If A and D
Than C
Your C is is my A', I think.
I understand it would be impossible to travel back in time to the same timeline, but why is it impossible all together?
I think you were hinting at this: where did A' (or your c) come from? What was it implied by? Before you travel back in time, A and A' would have an exact intersection, call it event P (for past). In other words, P implies A, yet P would also have to imply A'. This contradicts CD.
then everything we do will essentially be changing the events that happened even farther into the past, because in order for us to do this, a different set of events would have had to have happened to lead up to us doing this. And since everything has to change in order for something to change, the lottery doesn't have to turn out the same.
Exactly (the bolded part in particular).
What if there were no events leading up to us and our actions, but instead there are just new future actions caused from introducing a foreign entity that wasn't caused by previous reactions? This would sort of contradict CD in the sense that there is something that happened with nothing causing it, but that's slightly off point.
It entirely contradicts CD for exactly that reason. CD can only be valid if there are no loopholes, or at least no more than one*. If you think about it, You are allowing for something to happen randomly (the existence of a new entity) with no restrictions.
This makes statements like
If A, then B
Invalid, since you would have to stipulate that no no entities are introduced. Under CD, if you were to somehow posses all of the information in the universe, you could extrapolate as far into the past and future as you want. BUT, this would require that there be no time travelers to mess things up. And you would have no way to predict the effects of time travelers, thereby making all of your calculations useless.
You should be able to predict where/when time travelers would go, and what change they would bring to the new time. BUT, I don't see how you could extrapolate from this new timeline. If you had
A -> B-> C-> D -> E
And someone in A predicts someone (t1) in D travels back to B, AND someone (t2) in E travels back to C this would create
A -> B'-> C'-> D' -> E' (from T1)
AND
A -> B"-> C"-> D" -> E" (from T2)
Ignoring the fact that A is causing three events, (we'll go with your theory that the effects of time travel in CD must go back to the very beginning), this still creates the problem of E' and D". In either event the respective time traveler (T1 or T2) may or may not travel back again, and they definitely won't be able to travel back to the same event.
IE T1' might travel from D' to B"', and T1" might travel from D" to B"". By induction, this would create infinitely many possible events. So, our poor guy at A would never be able to predict events past B, (since each prediction would create another scenario), which means he would never get to predict the event of the time traveler in the first place, and certainly never get to the second time traveler, who would be creating future scenarios that effect the first time traveler.
This is a logical contradiction, since the reason he cannot predict event D is because of his prediction of even D.
(note that under CD these predictions are certainties).
*The one exception being the beginning of the universe, some sort of prime mover.
