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Then stop focusing on "being alive" bit. I was giving this solely as an example of why making statements about the future and basing arguments about some future

Then stop focusing on "being alive" bit. I was giving this solely as an example of why making statements about the future and basing arguments about some future state cannot work. Yet you take it as some trick to avoid having to explain the paradox. (Your analogy with pretending that the word false doesn't mean false is entirely off base. I don't see the correspondence. But no matter.) I think I've found a formulation that won't offend your sense: due to time's arrow and causality (which both go forward in time), one cannot make an induction that goes backward in time. This would cause a circular dependency in the inductive proof. In this case, the steps of the inductive proof go from Friday, down to Thursday, Wednesday, etc. Yet at the same time, causality goes from Wednesday to Thursday to Friday. One cannot simply dismiss causality. IOW, we have the inductive process N, N+1, N+2, where N is used to proove N+1, etc and where N = Friday, N+1 Thursday, all the while N state depends on N+1 because due to real-world causality, what happens on Friday depends on Thursday. You seem to wish to deny causality.

prof_hobart 15y ago
I'm not the one focusing on it. I'm saying it's pretty much irrelevant to the point of the paradox. It's not about being able to predict any future event except the date of the exam - as I've said, you could put all of the caveats you want in there about any other events either happening or not happening (e.g. "assuming that we're all still alive, and assuming that they don't rename the days of the week before next Friday, and that no-one's changed the terms of the teacher's statement etc") and it doesn't change the paradox. As for causality, I don't really see how that's relevant either. Assuming you've accepted whatever caveats we feel like adding, then nothing (apart from the test having happened) that happens on Monday, Tuesday, Wednesday or Thursday is going to change the fact that if you've got to Friday without the test having happened you'll have certainty that the test will be on Friday, and therefore won't be a surprise. In other words, the only things required for the paradox to be a paradox are the idea of a test happening on a day that the pupils can't predict and a deadline for when that test must happen by. (And the reason my analogy about the word false is relevant is that it's pretty clear what the bounds of both paradoxes are, and you "solve" either of them by throwing in things - whether that's events external to the point of the paradox, or word definitions external to the point - that are outside those bounds, but in either case it doesn't tell you anything useful about the paradox itself).

prof_hobart 15y ago

I'm not the one focusing on it. I'm saying it's pretty much irrelevant to the point of the paradox. It's not about being able to predict any future event except the date of the exam - as I've said, you could put all of the caveats you want in there about any other events either happening or not happening (e.g. "assuming that we're all still alive, and assuming that they don't rename the days of the week before next Friday, and that no-one's changed the terms of the teacher's statement etc") and it doesn't change the paradox. As for causality, I don't really see how that's relevant either. Assuming you've accepted whatever caveats we feel like adding, then nothing (apart from the test having happened) that happens on Monday, Tuesday, Wednesday or Thursday is going to change the fact that if you've got to Friday without the test having happened you'll have certainty that the test will be on Friday, and therefore won't be a surprise. In other words, the only things required for the paradox to be a paradox are the idea of a test happening on a day that the pupils can't predict and a deadline for when that test must happen by. (And the reason my analogy about the word false is relevant is that it's pretty clear what the bounds of both paradoxes are, and you "solve" either of them by throwing in things - whether that's events external to the point of the paradox, or word definitions external to the point - that are outside those bounds, but in either case it doesn't tell you anything useful about the paradox itself).