CAN I KILL MY YOUNGER SELF? Time Travel and the Retro-Suicide Paradox Peter B. M. Vranas The University of Michigan 15 September 2000

WHY CARE ABOUT TIME TRAVEL PARADOXES? l Traversable wormholes may allow TT. l Chronology Protection Conjecture (Stephen Hawking, 1992): “the laws of physics prohibit the construction of time machines”. l Motivation for the conjecture: TT paradoxes. John Earman: TT is compatible with General Relativity and is thus physically possible.  Is TT compatible with quantum gravity?  Even if TT is physically possible, the para- doxes are not trivial; cf. Zeno’s paradoxes.

OVERVIEW Part I: A critique of the standard solution Task 1: Identifying a lacuna in the solution Task 2: Showing that the lacuna is important Part II: New solutions to the paradoxes Task 3: Resolving the wide paradox Task 4: Resolving the narrow paradox

PART I: A CRITIQUE OF THE STANDARD SOLUTION Task 1: Identifying a lacuna in the solution  The Retro-Suicide Paradox (RSP)  The Standard Solution (SS)  The Hidden Assumption (HA) Task 2: Showing that the lacuna is important  Is the Hidden Assumption obvious?  Is the Hidden Assumption dispensable?  Is the Hidden Assumption innocuous?

THE RETRO-SUICIDE PARADOX u YS: my younger self. Dup: a duplicate of YS. u Situation 1: I can kill Dup (Dup is asleep,...) u Situation 2: YS is asleep,... (P1) My situation is like one in which I can kill Dup, except that YS replaces Dup. (C1) I can kill YS (i.e., I can commit RS). The paradox: l P1 entails both C1 and ~C1, so P1 impossible. l But P1 is possible if time travel is. l So time travel is impossible (contrary to GR).

THE STANDARD SOLUTION Ê Ability is compossibility with relevant facts. Ë Equivocation: is the survival of YS relevant?   C1 (“I can kill YS”) is ambiguous between: (C2) The relevant facts (which exclude YS’s survival) are compossible with my killing YS. (C3) The relevant facts (which include YS’s survival) are compossible with my killing YS.   P1 entails C2  ~C3, not C1  ~C1. Ì So in a sense I can kill YS, in another I can’t. It is reasonable to use ‘can’ in either sense.

THE HIDDEN ASSUMPTION l According to SS, P1 entails C2: (C2) The relevant facts (which exclude YS’s survival) are compossible with my killing YS. l If RS is impossible, it is not compossible with anything, so C2 is (false, hence) impossible and so is P1: the paradox is restored. l So SS presupposes that RS is possible: the lacuna in SS is that SS relies without argument on the Hidden Assumption that RS is (physically) possible.

TASK 2 Task 1: Identifying a lacuna in the solution  The Retro-Suicide Paradox (RSP)  The Standard Solution (SS)  The Hidden Assumption (HA) Task 2: Showing that the lacuna is important  Is the Hidden Assumption obvious?  Is the Hidden Assumption dispensable?  Is the Hidden Assumption innocuous?

IS THE HIDDEN ASSUMPTION OBVIOUS? The objection. Of course it is possible that I kill this boy; what’s impossible is the conjunction of “I kill this boy” and “this boy is YS”. Reply. l It is possible that I kill this boy iff there is a possible world w in which I do kill him. l But in w this boy is YS (‘this boy’ and ‘YS’ being rigid), so does he rise from the dead? l If resurrection is physically impossible, then apparently so is RS (so that HA is false).

IS THE HIDDEN ASSUMPTION DISPENSABLE? l Read C1 (“I can kill YS”) not as C2 but as C4: (C2) The relevant facts (which exclude YS’s survival) are compossible with my killing YS. (C4) Relative to the relevant facts (which exclude YS’s survival) I can kill YS. l Reply. C4 is also impossible if P2  P3 is true: (P2) RS is impossible (i.e., HA is false). (P3) Impossibility entails inability. So given P3, the possibility of C4 presupposes that P2 is false; i.e., that HA is true.

(P3) IMPOSSIBILITY ENTAILS INABILITY l I cannot perform miracles (even if God can). n P3 doesn’t follow: my killing YS is no miracle, it entails the miracle that YS is resurrected. l Then P3 follows from the claim that I cannot perform actions which are or entail miracles. n I can, given free will plus determinism: I can whistle even if laws plus state S entail I won’t. l No: in every world with state S in which I whistle a miracle occurs, but in some world with different state I whistle without a miracle.

IS THE HIDDEN ASSUMPTION INNOCUOUS? l If HA is false (i.e., if RS is impossible), then of course I can’t commit RS. No paradox then: contrary to initial appearances, I can’t kill YS. So HA must be true if a paradox is to arise. l Reply. This is unsatisfactory: what difference between the two situations explains the differ- ence in abilities? YS but not Dup causally related to me, but such differences irrelevant. l This irrelevance claim may be false, but HA just takes it for granted that it is false.

CONCLUSION OF PART I l The standard solution relies without argument on the hidden assumption. l The hidden assumption is neither obvious nor dispensable nor innocuous. l HA is not innocuous also because:  An easier (wide) and a harder (narrow) version of the paradox can be distinguished.  By relying on the hidden assumption, the standard solution just fails to address the harder version.

