All righty, back to respond yet again.
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.
I'm not so sure we do, about everything. I agree that 0, 1, and 2 are natural numbers (among other things), but I'm not so sure they "perfectly symbolize" the distinctions you use for OS 0 1 2. They can be made to symbolize the distinctions, sure, but so can a lot of things. As I've pointed out before, the specific values are only really important for doing set math on your logic problems.
In terms of naturally conferring your elements, those three values don't really do that. They're all defined values. If you wanted to pick a natural mathematical symbol for "mystery" I'm really not sure what you could use. I suppose you could use a variable (say, "x").
Plenty of logic systems use 0, 1, and 2, so they're as good as anything else. They're just nothing special when it comes to symbols.
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.
This is like saying "if 1+1=2 is mathematically true, then 1 and 1 is 2." We (humans) defined those numbers and their relations, so they work for the counting and ordering system designed using them because they were designed to.
Deciding that 0, 1, and 2 are something else, while pointless, would redefine the symbols used to count with. They're valid within the numerical system used by the developing world.
0=Natural Number Line
1=The Counting Number
2=The Ordering Number
0 does in no circumstances equal the natural number line. It is the beginning of it in many cases...
Unless, of course, you are defining "natural number" to mean an element of the positive integer set, which does not include 0.
Even with something as seemingly basic as the natural number line, there are variations in definition depending on the specific problem.
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.
Yes, we define things as "one" and "many" on a simple level, and it is possible to divide things up like that.
But here I'm starting to lose why this is an important distinction to make. As I said, you can simply conceptualize things as "one" and "many", but you can also make more distinctions, and that's done all the time. I'm not sure why you believe the ability to boil every distinction above "one" down into "many" (I will allow that you are not considering fractional amounts) has any practical value.
If you believe that the "many" distinction without further qualification is useful, please explain how. I understand it's useful in some kind of vague philosophical "this is the base of all higher numbers" way, but that's not particularly practical. I can't add "many" to anything and get a useful value.
There's another couple sticky matters you haven't really addressed: The null set in counting, and the possible systems of counting.
Counting could be seen as a movement along the natural number line (including zero), but it can also be seen as a set operation. For example, say you define the natural numbers as "an element of a set including all positive integers". That would exclude zero.
In that case, to count, you would essentially look at your "counting" operation as taking the next element from the natural number set and placing it into a new set, your "counting set" if you will.
"Nothingness", which is represented by "0" on the natural number line (including 0), would be represented by a null second set: you haven't yet placed any values into your counting set, so there's nothing in there.
Bear in mind I'm not saying the null set
is 0, because as I said before it isn't. I'm simply saying that in our new counting system, nothingness is defined as the null set (i.e. nothing present in the counting set). In the system where it's a movement along the number line, counting doesn't use a set operation, and thus the value 0 is used to represent "nothing".
Interestingly, this type of counting and ordering
does not require 0. That is the situation in which "nothing", "one" and "many" would be represented by a null set (but only your counting set, your natural number set has infinite values always), "1", and "2".
If you want to define counting in a really interesting way, you could use a set of
n number of 1's. If you want to count to 2, your set would consist of {1, 1}. Nothing would be represented by {} (an empty set). Ordering, in this system, is accomplished by comparing the size of various counting sets. Awkward, but very simple and fundamental. This is how someone might first learn to count and order: by grouping objects together.
Ordering based on numerical values is already an abstraction. Ordering in the real world uses physical characteristics, in the numerical world it uses relative values. The simplest, most innate counting system is actually the last one I mentioned: It simply groups objects by 1's and defines "nothing" as "nothing to count". Concepts like higher values, ordering numerically, and 0 are all non-innate concepts.
"Nothing" is innate, perhaps, but 0 is not.
If you want to acknowledge higher concepts like the quantification of "nothing" in specific cases (0), and numerical ordering (values higher than 1), you're moving beyond this "hard-wired" distinction you're interested in.
