A new grandfather paradox?

In an article in Scientific American (March 1994, pp. 68–74) entitled “The Quantum Physics of Time Travel”, Oxford physicist David Deutsch and Oxford philosopher Michael Lockwood give a defense of the physical possibility of time travel based on the “Many Worlds” interpretation of quantum mechanics. This positive view of theirs is not my concern, however—I want to quarrel with their argument that time travel cannot be accommodated in any other way.1 The best way to spell out the traditional “grandfather paradox” that appears to threaten the possibility of time travel involves the notion of ability, or personal possibility, or free will. An example of David Lewis’s: Tim travels back in time with the intent to kill his grandfather.2 Let us fix the case as one in which Tim in fact will not kill Grandfather; still, it seems that he can kill Grandfather because he is a good shot, has a gun, and is alone with Grandfather at close range. As Lewis says, Tim “has what it takes” to kill Grandfather. However, it is also compelling that Tim cannot kill Grandfather, because if Grandfather had been killed in his youth, Tim would not have existed to kill him. It is important to realize that the paradox essentially involves the notion of ability. No inconsistency results from supposing that Tim does not kill Grandfather. As for the case in which Tim does kill Grandfather, there are various possibilities. We could tell a consistent time travel story in which Tim kills Grandfather, but Grandfather is miraculously resurrected. Or one in which Tim kills Grandfather, but in which Grandfather has already had a child. Or one in which Tim kills Grandfather permanently, before Grandfather has any children, but in which Tim’s grandfather is someone other than Grandfather. As for the story in which Tim both kills Grandfather permanently in such a way that Grandfather has no children, and also is descended from Grandfather, this is an inconsistent time travel story; but of course the existence of some....
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DOI 10.2307/2953782
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