Earlier quoted context omitted.
> Try dealing with something of consequence, like killing your former self (as in: the person in that point of time-space which carries the mutable signifier of “yourself” which is younger than yourself) or giving yourself a kilogram of gold from the future, which I think would violate the law of preservation of energy or whatever. It is entirely irrelevant what it is . The point is that if the system is immutable it…
> It is entirely irrelevant what it is. The point is that if the system is immutable it is impossible to represent a combination of state transitions that alters an existing state, Alters? Aha! But you cannot alter that which is immutable! Seems that you still don’t get the concept. See how silly it is to language police people on such subjets? > would in that case [only include those] where the time travel does not…
If that was what I was doing, yes. But it wasn't, and your example is nonsensical because you referenced a statement where I explicitly pointed out that you cannot alter that which is immutable.
> Highlighted the problematic part with brackets. This is just hand-waving. “Only those”? Your theory would have to be able to explain concrete examples like the grandfather problem, or else it doesn’t rise to the level of being a theory that can explain the paradox.
No, that is not a problematic part at all. The grandfather paradox is a statement of a problem. You can not solve it without specifying a set of alterations or constraints on the unconstrained model that creates the problem. That is the point: The existence of the paradox suggests the model it is posed within is not possible. The solution to a paradox is to resolve the flaw in the model, as you yourself point out next:
> Irrelevant unless there is an actual elephant folding paradox that I’m missing. Impossible things can be explained; paradoxes cannot since they reveal a contradiction in the model.
That the reveal a contradiction in the model by pointing out a means by which the understanding of a model would allow an impossible thing is in fact the point. The solution is to identify constraints that makes the impossible thing impossible to represent in a model. Just like we can point out ways in which folding an elephant is impossible.
> “Determinism” is either irrelevant or non-sufficient. “Could not possibly” is pure hand-waving as there is nothing which makes sure that you are able to do something benign (like greet your former self) but not do something like kill yourself.
Immutability means you can not DO anything at all. No change ever happens. The passage of time in such a model is an illusion. You're still hung up on treating this as a series of events that are happening rather than a replay of an immutable state from a set of such states that needs to be possible to represent.
What makes "sure that you are able to do something benign" is simply an inherent constraint of needing to be able to represent graph of the transitions in an immutable way consistent with what we otherwise think we know about cause and effect. There's no other mechanism needed. A whole lot of seemingly benign things would also be impossible to express because it would cause interactions we're unable to account for, but we would never see the effects of that because those things also could never be expressed and so has never happened. The same way we can't express the states required to allow me to fold an elephant within the constraints of the universe we inhabit.
> You can’t resolve the Barber Paradox by simply saying that the Universe wouldn’t allow the barber to shave himself. That’s effectively what you’re doing here, only using vaguely hard science terms with a seasoning of “you still don’t get it”.
The Barber Paradox is an ontological paradox. We can certainly turn it into a space-time paradox by positing that the events in it are actually played out, in which case it is simply a restatement of the grandfather paradox.
And resolving such a paradox by introducing a constraint that ensures the paradoxical state is impossible is exactly how to do it.
I've not done any handwaving at all - I've given a very simple hypothetical model, and explained how it resolves it by making the impossible states impossible to represent.
Let me try one more time. S(t) represents the state at a given time. Each state is immutable, has always existed and will always exist exactly as it is, entirely unchanging in every way. That makes the following set of state transition a representation of the hypothetical example:
S(1) -> S(2)
S(2) -> S(3)
S(3) -> S(4)
S(4) -> S(2)
S(4) -> S(5)
Now, to introduce the paradox as stated, S(2) must involve you being killed. But immutability requires that S(2) has and always will be the same. It does not change when the time travel "happens", so any effect of the time travel must be consistent with what happened before it, in both previous states (S(1) and S(4)) and the next state - S(3). The time travel alters perspective, it does not alter the model. So in drawing up what goes into each of these states, you have a choice: Either you're always dead when transitioning to S(3) or you were never dead when transitioning to S(3). So either no killing happens, or it always happened and always will. In the latter case, the killing can not happen by you travelling back from S(4) to S(2), because in that case you never existed at S(4) and never will exist at S(4) and so future you never existed at S(2) and never will. To allow the paradox to exist, you need to be able to exist at S(4) to travel back in time, and so the only valid set of state transitions that involves you travelling back are ones where you're still existing in S(3) (and so in S(4)).
The paradox is explicitly the notion that we lack a clear understanding of whether there is a rule that prevents us from introducing an instability. Immutability in this case then introduces a rule that makes instability impossible to represent because that instability requires mutability, and so makes it impossible to represent the paradoxical state in question, and so if the universe is immutable, the paradox is resolved.
You can continue to argue this isn't the case, but you would simply be wrong.
[Incidentally, another way of resolving this paradox is a model where the instability is perfectly fine - where the system is mutable and if instabilities like this are introduced, the system will just keep oscillating between states as a "wavefront" of state transitions keep rolling through. This would require a model with a "memory" of past states to allow transitions to get "undone", but it's perfectly possible to define such a model. The only thing that makes this a paradox is that it appears to be at odds with what we think we know about the world, and so it tells us that what we think we know about the world is wrong.]