Consciousness is a hard problem for science, principally because no one quite understands what makes us the subjects of our experiences.
According to one critic, the problem that has preoccupied Stoppard throughout his career is “Are the materialists right, or is there more to man than mere flesh?”:
Hilary (Adelaide Clemens), the protagonist, is a youthful research psychologist-in-the-making who longs above all things to crack the hardest problem in to her field, the conundrum of human consciousness: “Who’s the you outside your brain? Where? The mind is extra….We’re dealing in mind-stuff that doesn’t show up in a [brain] scan—accountability, duty, free will, language, all the stuff that makes behavior unpredictable.” For her, a computer that plays chess can be conscious only if it “minds losing,” and the problem of consciousness is directly related to the problem of morality: … More. “Tom Stoppard’s new play tackles consciousness itself” at Mind Matters
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See also: Panpsychism: You Are Conscious but So Is Your Coffee Mug. Materialists have a solution to the problem of consciousness, and it may startle you
A short argument against the materialist account of the mind (Jay Richards)
What great physicists have said about immateriality and consciousness