= 27d567bc2d48d9f40e9ccc20ea370b15)
metaphysicist comments on Natural Laws Are Descriptions, not Rules - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (234)
Yes, I understand that; in fact, it was my express premise: "You can always add a finite number to an infinite set and not change the number of elements." That is, not change the number of quarks from one case to another.
Please read it again more carefully. My argument may be wrong, but it's really not that naive.
Added.
I see what you might be responding to: "So, there are more quarks than are contained in the set of all quarks." The second sentence, not the first. It's stated imprecisely. It should read, "So, there are other quarks than are contained in the set of all quarks." Now changed in the original.
You've collapsed the distinction between two possible worlds. You started out by saying, consider a universe containing infinitely many quarks. Then you say, consider a universe which has all the quarks from the first universe, plus a finite number of extra quarks. The set of all quarks in the second scenario indeed contains quarks that aren't in the set of all quarks in the first scenario, but that's not a contradiction.
It's like saying: Consider the possible world where Dick Cheney ended up as president for the last two years of Bush's second term. Then that would mean that there was a president who wasn't an element of the set of all presidents.
Replying separately to this now added comment. it still seems like this is an issue of ambiguous language. It isn't that there are other quarks that aren't contained in the set of all quarks." Is is that there's a set of quarks and a superset that have the same cardinality.
The problem seems to be that you are using the word "more" in a vague way that reflects more intuition than mathematical precision.
I think you responded before my correction, where I came to the same conclusion that my use of "more" was imprecise.
Added
I remember reading an essay maybe five years ago by Eliezer Yudkowsky where he maintained that the early Greek thinkers had been right to reject actual infinities for logical reasons. I can't find the essay. Has it been recanted? Is it a mere figment of my imagination? Does anyone recall this essay?