Ok I hadn't seen that before. Whatever shows at the end (if that even makes sense) it's certainly finite, since you're adding up finitely many finite numbers then resetting to 0. — fishfry
The counter resets to 0 after 9. It will only ever show the digits 0-9 — Michael
That is, the sequence is 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, ...
That sequence doesn't converge. — fishfry
I don't see how that follows at all. No mathematical thought experiment can determine the nature of reality. We can use math to model Euclidean geometry and non-Euclidean geometry, but math can never tell is which is true of the physical world. You can use math to model and approximate, but it is never metaphysically conclusive. — fishfry
So concluding something about the nature of time from thought experiments seems to put the horses behind the chariot or maybe to be analogous to ontological arguments, where we conclude something about the world by relying our own, perhaps mistaken, human intuitions. — Lionino
By the way the Thompson's lamp sequence is 1, 0, 1, 0, 1, 0, ... and that doesn't converge either. — fishfry
You seem to take issue with that first paragraph, but your reasoning against it doesn't make any sense. Unless the universe ceases to exist then 60 seconds is going to pass. The passage of time does not depend on the counter. — Michael
we already have the possibility of infinity as an assumption — Lionino
Now, you introduce another premise, "Unless the universe ceases to exist then 60 seconds is going to pass". This premise contradicts what is implied by the others which describe the supertask. — Metaphysician Undercover
Perhaps it would become an infinitely long counter showing an infinitely long line of 9s — Lionino
After 30 seconds a white square turns red, after a further 15 seconds it turns blue, after a further 7.5 seconds it turns back to white, and so on. — Michael
I would propose a parametric curve on the ball path, and, for fantasy sake, by whatever mechanism, the plate knows at what part of the parabola the ball is at, defining the counter. As time goes on, the revolution gets smaller and smaller. Eventually the ball will completely rest on the table, which is 0: — Lionino
by whatever mechanism, the plate knows at what part of the parabola the ball is at, — Lionino
This is just a meaningless hand-wavy rationalisation and is inconsistent with the specific timing intervals: — Michael
The description of the Thomson lamp only actually specifies what the lamp is doing at each finite stage before 2 minutes. It says nothing about what happens at 2 minutes, especially given the lack of a converging limit.
The description of the Thomson lamp only actually specifies what the lamp is doing at each finite stage before 2 minutes. It says nothing about what happens at 2 minutes, especially given the lack of a converging limit. — Lionino
Of course the solution doesn't work when you change the mechanism to be exactly like Thompson's lamp without the limit.
Likewise, Earman and Norton's solution doesn't work if you remove the limit (falling ball).
The paradox is this:I don't even understand what the supposed paradox is. — fishfry
There are no empirical differences, agree. Presentism is the movie reel being played (a sort of literal analogy of the moving spotlight version of presentism). The reel by itself is eternalism (even if it still represents a preferred frame, which eternalists typically deny). The photo is just a frame, and not even that, since it is just a mental state since nothing in the present can be detected. If the state is all there is, then all memories are false and do not constitute evidence of anything.ZENO'S PARADOX
Instead of presentism vs. eternalism, let's talk about the photo vs. movie reel. For the photo and every frame of the movie reel the characters believe they're in the present. — keystone
There is a way to disprove GR, but it is similar to proving/disproving an afterlife: You cannot report the findings in a journal. Both premises of SR contradict presentism, so different premises must be used to take that stance. This has been done, but the theory was generalized about a century after GR came out. It necessarily denies things like black holes and the big bang.Reconciling general relativity with presentism is quite challenging.
I beg to differ, but again, the addition of a premise of a preferred moment has nothing to do with the validity of Zeno's assertions. He makes no mention of the present in any of them. If you disagree, then you need to say how the additional premise interferes with Zeno's logic.Plus, adopting eternalism helps to render Zeno's Paradoxes largely non-paradoxical.
Not sure of the difference. If I cut a string, I don't get points, I get shorter strings.Consider reversing this perspective: adopt a parts-from-whole approach. Start with a single continuous line and then, as if it were a string, cut it to create discrete points (which correspond to the gaps). I encourage you to explore this mindset; I'm eager to discuss it more with you.
You can under some interpretations.You cannot directly observe a particle in a superposition state
I don't think QM states are like points. The analogy is going way off track it seems.I bring in QM, not to sound fancy, but there is an analogy here between observed states (which are like points)
It's one of the things I'm discussing. Zeno's arguments are of the form (quoted from the Supertask Wiki page):I believe you are discussing whether time is discrete or continuous.
Necessary only if the first premise is to be accepted.In the context of Zeno's Paradoxes, it's necessary to consider space and time as continuous (as you later noted).
Yet again, one's interpretation of time isn't relevant to the above analysis.I'm not sure what you're referring to with time being continuous or discrete from a presentist perspective, especially since Zeno's arguments suggest that time does not progress in a presentist's view of the world.
Fine, Then it's a mathematical line segment.I explicitly wrote abstract string.
You're going to have to spell out exactly how an eternalist stance makes a difference here. All I see is an assertion that it makes a difference, but I don't see how.let’s say that adopting an eternalist perspective allows someone to reframe the impossibility of supertasks, turning it's non-existence from having unacceptable consequences to acceptable consequences.
It takes some minimum time to explicitly comprehend/experience a step in a series of steps. Hence the explicit experience of each step of a supertask cannot be completed in finite time.Additionally, none of the paradoxes explicitly rule out (experience of each task) as a possible solution.
Hence needing to see them being irrelevant.If there is a continuous film reel capturing the ticking counter, the limits of observation dictate that there are just some frames that we cannot see.
The paradox is this:
1.The bottom of the stairs is reached at the 1 minute mark.
2.Reaching the bottom of the stairs entails taking a final step.
3. Therefore there is a final step
4.The steps are countably infinite (1:1 with the natural numbers)
5. There is no final (largest) natural number.
6.Therefore there is no final step
#3 & #6 are a contradiction. — Relativist
I would propose a parametric curve on the ball path, and, for fantasy sake, by whatever mechanism, the plate knows at what part of the parabola the ball is at, defining the counter. As time goes on, the revolution gets smaller and smaller. Eventually the ball will completely rest on the table, which is 0: — Lionino
Yes, but check the solution at https://plato.stanford.edu/entries/spacetime-supertasks/#MissLimiThomLamp — Lionino
We can determine whether or not something entails a contradiction. If time is infinitely divisible then supertasks are possible. Supertasks entail a contradiction. Therefore, time being infinitely divisible entails a contradiction. — Michael
You can argue that reality allows for the possibility of contradictions if you want, but most of us would say that it is reasonable to assert that it doesn't. — Michael
After 30 seconds a white square turns red, after a further 15 seconds it turns blue, after a further 7.5 seconds it turns back to white, and so on.
Mathematically, this sequence as a limit of 1.
The sequence never "reaches" 1; nor is there a last step. Neither of these statements is controversial once you understand what a limit is. Sadly, most people have never taken calculus; and most students who take calculus never really learn what a limit is — fishfry
By definition, a limit is not reached, — Relativist
However, the clock does reach 1. At time 1, the stairway descent must have ended — Relativist
That's because the physical steps map to an infinite series in an interval with an open boundary. One can't simply declare there's no final step because the mapping implies there isn't. The taking of steps is a repetitive physical process, and if a physical process ends, there has to be a final step.Certainly the relationship between time (independent of human control) and physical steps taken over a period of time has ended. — jgill
if a physical process ends, there has to be a final step. — Relativist
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