Jonny,
We are at a very critical stage of this discussion. We have a foundation that can be built upon. It is neccesary to appreciate this agreement to move forward.
We have agreement on the 0, 1, and 2. 0,1,and 2, as natural numbers on the natural number line, reflect and perfectly symbolize the distinctions that are used in OS 0 1 2.
So, when you say
Yes, in that limited context I can see what you mean. In the broader sense, though, I'm still in disagreement.
I should point out that this is limited to 0,1, and 2, yes, but it reflects the broader sense of what I am explaining.
0,1, and 2 as natural numbers, used in ordering and counting, are the foundation of this process. If that foundation was proven to be invalid, or magical as many reacted and assumed, then this system would also be such. If these distinctions are valid mathematically, then this foundation is valid.
Let me explain.
0=Natural Number Line
1=The Counting Number
2=The Ordering Number
We 'count' in orderings of 1, or in distinctions of 'one' and 'many'. One and many are also a set of oppositions, of dichatomies. We understand that distinction at a basic level because ordering and counting, as we agree, are hardwired into us. Although the set of distinctions of 'one' and 'many' are two distinctions, they are two distinctions that can come to represent a number of the highest magnitude, a number that can be understood as an almost infinite number of counting '1's.
That relationship, 'one' and 'many', is the same relationship as true and false, objective and subjective. These distinctions are exalted and refined into two major contributions in human culture, art and science.
And we can be certain of this.
Please note here, I wish to speak of 'certainty' in the same manner that a mathematicain uses 'certainty'
I see, so this is getting back to the philosophical realm. Well, mathematically speaking, there is also probability, which is a way of expressing and evaluating different degrees of certainty. I suppose that wouldn't really affect what you're talking about.
It (probablity) gives us the most likely outcome that we can assume to be either true or false. Like Zaay's arguments, for example. True unknowns and false unknowns, assigning degrees to the knowledge that the unknown can only be understood in terms of true and false, but only after it is known for certain, until then, we make assumptions, use probablity, or use hueristics (philosophy) to navigate our sense of true and false around an unknown event
I do, however, agree with an earlier poster who mentioned that in the strictest, "all knowledge is available" sense, every statement is either true or false. The concept of unknowability is a function of limited knowledge or limited understanding.
I dont disagree with that either, except with the claim that 'every statement' can be either true or false. Sure, at some point, we can determine the truth value after the fact, so it's true in princaple, but in reality, we have to analyze ideas critically in the present moment, and often we cannot tell one way or the other. "WMD exist in Iraq" is a perfect example. We now know for certain that is a false statement. We didn't know that in 2003, so we went to war to get rid of them, as the popular argument tells us.
So, OS 0 1 2 is about being absolutly certain in our statements and ideas, holding the exact same value of 'certainty' that is held in mathematics. I think as critical thinkers, the standard of certainty is certainly the most trusted one.
Also, I'm wondering if probability would have a role in human thought processes as well. We may not innately calculate it, but we do experience different degrees of certainty, that is, different degrees of "mystery".
yes! there is the mystery that is a 'puzzle', which in princaple we know we can figure out at somepoint although we dont have the answer currently, and then there are the 'great mysteries', such as death, humanities origins, purpose, etc etc.
I think I'd need to see more research on the link between numerical thinking and ideas, unless you mean the idea of breaking things down into categories like "true" and "false" (and yes, "unknown"), which I think is a function of the fact that real objects either are, aren't, or we don't know if the are or aren't. If that's what you mean, then I suppose it follows from our grouping and separation of objects.
that's what I mean,yes. We are hard-wired to order and count, and to break things down into true, false, and unknown.
Here is the kicker, however. I think that we have lost track of our natural ordering and counting and innate sense of t/f/m due to belief systems which do not aknowledge or utilize our natural ternary understanding of the world. I refer to this as 'irrationality'. Irrationality is relative to the 2 as rationality is relative to the 1. I am a highly IRrational human being as an artist, but a highly rational human being as a thinker. There is a natural place for our irrationality, humanity did not invent it consciously, but due to belief systems, we misappropiate it as something else, we confuse irrationality with rationality, we confuse ordering as counting, we confuse false as true. And we do this because we are 'irrational' in the face of the unknown, and confuse that 'irrationality' as a truth value of certainty to disregard what is unknown to protect our belief systems or guiding philosophy.
