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A theory of identity
that says that a person is the same individual
as any "other" individual that has the same or similar physical
The theory of identity is very relevant to people considering future technologies that have the possibility of duplicating or copying a "consciousness" or physical body (for example, transhumanists). Currently, a person's self-identity is consistent, as a person is born into a body, lives in that body their entire life, and dies, so there is little question about the identity in current society.
But imagine, that we had the technology of the transporter from Star Trek, where a person's entire chemical structure could be scanned, disassembled, and then recreated in another location. Would this truly be the same person? An answer from instinct would seem to say "yes" - after all, the body would be exactly the same, just in a different location. What happens, however, if there's a delay disassembling the person in the original location, and for at least a second, the person exists identically in two different locations? Since at this point, there are cleary two different people existing (even if they are almost identical), then one must wonder if, even during proper functioning, if the assembled person is the same person. This is where the theories come into relevance.
The pattern identity theory states that the two copies in the example above would, in fact, be the same person. That because the person in the destination site has the same physical "pattern", then self-awareness and self-identity would be continuous. The person would find themselves gone from location A to location B.
This would also be relevant for "uploading" - the possibility of transferring one's consciousness from the physical body into digital form inside a computer. That it would be you inside the machine, and not someone else who's just almost exactly like you.
Now, one must be aware that this is relevant only to the person being subjected to this procedure. To all outside observers, it would, obviously, be the same person. We determine a person's identity by appearance and actions - if the person in location a disappears, and a person appears in location B, looking identical, and acting exactly the same, then it is assumed that it is, in fact, the same person.
It's not quite as obvious when dealing with self. Let's reconsider the example above, with the transporter malfunction. You close your eyes, and the procedure is done - only there's a total failure to disassemble the body in location A. Now, there are two copies of you. When you open your eyes again, you're not going to be aware of being in both locations. You'll only be in one of them, and there will be a copy of you in the second location going through the same experience. Which location will you be in? (Note that there is a science fiction story written dealing with this very situation, unfortunately, I am not aware of the name)
I believe this theory states that this is, in fact, an invalid question. That both of them are you, and thus, there would be nothing wrong with eliminating one of the copies, since they aren't killing you. Thus the truth of this theory is very imporant for possible technologies like uploading and transportation to be truly useful - as a person needs to be the same person afterwards as they were before. How many people would willingly kill themselves for someone else, who just happens to be an exact copy of them, to exist somewhere else, or in some other form?
There are many strange ideas and possibilities that come along with discussing identity theory.
See Also: continuity identity theory, The issue of Teleportation and Self, Ship of Theseus