Unfortunately, the innate system of counting is more closely represented by two possible states: nothing in the counting set and something in the counting set. Higher level concepts require at least some basic development, including numerical ordering. Movement along a natural number line as counting is actually pretty high level, when you consider how abstract the concepts involved are.
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.
No, I totally disagree, they describe very different things.
-"One" and "many" describe quantity and vary by degree described.
-"True" and "false" describe truth (duh, I suppose) are are logically opposing.
-"Objective" and "subjective" describe a lot of things, are logically opposing, and have considerably more definitional variation than the other four terms.
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.
I didn't say "in reality". I said that in the case where
all knowledge is available, everything is either true or false. In that case, uncertainty does not exist. You know
everything, whether there are WMDs in Iraq, what I had for breakfast, whether there is a God and what it's like, etc.
I understand you're not talking about that situation, but I just wanted to point out that every statement subject to true/false evaluation is either true or false in the universal sense, regardless of whether or not we know the answer.
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.
"Certainty" doesn't have a precise mathematical definition that I am aware of. If you mean "100% probability" then I don't believe any statement in the real world can ever be there, because there's always those lingering issues like "what if this is all a dream?" Sure, I'm 99.9999999999... (x10^1000) ...9999999999% sure I'm not really a hedgehog dreaming this all, but there's always that infintesimally small chance I'm just a hedgehog.
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 was just talking about statements like "I'm quite sure I'm not a dreaming hedgehog". There's still that lingering infintesimal, and you will probably never know the universal truth.
that's what I mean,yes. We are hard-wired to order and count, and to break things down into true, false, and unknown.
Yes, we are, but I still don't think those things are all that connected.
Also, as I said above, the concept of numerical ordering does not seem to be hard wired. For example, a simple system of counting and ordering like a check mark-based system does not have numbers greater than 1, it has little bundles of 1's. It resembles the one-value set counting system I mentioned above.
Innately, I think we order things by physical characteristics. Values are an abstraction of things like "there are more of these" or "this one is bigger than that one", but the values are by no means innate.
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 you're totally off base here, if I understand your correctly.
I don't believe that we've lost our "innate" understanding of ordering and counting. I believe that as humans we really don't have a very good "innate" understanding of the world around us. We tend to attribute things to stuff like "magic" or "God" without examining those beliefs. I think that the best tools we have are those that bring us away from our innate drive to assign everything anthropomorphic characteristics to everything and make judgments without evidence.
I think our senses and our brains are poorly equipped to innately determine anything, which is why we developed tools like mathematics, the scientific method, or technology to help us.
I also don't think our very simplistic "innate" ordering and counting has anything to do with our understanding of the true or false of anything.
I think the issue with irrationality is not the loss of some ability to distinguish between a true statement, a false statement, and an unknown statement, but an unwillingness to examine beliefs to determine if they are supported by evidence or some kind. This isn't the issue of some "lost ability", I just think there always have been and always will be large numbers of people that don't want to bother examining their beliefs.
If you believe that humans ever had the innate ability to do this, I think you're simply applying the "beautiful people" myth to our reasoning abilities. History does not support the idea that people were ever particularly rational as a whole.
I don't think anyone confuses ordering and counting, and I don't think that has anything to do with rationality. They may believe they're being rational when they aren't, but it's got more to do with an unwillingness to be critical rather than some mix up of their innate understanding of anything.
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.
Yes, hence honesty is evolutionary. It helps society, and became a valued trait. Those societies that placed a higher value on honesty survived, those that did not failed. Anecdotal, yes, but I think history bears it out.
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.
How does OS 0 1 2 provide "certainty"? The only way something could provide an additional degree of certainty is to provide more information about the real nature of something. How does OS 0 1 2 do this?
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'
This is a whole discussion by itself.
Now, to keep our discussion on tract, I queried "is not 1,000,000, (M) not 'one million' ones?
To which I answer: What counting system are you using?
