Since quite literally every term is occupied, including true, false, and real, let me revise what I propose:

Axiom: Meaning is the ascription of value to information independent of its representation

Information has no worth to a human unless it means something, therefore “having meaning“ or “not having meaning“ is an innate property of logical and mathematical valuation, whether mechanically derived or sensorially observed.

Proof: 3 < 6 has meaning. 6 < 3 does not. QED.

If something is not known to have meaning, it is meaningless until it does.

I propose the following:

O = {MEAN, NO-MEAN}

A 2-state set to denote the ontological distinction of ascriptive value independent of information and computation.

There is a bijection between set O and the set of integers {0, 1}
There is a bijection between set O and the set of logic states {T, F}

This bijection permits a computer to use base 2 integers and 2-state logic states to evaluate logic and arithmetically compute any meaningful value.

Thoughts?

 

So information doesn’t exist as an independent some “thing” unless something else registers this fact?

How do you logically conclude that from what I said?

You wouldn’t call “5” or “dog” information?

No, just like I wouldn't call "5" or "dog" energy.

 

How do you logically conclude that from what I said?

I’m taking it in context to what you said very early on, that we have no definition for information. This is another semantic clusterf*ck. How can we truly say a quantity is not a piece of “information?”

Here‘s a common definition:
”the amount or number of a material or immaterial thing not usually estimated by spatial measurement”

This sounds like a definition for information to me no different than characterizing information by a measurable quantity!

Can a machine define information any different than a number of voltage states or switches high or low?

No, just like I wouldn't call "5" or "dog" energy.

Words and the science of their interrelation are not information then?

 

Because you can’t insist anything else exists, including mathematical theorems, unless you exist first to know the difference.

The existence of a mathematical theorem doesn't have anything to do with whether I insist it exists or not.

What if “machine” is just one component of your existence, and the term is not comprehensive?

What if machine is the whole enchilada and there is nothing else?

Because a univac is as much a machine as is a DWave or iPhone, or a T-800. What does quantity have to do with qualia?

You don't recognize that a cell is a molecular machine? You don't recognize that there is both a quantitative and qualitative difference between a single-celled organism and one that's comprised of trillions of cells?

At what point does an apple become a car?

Well, at one point the apple was just a bunch of CO2 and H2O molecules.

No amount of sand particles changes the definition of a beach. Just its size.

What does the definition of a beach have to do with anything? You're not being reasonable. What kind of structures can you (or nature or whatever) make with a grain of sand? What kind of structures can you make with a beach of sand? See the difference? Complexity matters.

 

If the machine does not experience the difference, why is an interpetation considered an illusion and not just a different interpretation?

You didn't answer the "2+3=4" question. Anyway, you've answered your own question (keyword bolded).

 

Considering ℝ is essentially a term that encapsulates all except for imaginary numbers, it’s incongruous to me to insist they knew of “sets.” They all ”knew” of one “set“ that effectively, operationally disappears: “numbers and fractionated phenomena.”

You're wrong. For Pythagoras, we know from history that he considered what we would call rational numbers sacred, and that he was horrified by the discovery of an irrational quantity (the diagonal of a unit square). Newton and Leibniz were far more mathematically sophisticated. They certainly could appreciate the difference between integer equations (Diophantine equations) and real equations, In particular, they thoroughly understood that a calculus of increments required numbers even more finely spaced than the rationals. Newton called them "fluents" (flowing numbers), Leibniz called them infinitesimals. They were of course talking about the continuum of ℝ.

 

If you accept a metaphysical component, that’s the “how”.

Ah, so the key to understanding your logic is to accept magic.

No operational difference between you and the non-living replicant “you“ that Skynet makes in 2090.

Other than the fact one is alive, can know he is, can feel it, as a function of being IN the machine, and the machine is just an interface...

...vs. the other is a throwaway device. :—)

There is no dispute that the brain is biological life and the computer is not. But if there's no operational difference (except "feeling"), then we don't need to invoke magical powers for animation.

I'm interested in finding the minimal set of properties that you believe require metaphysical explanation. We can put animation/motion in the set of things that a computer can do. What's the minimal set of things that only a metaphysically endowed human can do?

 

What!??? How do you know it’s true?

I didn't until I learned mathematics, including set theory. ;--)

 

See, this is what I consider the “Grokk” in motion:

”The determinant of a singular is zero“

is really saying,

”Using the laws of The Grokk, it is ontologically true to ME based on my internal order system, that the ‘determinant of a singular matrix is zero‘ follows from prior axioms.”

