For the record, just so you know the general tact I would take in responding to some of those points—because it's frustrating to get NO reply—ontologically we're interested in absolute BASE, indivisible phenomena all definitions are based on.

So that means, for example, a "trit" is just another axiomatic element being defined as a subset of bit. Indeed, you can define a trit componentally in terms of a bit. That means it's an axiom, not an ontological fundament. One trit is equivalent to log2 3 (about 1.58496) bits of information.

Same applies to an XOR gate. I'm not on board with that QED because an XOR gate is ontologically a contraption of 4 inverted OR gates (NAND gates). The OR gate is the ontological fundamental building block, which is in fact employing the "OR" axiom, or ADDITION operator. An XOR is simply a steroidal, mutually exclusive OR gate. The carry bit is an essential element of the TRUE-FALSE superposition and is being ferried to the next circuit to complete the addition (because a computer is an ADDING machine alone, and it ADDS via OR gates and inverters! — QED AF!).

 

The voltages are nondescript and have no definability one to another!

Definability, deshminability. Information processors use the relations between the voltages.

On the table is your brain, with each neuron representing one or more bits, if you space them all out, none of them know anything. The “weather” is a concept in Siri that it’s aware of or “sees” different than any other bag of bits like wikipedia or wolfram alpha? C’mon man!!

If we take a 2x2 section of pixels from the image of MARIO, is it still MARIO? Nope. MARIO is the relationship between all the pixels. Likewise, "weather" -- a much more complicated "picture" than MARIO -- is the relationship between all the subsets of states that comprise the CONCEPT of "weather". Siri has its own CONCEPT of "weather", as does Wikipedia, Wolfram, and me.

That’s why you don’t put a tritone in a crib, lest you breed Jason Krueger.

ROFL. Actually, I used to play "harmonically interesting" chords -- especially tritones! -- to my infant daughter. It was my hope that she'd develop interesting neural pathways beyond what "Twinkle, twinkle" could inspire. She's 13 now and a pretty cool kid; I secretly attribute some of that to tritones.

 

Totally disagree. I close my eyes and imagine a dog. What's happening is that, having read your sentence, several sub-states of my brain are activated, including sub-states that are associated with my CONCEPT of "dog". The mental images I experience are not spawned from nothing; they were created, stored, and evolved from all my previous experiences of dog-related stimuli.

Nope. Lol. You're a brain, and you have no idea what your brain is doing. Does Siri, with n⁹⁹⁹⁹⁹⁹⁹ yottabytes of Watson as a backend enable her to see or know the weather her faux-voice is reflecting (and which itself has no connection to the weather)?

The "thought form" is just a set of sub-states. Being states, they can be described by n-bit strings. Such a description doesn't exist in my brain, but the states it represents does.

Nope, because no n-bit strings can know about those "thoughts" (another non-bit axiom) and you're just n-bit strings.

Perhaps it's about time you defined 5D INFINITY.

We'll get there.

If I have to be assigned to a church, I suppose it'd be the Church of Information. In this church, brains are just a very tiny subset of things that process information, only slightly more interesting than computers.

This church doesn't exist though, because it doesn't know what anything is, including itself. As such, it is an indirect regional distributor for Kraft-Heinz, storing gaylord pallets of 55-gallon drums of Kool-Aid® in the basement next to Michelangelo's David-esque statues of Darwin and Hume.

 

We're getting rid of existing propositional logic then, and inventing a new one, because the hardware proves otherwise. I don't care what anyone says — the 0's and 1's as voltages are able to be used as logic states and base 2 numbers and added using "+" or "OR" (as in base-line human awareness of what those things mean). I don't care what towns we set on fire here, if 50% of it has to go, it has to go in the quest of an authentic ToE.

As fun as conceptually burning everything down and rebuilding can be, we've got to leave something in the fire-proof box. And since logic is the very foundation on which everything reasonable stands, I say we spare having to re-invent propositional logic.

Umm... Again, going back to the fact that you are a brain examining another "brain/computer." You are "bits examining bits."

And? Bits responding to other bits is how we're defining processing. I'm processing process.

What do you mean "where are the numbers?" Is not a calculator doing calculations with numbers?

Most definitely not! There are no numbers inside of a calculator. Open up a calculator and try to find a single number, I dare ya.

The numbers ARE the unique combinations of 0's and 1's! They're in base 2! And the same string can be used as logic states to evaluate against others. How do you know they're NOT numbers or logic states?