PART II Part I: A critique of the standard solution Task 1: Identifying a lacuna in SS Task 2: Showing that the lacuna is important Part II: New solutions to the paradoxes Task 3: Resolving the wide paradox Task 4: Resolving the narrow paradox

THE WIDE AND THE NARROW PARADOX l Wide paradox. I cannot kill YS because: (W1) My killing YS would change the past; (W2) I cannot change the past. l Narrow paradox. I cannot kill YS because: (P2) My killing YS is impossible; (P3) Impossibility entails inability. [P2 is the negation of the hidden assumption.] l If my inability to change the past is the whole story, then my inability to kill YS is on a par with my inability to kill (e.g.) Hitler: ‘wide’.

RESOLVING THE WIDE PARADOX The reasoning: (W1) To kill Hitler would be to change the past. (W2) I cannot change the past. Thus: (W3) I cannot kill Hitler. The past of what? (W1) To kill Hitler in 1920 would be to change the past of 2000 [but the future of 1920]. (W2) In 1920 I cannot change the past of 1920 [but I can change the future of 1920].

OBJECTION 1: CAN I CHANGE THE FUTURE? Objection: In 1920 I can no more change the future of 1920 than I can change the past. Reply: Two senses of ‘I change the future of t’: Ê I bring about a (logically impossible) state of affairs in which an event both does and does not occur at some moment after t. (I cannot.) Ë I actualize a non-actual future of t. (I can.) Hard determinism: I can do only what I do. Reply: Then the wide paradox does not even get off the ground (not so for narrow paradox).

OBJECTION 2: CAN I NOW KILL HITLER? Objection: Even if in 1920 I can kill Hitler, can I now kill him? I cannot at t actualize a non-actual past of t: it’s too late for that. Reply: Even if you are too far away for me to kill you, I can still kill you if I can approach you. Similarly, even if now it’s too late for me to kill Hitler, I can still kill him if I can go to 1920—since in 1920 I can kill him. Isn’t it too late now to go back to 1920? No: by assumption I meet Hitler in 1920.

TASK 4 Part I: A critique of the standard solution Task 1: Identifying a lacuna in the solution Task 2: Showing that the lacuna is important Part II: New solutions to the paradoxes Task 3: Resolving the wide paradox Task 4: Resolving the narrow paradox

RESOLVING THE NARROW PARADOX l The narrow paradox again: (1) I can kill YS because I can kill Dup. (2) I cannot kill YS because: (P2) My killing YS is impossible [because: (P4) Resurrection is impossible]; (P3) Impossibility entails inability. l P4 alone does not entail P2. P5 is also needed: (P5) It is impossible that YS coexists with me without being an earlier stage of mine. l My solution: P5 is false, so (2) unsound.

DOES ORIGIN ESSENTIALISM ENTAIL P5? l (P5) It is impossible that YS coexists with me without being an earlier stage of mine. l (OE) If p is a descendant of s & e, it is impossible that p exists without being a descendant of s & e. l OE need not entail P5: YS and I are both descendants of s & e, but maybe in some w YS and I are post-fission stages of identical twins. Then in w P5 is false: YS and I coexist but YS is no earlier stage of mine.

AGAINST P5 l OE is false: what matters for organism identity is matter-plus-configuration identity, not identity of precursor organisms (Forbes). l In α: YS exists in 1975, OS originates in 2000 from OS- with matter M in configuration F. l In w: YS exists in 1975, OS originates in 2000 from a machine which happens to put together M according to configuration F. l In w YS no earlier stage of OS: no causal connection between states of YS and of OS.

REACTION 1: WE CARE ABOUT THE ACTUAL WORLD l I want to know whether I can kill YS in α. n YS in w = YS in α. Moreover, it’s in α that “I can kill YS” is true. l But how does the fact that I kill YS in w make “I can kill YS” true in α? n It doesn’t. I’m not saying I can kill YS because my killing him is possible. I’m saying I can kill YS because I can kill Dup, and be- cause the possibility of my killing YS removes the obstacle to concluding I can kill him.

REACTION 2: WE CARE ABOUT PERSONS, NOT STAGES My solution does not work for persons: Let ‘Peter’ be the person whose stages OS and YS actually are. In w OS and YS are not stages of the same person; so even if in w OS kills YS, Peter does not thereby kill Peter. We need stages to even formulate the paradox: The question is whether I can kill this boy. If ‘I’ and ‘this boy’ are persons, then they are both Peter; but the question whether Peter can kill Peter is trivial.

CONCLUSION OF PART II l The wide paradox is resolved by clarifying some ambiguities, so it’s relatively easy. l The narrow paradox requires investigation in- to metaphysical issues, so it’s relatively hard. l The narrow paradox relies on the negation of the hidden assumption, so the standard solu- tion doesn’t even address the harder paradox. l I resolved both paradoxes without appealing to equivocation about relevance, so the appeal of SS to such an equivocation is redundant.

WHAT DID WE LEARN? Ê There is a family of related retro-suicide para- doxes: (1) Narrow/Wide; (2) Rigid/Nonrigid. Ë Maybe now I can kill Hitler if: (a) Now I can go back to 1920, and (b) In 1920 I can kill Hitler (because in 1920 I can change the future of 1920). Ì Retro-suicide may be possible even if resur- rection is not: it is possible that YS coexists with me without being my younger self. Í Equivocation about relevance redundant.