Continuing A Combox Discussion

I wanted to continue a discussion in the combox for Upstairs Of The Turning Point but my combox comment would have become a lengthy one so why not make it a post instead?

Discussing time travel paradoxes in Poul Anderson's Time Patrol series, S.M. Stirling comments:

"...if you prevent your parents from meeting, as long as you're there in the past prior to the change, you continue to exist, but the chain of events that resulted in you is gone.

"It's sort of... disturbing..."

A single discontinuous timeline in which a time traveler can arrive from a prevented future and in which some events are remembered even though they never did happen and never will happen is disturbing and counter-intuitive but logically possible because not self-contradictory. However, there is a contradiction in the Time Patrol series:

at one stage, Manse Everard is in the timeline where Keith Denison is Cyrus the Great;

therefore, that timeline exists;

however, Everard, while in that timeline, says that it might be brought about that that timeline does not exist;

this is a contradiction;

we can, without self-contradiction, believe that "remembered" events did not happen, i.e., that the "memories" are false, but we cannot, without self-contradiction, believe that an event that IS now happening might be caused NOT to happen.

My way of making logical sense of this story, "Brave To Be A King," is as follows. At the end of the story, the entire timeline in which Denison was Cyrus is in the past of the second temporal dimension. Each moment of the first temporal dimension contains a three-dimensional universe. Each moment of the second temporal dimension contains a four-dimensional spacetime continuum. At the end of the story, it is true to say that Denison never was Cyrus in the past of the current timeline but it would not be true to say that he had never been Cyrus in any previous timeline. In this context, "current" and "previous" refer to temporal relationships within the second, not the first, temporal dimension. The Temporal language has appropriate tenses and terminology.