s a necessary belief for any kind of real engaged socially-oriented action and actually practical action in general. That’s why this is never really a problem for us until we stand back and reflect on it in a detacted, world-less kind of way. So, most of the time, we have no problem of other minds. But I admit when you step back and reflect as you are doing, it is probably an insoluble problem again, unless something like neural state-phenomenal thought identity is true.
But then we go back to our practical lives and it is no longer a problem again. : )
I might suggest that you prefer that guess because the only alternative would seem to be Solipsism, which would essentially be the actions and words of the other are merely a construct of your mind (along with everything else, for that matter) and that conclusion is unacceptable for more reasons than I can possibly list, thus, we accept that the others have thoughts, and given that it is our own thoughts that direct our own actions, we assume it is the thoughts of the other that direct the actions and words of the other.
Simply put, we assume to at least the most rudimentary extent, that others are like us.
The conclusion would make sense, unless one is somehow to see oneself as elevated to a higher degree than others, a lone sentient being surrounded by a seemingly infinite legion of automatons that act automatically and robotically.