0, 1, infinite model, question

[Moonrat]

If you are now going to declare the "infinite environment is 2 through infinity and 0" then I don'et know what you're remotely getting at. .

I am getting the funny feeling that I may be overcomplicating this in an attempt to match all of your expertise, so please bear with me a bit...


Let's say all number sets can be divided into two distinctions. Finite sets, and infinite sets. An infinite set, according to how I am defining this in the dialectic, by default, has two distinctions inside of it that cannot be escaped or excluded. I know that there are many different sets of infinite in mathematics, but this is not how I am defining it here, this is about how infinity is or can be 'percieved' naturally. Infinity, by it's nature, is not 1, but '2'.

First, there would be what we would call the 'ding an sich' of infinity, which can find no 'true' expression. the philosophical question to this would be 'What is the thing in and of itself of infinity? what can infinity be deconstructed down into? How can we define that which is continuous?'

In math, I would assume this is the same principle that there is no 'infinite number' as there is no 'total' in an infinity, right?

So what is this number then? what is the number that can define that which has no final or finite value other than 0? For this, I assign 0. 0 has no final value, no finite ( at least in the environment of order and addition as Honestrosewater suggested) just as infinity has no final value. Indeed, all infinity can be said to be is merely the 'collection' of finites, which are defined as 1's.

Now, since we have defined this infinity has having no grand total, or a value equal to 0, next, we define how we arrive at all numbers that are 'finites' inside of this grand collection. The grand collection of 1's is what is referenced as the '2', false. There is no such thing as a singular '2' in this infinite set. If there was, then there would be an infinite number of '2's none the less. So in this set, we can then define all numbers as being infinite. We could say the same thing about 3, 4, 5, etc etc that we do about 2. 2 is just the first pure false number, and we refrence it for false for simplicity sake since two is the first distinction of 1. Here, there is no distinction between the numbers 2 through infinity, they are all false. there is only 1 true number, and that is 1 itself. all other numbers are abstractions of the infinite defining the finite for the sake of order and simplicity.

So when 2 is defined as false and assigned to another description of infinity, we define this in the extreme literal sense. 2 is false. there is no '2'. there is no such thing, there is merely a infinite collection of 1's, and nothing more.


You mentioned that mathematicians don’t care if the math is 'real' in the sense that if it has representation in the real world, it is only concerned with the 'rules' of how it is defined conceptually.

I accept that,however, how I am using 0, 1, and 2 has every bit to do with the real or objective world. It is the translation to how we perceive the objective world, so it must. I see that where I need the most work is to understand how the conceptual rules overlap, if at all, in mathematics or mathematical principles, but these principles are very 'real' as they function all the time.

Why is 1 not in this set?

From the pov of what I am referencing, 1 is the only number in that set in the true sense (of 0, 2 through infinity). Now, of course I am not saying that 0 is not a number, or 2 through infinity are not numbers, I am only saying that '1' is the only number with 'balls' if follow my drift. Every thing else is either mystery (like the ding an sich of infinity) or false (like every expression of the combinations of 1)

Because it is "the finite"? This is a departure from the usual ideas, and almost certainly wouldn't agree with whatever notion of numbers the bloke from Princeton had.

well, he did agree, but again, I explained it different to him...remember this is how we 'perceive' these numbers not just inside of us in the conceptual sense, that mathematicians do, but how 'we' in the collective sense perceive them outside of us, and how they apply outside of us.

I don't see why you need to make a distinction between different symbols for the same object: 3=1+1+1.

Ahh! it is not the same object from this POV. 3 is the one 'conceptual' object for THREE real or true objects in objective reality.

I have three bucks in my pocket. In my head, I make '1' distinction that I have '3'. however, when I take the money out of my pocket, I now have 'three' distinctions of 1 dollar. 1 dollar + 1 dollar + 1 dollar. There is no such thing as a three dollar bill ;-)

THAT is the only thing I am talking about, that, and no other. The basic perception of number that if it did not exist, we could not percieve very much, much less mathematics!

You are reading more into it than I do (what I termed "personifying", such as assigning terms like mysterious to 0).

that is the point, however, of this particular work, to 'humanize' these rational principles and define how we humanize them mathematically.

If however, all this princetonian was doing was explaining to you that there is a initial ordinal, successor finite ordinals, and that the set of finite ordinals is infinite, then I can see what he was getting at.

yes...that is where I am getting at too, thank you...

To see this, hold up two fingers and then two more fingers and you have "1+1=3" by counting the spaces between them. So 0 is only special with respect to your common notion of addition

great, now your going to keep me up all night again counting my fingers...hehe, 1, 1, 1,1, 1...

MR

 

[CRGreathouse]

Let's say all number sets can be divided into two distinctions. Finite sets, and infinite sets. An infinite set, according to how I am defining this in the dialectic, by default, has two distinctions inside of it that cannot be escaped or excluded. I know that there are many different sets of infinite in mathematics, but this is not how I am defining it here, this is about how infinity is or can be 'percieved' naturally. Infinity, by it's nature, is not 1, but '2'.

For communication purposes, you're saying that you're dividing sets into three categories: the null set, nunnull finite sets, and infinite sets, and that your number system is based on their respective cardinalities.

