I agree has a broken link.
I don’t know LW editing. (First post.) How do internal links work ? Edit : Simple HTML internal links, I had to add “#”.
By meta-epistemy do you mean something that can explain how the current rationalist epistemology came about or do you want something that can explain how one should make it better in the future?
By meta-epistemy, I meant an epistemy that we should follow to define and evaluate new sub-epistemies.
Can you clarify what sub-epistemies are in this framework?
Basically, instead of coming with a new thought. Trying to see to which more general field that thought belong too, and if there are basic associated rules that could help checking the validity of the thought. It’d be easier with some examples, but that could be taken negatively by the source material’s author. It’s late where I am. If you want an example, I can produce an artificial one tomorrow.
“summation of {i = 0} to n of (n combination i) = 2^n”
This is not a proof that “2^{aleph_0}” is the cardinality of the set of the subsets of natural numbers. You assume it works in the infinite cardinal case (without proving it), and then say that you thus proved it. You got confused by notation.
“I shall proffer a mathematical proof to show that for any infinite set of cardinality aleph_0 (the cardinality of the set of natural numbers) there are aleph_1 (2aleph_0) distinct infinite subsets.”
No. 2^{aleph_0} is /by definition/ the cardinality of the set of the subsets of the natural numbers. It’s named that way to allow the intuition of “summation of {i = 0} to n of (n combination i) = 2n” to work with cardinalities.
“aleph_1 (2^{aleph_0})”
aleph_1 = 2^{aleph_0} has been shown to be independent from ZFC. ie, if we haven’t worked within inconsistent math for that past 60 years, what you just said is unprovable. You might have confused aleph and beth numbers.