This re-instated what passes for faith in humanity

[LemmingofGlory]

The R-H Dictionary, to offer a  typical example, defines a mathematical set to be “[A] collection of objects or elements classed together.”

Mathematicians say that "set" is a notion without (rigorous) definition. It's a "primitive" concept; definitions of it end up being recursive in nature.

Further, isn’t it an essential property of infinity that it be infinite in regards to either increase or decrease of the property it describes? and thus that infinity must possess direction? For even if something is infinitely the same, how can it be so except in  regard to an increase of time? 

I'm going to say no. Increase, decrease, and constant aren't the only behaviors that exist. And if you want to talk about behavior, that's getting into the realm of sequences.

“If” begins a conditional sentence, as  in my writing “ If one supposed an ordered set...”. If one doesn’t grant the premise supposed by the “if” then there no point to arguing against the “then”, as, in a conditional sentence, the “then” is  predicated upon the “if”.

I wasn't disagreeing with your implication, but rather with your use of jargon. When I see "set" used as loosely as it's been used in this thread, I have this filthy urge to see it used more clearly. I know, it's my problem but so help me if I keep my mouth shut, I'll eat twelve jars of olives until I stop thinking about it.

If I would accept your assertion that a set may only have “order,” not order, then I wonder how I would  know whether a set is actually more than just a “set”? In other words, why is the classifying of elements into a group and calling it  a  set more than just “your doing”? In yet other words: The  organization of elements into any given set is done to reflect some general classifying principle (ex. a group of all integers, a group of all flatware, a group of some interval,  etc.). How do I know that the very act of organizing  items into collections called sets isn’t equally as arbitrary as you claim the order of the elements in those sets must be? If the choice of items to include or exclude from a set is also arbitrary (thus the set has “organization”, not organization), then what one has isn’t a set, it is a “set”- a thing  that is arbitrary and therefore reflective of nothing more than “your doing.” If a “set” is nothing more than “your doing,” then how can any conclusion be expected to be drawn from it that is other than only a reflection of  “your doing”, including, therefore, the assertion that it is unordered?

I think your philosophical tangent here is some objection to the notion of something being arbitrary... but I don't see any benefit to me reading it when it looks like one of Doc's windy episodes.

The question is about quantity, not value; how do negative integers pertain? In other words, doesn’t the set {100, 101, ...} contain elements that, if one were to enumerate them, would form the set  {1,2,3,...}? just as the set {..., -101, -100} likewise would? or any similar set? Is it possible for a set that contains 100 elements, regardless of what the elements are, to not also contain 99 elements, 98, and so on? If I construe correctly your objection it would seem to rest on the claim that a set may contain a negative quantity of elements.

The last sentence was all you needed. Honestly, I don't know what the rest of that is all about.

While your proffered summary, that "I believe that effect has a cause, in much the same way that any listing of a set has a first element,” may be, and I have no cause to doubt you, a “neat” sentence to read, it isn’t my argument.

At the same time, you must admit that it would be absolutely silly for me to ask you to provide a more concise presentation of your argument if I was able to accurately summarize it in a single sentence. For were it possible to do that, I would not desire a concise statement -- I would already have it! -- so surely I would not need another.

Given that, rather than replying as you did it'd be quite to your advantage to admit that I managed to offend you and either demand a duel at dawn or, equally satisfying (to me, naturally), explain why you still persist in carrying an abundance of words with which you hunt paragraphs to extinction.

-Lemmy