I take it that a person is one who values. I am a person (I cannot help but be one who values). Because I have values, I must order these values: I must be consistent.
You gesture towards your mind. I must take that as either a gesture toward a mind or a lie. If a lie, I should stop using those gestures to indicate my own mind, thus, I take the gesture to be honest. Therefore I believe you have a mind.
There is more to it than this (what I have here given has certain gaps left in it), but I have little interest in writing it all out at the moment. What I have given seems sufficient to allow one at least to be able to take breaks from the problem, and this is all I feel the duty to do.