On coincidence in causal loops

Abstract

The existence of closed time-like curves in Gödel's solutions to Einstein field equations would allow for the physical possibility of backward time travel. Since Gödel's publication in 1949, philosophers have examined the logical constraints surrounding the possibility of backward time travel. A popular objection to this claim, known as the autoinfanticide paradox/grandfather paradox, holds that if backward time travel were possible, then it would be possible to travel back in time and kill one's younger self or prevent their birth from ever occurring. Authors such as David Lewis (1976) have responded to the autoinfanticide objection by arguing that attempts by time travelers to kill their younger selves would result in "coincidental events" such as gun jams and banana slips, which prevent such autoinfanticide attempts from succeeding. Paul Horwich responds to Lewis in his book Asymmetries in Time: Problems in the Philosophy of Science by arguing that such coincidences would be improbable. In this paper, I will argue that Horwich's improbability in describing these coincidental events is misguided due to the failure of the frequency principle. Utilizing Berkovitz's response in his paper "On Chance in Causal Loops," which responds to Mellor's argument for the impossibility of causal loops from his book "Real Time II". I will show that the frequency principle fails due to the frequency of events in causal loops always having biased reference classes.