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 ABOUTTIME TRAVEL PARADOXES?

Traversable wormholes may allow TT. Chronology Protection Conjecture (Stephen

Hawking, 1992): “the laws of physics prohibit the construction of time machines”.

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 OFTHE 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

YS: my younger self. Dup: a duplicate of YS. Situation 1: I can kill Dup (Dup is asleep, ...) 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: P1 entails both C1 and ~C1, so P1 impossible. But P1 is possible if time travel is. So time travel is impossible (contrary to GR).

THE STANDARD SOLUTION

Ability is compossibility with relevant facts. 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.

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

According to SS, P1 entails C2: (C2) The relevant facts (which exclude YS’s survival) are compossible with my killing YS.

If RS is impossible, it is not compossible with anything, so C2 is (false, hence) impossible and so is P1: the paradox is restored.

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. It is possible that I kill this boy iff there is a

possible world w in which I do kill him. But in w this boy is YS (‘this boy’ and ‘YS’

being rigid), so does he rise from the dead? If resurrection is physically impossible, then

apparently so is RS (so that HA is false).

IS THE HIDDEN ASSUMPTION DISPENSABLE?

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.

Reply. C4 is also impossible if P2P3 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

I cannot perform miracles (even if God can). P3 doesn’t follow: my killing YS is no miracle,

it entails the miracle that YS is resurrected. Then P3 follows from the claim that I cannot

perform actions which are or entail miracles. I can, given free will plus determinism: I can

whistle even if laws plus state S entail I won’t. 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?

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.

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.

This irrelevance claim may be false, but HA just takes it for granted that it is false.

CONCLUSION OF PART I

The standard solution relies without argument on the hidden assumption.

The hidden assumption is neither obvious nor dispensable nor innocuous.

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 THENARROW PARADOX

Wide paradox. I cannot kill YS because:(W1) My killing YS would change the past; (W2) I cannot change the past.

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.]

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 THEWIDE 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’: 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.)

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 THENARROW PARADOX

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.

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.

My solution: P5 is false, so (2) unsound.

DOES ORIGIN ESSENTIALISM ENTAIL P5?

(P5) It is impossible that YS coexists with me without being an earlier stage of mine.

(OE) If p is a descendant of s & e, it is impossible that p exists without being a descendant of s & e.

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

OE is false: what matters for organism identity is matter-plus-configuration identity, not identity of precursor organisms (Forbes).

In α: YS exists in 1975, OS originates in 2000 from OS- with matter M in configuration F.

In w: YS exists in 1975, OS originates in 2000 from a machine which happens to put together M according to configuration F.

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

I want to know whether I can kill YS in α. YS in w = YS in α. Moreover, it’s in α that “I can

kill YS” is true. But how does the fact that I kill YS in w make “I

can kill YS” true in α? 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 STAGESMy 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

The wide paradox is resolved by clarifying some ambiguities, so it’s relatively easy.

The narrow paradox requires investigation in-to metaphysical issues, so it’s relatively hard.

The narrow paradox relies on the negation of the hidden assumption, so the standard solu-tion doesn’t even address the harder paradox.

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?

There is a family of related retro-suicide para-doxes: (1) Narrow/Wide; (2) Rigid/Nonrigid.

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).

Retro-suicide may be possible even if resur-rection is not: it is possible that YS coexists with me without being my younger self.

Equivocation about relevance redundant.