Bubble,
I'm really not convinced that OS 0 1 2 really solves any kind of problems, makes any useful predictions, or really does anything useful that hasn't already been addressed by some other discipline. I'm fairly sure I'm following the arguments, I just don't see it as being unique. You've been making your points for a while now, and I'm really not convinced.
I see you kind of dodged my set counting issue by stating that counting dates back 50,000 years and it's really got 2 in there. You are correct that we do create symbols to represent amounts, but we don't necessarily have to. If I were to draw this on a wall;
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You would recognize it as two objects, but you wouldn't need the symbol "2" to do anything. "2" just represents the thought that is evoked by seeing two of a particular object.
Mathematically, this is shown as {1, 1}.
There isn't a symbol for 0 in this system, there is simply nothing. There isn't a symbol to conceptualize this, as 0 took humans a long time to figure out.
Really, 0 is hardly innate. The simplest human counting system has a series of marks. Properly speaking, it would be a one-value system. If you want to go down the road of calling higher groupings of marks different "values" or "distinctions" or whatever, then it becomes an infinity-value system.
That's all splitting hairs, but that's what math is all about. Yes, you can conceptualize human counting as 0 (nothing), 1 (a single value), 2 (the first value made up of a whole fraction of 1's), but there really isn't a particular reason to do this. Binary also has a value for greater than 1, despite being based on only two numbers. Again, you can claim they really included "2" in there with that value, but it's imprecise to do so.
My issue is that you keep saying that 2 is a conceptual concept, but it really isn't. Groups of things are conceptual concepts, numbers are not. Numbers are a way of describing conceptual concepts precisely and relating them to other concepts. I'm going to get into this issue in more detail when I talk about summation below.
You still need to address a few problems with mathematics. These are simple things critical to describing the real world, but currently appear to be totally outside the concept of 0, 1, or 2 even as you set it up.
These don't have anything to do with truth values, but have a lot to do with human conceptualization of numbers. In fact, they are required to fully describe numerical concepts precisely.
If you're going to lump this stuff in with "many", "mystery", "infinity" or whatever and still try to claim the mathematical elements of OS 0 1 2 have any ability to describe reality as we perceive it, you're going to have serious problems.
√-1 or say it's unsolvable. If you're willing to include i on your list of things, then the problem can be solved.
Number theory is considerably more involved than ordering and counting.
I'll address the concept of absolute certainty again. I wouldn't even go so far as to say that you can be absolutely certain about the ending of your sentence, because there is always the small chance that I am perceiving it incorrectly or none of this is real, in which case your statement wouldn't reflect objective reality.
I agree you can be 100% certain about what you think you perceive at any given moment, and you can be 100% certain that you are perceiving (unless you want to get really weird, philosophically). Other than that, nope.
And finally, I'd like to talk about your idea that human experience can be perfectly "noted" as objective, subjective, 0, 1, and 2 (I'll assume you mean true, false, and mystery).
No, I disagree. You even said that things like emotions work into the "mystery" category. This by itself indicates your system does not perfectly describe human experience at all, it simply attempts to simplify and model it in some way. I don't think human experience can ever be perfectly described by anything.
Is "mystery" by any chance a scalar value?
I'm really not convinced that OS 0 1 2 really solves any kind of problems, makes any useful predictions, or really does anything useful that hasn't already been addressed by some other discipline. I'm fairly sure I'm following the arguments, I just don't see it as being unique. You've been making your points for a while now, and I'm really not convinced.
I see you kind of dodged my set counting issue by stating that counting dates back 50,000 years and it's really got 2 in there. You are correct that we do create symbols to represent amounts, but we don't necessarily have to. If I were to draw this on a wall;
||
You would recognize it as two objects, but you wouldn't need the symbol "2" to do anything. "2" just represents the thought that is evoked by seeing two of a particular object.
Mathematically, this is shown as {1, 1}.
There isn't a symbol for 0 in this system, there is simply nothing. There isn't a symbol to conceptualize this, as 0 took humans a long time to figure out.
Really, 0 is hardly innate. The simplest human counting system has a series of marks. Properly speaking, it would be a one-value system. If you want to go down the road of calling higher groupings of marks different "values" or "distinctions" or whatever, then it becomes an infinity-value system.
That's all splitting hairs, but that's what math is all about. Yes, you can conceptualize human counting as 0 (nothing), 1 (a single value), 2 (the first value made up of a whole fraction of 1's), but there really isn't a particular reason to do this. Binary also has a value for greater than 1, despite being based on only two numbers. Again, you can claim they really included "2" in there with that value, but it's imprecise to do so.
My issue is that you keep saying that 2 is a conceptual concept, but it really isn't. Groups of things are conceptual concepts, numbers are not. Numbers are a way of describing conceptual concepts precisely and relating them to other concepts. I'm going to get into this issue in more detail when I talk about summation below.
You still need to address a few problems with mathematics. These are simple things critical to describing the real world, but currently appear to be totally outside the concept of 0, 1, or 2 even as you set it up.
These don't have anything to do with truth values, but have a lot to do with human conceptualization of numbers. In fact, they are required to fully describe numerical concepts precisely.
If you're going to lump this stuff in with "many", "mystery", "infinity" or whatever and still try to claim the mathematical elements of OS 0 1 2 have any ability to describe reality as we perceive it, you're going to have serious problems.
- Irrational numbers: These cannot be reduced to fractions of 1. They are not natural numbers, but several of them are absolutely essential to describing reality. Pi, for example, is critical to describing numerous geometric shapes accurately.
- ∑: This is the mathematical symbol for summation. Interestingly enough, it would provide a far more logical symbol to connote "everything more than one" than 2.
In fact, there is a specific formulation using ∑x with "1 < x < ∞" written below it (sorry, I'm not good with LaTeX so I can't make it all purty-like) that would mean "the sum of all numbers greater than 1 and less than infinity" without including any symbol for "2" at all.
You want to use set notation, you could even restrict it to natural numbers. I think this is the closest mathematical representation of "many" you can get.
- ∆: The mathematical symbol representing "change". I would think that, since you say this system is supposed to represent human experience, that this would be important.
- ∞: Interestingly enough, 0, 1, and 2 does not explicitly contain the concept of infinity (you keep mentioning it, but didn't include it as a symbol). The concept itself is separate from "an infinite number of 1's" and can't really be mathematically described as such. You see, the concept of "an infinte number of x" is not really the same as the concept of infinity itself.
√-1 or say it's unsolvable. If you're willing to include i on your list of things, then the problem can be solved.
Number theory is considerably more involved than ordering and counting.
I'll address the concept of absolute certainty again. I wouldn't even go so far as to say that you can be absolutely certain about the ending of your sentence, because there is always the small chance that I am perceiving it incorrectly or none of this is real, in which case your statement wouldn't reflect objective reality.
I agree you can be 100% certain about what you think you perceive at any given moment, and you can be 100% certain that you are perceiving (unless you want to get really weird, philosophically). Other than that, nope.
And finally, I'd like to talk about your idea that human experience can be perfectly "noted" as objective, subjective, 0, 1, and 2 (I'll assume you mean true, false, and mystery).
No, I disagree. You even said that things like emotions work into the "mystery" category. This by itself indicates your system does not perfectly describe human experience at all, it simply attempts to simplify and model it in some way. I don't think human experience can ever be perfectly described by anything.
Is "mystery" by any chance a scalar value?
