December 2015 1 Resolving the Grandfather Paradox: Do the accounts of Sider and Horwich improve the plausibility of constrained time-travel? If time-travel were possible and you managed to travel back in time and kill your grandfather, a paradox would emerge in which you are both born and not born. Can Ǯconstrained time-travelǯ, which holds that you could travel back in time but would be unable to kill your grandfather, plausibly resolve this paradox? Sider and Horwich attempt to defend the plausibility of constrained time-travel, but I show that their arguments are flawed: to someone troubled by time-travelǯs consistency constraints, the arguments of Sider and Horwich can offer no reassurance Word count: 1,500 If you were to travel back in time and kill your grandfather then the events that led to your birth and your subsequent time-travel could never occur, leading to a paradoxical state in which your grandfather is both killed and not killed, and you are both born and not born. Philosophers such as Lewis (1976) have tended to respond that if you were to travel back in time then your actions would be constrained by consistency such that you could not kill your grandfather (since this would lead to contradiction), but you can nonetheless go back in time and interact with him. The impossibility of your killing him, however, means that any attempt to do so will fail. You will miss, lose nerve, or slip on a banana peel when the killing is attempted. ) refer to this attempt to resolve the paradox as Ǯconstrained time-travelǯ. )t accounts for time-travel within a closed time-like curve – a curve whose final event is synonymous with its first event, leading to a consistent Ǯloopǯ of events. Some people argue that these consistency constraints have implausible implications which count against the possibility of time-travel. I make no attempt to evaluate this claim here; instead, I argue that if these constraints are taken to be problematic for the possibility of time- travel, then these problems remain despite the arguments of Sider (2002) and Horwich (1975), which both fail in their respective attempts to improve the plausibility of constrained time-travel. Siderǯs Ǯgenuine coincidencesǯ Sider (2002) defends constrained time-travel by arguing that a time-travellerǯs persistent failure to kill his grandfather ȋor, in Siderǯs paper, his Ǯformer selfǯȌ, does not require that there are any Ǯstrangeǯ and Ǯimplausibleǯ shackles on him. Consider the following counterfactual: Ǯ)f there was a person who was a permanent bachelor and who attempted to get married, it would have been the case that he failed due to some coincidence such as slipping on a banana peel and dying before the ceremony takes placeǯ (Sider, 2002, pp. 125-127). Is it strange that this person would always have failed if he had attempted to marry? No, because the fact that the person will never marry is contained within the antecedent of the proposition, which specifies that the person is a permanent bachelor. That he will never marry does not imply that he could not have married – his failure to marry may well be due merely to some coincidences, and we would not regard these as undermining a personǯs freedom ȋSider, ʹͲͲʹ, p. ͳʹ6Ȍ. In the same way, if a time-traveller were to attempt to kill his grandfather or former self he would slip on a banana peel or fail due to some other coincidence. Yet this does not undermine the time-travellerǯs freedom: that the time-traveller cannot kill his grandfather is simply implied by the antecedent of our proposition, which specifies that he is a time-traveller. Due to the type of world we have concerned ourself with there are many different failures that plague all the attempted killings, but these can still be genuine coincidences (Sider, 2002, 127-128).