Timeline for Doesn't infinite regress go backward forever? Is SEP wrong?
Current License: CC BY-SA 4.0
13 events
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| Jul 26, 2021 at 1:46 | comment | added | Ted Wrigley | @user4894: I understand your intuition. I disagree with it, for the reasons I've outlined. | |
| Jul 26, 2021 at 0:23 | comment | added | user4894 | @TedWrigley My intuition is based on the mathematical interpretation. In set theory, upward infinite membership chains are common; while downward infinite membership chains are explicitly outlawed by the axiom of foundation. So set theorists, at least, draw a sharp distinction between the two directions; even if a case can be made that the distinction is mostly meaningless. Set theorists find it meaningful and perhaps that's the biggest influence on my intuition. I appreciate your point of view, you're not wrong. | |
| Jul 26, 2021 at 0:17 | comment | added | Ted Wrigley | @user4894: I think you're missing the forest for the trees, here, but I don't see value in repeating what I've said a third time. I'll leave it for others to decide... | |
| Jul 25, 2021 at 22:18 | comment | added | user4894 | @TedWrigley Re Zeno, right. Zeno can't even get off the starting line. Whereas in a different version of Zeno, he can go 1/2 way then 3/4 then 7/8 but he can never reach the finish line. The two cases exemplify infinite regress versus mathematical induction. Turtles all the way down versus all the way up. | |
| Jul 25, 2021 at 22:16 | comment | added | user4894 | @TedWrigley Recursion always has a base case, that's part of the definition. So recursion is like mathematical induction and NOT like infinite regress. Humean and mathematical induction are more different than alike. Mathematical induction is a logically deductive method. It's absolutely certain. Humean induction just says "well it's always been this way so we'll hope for the best in the future." it's philosophically questionable and often proven false in practice. | |
| Jul 25, 2021 at 22:06 | comment | added | Ted Wrigley | @user4894: Regression says the opposite (in English): "This can only hold if some prior condition holds." When the prior condition is recursive — in other words, if it repeats the aspect of this that it was meant to resolve — then the regression is infinite, meaning you can never resolve it. A mathematical example would be Zeno's paradox, where Achilles can't cross the finish line until he reaches the halfway point, and he can't reach the halfway point until he's crossed a quarter of the distance, and he can't... until we see that Achilles can't even manage to get off the starting line. | |
| Jul 25, 2021 at 21:59 | comment | added | Ted Wrigley | @user4894: As I said, mathematical induction and Humean induction are cognates; not different things. Induction says (in English): "If I know that this holds, then the next thing I see after this will also hold." The concept of 'the next thing' is far more rigorously defined in math than in philosophy, obviously, but the intent is the same. | |
| Jul 25, 2021 at 20:19 | comment | added | user4894 | @TedWrigley "without the invocation of an infinitely long string of elements to support it." -- But then you are saying 2 supports 1, 3 supports 2, etc. In your model, it's "turtles all the way UP!" Isn't that the opposite of an infinite regress? Please see my edit to my question in case that makes my intent more clear. And of course I did mean mathematical induction, which is completely different than Humean induction. Mathematical induction is a deductive principle, confusingly named perhaps since it's very different than philosophical induction. | |
| Jul 25, 2021 at 19:18 | comment | added | user4894 | @viuser Thanks, you're the only one so far who even understands what I'm saying! | |
| Jul 25, 2021 at 19:12 | comment | added | Ted Wrigley | @viuser: The difference between mathematical and empirical induction is minimal; they share the same forward declaration that if x(n) holds, x(n+1) will hold. An infinite regress is the opposite, a reflexive declaration that x(n) holds if and only if x(n+1) holds. | |
| Jul 25, 2021 at 18:15 | comment | added | viuser | I suspect OP means mathematical induction (a valid proof technique), not empirical induction. And the SEP description “a first member but no last member, where each element leads to … the next” sounds like mathematical induction. | |
| Jul 25, 2021 at 16:35 | history | edited | Ted Wrigley | CC BY-SA 4.0 |
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| Jul 25, 2021 at 16:22 | history | answered | Ted Wrigley | CC BY-SA 4.0 |