If infinite sets and brutely distinguishable elements exist, infinite sets with brutely distinguishable elements should exist.

Why? It doesn't follow. (As a trivial case, imagine that there are only two brutely distinguishable things in the world.) (Assuming that by "infinite sets with brutely distinguishable elements" you mean "set with infinitely many b.d. elements".)

Also, you say that sets are distinguishable whenever there is a predicate which applies to one and doesn't apply to another. That is, X and Y are distinguishable iff for some P, P(X) and not P(Y). Right?

But then you argue as if the only allowed predicates were those about cardinality. To closely follow your example, let's denote X = "the former set containing infinitely many b.d. points" and Y = "the latter set containing all those points plus the additional one which 'popped into existence'". Then we have a predicate P(Z) = "Z is a subset of X", and P(X) holds while P(Y) doesn't. What's wrong here?

Are my aesthetics off? [...] Perhaps its a status thing, as the research journals don't use it.

Your aesthetics are incompatible with most of the readers. You've got quite a lot of negative responses to your formatting, not a single positive response (correct me if I am wrong), yet you still persist and speculate about status reasons. Even if it were true, I'd suggest taking the readers' preferences more seriously, if you want the readers take you more seriously.

To me, coloured text really doesn't seem more legible than bold or italics. Moreover I like when a website has a unified colour scheme which your colours break. All violations of local arbitrary design norms are distracting; the posts aren't art, therefore aesthetics shouldn't trump practical considerations. But if you really that much insist on using colours for emphasis (but consider there may be colourblind people reading this), please at least use the same font and background colour as everybody else.

First, I second the other's requests to define "exist".

Second, I don't understand the arguments.

But the identity of indistinguishables does apply to sets: indistinguishable sets are identical. Properties determine sets, so you can’t define a proper subset of brutely distinguishable things.

"Let A and B be brutely distinguishable points. Define the sets M and N as M = {A, B} and N = {B}. N is a proper subset of M."

What I have done wrong in the preceding quotation? It seems like something a mathematician could easily say.

To show that the existence of an actually existing infinite set leads to contradiction, assume the existence of an infinite set of brutely distinguishable points. Now another point pops into existence. The former and latter sets are indistinguishable, yet they aren’t identical. The proviso that the points themselves are indistinguishable allows the sets to be different yet indistinguishable when they’re infinite, proving they can’t be infinite.

1. You say that the points are brutely distinguishable and later you say that they are indistinguishable, which nevertheless you hold to be different properties.
2. Why are the sets indistinguishable? Although I don't particularly understand what predicates you allow for brutely distinguishable entities, it seems possible to have X = set of all brutely distinguishable points (from some class) and Y = set of all brutely distinguishable points except one. It is, of course, not a definition of Y unless you point out which of the points is missing (which you presumably can't), but even if you don't have a definition of Y, Y may still exist and be distinguishable from X by the property that X contains all the points while Y doesn't.
3. If the argument were true, haven't you just shown only that you can't define an infinite set of brutely distinguishable entities, rather than that infinite sets can't be defined at all?
4. What is your opinion about the set of all natural numbers? Is it finite or can't it be defined?
5. And how does the argument depend on infiniteness, after all? Assume there is a class of eleven brutely distinguishable points. Now, can you define a set containing seven of them? If you can't, since there is no property to distinguish those seven from the remaining four, doesn't it equally well prove that sets of cardinality seven don't exist?

The frequency of heads and of tails is then infinite, so the relative frequency is undefined.

The frequentist definition of probability says that probability is the limit of relative frequencies, which is the limit of (the number of occurrences divided by the number of trials), which is not equal to (limit of the number of occurences) divided by (limit of the number of trials). Note the positions of the brackets.

The sequence {2n/n} = {2/1, 4/2, 6/3, 8/4, ... } = {2, 2, 2, ...} has an obvious well defined limit, even if the limits of both {2n} and {n} are infinite.

A note about formatting: consider not copying a text from a word processor or a web browser directly to the LW post editor. The editor is "smart" and recognises the original font size and type and grey background color and whatever else and imports it to the post, which therefore looks ugly. I'd suggest copying to a Notepad/gedit-style editor first which kills the formatting and then to LW. (And emphasis is usually marked by italics, not red.)

As an abstract entity, infinity has been quite useful in describing the real world. Perhaps the question would be easier to answer if it were rephrased with "exist" tabooed.

Seems like yet another confusion about the definition of "exist", which you conveniently don't give.

If you rephrase it as "Can infinite quantities be observed?" then the answer is negative. If you phrase it as "Can models with infinities in them fit the observations better then those without?", then the answer is affirmative. If you are interested in a metaphysical answer, such as "Do numbers exist?", then you have to be clear in what you mean by each term.

Sorry, but I do not think this is a well written article. The formatting is strange and hard to read, and your points meander a lot. You also need to give coherent summaries a lot more. As written now, your post is hard to read, and I can't quite tell what points you are really trying to convey. Please take this as constructive criticism, and work to make your post better.

Seems like yet another confusion about the definition of "exist", which you conveniently don't give.

If you rephrase it as "Can infinite quantities be observed?" then the answer is negative. If you phrase it as "Can models with infinities in them fit the observations better then those without?", then the answer is affirmative. If you are interested in a metaphysical answer, such as "Do numbers exist?", then you have to be clear in what you mean by each term.

Reminds me of another question I read recently: "Has anyone really been far even as decided to use even go want to do look more like?" I may have better luck parsing your post if you chose to work on its formatting. Feedback you've received on LW in the past, to little avail. Avast! (?)

I'm also not sure about your apparently new concept of "brute distinguishability", my only association is "et tu, brute?" which of course is historically inaccurate.

(during the eridu radical-feminist debacle)

I don't know that 'debacle' and there seems to be a lot of content that could be part of it (you meant something in the comments of this same article apparently). If you think it is very relevant, i'd be grateful for one or several specific links to start from.

allowed me to notice that it seems highly likely that nearly all female feminists I've encountered in person with common knowledge of such were mostly of the kind that had one or few strong very bad near-type personal experiences with men, or many small but memorable such near-type experiences.

Where can i find out what "near-type" means here? This appears important enough to postpone my reply to this part.

because if the contrary were true, the feminist movement as a whole would be spectacularly self-hindering and shooting itself in the foot constantly, since such behavior as I've observed would basically cause very destructive conflict and wouldn't actually help further their goals.

I didn't mean it in that way. And i think the feminist movement, as a whole or in part, doesn't necessarily want to be lightly told by men what behaviour is or is not "furthering their goals" =P

(This instance seems to me like one in which you did so lightly, because it didn't seem highly relevant / on-topic.)

Well, using pragmatist's cited definition of correspondence theory, a proposition is true if and only if it bears some sort of congruence relation to a state of affairs that obtains.

What state of affairs is "correspondence theory is true" congruent with?

I can't think of any.

If you can, I'll happily be convinced my argument doesn't hold, but basically it seems to me that correspondence theory lays out a framework for thinking about truth, just as governmental constitutions lay out a framework for thinking about law. Correspondence theory itself is no more true (or false) than constitutions are legal (or illegal).

If correspondence theory is true, you aren't allowed to use the Piercian limit. It's a vacuous concept.

(blink) If I accept acorrespondence theory of truth, it seems that correspondence theory is not the sort of thing that is allowed to have a truth value. And if I reject a correspondence theory of truth, then I ought not believe that correspondence theory is true. So it seems that "correspondence theory is true" is necessarily false. No?