I think that concepts like "honesty" are things developed over millions of years of human biological and social evolution. Those concepts don't exist innately in all animals, but they have a distinct advantage in human society. I think it can be argued that those traits provided a survival advantage in the form of an improved society.
Honesty is essential to the spread of accurate information. We need accurat information to evolve society. When there is dishonesty, we are spreading false ideas believed to be true, mysterious ideas believed to be false, and true ideas assumed to be mysterious.
Well, you can be dishonest doing math, but you won't arrive at the correct answer.
exactly, and the same thing with OS 0 1 2. OS 0 1 2 provides 'certainty', and if we are dishonest, we simply cant be 'honestly' certain our truth value is accurate.
I agree that rationality is key to developing higher math. You have to observe, model, refine the model, etc. a lot to develop concepts. Once you have a decent set of mathematics, you start to refine within the context of math itself with concepts like number theory.
Then let's make the connection between honesty and rationality. What do both of them share in common? Truth. The ability to distinguish what is true, and what is not true. Rational thought is simply an extention of honesty thought. I would imagine they are apart of a similar set of hardwires. They both exalt into 'objectivity'
Now, to keep our discussion on tract, I queried "is not 1,000,000, (M) not 'one million' ones?
Yes, but my argument is that no one conceptualizes it that way. They conceptualize the abstract concept of the million rather than the idea of "one million repetitions of the unit one". Especially with large numbers, the conceptual framework has to extend beyond imagining a group of n objects.
agreed, we understand at a very basic level the rational and logical neccesity of 'ordering' things into symbols which contain the full information. We 'compress' high amounts of information into 'symbols' that allow us to compute and consider larger and larger amounts of information. It's built into us, so we dont need to conceptualize the full set of '1's in a million, but we can, as critical thinkers, deconstruct it down to a million ones, and be certain that our deconstruction was accurate. That's all I'm saying. And we can do this at a very basic level because of the simple distinctions between 'one' and 'many'.
You know, I'm going to turn it around here: I think that numbers are a representation of the external reality. Sure, there's a distinction... because we created it that way. Numbers exist as a way of understanding and working with concepts like "I see a bunch of apples here". If that's what you mean to say, then I agree.
that's what I mean, and to turn it fully around 360 into harmony, we can say that our evolution was interwoven with objective reality. Hence, in OS 0 1 2 basic, which is an intuitive presentation of this process, it says "Simply, our ideas of the world shape the world. And the world shapes our ideas. We create them and they create us."
This is what is called 'comprehensive' thinking. to observe the whole sum functioning together. It's a synergy. Now, I use that word critically. It was coined by my biggest hero of all time, Buckminster Fuller. Synergy is defined inside of OS 0 1 2 as 'all sides contribute, all sides win the collective output of all contributing'. Bucky defined synergy as 'behavior of whole systems unpredicted by the separately observed behaviors of any of the system’s separate parts or any subassembly of the system’s parts'.
I just wouldn't say it as if the concepts are found outside of numbers. That seems to imply that reality is comforming to number theory, rather than the other way around.
in the 21st century, both are conforming to each other. We now make very critical impact on environment and reality. We even understand how to make 'black holes'!
Well, just as true/false has limits, so does true/false/unknown. For example, T/F/U fails to address degrees of certainty or probability.
agreed, but probablity is not certainty, it is a way of navigating uncertainty. I dont think you can compare them against each other. all are neccesary intellectual tools for arriving at truth.
Sure, you could address that casually, but in casual discussion you can also include "unknown" into a generally true/false discussion. You can also divide things up into multiple frameworks, if it would be useful.
agreed. but reality can only be 'understood' in certain terms as true, or false, or unknown. Probablity is a way of analyzing 'unknown' or the third value. If there was no third value, there would be no need for probability.
I think it's extremely difficult to describe human experience in precise, non-amibiguous terms, so we invent all kinds of systems to describe different aspects. We invented mathematics to define our perception of objects and quantify our experience with the real world. We invented logic frameworks to help describe concepts like "truth".
I dont think it is hard at all to describe human experience in precise, non ambigous terms. human experience is the 'many' as opposed to the '1' of human knowledge. It's either objective, subjective, or some combination.
As far as I know, we don't get to step outside ourselves. That sucks, but we just have to deal with it, so we invent systems to help convey things to other people.
well here is where dialectic and this system is very useful. We cant step outside of ourselves, no, but everyone else is outside of us! Through honest tit for tat with others, we can come to be very certain about ourselves. This is nothing more than common integrity. A human being with integrity will come to find identical ideas about self as others have with him or her.
