It is a bootstrap paradox. A self-guaranteeing causal event cycle.
- The group THINKS they see Crono dying while in reality it is the doll as the group already went back in time to save Crono (as they also saw the doll, thinking it was Crono, etc.)
- They get the Chrono Trigger
- The Chrono Trigger causes the event that opens the time rift right when Lavos attacks
- They use the doll.
- The heroes THINK they see Crono dying
- They get the Chrono Trigger
- The Chrono Trigger, et cetera ...
You say "the moment itself and all that derives from it is unchanged" and that is exactly what a bootstrap paradox is: Whatever happened, happened. The cause influences the effect and vice-versa. And it always does and always did. A moment that would be changed would be a so-called "consistency" or "grandfather paradox". A Bootstrap Paradox is not called "Paradox" because it is impossible or anything but for the very reason that, as you mention does not need anything but itself. It is not called "Paradox" because it is causally impossible. "Paradox" is often used synonymously to "Anomaly" or "Problem". Just as in science we often call something "Theory" even though it is already proven. A Bootstrap Paradox functions with closed and consistent logic as it uses a cycle, functioning as its own "proxy beginning" that is legitimate for the very fact that it is a cycle. Other than a consistency paradox the Bootstrap is no actual problem and highly misunderstood by many. If Crono's "saving" would not be a bootstrap paradox, it would be a consistency paradox and that is the form of impossible paradoxes (CT also has a lot of them), because "just replacing something" still is a change of things, thus you would automatically overwrite the reality you came from, even if that change seems insignificant, hell, even moving a pebble for 1 mm is already a different reality for the very fact that it has not before existed in this state of truth. It is very true that CT uses a lot of consistency paradox, but Crono's event works very well as Bootstrap Paradox.
(SPOILER)
- Link learns the Song of Storms from a guy who has heard it from Link
- He plays it so the other guy can play it
- Squall, a SEED finds himself in the past and tells Edea about being a SEED from Balamb Garden
- Edea opens up the Garden and creates the concept of the SEEDs
- Squall becomes a SEED
- Squall fights Ultimecia and finds himself back in time
- Harry is warned by is Future Self without knowing it is his Future Self
- He sees his Future Self casting the Patronus thinking it is his father
- He travels back in time
- He warns his past self without his past self knowing it is his own future self
- He waits for his father realizing he will not come and that he has seen his own future self casting the Patronus
- Past Harry sees Future Harry casting the Patronus
- Future Trunks flees from Goku Black
- Events start that provide the ground for Zamasu becoming Goku Black
- Goku Black terrorizes Trunks
- Trunks flees
Twelve Monkeys:
- Bruce Willis is sent back in time to initiate an event that can make the outcome different
- It is revealed at the end that his try to do so - in vain - caused it (Bootstrap/Predestination Paradox)
- Kim Possible A Sitch in Time Tempus Simia Cycle
Supernatural:
- Dean convinces his Past Father to get the Impala
- John buys the Impala
- John gives the Impala to Dean
- Dean is sent back to the past
What is an impossible consistency paradox?
Back to the Future: Marty begins to fade away
Futurama: Fry is his own grandfather
Bootstrap Paradox?
Back to the Future: Johnny B. Goode
I have not seen the movie but if what you say is true then there is no problem with that. That exactly is a bootstrap paradox. You say "if he would not have jumped back in time". But he did. Before. And before. And before. And before. And before. Always. It just exists and that is all.
Sure, they could have easily went in CT with "we just changed it by using a doll that was never used before because before that what we have seen was really Crono's body and not just as assuming it was" and not have cared about it. And in this case they could have even excluded the doll, because if it really was Crono's body and they overwrote time by swapping him out for the very first time, no matter the replacement, it would still be a consistency paradox. But the inclusion of the doll + the possibility with it to say "okay we have not actually for the first time replaced him but what we thought of the dead Crono was also already the doll" makes it possible for the causality cycle, the bootstrap, to exist, and going with something that is no grandfather paradox is normally nicer. You are mixing a few aspects of multiple concepts together to confuse yourself. I have seen that with a few people by now. You already had the answer in your own post but then proceeded to bring in a few more things that messed it up. Even though it is pretty easy. They always travelled to save Crono because the thought he was dead, therefore saved him, making their past selves believe he was dead while the past self of Crono in reality actually was already in the future. They themselves then proceed doing the exact thing. And that very well is a bootstrap paradox. No change, nothing. Whatever happened, happened. Now I don't remember Chrono Cross so maybe they messed it up by bringing it back there and saying that in that moment they changed something but then they would have messed up the opportunity. However, what they thought of for Chrono Trigger specifically and if the thought about that does not matter when it comes to the overall concept in terms of functionality whenever it is used (so everwhere else), even if the creators of Chrono Trigger would one day say "oh, well, here we did not mean that".
Bootstrap Paradoxes are way more solid, functional and consistent than e.g. Alternative Timelines (the things that people use as explanations to exclude consistency paradoxes) which are nowadays a part of popular internet science as Alternate Timelines have actual causality problems (e.g. Regressus ad Infinitum as the reason for a split can be questioned with "what made that reason exist?" and when someone provides the answer of a difference the answer would be "but then that earlier reason must have already caused the split and what caused the earlier reason and difference to exist - and again and again and again; Regressus ad Infinitum). The Bootstrap has none such as the context of it being and eternally running cycle excludes the necessity of "a normal beginning" in the first place; it only needs itself and working as a cycle is allowed to actually do so. Bootstrap Paradoxes are already stable time loops. The problem that so many people have with it is that they fail to realize that within the context of the everlasting cycle that has no beginning and end it is fully legitimate to power itself. Insisting on "no, things need a beginning" is forcing yourself to not think within the context of the cycle that has no beginning and end and therefore running totally past what a bootstrap paradox is. A bootstrap paradox cheats its way out needing something other than what it consists of to happen and scientists who actually invest a bit more time in that than just thinking "uh but it needs a beginning" very well know its functionality. Guys, do not fall for the word "paradox". Paradox does not automatically mean it is an impossible concept in nature. Nature does include paradoxes. Not all paradoxes are inconsistent and thus impossible. You must be under the impression that you are the first one I am telling this. I assure you, you are not. By far.




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