David Lewis, “The Paradoxes of Time Travel”

Posted: Wed, Oct 22, 2025

Some background

Time travel

  • Do nothing
  • Hop on a train
  • Hop on a plane
  • Relocate the time traveler, much like space travel
  • Relocate the objective present

Lewis’s definition of time travel: Disagreement between “personal time” and “external time.”

  • I missed the Times Square ball drop in 2000. I hop into my time machine on December 31, 2025, stay in the time machine for 5 year exactly, and come out on December 31, 1999.
  • On December 31, 1999 “the second time around”:
    • My personal time: I’m now a 33-year-old.
    • External time: Today is December 31, 1999.

What if you have two time travelers?

  • I hop into my time machine on December 31, 2025, stay in the time machine for 5 year exactly, and come out on December 31, 1999.
  • When my time machine arrives with its funny noise on December 31, 1999, a 5-year-old cat sees it and jumps in. She spends a year getting to December 31, 2025.
  • I live another 26 years to December 31, 2025.
  • On December 31, 2025 “the second time around”:
    • My personal time: I’m now 59 years old.
    • The cat’s personal time: She is now 6 years old.
    • External time: Today is December 31, 2025.

“Hypertime”: An extra dimension to allow us to hyper-chronologize times that happen “a second time.”

  • December 31, 1999 happens the first time at ht1.
  • December 31, 2025 happens the first time at ht2.
  • December 31, 1999 happens the second time at ht3.
  • December 31, 2025 happens the second time at ht4.

The traditional worry: Time travel is physically possible but logically impossible.

  • Killing your grandfather
  • Causal loops

Killing your grandfather

Can you kill your grandfather before he meets your grandmother?

  • You can: You can pick up your weapon of choice and do it.
    • A time traveler and a non–time traveler both trying to assassinate the time traveler’s grandfather.
  • You can’t: If you succeeded, then you wouldn’t exist, and so you couldn’t.
    • In fact, neither can the non–time traveler.

The semantics of ‘can’ developed separately by Angelika Kratzer and David Lewis:

  • I can do A just in case my A-ing is compossible with the relevant set of facts.
  • Sometimes it’s clear which set of facts is relevant; sometimes it’s less clear.
    • Can I travel faster than the speed of light? -> Is my traveling faster than the speed of light compossible with the relevant set of facts?
    • Can the president violate the law? -> Is the president’s violating the law compossible with the relevant set of facts?
  • Can the time traveler kill their grandfather?
    • It is compossible with the fact that they carry and are capable of using a weapon.
    • It is not compossible with the fact that the grandfather lived.
  • This does not threaten free will:
    • We know that the non–time traveler didn’t succeed because the grandfather lived, but that’s fine.
    • So it should also be fine in the time traveler’s case.

A residual worry: This story does not allow us to genuinely change the past.

  • Hypertime travel: In order for the time traveler to succeed in killing their grandfather, they may need to travel with hypertime—they need to “reset” the objective present for everybody, that is, relocate the location of the objective present in hypertime.
    • In 2000 the first time around, grandfather lives.
    • In 2000 the second time around, grandfather dies.
  • Hyertime travel is not a branching universe view.
    • In 2025 the first time around, father exists.
    • In 2025 the second time around, father does not exist.
    • Hypertime travel rewrites the chronology without rewriting the hyper-chronology.
    • Father exists in hypertime but not in time.
    • Father “didn’t happen”; he only “hyper-happened.”
  • What happens to the time traveler?
    • Something else has to change: Perhaps they have a different grandparent, perhaps they are a hypertime nomad.
    • From the perspective of non–time travelers, the time traveler has always had the hyper-new grandparent.
  • Hypertime travel seems to raise more moral and political problems than logical problems.

Causal loops

I get into my time machine to travel back to tell my younger self how to build a time machine.

  • I know how to build a time machine because my younger self knew how to build a time machine.
  • My younger self knew how to build a time machine because I told her how to build a time machine.
  • I could tell my younger self how to build a time machine because I know how to build a time machine.

Lewis: Every event in the causal loop is fully explained; what’s unexplained is how the causal loop got started. But this is no more puzzling than how some other happenings got started, think the Big Bang or radioactive decay.