I say "God" simply as shorthand for the mechanism of innate "meaning determinator" that allows us to declare "X is potentially illusory or not".

What do "meaning" and "illusion" have to do with each other? And what does any of that have to do with "god"?

You seem to like entangling independent concepts. The McGurk effect is a famous and powerful cross-sensory illusion. We can know the meaning of the illusion -- know fully well that what we are experiencing is an illusion -- and are nonethless powerless to stop the illusion. Meaning and illusion are different kinds of things. I still have no idea why "god" was invoked.

So by that definition, you said, "In that sense, all is illusory, including ℕ [thus saith God]."

It's interesting how much you're running with this statement that I made sarcastically.

Because we can use this very mechanism to say, "Perhaps all mathematical theorems are illusory" — the very mechanism to do so lies outside of the theorems to determine any one of them "make sense."

Mathematical theorems cannot be illusory. An illusion is a confusion of the senses. Math theorems are non-sensorial. Furthermore, theorems are unequivocally valid. Their proofs are mechanical -- a computer can verify them.

I invoked him when I used the "inverse-proof" approach to saying "the reason you thought the axioms I made were a mess" was because you had a mechanism to do so that was transcendent to the math itself, which was a proof that the axioms were real.

Huh? There is no such thing as a proof of the realness of axioms. An axiom is a given (unproved) theorem of a formal system. There's no notion of realness or unrealness to an axiom. When making a formal system, anyone is free to include whatever axioms they wish -- you can even choose axioms that make the system self-contradictory. But few will find such systems useful, and we tend to pick formal systems for their utility.

This is the first definition of "proof": The ability to identify a proof by the Grokk's permission. That which is real is that which the Grokk informs us is real by letting us feel the value of the information and its countless relationships, including moral, in relation to information referring to itself or information referring to physical space—something a conscious being does, but an inert non-living mechanical device does not (insofar as we can observe—generally those in caskets and on gurneys don't appear to be doing such).

A proof is a description of a mechanical deduction.

 

The distinguishment isn't something it knows.

So one can have "distinguishment" without knowing. Not sure how, but fine.

It can, it doesn't know or experience it. That's the issue.

Wait a second, if the computer doesn't need to know and can do things like navigate buildings just by distinguishing, then why can't my brain not know and still do things by distinguishing?

What's the operational distinction? <-- this is the crucial question.

We said before that the "dog in the light" problem is about being able to address the dog and its capacities directly. If we can't do that about the dog, how are we to do it about the brain that's supposedly "asking about the dog?"

There is no connection between the brain and the dog.

Huh? There is a connection between the brain and the dog. The dog reflects light, which conveys information about the dog to the brain. The brain doesn't need to "know" the dog; like a computer, it only needs to distinguish the light from the dog.

I think there are perhaps 3 principal "infinite-bit" shapes within the mind — circle, square, triangle — all 3D, and these things are resonating a value of meaning and quantity.

I get what you mean, but I can't help but mention that those shapes are not 3D. ;--)

 

It’s not that I’m trying to get us not to use them, I’m trying to identify the most rudimentary foundational building blocks that drive them all for a ToE. It has to do with “meaning,” feeling and the capacity to grok.

But you are using elements from formal systems to do it. You say that "{0,1}" is an ontological set, both numbers and logic states at the same time. Can you see how this is filled with presumptions about numbers and logic?

The rudimentary foundation of everything is the physical laws that drive the universe. I take these as axiomatic, for there is no way to derive them from something more elemental.

Are you willing to think about numbers without the set theory? (Serious question).

I'm not sure exactly what you mean by this. Can I think of specific properties of numbers that are independent of sets? Sure, no problem. But when we start talking about types of numbers -- i.e., a set of numbers that share certain properties -- how am I supposed to not think of sets?

How is it Pythagoras came up with his theories having no concept of them? Or Newton or Leibniz or anyone else?

You're wrong that they had no concept of number sets. Even old Pythagoras recognized that there was something different between \( 2 \) and \( \sqrt{2} \). Newton and Leibniz could not have invented calculus without having some concept of ℝ.

Exactly what do they afford us with respect to their application in physical space that not knowing about them didn’t?

What does "application in physical space" have to do with numbers?

For example, if we distinguish between grunts and grunt-processes, we can perhaps see numbers in a different, elementary, and unifying light?

You keep forgetting that the counting numbers are an abstraction of the counting process. There are no grunts without the grunt-process.

 

Sorry... that was, “WITHOUT information you can’t insist your brain exists.”

What does it matter if I can or can't insist that my brain exists?

“My brain is a set of states that store (and convey) information” <— No machine can declare such, because there is no “Grokk“ to make the definitional distinction between the physical, their states and information itself. At what complexity level of physicality would such a delineation exist?