I don't think anyone here has been arguing that the unknown is not a component of human experience.
That's just it, they have! They are not realizing it fully, but they have been arguing for it, their statements, which we can accept that they believe as true, reflect that the third value is meaningless, it doesnt exist. How many times have people said that on this thread?
Unknown in the human experience is the third value. The third value is nothing more than the unknown in human experience.
I agree that humans often have a deep fear of the unknown.
very deep. and when we are faced with the unknown, all we have are our ideas about what it 'maybe' to go on. And then, at a very deep level of metaprogramming, we tag those 'maybe's as 'true'. Thus, we get religion, the supernatural, and bad philosophy.
Put from the position of probability, you could say that humans have a fear of situations in which they have a low percentage of certainty regarding the outcome. The degree of uncertainty and specific situation required to cause fear would vary from person to person, I suppose.
I like that
However, what's the deal with fractions, then? If you break an apple into two, are you looking at 1/2's of an apple, or are you looking at two units of 1 apple half? When you look at the apple, are you really looking at several million units of 1 molecule?
all of the above, 1 recapitulates, no?
Do you see where I'm going with this? You can say that 1 unit is the smallest unit you can divide any real object into, but 1 of what? If you're going to abstract the concept, you might as well go all the way and acknowledge that the concept of "1" is in and of itself an abstraction of what we observe. It's not the real object, it's an abstraction we use to meaningfully distinguish the apple from the ground.
yes, it is an abstraction, a 'true' idea, not the ding an sich. I loved that line in Godel, esher, and bach, when the author states '1 +1 = 2' most of the time, except when adding drops of water together!
What is important is the distinction between the 'one' and the 'many'. It recapitulates in ordering and counting.
Even if your a QM scientist and put forth a theorum, you are still going to have x number of steps taken, written on x number of pages, worked on for x number of days, applying to x number of particales. Ordering and counting is the highest 'order' that surrounds all other concepts we have.
I think that the unit of 1 is just as much a conceptual abstraction as 3, 10, 50, or 5 trillion. When dealing with abstract numbers, I think the abstraction of 1 is lost in the general abstraction that is mathematics.
It is just as much as a conceptual abstraction, but what is important is the distinction amongst the conceptual abstractions, the relationship. One to the Many is a very important distinction that governs the abstractions.
We may know that 5 means five groups of 1 (or 10 of 1/2 or whatever), but we don't conceptualize it like that. 5 exists as an abstract entity just like 1 does.
but the distinction of 'one' and 'many' still holds.
Even when dealing with physical objects, these are abstract concepts. Do you think of your computer as a group of 8 or so components or 1 computer? Do you think of yourself as billions of atoms?
we dont need to deconstruct everything down unless it is neccesary to. It's not neccesary that I do that with my computer to refer to my computer. My computer in language assumes all that information by default.
It's especially difficult when dealing with very large numbers. If you want to see abstraction, try thinking about a trillion. Try to conceptualize just how many "things" that would represent. I would wager that you do not have a distinct picture in your mind of, say, one trillion apples... or anything else, for that matter. It's become a distinct abstract concept from the concept of a singular object in order for you to work with such a large number.
I only need to make the abstraction that 'one trillion' apples is very very very many apples!
As these are all abstract models for underlying reality, I'm not sure 1 and 2 have all that much inherent meaning. You might use them to define concepts with inherent meaning, but I conceptualize in terms of different units, or even different objects.
How I mean them is 'one' and 'many'
If you wanted to quanitify a problem using "unknown" as a value, it would be useful. Say you wanted to formally propose something like "God exists" (I know, I know... can of worms) but wanted to include the possibility that, say, the concept of God was unknowable at this time.
That would be a certain statement. For certain we can say that. Everything else is probability based on our knowledge (which is limited) and our belief system.
That is how I think agnosticism is the purest rational argument, to really open up that can of worms further. I think atheism and faith are both equally irrational and niether certain.
agnosticm is the third value, by the way, in this triad.
It's because mathematics has defined rules. There is a right and a wrong answer when discussing mathematics, and if something is unknown, it's plainly stated as such (for example, there are plenty of unsolved problems in mathematics).
Same thing in OS 0 1 2. We must have certainty. Certainty is very important in critical thinking, and it has nothing to do with opinions.
Really good pass, Jonny. I have to say, you are one of the most rational people I have found on the internet!
Bubblefish