Is identity determined by your physical appearance or something like a "soul"? If someone was to receive a brain transplant and be inside another body, would they really be the same person they were before even if they had the same thoughts, ideas, and memories? Would the new body with the same brain just be a fake duplicate?

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This is a deep and interesting question, which goes to the heart of the topic of personal identity, and reflects a tradition that stretches back to John Locke's treatment of the topic in the Essay Concerning Human Understanding. A preliminary note is in order, however: most contemporary treatments of personal identity--and that of Locke as well--do not turn on whether personal identity is determined by the body (one's 'physical appearance') or the soul, but in terms of whether personal identity is determined by the identity of the body or the mind. (By framing the question in this way, philosophers who are agnostic about the existence of the soul, or thinking substance--like Locke--or who deny its existence--like many participants in recent philosophical debates on the topic, can engage it without having to take up the issue of whether there is such thing as a soul.) Interestingly enough, the kind of 'thought experiment' that you propose to illustrate your question is one that Locke himself considers and with which philosophers continue to grapple. But let's set aside Locke for now, since his own treatment of the issue is complicated by his own views about the point of personal identity and the nature of our knowledge, and focus on the question itself.

I'm not altogether clear about the case that you're proposing, so I'll present my own way of framing it. The issue that you are raising seems to be the following: if a person's brain is transplanted into another body--assuming, I take it, that a person's psychological life supervenes on her brain and so a person would continue to have the same thoughts, ideas, and memories despite the fact that her brain is 'housed' in another body--would the person be the same person as before? The answer to this question is: it depends. If one takes the identity of a person to be constituted by her psychology, that is, ,her thoughts, ideas, and memories, then she would be the same person, even if she was occupying another body. But if one takes the identity of a person to be constituted by the identity of her body--and, after all, we normally identify and reidentify people on the basis of their physical appearance--then one might maintain that the person is different. For when a person undergoes a fundamental change in her worldview--think, for example, of Paul on the road to Damascus--one might claim that that person remains the same person. (Of course, in the case just cited, the person in question didn't think that he was the same person after his conversion: Saul became Paul.)

Now in such a case, would the person be a "fake duplicate"? (I presume that you mean that the person after the transplant would be a "fake duplicate" of the person before the transplant, as in John Woo's movie Face-Off, in which the thoughts of one person are transplanted into the body of another--and vice versa, but let's set that complication to the side.) Well, if the person whose psychological life had been transplanted into another body knew of the transplant, she could try to 'pass' as that person, and she might be successful, especially if she knew enough about the thoughts, ideas, and memories of the person whose body she was occupying, since, of course, from the outside, the fact that a new psychological life was being housed in that body wouldn't be apparent. If, however, no such attempt at 'passing' was made, then I'm inclined to say that the person wouldn't be a "fake duplicate," but would simply be occupying another body.

Now my last remark indicates my sympathy for the idea that personal identity is constituted by psychology. However, since I'm not inclined to think that psychology can simply be transplanted into another body--either by transplanting a brain or by any other means--and since in fact I'm inclined to think that one's psychology may well be constituted by one's body, I'm drawn to the idea that personhood isn't constituted either by psychology or by the body but by both. (I believe, although I may well be mistaken, that this position is known as 'animalism' in the contemporary literature, and is distinct from positions that take personal identity to be constituted by identity of the body or by psychology.)

This is a fascinating topic, that continues to receive lots of attention from philosophers--and which figures in various movies, ranging from Total Recall to Face Off to Eternal Sunshine of the Spotless Mind to All of Me. If you're interested in pursuing the issue a bit more systematically, a very nice starting point is a dialogue on the topic by John Perry.

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