You would not say the statement follows unless the order system within let you.

You mean the laws of physics? If I set up a bean machine (https://en.wikipedia.org/wiki/Bean_machine) to demonstrate the central limit theorem, would I say "it is ontologically true to ME based on my internal order system"? If I set up a sequence of gears and levers that computes a Fourier series (

), would I say "it is ontologically true to ME based on my internal order system"?

The universe doesn't give a f*ck about my "ontological truth". My internal order system is the laws of physics, same as the external order system.

 

Important: Also, by replacing every False with True and True with False in a formal system ALL you have done is switched the words being used to denote the same underlying meaning!

But you can't do that with integer arithmetic, which was my whole point. You've been claiming that logic states -- which hopefully you now agree are arbitrary symbols -- are equivalent to numbers, but you can't swap 3 and 6 in " 3 < 6".

The ONLY difference between a true and false statement in a theorem is its Grokk Meaning Value (GMV).

What do you think I've been saying this entire time? Sweet lord. The theorems of a logical system are empty of meaning until we apply an interpretation (model) and assign each variable a \( \top \) or \( \bot \) value. Logic is purely syntactic.

Your first grade teacher told you 3 < 6 and you GROKKED it experientially! AKA “AHA! YES! I SEE THAT!” difference between information and “knowing” information as an ORDER! You experienced the order!

Nah, I really didn't grok 3 < 6 until many, many years later. In fact, I'm still learning the complexities of order theory.

 

How does a machine (you) differentiate between axioms, theorems, numbers, true, and false with just unary or binary states of voltage?

Same way a machine differentiates anything, by developing concepts about the things.

 

You mean the laws of physics? If I set up a bean machine (https://en.wikipedia.org/wiki/Bean_machine) to demonstrate the central limit theorem, would I say "it is ontologically true to ME based on my internal order system"? If I set up a sequence of gears and levers that computes a Fourier series (

), would I say "it is ontologically true to ME based on my internal order system"?

The universe doesn't give a f*ck about my "ontological truth". My internal order system is the laws of physics, same as the external order system.

Bitter Lord. And you say that I'M not being reasonable???

I just don't understand how you can't see how utterly "blanket" that statement is.

You attribute "knowability" and "grokability" to discrete voltage states. As a machine, you don't know the difference between "information," "representation," the "laws of physics" are. "Gravity" is what again in your states?

#!##!!!##!##!##!!!!!###!###!##!#!# <- THAT is gravity to you (where each symbol represents a logic state)

What kind of fairy dust is on those states that "knows" what gravity is vs. magnetism vs. polarity vs. electromotive force? There is positively ZERO "knowledge" of those things. Simply logic states that represent symbols that represent information that represents meaning to a human.

A "machine" is nothing more than a mechanical device that's reflecting the pre-programmed states of voltages that ONLY make "sense" or have "meaning" to a human. There is no MEANING in a mechanical machine. Positively none.

MrAl, if you're still here — just curious: what's your "feeling" on this? Do you believe a "machine" knows anything? Or would you say it's simply just states reflecting its programmer's intention that KNOWS the difference??

 

What do you think I've been saying this entire time? Sweet lord. The theorems of a logical system are empty of meaning until we apply an interpretation (model) and assign each variable a \( \top \) or \( \bot \) value. Logic is purely syntactic.

Due to the semantirrhea that's going here, we have to spend 3,000 messages coming to terms with what's being conferred. I've know that's what you're saying, but I'm trying to get at the very MECHANICS of that differentiation system. It's frankly nonsense that "T" and "F" and "REAL" are all occupied to me. That was what my whole "grokk dragon" thing was about, if you could catch what I meant.

There is a meaning system — it's the "Theorem Kit" we purchase in the womb: It comes with the mathematical theorems AND ABSOLUTE value of truth vs. falsity to them. This was my whole point in trying to create an ontological truth set that both logic AND arithmetic is derived from. Clearly they are branches on a single "grok" trunk. Do you vibe what I'm pitching?

Nah, I really didn't grok 3 < 6 until many, many years later. In fact, I'm still learning the complexities of order theory.

No, correct me if I'm wrong, but you positively grokked some kind of baseline of understanding of "less than," and then grokked MORE about it later on.

