Humans have (or seem to have) both physical properties and mental properties. People have (or seem to have) the sort of properties attributed in the physical sciences. These physical properties include size, weight, shape, colour, motion through space and time, etc. But they also have (or seem to have) mental properties, which we do not attribute to typical physical objects These properties involve consciousness (including perceptual experience, emotional experience, and much else), intentionality (including beliefs, desires, and much else), and they are possessed by a subject or a self.
Source: Stanford Encyclopedia of Philosophy
The problem, which has been debated for (at least) a two thousand years, is yet to be resolved.
In sum, we can say that there is a mind-body problem because both consciousness and thought, broadly construed, seem very different from anything physical and there is no convincing consensus on how to build a satisfactorily unified picture of creatures possessed of both a mind and a body.
Recent 'Thought experiments' which imagine a time when a person's mental state and content could somehow be stored as digital information (currently completely unrealisable) have added to the debate as to whether a 'mind' could exist without a 'body'.
In the reverse direction, 'Artificial Intelligence' (AI) proponents argue that an AI system might somehow become 'conscious' - without a 'body' in the traditional sense. As yet there is no evidence that this has, or could, happen.
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