Well, I am machine that can declare such a statement. I don't understand what declarations have to do with anything, though. Humans declare stuff, jellyfish not so much. "Declarations" is an anthropocentric metric.

More switches and wires and their more complex interrelation does no such thing.

How do you know?

 

You are saying quantity is not information itself. Can you elaborate on this?

Information is conveyed by change of state. A "quantity" on its own, in a vacuum of context, conveys no information. A quantity in relation to other quantities, or in context of a measurement (i.e., in relation to a process), conveys information.

 

Unless God IS those things.... also, what is “illusion?“

Unless god is what things? An equation? A ring of integers? Please show me how "2 + 3 = 4" can be a theorem in a ring of integers (i.e., elementary arithmetic).

What is an illusion? It is the phenomenon of the brain misinterpreting sensory data.

 

So one can have "distinguishment" without knowing. Not sure how, but fine.


Wait a second, if the computer doesn't need to know and can do things like navigate buildings just by distinguishing, then why can't my brain not know and still do things by distinguishing?

What's the operational distinction? <-- this is the crucial question.


Huh? There is a connection between the brain and the dog. The dog reflects light, which conveys information about the dog to the brain. The brain doesn't need to "know" the dog; like a computer, it only needs to distinguish the light from the dog.


I get what you mean, but I can't help but mention that those shapes are not 3D. ;--)

Correct! I meant comprising 3D! %-)

 

Information is conveyed by change of state. A "quantity" on its own, in a vacuum of context, conveys no information. A quantity in relation to other quantities, or in context of a measurement (i.e., in relation to a process), conveys information.

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

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

 

What does it matter if I can or can't insist that my brain exists?

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

Well, I am machine that can declare such a statement. I don't understand what declarations have to do with anything, though. Humans declare stuff, jellyfish not so much. "Declarations" is an anthropocentric metric.

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

How do you know?

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? At what point does an apple become a car?

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

 

Unless god is what things? An equation? A ring of integers? Please show me how "2 + 3 = 4" can be a theorem in a ring of integers (i.e., elementary arithmetic).

What is an illusion? It is the phenomenon of the brain misinterpreting sensory data.

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

 

You're wrong that they had no concept of number sets. Even old Pythagoras recognized that there was something different between \( 2 \) and \( \sqrt{2} \). Newton and Leibniz could not have invented calculus without having some concept of ℝ.

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.”

 

So one can have "distinguishment" without knowing. Not sure how, but fine.

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

Wait a second, if the computer doesn't need to know and can do things like navigate buildings just by distinguishing, then why can't my brain not know and still do things by distinguishing?

What's the operational distinction? <-- this is the crucial question.

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. :—)

 

Ok, I feel we have to fundamentally shift roles here... How about you start off a ToE with your concepts of words, feeling, grokking, physical space, information, being, infinity, numbers, etc. and I will attempt to agree/disagree/tweak.

Let‘s do 1 axiom at a time. Shoot...

 

You jump into a pool, you come out of the pool... “wet” would be a word token to describe yourself, right?

Anyone else jumps into the pool and does the same, you’d describe them the same.

Would you consider that a “true statement“ that holds the same “weight” as a mathematical one involving sets?

I can't emphasize enough how important it is to distinguish between logical "truth" and the human idea of "truth" as a measure of correspondence. To clarify this distinction, I'll use symbol \( \top \) to mean logical "true" and symbol \( \bot \) to mean logical "false".

In propositional logic, the statement \[ A \vee \neg A \] is \( \top \) for any value of \(A\).

Leaving the system of logic, is the statement "true" in some universal sense? We don't actually know, but at human scales it seems to hold -- it corresponds with our experiences -- so we tend to call it "true". A quantum physicist, however, might say differently.

In the ring of integers, the statement "1 + 1 = 2" is a theorem. It is neither \( \top \) nor \( \bot \) because it is not a statement of logic. Leaving the systems of logic and arithmetic, is the statement "true"? It corresponds with our usual experience, so we say that it's "true". Importantly, there are cases when our experience does not jibe with the theorem. When two rain drops slide down a windshield and merge into one rain drop, we might describe that as a "1 + 1 = 1" correspondence. We can recognize the "truth" of both theorems, even though they are strictly incompatible at the level of integer arithmetic.

Finally, when someone jumps in a pool, we say they are wet. "Abraham Lincoln jumped in the pool; he is wet." Within the system of English language, by definition of "pool" and "wet", this statement is "true". It is neither a logical statement nor an arithmetical statement, and so it is not a theorem. Furthermore, it doesn't speak to the correspondence of experience -- maybe Lincoln never jumped in a pool. The statement's "trueness" is a function of the definitions of its words.

