All of this discussion of time travel is relevant to several works by Poul Anderson, of course, and Anderson explores every option. The two basic premises are "the past can be changed" and "the past cannot be changed." The "can be changed" premise causes endless confusion and can be rationalized in several different ways. See here.
Anderson's Time Patrol series:
is superb historical sf;
presents the circular causality paradox within a causality violation scenario;
in fact, shows the Patrol completing causal circles in order to prevent causality violations;
is subtle in its presentation of paradoxes so that any incoherencies are not immediately apparent;
is ambiguous - is there a single discontinuous timeline or a single mutable timeline or are there divergent timelines?
Everard's language alternates between discontinuity and mutability but, in "Star of the Sea," he refers to a fork in events, which implies divergence.
Back in Nantucket:
"...presumably they were still - the word made no sense, but English grammar wasn't well adapted to time travel - all right, up in the twentieth."
-SM Stirling, Against The Tide Of Years (New York, 1999), Chapter Three, p. 39.
The Nantucketers need the Time Patrol language, Temporal.