 

My question was, “all things equal.” It is unequivocally TRUE on the same level of any theorem, “all are wet.”

No, of course not. Unequivocally true means to be beyond doubt. An experiential "fact" is always doubtable.

I'm not sure what to make of this. Do you not see the difference between the necessity of a theorem and the interpretation of a perceptual experience?

Crucial: It is as TRUE you learned 3 < 6 from your 1st grade teacher as it is that 3 < 6. Yes??

Of course not. The word "true" is perhaps the most confusing word in the English language.

Within a formal logic system, "3 < 6" is not a well-formed formula and is neither true nor false. The statement

"3 < 6" is a theorem of integer rings

is a "true" statement in the sense that it corresponds to experience, in the same way that "Liquid water is wet" is a "true" statement. Note that if someone doesn't know what an integer ring is, they might not necessarily believe in the "truth" of the statement. Someone might plausibly suspect that it's a trick question, that 3 is actually greater than 6 in whatever "integer ring" means.

The statement of a theorem is not a theorem.

Most importantly, the notion of truth as used in formal logic systems is entirely different from the notion of truth that we use in casual conversation. Formal truth is an arbitrary classification that has no bearing or resemblance to experience. An experientially false thing can be formally "true". In propositional logic, the statement "If 2 = 3, then Chuck Norris is the president" evaluates to true. When we speak of "truth" in casual conversation, we're speaking of how closely something corresponds to our experience of things. It's true that it always rains when we wash the car. It's true that Canada is a country in the U.N. It's true that Linda has six kids.

The "truth" -- in the casual sense -- of when I first learned that 3 is less than 6 is not entirely clear to me. It might have been first grade, it might have been kindergarten, or second grade. I can't remember exactly. I have a vague notion of the "truth". There are no vague notions of theorems -- a statement is either a theorem of a system or it isn't, for always and ever.

 

I didn't until I learned mathematics, including set theory. ;--)

Nahhhh... if you didn't grok it as truth at some level to begin with, you wouldn't even bother studying it. I'm sure you were teaching the teacher at 4 about these things, don't lie. Lol.

 

Axiom: Meaning is the ascription of value to information independent of its representation

What does "value" mean in this context? What exactly is being ascribed to provide meaning?

Information has no worth to a human unless it means something, therefore “having meaning“ or “not having meaning“ is an innate property of logical and mathematical valuation, whether mechanically derived or sensorially observed.

What does "worth" have to do with anything? At this very moment, there are a bunch of molecules in Jupiter's atmosphere transferring information. It is very unlikely that they have any worth to any human on Earth. What does it matter to the molecules?

Proof: 3 < 6 has meaning. 6 < 3 does not.

You think that "6 < 3" doesn't have meaning? It's certainly not meaningless. I can interpret the symbols and connect them with their usual meaning. I could even explore the consequences of "6 < 3" being a theorem of some system. That doesn't seem meaningless to me.

I propose the following:

O = {MEAN, NO-MEAN}

A 2-state set to denote the ontological distinction of ascriptive value independent of information and computation.

There is a bijection between set O and the set of integers {0, 1}
There is a bijection between set O and the set of logic states {T, F}

This bijection permits a computer to use base 2 integers and 2-state logic states to evaluate logic and arithmetically compute any meaningful value.

Thoughts?

Kudos on the significant improvement in precision and clarity! Seriously, nicely done.

I would ask this: if {MEAN, NO-MEAN} is ontologically fundamental, then how does a computer use it? I've interpreted your stance as being that one of the essential differences between humans and computers is that the latter cannot ascribe meaning to their data. If so, then how does a computer use {MEAN, NO-MEAN} to compute?

 

I’m taking it in context to what you said very early on, that we have no definition for information.

But you said that I implied that information doesn't exist until it's registered. I implied no such thing.

How can we truly say a quantity is not a piece of “information?”

Saying piece of information suggests that you're thinking of information in the casual sense, e.g., "George Washington was the first U.S. president" is a piece of information. That's a human-level use of information. I'm talking about information as a fundamental property of the universe. It's general and devoid of intrinsic meaning.

A quantity is a high level abstraction, on the same level as numbers. We use raw, low-level information to create the abstractions that allow us to describe phenomena in terms of quantities.

When I say that information is a measurable quantity, I'm speaking at the level of an agent measuring things and describing theories, i.e., a very high level. I don't claim that "measurable quantity" is a great definition of low-level information, but it's a start.

