I downvoted common_law’s post, because of some clear-cut math errors, which I pointed out. I’m downvoting your comment because it’s not saying anything constructive.
There’s nothing wrong with what common_law was trying to do here, which is to show that infinite sets shouldn’t be part of our ontology. Experience can’t be the sole arbiter of which model of reality is best; there is also parsimony. Whether infinite quantities are actually real, is no less worthy of discussion than whether MWI is actually real, or merely a computational convenience. I only agree with you that the math lacked rigor. This is discussion, so I don’t see a problem with posting things that need to be corrected, but I had to downvote the post because it might have confused someone who didn’t notice the errors.
There are arguments which are wrong because they lack rigor, but in my opinion this isn’t one of them. The main problem is asking a question about “actual existence” of abstract objects without clear understanding what such “actual existence” would represent. I can imagine a rigorous version of this post where “actual existence” was given a rigorous definition, but I doubt it would convince me about anything (as I remain unconvinced that e.g. modal logic is a useful epistemological tool although it can be formalised).
Note that (one of) the apparent motivation(s) of all recent anti-infinity posts is rejection of many-world interpretation of QM, i.e. it is unlikely that the author is aiming at constructing a neat rigorous theory.
I downvoted common_law’s post, because of some clear-cut math errors, which I pointed out. I’m downvoting your comment because it’s not saying anything constructive.
There’s nothing wrong with what common_law was trying to do here, which is to show that infinite sets shouldn’t be part of our ontology. Experience can’t be the sole arbiter of which model of reality is best; there is also parsimony. Whether infinite quantities are actually real, is no less worthy of discussion than whether MWI is actually real, or merely a computational convenience. I only agree with you that the math lacked rigor. This is discussion, so I don’t see a problem with posting things that need to be corrected, but I had to downvote the post because it might have confused someone who didn’t notice the errors.
There are arguments which are wrong because they lack rigor, but in my opinion this isn’t one of them. The main problem is asking a question about “actual existence” of abstract objects without clear understanding what such “actual existence” would represent. I can imagine a rigorous version of this post where “actual existence” was given a rigorous definition, but I doubt it would convince me about anything (as I remain unconvinced that e.g. modal logic is a useful epistemological tool although it can be formalised).
Note that (one of) the apparent motivation(s) of all recent anti-infinity posts is rejection of many-world interpretation of QM, i.e. it is unlikely that the author is aiming at constructing a neat rigorous theory.