Logic, Mathematics, Physics And Time Travel

 

Time travel fiction raises some basic questions, none more so than in Poul Anderson's works.

Logic

Philosophy undergraduates receive at least an introduction to logic in the form of symbolic logic. The first logical premise, "if p, then p," expressed with a hook symbol that is not on my keyboard, means simply that, if a proposition, p, is stated at any point in an argument or narrative, then the truth of p must be assumed at any subsequent point in that same argument or narrative. Whether p is in fact true is beside the point at this stage. Of course, most propositions are dated. Thus, "Boris Johnson is the Prime Minister of the United Kingdom" is true at some times but not at others. However, we can be more precise. Thus, "Bojo is the UK PM at 1:30 pm on Monday 16 May, 2022 AD in Timeline A." I specify a timeline just in case there are multiple, alternate, divergent or successive timelines. A single line of argument cannot coherently affirm, then deny, a sufficiently precise proposition.

A familiarity with logic must affect how philosophy students and graduates read Poul Anderson's Time Patrol series. One fellow sf fan did not accept my logical arguments about time travel on the ground that we do not know how time travel would work. But we do know whether one proposition follows from another. We do know that, if someone prevents my parents from meeting, then he initiates a sequence of events in which I was never born, not a sequence of events in which I am born, live into adulthood, then disappear!  That cannot happen, however time travel works.

Mathematics

I was not introduced to calculus at school but had to work out the most basic principle of calculus for myself just to think about time travel. We can travel through space at 60 miles per hour but do not travel through time at 60 minutes per hour hour because 60 minutes = 1 hour. Motion and therefore velocity require two quantities or sets of units changing in relation to each other. We can accelerate from 60 to 100 miles per hour but not from 60 to 100 minutes per hour. HG Wells in The Time Machine and James Blish in The Quincunx Of Time get this wrong. Poul Anderson does not.

Physics

I know nothing about it. Physical laws determine whether time travel is physically possible. If logic or mathematics could predict physical laws, then there would be no need for empirical science.