Heh, that was really just me trying to come up with a justification for shoe-horning a theory of identity into a graph formalism so that Konig's Lemma applied :-)
If I were to try to make a more serious argument it would go something like this.
Defining identity, whether two entities are 'the same person' is hard. People have different intuitions. But most people would say that 'your mind now' and 'your mind a few moments later' are do constitute the same person. So we can define a directed graph with verticies as mind states (mind states would probably have been better than 'observer moments') with outgoing edges leading to mind states a few moments later.
That is kind of what I meant by "moment-by-moment" identity. By itself it is a local but not global definition of identity. The transitive closure of that relation gives you a global definition of identity. I haven't thought about whether its a good one.
In the ordinary course of events these graphs aren't very interesting, they're just chains coming to a halt upon death. But if you were to clone a mind-state and put it into two different environments, they that would give you a vertex with out-degree greater than one.
So mind-uploading would not break such a thing, and in fact without being able to clone a mind-state, the whole graph-based model is not very interesting.
Also, you could have two mind states that lead to the same successor mind state - for example where two different mind states only differ on a few memories, which are then forgotten. The possibility of splitting and merging gives you a general (directed) graph structured identity.
(On a side-note, I think generally people treat splitting and merging of mind states in a way that is way too symmetrical. Splitting seems far easier - trivial once you can digitize a mind-state. Merging would be like a complex software version control problem, and you'd need very carefully apply selective amnesia to achieve it.)
So, if we say "immortality" is having an identity graph with an infinite number of mind-states all connected through the "moment-by-moment identity" relation (stay with me here), and mind states only have a finite number of successor states, then there must be at least one infinite path, and therefore "eternal existence in linear time".
Rather contrived, I know.
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Here is a second Simulation Trilemma.
If we are living in a simulation, at least one of the following is true:
1) we are running on a computer with unbounded computational resources, or
2) we will not launch more than one simulation similar to our world, or
3) the simulation we are in will terminate shortly after we launch our own simulations.
Here 'short' is on the order of the period between the era we start the simulation at and when the simulation reaches our stage.
Why would us launching a simulation use more processing power? It seems more likely that the universe does a set amount of information processing and all we are doing is manipulating that in constructive ways. Running a computer doesn't process more information than the wind blowing against a tree does; in fact, it processes far less.