On the natural number line, no it kind of isn't. Using a set operation it could be. In the most simplistic counting system, it is. Then again, that system doesn't even have 0 (or 2, or anything other than 1 and nothing), so it's not really in line with your whole ternary theme.
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'.
Yes, we
could deconstruct it into a million units of one, but we don't need to.
Now I think it's time to bring up the concept of irrational numbers again. An irrational number
cannot, by definition, be reduced to any division of ones. Their relationships are supremely abstract, and yet they are extremely useful (think pi). How does this fit into your system? Is it out because it's not "ordering and counting"?
Again, I have to ask which ordering and counting system you mean? If you're going to introduce numerical abstractions like 0 (which you admitted was hardly an innate concept, as it took humans thousands of years to define it), why not things like irrational numbers?
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."
How do our ideas shape objective reality? Do you mean the actions or ideas provoke?
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'!
Theoretically, yes. Micro black holes could theoretically be created in limited circumstances, that would exist for a minute fraction of time and then vanish.
That has nothing to do with number theory. How does number theory directly influence reality?
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.
Probability is degrees of certainty. I just don't think you can ever have 100% certainty in the real world.
Sure, a ternary system has its place, but it still doesn't address degrees of certainty directly.
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.
All right, but "unknown" is simply a way of stating that we aren't 100% certainty about the ultimately binary reality (based on the magical situation where everything is known, not in the real world). Utilizing probablistic analysis takes the quality "unknown" and does something useful with it: determines what the most
likely answer is, based on currently available data.
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.
I don't want to get all personal with this, but how would you precisely describe how you feel about your child? I just don't think you can reduce subjective experience into something where a third party will know exactly how you feel. I could compare it to similar situations in my life (say, how I feel about my wife), but I wouldn't really
feel exactly the same as you do. I wouldn't know exactly what you're feeling.
That's what I mean when I say "describe 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?
I don't think that you've understood what they said. I don't think anyone here has said that the concept of "unknown" doesn't exist.
In fact, they've said several times that it's dealt with in many logic systems, as well as informal logic.
Unknown in the human experience is the third value. The third value is nothing more than the unknown in human experience.
Then that is well accounted for in reasoning and human thinking, as well as most non-hypothetical logic.
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.
This is the kind of statement you need to show some research to support. I would be inclined to believe we tag the "maybes" either true
or false, depending on what we believe when we observe the unknown.
Thank you.
all of the above, 1 recapitulates, no?
No. 1 is an abstraction to describe the experience of seeing an object. What "1" represents depends on context, in the real world.
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.
It's also important to divide "many" into units, if you want to do anything advanced. As I have stated above, I don't think that defining higher numbers is innate. We see something and we define it to make what we see clear. We all agree on definitions. When we talk about cars, we all agree what represents "one car". The innate observation of "many" is impossible to quantify without some kind of number system. Without that,
n has no meaning, it's just a bunch of stuff you see and can't describe very well.
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.
1 to "many" isn't a very useful distinction, however. Define "many"? How am I supposed to do anything with "many" other than know you mean "more than one"? Heck, "one" of what? "Many" of what?
If you're going to stick with something so vague, why not "nothing" and "something"? It's about as mathematically useful as "many".
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.
Yes, it does. Your definition of "one" is very grounded in the real world, not at all numerically self evident.
I only need to make the abstraction that 'one trillion' apples is very very very many apples!
Depends on what you're trying to do with that information.
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.
You're not familiar with "weak atheism", are you? Weak atheism is basically "I am not 100% sure, but I haven't seen any evidence that there is a God yet, so I will work under the assumption there isn't one unless proven otherwise".
You're talking about "strong atheism": "I know for sure that there is no God." I agree that this is an irrational statement to make, unless you narrow the definition to specific Gods that couldn't exist, say, because they are logical absurdities.
Looking forward to your reply. In particular, I'm interested in what you've got to say with regards to my points about the concept counting and set math. As you can see, the most fundamental system of counting and ordering can be described as a mathematically one-value system using sets.
