Essay talk:Of Islands

You might want to put them in your "user" space, or, if you think they are "ready for prime time", put them in "essay". Because your talk page is community property, etc. Ask me what I mean if you don't understand, at my talk page. human 02:38, 9 January 2008 (EST)

I think that I may need to read "islands" a few more times. But, as Human says, you might wish to consider the essay space for some of your stuff as that should invite more comments. :-) (Hail the goat!)--Bob^{bing up} 04:44, 9 January 2008 (EST)

Yes, I have been thinking about that. At least about putting them in my userspace with simply links to them on this page. I suppose I have something to do now besides correcting arguments that are in slight err, or developing bullet proof logical arguments myself. You know, at least for philosophy, science, and logic pedantism is a really good thing. However, of course, not so much for light reading... I am very verbose. --Eira ^yay! The Goat be praised. 12:33, 9 January 2008 (EST)

Done, and done. --Eira ^yay! The Goat be praised. 13:18, 9 January 2008 (EST)

Minor details

• Since length of description (as one or more statements) is not necessarily finite, the cardinality of the set A (it may take more than one sentences to describe an element in "Everything") should be uncountably infinite (array of infinite length of a finite number of elements, similar to Cantor's diagonal argument), so in "It follows that"(6,4) it may be better to use "real numbers" instead of "rational numbers"
  • Note if a one-string identifier is used, the cardinality would still be uncountable as long as the length of the string is infinite (like real number, array of finite number of possible elements(alphabets) with infinite length)
• It may be better to write it in formulae for your logic statements so there is less ambiguity.
• In "Given that"(6) and "Given that"(9), is the g()'s the same function that spans different domains?

These are the suggestions I have so far. Maybe more will come up later. [[User:K61824|]][[User_talk:K61824|]] 20:03, 9 May 2009 (UTC)

I had not taken into account any amount of countability in this matter... Now considering it, the cardinality of the set A in fact is actually significantly larger than the cardinality of even the real numbers. Case in point, the set A must by definition contain the real numbers, but not only that, but it also contains an infinite number of imaginary numbers composed from each real number. But A does not stop just there, it also contains an infinite number of sets, and an infinite number of functions upon those sets. It is thus easy to see that set A has a cardinality of no less than Aleph-Null up-arrow to the Aleph-Null Aleph-Null. Thus regardless of a choice of rational or real numbers, the cardinality of the number set would still technically be insufficient to map from A to that set of numbers. So, I don't think it matters using a "countable set" vs the "uncountable set" of real numbers, regardless it will be "insufficient". The only thing we can rely upon is the handwavy ability of pointing out that with an unbounded number set, one can always produce a new number.

I considered writing my statements with formal logic, I gave up, as I think it produced an intimidating piece of work, and had a higher entry-level simply to understand. I think if you look back in the fossil record, you might find some of the early versions with formal logic formulae.

Oops, I defined two functions with the same name. I'll fix that for sure. --Eira ^omtg! The Goat be praised. 10:20, 3 July 2010 (UTC)

More descriptive names & f()

The essay would be easier to read if the sets and functions had more descriptive names.

Instead of talking about the function f(), you can simply say that the set B (or equivalently the set A) is well-ordered, and the meaning of this ordering is increasing perfection. This is always possible due to w:Zermelo's well-ordering theorem. --Tweenk (talk) 03:18, 13 March 2011 (UTC)

Good point. I will work on that. --Eira ^{OMTG! _{The Goat be Praised.}} 01:14, 14 March 2011 (UTC)

Russell's paradox

"There exists a set, A, that contains everything": Russell's paradox! In particular, the combination of (1)/(2) and (3) lead to Russell's paradox directly. You can't have both (unless you want to be paraconsistent). --Maratrean (talk) 07:32, 13 March 2011 (UTC)

I don't see how Russell's paradox applies. My universal set does not exclude anything, and thus no paradox can be made from "it must include x, but by including x it therefore cannot include x". As a point, it is a level of abstraction above the paradoxes that it contains, because since it includes everything it includes all paradoxes, not just Russell's paradox. Specifically, the set must specifically include more set theories than just ZF set theory. So, more precisely, I am discarding comprehensibility, not consistency. --Eira ^{OMTG! _{The Goat be Praised.}} 01:29, 14 March 2011 (UTC)

When you start talking about sets, people will just assume you are adopting ZF. If you aren't adopting ZF, what are you adopting? NFU? --(((Zack Martin)))^™ 11:47, 18 March 2011 (UTC)

Actually, I now realize, reading what you have written a bit more carefully - As a point, it is a level of abstraction above the paradoxes that it contains, because since it includes everything it includes all paradoxes - that is a pretty explicit embracing of paraconsistency. Which is fine, but it's so nonstandard, if that is what you are going to do, you better be upfront and explicit about it. I don't see anything in your essay about rejection of ex contradictione quodlibet.

And by the way, you say I am discarding comprehensibility, not consistency - but you have (3), There exists a set, E, that is any arbitrary subset of A seems to be a statement of, or an application of, the axiom of comprehension. --(((Zack Martin)))^™ 11:54, 18 March 2011 (UTC)

The subset E has comprehension, and possibly obeys ZF set theory or something. It's should be at least kind of apparent that since ZF doesn't have a universal set, that there exists some set that includes ZF sets and non-ZF sets. Honestly, you're talking well above my naive understanding of sets, I was simply using "sets" as the mathematical basis for understanding the concept of a theoretical collection of stuff. The universe exists, and has things within it that exist, so a set E must exist that contains all things that exist. There are also things that are know (as well as can be established) to not exist, thus there must be a set of things that don't exist, which unfortunately also includes paradoxes, and contradictory sets, and all sorts of things that we can't deal with in reality, because: they don't exist. The union of an incomprehensible set and a comprehensible set should most understandably be an incomprehensible set, but it doesn't mean that there is not a subset of that incomprehensible set that is comprehensible. --Eira ^{OMTG! _{The Goat be Praised.}} 21:39, 20 March 2011 (UTC)

The term you are looking for is a class of sets. The problem is that such a "set of sets" naively put forward could be used to "prove" that reality doesn't exists, and that it does, and God is a unicorn, and he isn't, etc. All theorems follow from contradiction, unless you are embracing paraconsistency, but then you need to establish your logic used, as this is very unorthodox logically speaking. -Adam Myers, random dude on the internet. ^{— Unsigned, by: 107.77.193.51 / talk / contribs}