Time travel and the issue of autoinfanticide

In the first place, it is quite obvious that there are constraints on the timelike curves may act as loci for particular sorts of causal chain. The spatiotemporal interval between distinct events of a type of causal process if commonly determined by laws of physics. Second, any causal chain must be consistent with those chains which are located along intersecting lines.... Such systems [of self-defeating systems -DHC] are excluded by just those restrictions on causal chains and their interrelationships that ordinarily apply in open time. [Paul Horwich, Asymmetries in Time: Problems in the Philosophy of Science (Cambridge, MA: MIT Press, 1992), 118-9]

The problem with the possibility of time travel is that it opens up paradoxes. In particular, if one can travel to the past and alter history, could one kill one's infant self, thus result in an unresolvable contradiction? Or one can cause any change in world history, resulting in one not being born at all. There are a couple of possible ways such time paradoxes could be resolved. One way is for one to be threatened to be erased from time (and would be erased from existence) if one attempts to kill one's infant self or do anything which prevents one's being born (as seen in Back to the Future). Another way is one can kill "one's infant self" and realize when one returns that one has a different pedigree altogether (because of actions committed in the past), with perhaps even a different set of memories and life experiences when one returns (or having both sets simultaneously). Since nobody has ever witnessed time travel neither it is at present feasible to attempt time travel, anything we have now about time travel is mere speculation.

As a thought experiment however, thinking about time travel tells us more about one's philosophy of time. The philosopher Paul Horwich, in dealing with the problem of time travel and the problem of autoinfanticide, suggests that the nature of causal chains make it such that overlapping and contradictory timelike causal chains are impossible since "any causal chain must satisfy consistency conditions imposed by its surroundings" (p. 119). In other words, paradoxes such as autoinfanticide are impossible because consistency in spacetime conditions must be maintained, and therefore a subsequent causal chain cannot disrupt the former conditions in the spacetime environment, laid out in the causal chains that are already present there. When one attempts to kill one's infant self, circumstances will ensure that that would not be possible no matter how hard one tries to do so.

My question to such a solution to the paradox however is why we must state that circumstances must prevent autoinfanticide from happening, instead of conceding that a genuine paradox might occur in the timeline of the world. Postulating that a subsequent causal chain cannot disrupt previous chains because of "consistency conditions" is merely to answer the question with a restatement of the question in the form of an answer. "Why must another causal chain NOT disrupt previous chains," when analyzed, is the essence of the question "Why must one not be able to murder one's earlier self," which is our initial question. Horwich's claim that autoinfanticide is impossible it seems boils down to the assertion that it is impossible, which is not a good answer at all.

Subsequently, speculations about the physical and technological possibility of time travel are stated, and that might be true impediments to time travel. But arguments based upon human psychology (why would one wants to kill one's former self), and the strange physical inability to kill oneself, are unconvincing. Unless one rejects that man has free agency, man is naturally able to choose to do what one desires to do. It does not matter whether one wants to do action X or not. If man has the natural ability to choose action X, then the paradox remains. Likewise, postulating all manner of circumstances (gun misfire, fall ill on the day when one will try to kill one's former self) does not solve the problem because these contingent factors can be resolved to satisfaction in other possible worlds, and therefore the paradox remains.

It seems therefore that the paradoxes of time travel has not been well resolved in Horwich's book. The autoinfanticide paradox, as well as the time travelers' paradox, remain problems that seem to suggest the impossibility of time travel in this universe.