ILLUSTRATION BY DANIEL HERTZBERG
Births, deaths, and other time travel paradoxes.
Idoubt that any phenomenon, real or imagined, has inspired more perplexing, convoluted, and ultimately futile philosophical analysis than time travel has. (Some possible contenders, determinism and free will, are bound up anyway in the arguments over time travel.) In his classic textbook, An Introduction to Philosophical Analysis, John Hospers tackles the question: “Is it logically possible to go back in time—say, to 3000 B.C., and help the Egyptians build the pyramids? We must be very careful about this one.”
It’s easy to say—we habitually use the same words to talk about time as we do when talking about space—and it’s easy to imagine. “In fact, H. G. Wells did imagine it in The Time Machine (1895), and every reader imagines it with him.” (Hospers misremembers The Time Machine: “A person in 1900 pulls a lever on a machine and suddenly is surrounded by the world of many centuries earlier.”) Hospers was a bit of a kook, actually, who achieved the unusual distinction for a philosopher of having received one electoral vote for President of the United States. But his textbook, first published in 1953, remained standard through four editions and 40 years.
His answer to the rhetorical question is an emphatic no. Time travel à la Wells is not just impossible, it is logically impossible. It is a contradiction in terms. In an argument that runs for four dense pages, Hospers proves this by power of reason.
“How can we be in the 20th century A.D. and the 30th century B.C. at the same time? Here already is one contradiction … It is not logically possible to be in one century of time and in another century of time at the same time.” You may pause to wonder (Hospers doesn’t) whether a trap is lurking in that deceptively common expression, “at the same time.” The present and the past are different times, therefore they are not the same time, nor at the same time. Q.E.D. That was suspiciously easy.
The point of the time-travel fantasy, however, is that the lucky time travelers have their own clocks. Their time can keep running forward, while they travel back to a different time as recorded by the universe at large. Hospers sees this but resists it. “People can walk backward in space, but what would ‘going backward in time’ literally mean?” he asks.
And if you continue to live, what can you do but get one day older every day? Isn’t “getting younger every day” a contradiction in terms—unless, of course, it is meant figuratively, as in “My dear, you’re getting younger every day,” where it is still taken for granted that the person, while looking younger every day, is still getting olderevery day?
(He gives no hint of being aware of F. Scott Fitzgerald’s short story in which Benjamin Button does precisely that. Born as a 70-year-old, Benjamin grows younger every day, until infancy and oblivion. Fitzgerald would have admitted the logical impossibility. The story has many offspring.)
Time is necessarily simple for Hospers. If you imagine that one day you are in the 20th century and the next day your time machine carries you back to ancient Egypt, he retorts: “Isn’t there a contradiction here again? For the next day after January 1, 1969, is January 2, 1969. The day after Tuesday is Wednesday (this is analytic—‘Wednesday’ is defined as the day that follows Tuesday)” and so on. And he has one final argument, the last nail in time travel’s logical coffin. The pyramids were built before you were born. You didn’t help. You didn’t even watch. “This is an unchangeable fact,” says Hospers and adds: “You can’t change the past. That is the crucial point: the past is what happened, and you can’t make what happened not have happened.” We’re still in a textbook about analytical philosophy, but you can almost hear the author shouting:
Not all the king’s horses or all the king’s men could make what has happened not have happened, for this is a logical impossibility. When you say that it is logically possible for you (literally) to go back to 3000 B.C. and help build the pyramids, you are faced with the question: Did you help them build the pyramids or did you not? The first time it happened you did not: You weren’t there, you weren’t yet born, it was all over before you came on the scene.
Admit it: You didn’t help build the pyramids. That’s a fact, but is it a logical fact? Not every logician finds these syllogisms self-evident. Some things cannot be proved or disproved by logic. The words Hospers deploys are more slippery than he seems to notice, beginning with the word time. And in the end, he’s openly assuming the thing he’s trying to prove. “The whole alleged situation is riddled with contradictions,” he concludes. “When we say we can imagine it, we are only uttering the words, but there is nothing in fact even logically possible for the words to describe.”…