Floating cork paradox

A floating cork paradox is a paradox to show that it is impossible to intentionally prevent an event from occuring using time travel. This paradox build on the predestination paradox, which states that any even that occurs in the past while time traveling is predestined to occur when that person travels in time because the event already happened, by showing that elements of this paradox and the grandfather paradox, which states that you cannot travel back in time and kill your grandfather because you would then never be born, are not mutually exclusive. The paradox shows that because you cannot change something you do not know exists, accidents during time travel are the only possible predestined events that can occur.

Thought Experiment

This is the original thought experiment as written by Matt Pfaff:

Just as a river flows in one direction, time always flows in one
direction at a constant speed. A man flows constantly through time
like a man sitting in a boat. This man ties his boat to the shore,
gets out, walks back toward the start of the river, and drops a cork
in the river. Because the river moves constantly forward, the cork
will then exist at all stages of the river extending in to infinite.
If you then look at each point in the river as a moment in time, the
cork existed in each moment in time after it is dropped, regardless of
what happened in that spot before it was dropped. Similarly, if a man
travels back in time and changes an event, that event will forever be
changed at every moment after that time. Therefore, anything we are currently aware of
occurring cannot be changed through time travel, because if it could
be changed then it would already have been changed and we would not
currently be aware of it.

Dilemma

If a person were to travel back in time and change Event A to Event B, everyone, including the time traveler, will be born without knowledge that Event A ever occured. Likewise, if another person travels back in time and change Event B to Event C, everyone, including both time travelers, will be born without knowledge that Event A or Event B ever occured. This means that the only events that can possible be known are the very last events to occur. As these are the very last events to occur, it is logically impossible to change these events.

This raises the key question:
Is it possible to travel back in time and change an event if you never knew that event occured?

The obvious response to this dilemma is that it is possible to prevent an event from occuring if you first travel to a past version of yourself, who by the laws of the flowing timeline already does not know Event A ever occured, and convince him that it is necessary to do this. However, by the same flowing timeline laws that govern the previous version of yourself mean that at the exact moment you change history, all version of yourself will never know that Event A ever occured. This means you will later be born without knowing that Event A ever occured and have no way of knowing that you need to travel back in time and warn a past version of youself.

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