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Stephen Kearns, Tit for tat for tit: On reactive loops and regresses, Analysis, Volume 83, Issue 1, January 2023, Pages 55–60, https://doi.org/10.1093/analys/anac032
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First, a story:
At time tʹ, Dawn reprimands Jennifer, for reasons soon to be divulged. Dawn leaves, but the next time Jennifer sees her, at t*, Jennifer reprimands Dawn in reaction to being thus reprimanded. Jennifer then leaves. The next time Dawn sees Jennifer, she reprimands Jennifer in reaction to being thus reprimanded. But here’s the twist: Dawn’s reprimand of Jennifer is the same reprimand with which we started this story (the one at time tʹ), because Dawn and Jennifer exist within a temporal loop – a closed timelike curve in which tʹ rests in both the future and the past of t* (and vice versa). In essence, each reprimand is given in response to the other.
This story, while fanciful, is not obviously impossible. It involves a causal loop, but it is argued by several philosophers that there is no compelling reason to think that causal loops are impossible (e.g. Meyer (2012), Wasserman (2018: ch. 5) and Effingham (2020: ch. 5, ch. 12), though see Pruss 2018: 61–63, 162–63 for an opposing view). Indeed, if people can exist on closed timelike curves, it seems that such a scenario could indeed play out (for work on the possibility of timelike curves see the above references, plus Gödel 1949, Gott and Li 1998).
