I am unconvinced that the mind is so special. The way it is decided that a mind exists is through behavior. The observation of behavior is how the mind is, to use your words, "tested, detected or measured" and such observation is "by natural means." We make all sorts of determinations of the intelligence of minds (IQ tests, etc.), and there is nothing supernatural about how that is done. We do the same sorts of things for determining how minds feel about various things.
The fact that it is "indirect" observation, in that one views the behavior rather than the mind itself, does not make the situation special. We do the same with gravity. We do not observe gravity as a thing in itself, but as it affects other things.* That does not make gravity supernatural or unreal.
Additionally, with examinations of damaged brains, we know that the mind is altered by altering the brain. We can be pretty certain that the mind is a subset of the activities of the brain. (One also can do a self-test, where one drinks enough alcohol to become drunk, and one can notice the subjective aspect of mind changing, while others can observe differences in our behavior. The alcohol in the brain affects the activities of the brain.) Granted, the details are not all worked out yet, but before modern astronomy, we did not know what the stars were and could not be sure about them. That did not make them supernatural. That just made the details unknown. Unknown details is not the same as "supernatural."
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*By all means, ask Alex K, our resident expert on such things, to weigh in on my characterization of gravity. I'll concede almost anything he says about gravity, if we get him in a serious mood.
The fact that it is "indirect" observation, in that one views the behavior rather than the mind itself, does not make the situation special. We do the same with gravity. We do not observe gravity as a thing in itself, but as it affects other things.* That does not make gravity supernatural or unreal.
Additionally, with examinations of damaged brains, we know that the mind is altered by altering the brain. We can be pretty certain that the mind is a subset of the activities of the brain. (One also can do a self-test, where one drinks enough alcohol to become drunk, and one can notice the subjective aspect of mind changing, while others can observe differences in our behavior. The alcohol in the brain affects the activities of the brain.) Granted, the details are not all worked out yet, but before modern astronomy, we did not know what the stars were and could not be sure about them. That did not make them supernatural. That just made the details unknown. Unknown details is not the same as "supernatural."
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*By all means, ask Alex K, our resident expert on such things, to weigh in on my characterization of gravity. I'll concede almost anything he says about gravity, if we get him in a serious mood.
"A wise man ... proportions his belief to the evidence."
— David Hume, An Enquiry Concerning Human Understanding, Section X, Part I.