It is incredibly easy to get confused about these different uses of "true", especially given the terribly Rene-esque choice of labeling the constants of bivalent logic "true" and 'false". The most important thing to remember is that formal "truths" -- theorems -- are mechanically necessary and need no correspondence to the external world. In a logic system, we can replace every "true" with 'false", and every "false" with 'true", and derive precisely the same theorems.

Mathematical theorems are also necessary consequences. We casually say "it is true that ...", but the theorems are neither logically true nor logically false, nor are they "true" in the human experience sense. A theorem such as "The determinant of a singular matrix is zero" doesn't have a "true" or "false" correspondence; it simply follows from the axioms.

Serious question:

If someone else jumped into the pool, came out, had water all over them in like manner, and they claimed they were dry, what would you call that?

I mean, it's not inconceivable that the person had covered themselves with a hydrophobic substance prior to jumping into the pool. They might look wet, but their skin would not be touching water. Are they really wet, then? Can you see the distinction between the necessity of a theorem and the degrees to which an experiential statement might be "true".

 

Prior to your knowledge of sets, could you say 3 < 6, and if so, why?

Yup, my first grade teacher told me.

 

Yup, my first grade teacher told me.

What!??? How do you know it’s true?

 

I can't emphasize enough how important it is to distinguish between logical "truth" and the human idea of "truth" as a measure of correspondence. To clarify this distinction, I'll use symbol \( \top \) to mean logical "true" and symbol \( \bot \) to mean logical "false".

In propositional logic, the statement \[ A \vee \neg A \] is \( \top \) for any value of \(A\).

Leaving the system of logic, is the statement "true" in some universal sense? We don't actually know, but at human scales it seems to hold -- it corresponds with our experiences -- so we tend to call it "true". A quantum physicist, however, might say differently.

In the ring of integers, the statement "1 + 1 = 2" is a theorem. It is neither \( \top \) nor \( \bot \) because it is not a statement of logic. Leaving the systems of logic and arithmetic, is the statement "true"? It corresponds with our usual experience, so we say that it's "true". Importantly, there are cases when our experience does not jibe with the theorem. When two rain drops slide down a windshield and merge into one rain drop, we might describe that as a "1 + 1 = 1" correspondence. We can recognize the "truth" of both theorems, even though they are strictly incompatible at the level of integer arithmetic.

Finally, when someone jumps in a pool, we say they are wet. "Abraham Lincoln jumped in the pool; he is wet." Within the system of English language, by definition of "pool" and "wet", this statement is "true". It is neither a logical statement nor an arithmetical statement, and so it is not a theorem. Furthermore, it doesn't speak to the correspondence of experience -- maybe Lincoln never jumped in a pool. The statement's "trueness" is a function of the definitions of its words.

It is incredibly easy to get confused about these different uses of "true", especially given the terribly Rene-esque choice of labeling the constants of bivalent logic "true" and 'false". The most important thing to remember is that formal "truths" -- theorems -- are mechanically necessary and need no correspondence to the external world. In a logic system, we can replace every "true" with 'false", and every "false" with 'true", and derive precisely the same theorems.

Mathematical theorems are also necessary consequences. We casually say "it is true that ...", but the theorems are neither logically true nor logically false, nor are they "true" in the human experience sense. A theorem such as "The determinant of a singular matrix is zero" doesn't have a "true" or "false" correspondence; it simply follows from the axioms.

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.

As one machine unit, to divorce the experience element entirely cannot be on the level.

 

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!

It is the CONTRAST that is what logic is about. The ONLY difference between a true and false statement in a theorem is its Grokk Meaning Value (GMV).

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!

are you on board with this?

 

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

 

I mean, it's not inconceivable that the person had covered themselves with a hydrophobic substance prior to jumping into the pool. They might look wet, but their skin would not be touching water. Are they really wet, then? Can you see the distinction between the necessity of a theorem and the degrees to which an experiential statement might be "true".

Yes, but of course... I aim at making a new kind of theorem, and I hope you’re on board with this:

“Base grok value.”

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

One cannot divorce the origin of the use of words and experience completely(!) from theorem development. Words themselves are experiential in nature and underly the acquisition of knowledge and meaning.

Crucial: It is as TRUE you learned 3 < 6 from your 1st grade teacher as it is that 3 < 6. Yes?? I.e., the same empirical “truth” system we employ to study medicinal effects and able to create order in society like stop signs?

(Notice the use of “really“ there... as in “truly” wet, and “I mean” as the opening... these are PART of the scientific pursuit inextricably, and need hi-res definition)