(continued)
But at this point a more formidable objection to time travel may be lodged: time travel seems to entail the possibility of the existence of a logically pernicious self-inhibitor. The objection is a reminiscent of the argument against tachyons. Earman asks us to consider a rocket ship that at some space-time point x can fire a probe that will travel along a timelike loop into the past lobe of x's light cone. Suppose the rocket is programmed to fire the probe unless a safety switch is on and the safety switch is turned on if and only if the "return" of the probe is detected by a sensing device with which the rocket is equipped (230-232). Is the probe fired or not? The answer is that it is fired if and only if it is not fired, which is logically absurd. Again, this contradiction does not suffice to show that time travel per se is impossible. Rather the whole situation is impossible, and this includes assumptions about the programming of the rocket, the safety switch, the sensing device, and so forth. But, although the contradiction could be avoided by giving up some of these assumptions, Earman suggests that we have good evidence that rockets can be so programmed. Earman concludes, "Thus, although we cannot exclude closed timelike lines on logical grounds, we do have empirical reasons for believing that they do not exist in our world" (232). His conclusion may be strengthened: it is not just the feasibility in our world of such rockets which generates the paradox; so long as such machines are nomologically possible, the contradiction could arise. Given the nomological possibility of such machines, then, timelike loops must be nomologically impossible if the contradiction is to be avoided. The conclusion would therefore appear to be similar to that in the tachyon case: that, although time travel is logically possible, there are no nomologically possible accessible worlds in which time travel can occur.
Paul Horwich has, however, disputed Earman's reasoning, claiming that he invalidly infers that, since the various assumptions are logically incompossible and since the rocket, safety switch, and so forth are physically possible, therefore timelike curves do not exist (440).{20} But there could exist timelike curves in the actual world or in any physically possible world in which the rocket, switch, and so forth do not exist. Letting p = "The rocket, probe, safety switch, and so forth exist and function properly," q = "Timelike loops exist," and r = "The probe is fired," Horwich's argument appears to be that the following reasoning, which is Earman's, is invalid:
http://www.leaderu.com/images/article/offices/billcraig/tachyons/argument5.jpg The problem is that (v) does not follow modally from (i). Although the conjunction of p and q implies an absurdity, the conjunction of q with <> p implies neither a contradiction nor even the possibility of a contradiction. In other words, timelike loops can exist in any world in which such rockets, switches, and so forth are possible but never in fact exist or function correctly; similarly for tachyons and the tachyonic antitelephone.
The opponent of time travel (and tachyons) has thus apparently committed precisely the same fallacy as the theological fatalist, and the response to them has the same form. The opponent of fatalism asserts that from God's foreknowledge of a future contingent proposition it follows, not that the future event cannot occur but only that it will not occur; the proponent of time travel maintains that from the fact that timelike loops exist it follows, not that such rockets cannot exist or function properly, but only that they do not exist or function properly. Further, the opponent of fatalism maintains that, if the contingent event were not to occur, then different propositions would have been true and God's foreknowledge would have been otherwise; the proponent of time travel contends that, if such rockets were to be built and function properly, then the timelike loops would not exist. Thus, the two situations seem quite parallel.
Also, look at IV. Tachyons, Time Travel, and Theological Fatalism.