Can a machine define information any different than a number of voltage states or switches high or low?

Voltage states and switches are abstractions, too. I think what you're trying to get at is can information describe itself? As I can describe myself, I would say yes.

Words and the science of their interrelation are not information then?

In the causal sense, of course. In the fundamental sense, words are closer to raw information than science. The vocalization of words is an information process. We transform information -- by modulating air molecules -- to speak words. At a higher level, our brains associate the words with concepts (definitions and such) and derive meaning from the raw vocalizations.

Science is on another stratosphere, abstraction-wise. There is no physical thing we can point to and say "science!" Like math, it's entirely conceptual. But unlike math, science concepts are almost entirely reflective of external states. They are states about how best to conceptualize external states. Ultimately, science is the combined memory of innumerable such concepts.

So, is science information? Yes, but it's complicated. ;--)

 

You attribute "knowability" and "grokability" to discrete voltage states. As a machine, you don't know the difference between "information," "representation," the "laws of physics" are.

Of course I do. Wolfram Alpha knows, too.

"Gravity" is what again in your states?

Gravity itself is just a set of state transformations. The universe made these state transformations different from the state transformations that characterize the laws of electricity. I don't get why you think "magic" has to happen to distinguish that the two are different.

#!##!!!##!##!##!!!!!###!###!##!#!# <- THAT is gravity to you (where each symbol represents a logic state)

Not even close. How many megabytes of RAM do you think that Wolfram Alpha uses for its conception of gravity? Seriously, think about it. Then consider how many neurons are working in my brain to allow me to hold the concept of gravity.

What kind of fairy dust is on those states that "knows" what gravity is vs. magnetism vs. polarity vs. electromotive force? There is positively ZERO "knowledge" of those things. Simply logic states that represent symbols that represent information that represents meaning to a human.

You can ask Wolfram Alpha the difference between gravity and magnetism yourself. How could it possibly answer those questions if it couldn't even recognize there was a difference?!

If you're tempted to say "it was programmed", don't forget that you were, too!

A "machine" is nothing more than a mechanical device that's reflecting the pre-programmed states of voltages that ONLY make "sense" or have "meaning" to a human. There is no MEANING in a mechanical machine. Positively none.

Even if I grant you that no currently available electronic machine has any notion of "meaning", so what? If indeed meaning is a matter of complexity -- and it surely seems to be, talking to you snails! -- then it is entirely possible that a sufficiently complex electronic machine will have meaning. You're denying that possibility outright without any justification other than "magic".

 

I've know that's what you're saying, but I'm trying to get at the very MECHANICS of that differentiation system.

What differentiation system? The capability of recognizing theorems from non-theorems? As I see it, that capability is the very same one that allows us to distinguish between physical phenomena. The same capability that allows an amoeba to detect changes in temperature in its environment, allows us to experience the world. Due to environmental pressures and luck, our species was fortunate enough to evolve an exceptionally complex cerebral cortex, allowing us to direct that distinguishing capability inward, as it were.

Being able to recognize mathematical theorems are just one of the many interesting things that can happen.

There is a meaning system — it's the "Theorem Kit" we purchase in the womb: It comes with the mathematical theorems AND ABSOLUTE value of truth vs. falsity to them.

Totally disagree. We are not born knowing mathematical theorems or absolute anythings. It takes a lot of work to get to the point where we can even conceive of such things. The fancy cerebral cortex gives us the capability, not the ability.

No, correct me if I'm wrong, but you positively grokked some kind of baseline of understanding of "less than," and then grokked MORE about it later on.

Sure, I had a practical idea of what "more" and "less" meant. Give me more candy, please. Give me less homework, please. That's a long way from grokking the mathematical implications of "3 < 6".

 

Nahhhh... if you didn't grok it as truth at some level to begin with, you wouldn't even bother studying it. I'm sure you were teaching the teacher at 4 about these things, don't lie. Lol.

Quite the opposite, on both counts. I was a dreadful student and especially hated (mostly out of fear) math. Had I just accepted that 3 is less than 6, that would've been the end of that. But, rather than simply follow the instructions, learn the rules, and get an 'A', I would ask "why?", complain when the teacher gave a perfunctory answer, and get a "C-". Many years later, when I finally got over my fear of math, I learned that asking "why?" is actually the most important mathematical question. And that's when "boring" theorems like 3 < 6 started becoming very interesting.