Logic

"'I think you're describing a logically impossible situation. I'll grant the possibility of time travel, seeing that we're here, but an event cannot both have happened and not happened. That's self-contradictory.'"
-Poul Anderson, Time Patrol (New York, 2006), p. 9.

The statement that this event happened does contradict the statement that this event did not happen. How does the Time Patrol instructor respond?

"'Only if you insist on a logic which is not Aleph-sub-Aleph-valued,' said Kelm." (p. 10)

This sentence is completely meaningless. Just in case it did turn out to have some meaning, I have just googled "Aleph-sub-Aleph-valued logic" and all that came up was this sentence in the first Time Patrol story.

Surely all that needs to be said is either that there is a single discontinuous timeline in which an event did not happen even though there are what have to be regarded as spurious memories of it or that there are two timelines? Discussion in the Time Patrol series alternates between these two accounts although I think that the second account is the only way to make overall sense of the series. While they are in a timeline, Time Patrollers state that it is possible that this timeline does not exist and that is self-contradictory.