 

[Moonrat]

I can see a particular argument for 0, 1, and infinity as the building blocks for numbers (taken to be the set $$\{0,1,2,\ldots\}$$ adjoin infinity): 0 is the base element, and is the successor of no other; 1 is the 'typical' number, the first successor of 0, and the additive building block of the counting numbers (1, 1+1, 1+1+1, ...). Infinity is the only 'number' that is its own successor.

Please let's eloborate on this! That seems to pinpoint this environment. Now, what are the 'distinctions' that make those what you just mentioned? how does 0 imply a base element? how does 1 imply a 'typical' number? How is infinity it's own successor? what are the percievable distinctions that can be observed not just by mathematicians, but by all in this regard?

Notice how both me and you can see the same distinctions, and you describe them above, and me another way, yet the distinctions remain none the less, even outside of our language or pov.

However, outside of some unusual philosophy, I can't see the relationship between 0 and mystery, 1 and true, or 2 and false. That's arbitrary at best. This is better done as abstract algebra, perhaps...

some say symbolic, someone else told me recently propositional calculus with three truth values.

I really don't know, that is where I am stuck!

T, F, U (representing true, false, unknown). Would you like to define for us how you think these should combine?

hmm, well the first thing is to say that they are already combined, the trick is to find where they are distinguished!

True and true is true, mystery and mystery is mystery, but what of the other 7 combinations? Maybe then we can better understand how these relate to numbers and give you input regarding how well 0, 1, and 2 work for these.

I am not sure if I can answer this question properly or not. this may require me to parse something in a language I do not fully understand. I am not even sure how that question would apply because of 'mystery', but let me try this...

First off, mystery is both true and false at once, and as such, we cannot distinguish that which is true, from that which is false. it's mystery, if we could distinguish it, it would not be mystery, but either true, or either false.

Secondly, remember this is a placement for perception, and ideas. So all ideas or perception 'morph' into true, and false, and mystery. Those are just three ways to 'percieve' ideas, each with a distinctive function.

What this dialectic does with these three placements is allows us to 'resolve paradox'.

I don't know if this is going to complicate things, or confuse your question, but in normal bivalency, we are given a choice between truth and falsity. All answers must be either or, and before we can tell, all answers are defaulted to false until proven true. Right?

This relationship only defines the truth, it does not define then what is false, other than false is not true. It does not define what function false serves in relationship to truth, or even outside of truth. we are only given the relationship that false is not true.

however, when we pair false with 'mystery', or unknown, and then allow that to be our dualistic set, false and mystery instead of true and false, well some interesting things begin to occur. The first of which is an objective definition of 'mystery' must take place, and then we must see how 'truth' is 'hidden' in this very elusive relationship between 0, and 2.

And then, the other opposite, mystery and truth. What is the opposition of mystery and truth?

again, these sort of relationships we begin to observe with perception, and when we apply this mathematical 'stigma' to perception, then we must also i nclude ourself into the equation percieving it, no?

So, here are the basic sets of opposition in the dialectic. Now,this is more the advanced stuff, and i am still working out the basics, so again, this is where I also could use some great help and insight.

To resolve all paradox, simple input a tertiary princaple or distinction for that which distinguishes 'both bivalencies' at once, in addition to them seperate.

true and false
false and mystery
mystery and true.

so in perception, to true we can assign objectivity, to false subjectivity. In perception we can assign to 1, order and to 2, choas. To 1 we can assign the distinctions of applying what we percieve, or process, so now we can say that 1 is science, 2 is art...

and mystery is always that which you can't tell which is true, or which is false, where the science ends and the imagination begins, or where there is order, or where there is chaos.

How is it that the word 'mystery' is used, and not 'unknown'? Because mystery, as a signifier of 0, is both true and false, art and science. it is a word that 'invokes' imagination (2, false), yet still defines that there is 'unknown' (1, true)

Now, to bring this into practical application, let's take recent history, war in iraq, and before the invasion, the public dialouge about war. This is certainly not to get political, just refrencing a common shared event to explain something simple.

In jan and feb of 2003, WMD where either true, or they were 'false' right? Note how the perception of 'true' on the idea of WMD altered history one way, and then the perception of WMD as false altered it another way.

now imagine what sort of history we may have if, in basic arguement, common arguement, WMD were allowed to be in the 'truthful' category of 'mystery' until proven one way or another?

Just like we can decontruct all numbers down into a combination of 1's, we can decontruct all ideas down into what is true (1), what is false (2), and what is mystery. And we can do this with complete and utter certainty with the dialectic.

Now i would imagine here is where you mathematicians would start having fun with us 'filosophers', so go to it!

I still have a few more responses to get too, Honestrosewater and arildno have made some powerful suggestions, and I may not get to them til tommorow..


MR

 

[Moonrat]

For communication purposes, you're saying that you're dividing sets into three categories: the null set, nunnull finite sets, and infinite sets, and that your number system is based on their respective cardinalities.

hehe, that sounds good, but which is which? 0, 1, 2?? also, is the spelling on nunnull really non-null?

where do you wish me to send the check?;-)

MR