An abacus is a calculator. Most of them are not base-2, and none uses 0s and 1s -- they use stones or beads. Where are the numbers there? A traffic light is a state machine with three logical states. "IF RED, THEN STOP" and so on. So, if RED is a logic state, is it also a number?

 

Definability, deshminability. Information processors use the relations between the voltages.

Relation shmlation! There are no RELATIONS between bits in a bit-processing machine!! NO one bit in Mario knows WTF any other bit means. Mario could be stored across 900 servers in 40 countries. He is as componental and 1D as the day is long!
Your concept of "CONCEPT" is just as axiomatic as INFINITY!

If we take a 2x2 section of pixels from the image of MARIO, is it still MARIO? Nope. MARIO is the relationship between all the pixels.

Hahaha... yes! Again, says the BRAIN who doesn't "know" the difference or relationship between any one bit???? This is PRECISELY my argument! The "real" MARIO MUST BE INFINITE! Otherwise, there is NO first order definition of MARIO used to define any other Mario ever!! Can you use bits to define INFINITY? No. Nor can you use them to define symbol or axiom Mario!

Likewise, "weather" -- a much more complicated "picture" than MARIO -- is the relationship between all the subsets of states that comprise the CONCEPT of "weather". Siri has its own CONCEPT of "weather", as does Wikipedia, Wolfram, and me.

Again, here is a brain "rolling its own axioms" with no permission. "CONCEPT" is invoking the concept of supra-bit "indivisible definition."

ROFL. Actually, I used to play "harmonically interesting" chords -- especially tritones! -- to my infant daughter. It was my hope that she'd develop interesting neural pathways beyond what "Twinkle, twinkle" could inspire. She's 13 now and a pretty cool kid; I secretly attribute some of that to tritones.

...and little do you know she's actually wanted in 50 states. Cue Robert Stack's voice: "IF YOU have any information concerning the whereabouts of the Tritone Killer, please contact the Unsolved Mysteries Hotline..."

 

For the record, if someone with the stature of Kronecker can call into question all existing number theory and say "God created the integers, the rest is manmade contrivance" (and I think he was essentially on the right path) and also have the respect of others in the field, then we can do the same here with logic. You don't think you're as smart as him? You ARE Boole. And I'm Kronecker's secretary. So let's get this thing rollin'. Obviously there's *quite a bit of unexplored territory* in the infinity/consciousness/knowledge/reason space coming from a more logic/math/info theory approach (albeit bespoke). Mankind doesn't exist, thinks he does, and doesn't know what something is, but insists he does as a bag of wires hooked to a battery on a table. We got work to do.

Just wanted to say that I love this paragraph.

 

1) QED's on machinery/information processor with 2ⁿ limit
2) INFINITY as supra-numeric phenomenon

This is a VERY sound foundation.

Yup.

So, for #3, I propose:

INFINITY represents indiscrete, unboundability. A bit is a discrete, bounded element. No n number of bits is modulating this definition or cascading into unboundability.

Nope. The unboundedness of INFINITY is orthogonal to the discrete/continuous distinction. If we associate INFINITY with boundless process of counting the natural numbers -- which is were the CONCEPT of INFINITY initially comes from -- then INFINITY has a discrete flavor. Counting can be performed only on discrete things, hence the (discrete) natural numbers.

Can INFINITY as defined as the supra-numeric unbounded axiom truly be represented as a voltage or group thereof without compromising #2's definition?

Yes, the CONCEPT of INFINITY can be stored in finite bits. Interestingly, taking voltage levels as a continuum (rather than binary levels) inspires the CONCEPT of uncountable infinity (_INFINITY). But we don't need to go there.

 

ROFL. Actually, I used to play "harmonically interesting" chords -- especially tritones! -- to my infant daughter. It was my hope that she'd develop interesting neural pathways beyond what "Twinkle, twinkle" could inspire. She's 13 now and a pretty cool kid; I secretly attribute some of that to tritones.

Also.... "Daughter," he says. You mean the parts and schematic to the T-8500 you brought over with you in the trunk of the time-deplacement equipment? Because that's the only thing that should be hearing a tri-tone in its "crib" FFS!

 

Yup.


Nope. The unboundedness of INFINITY is orthogonal to the discrete/continuous distinction. If we associate INFINITY with boundless process of counting the natural numbers -- which is were the CONCEPT of INFINITY initially comes from -- then INFINITY has a discrete flavor. Counting can be performed only on discrete things, hence the (discrete) natural numbers.

Yes, the CONCEPT of INFINITY can be stored in finite bits. Interestingly, taking voltage levels as a continuum (rather than binary levels) inspires the CONCEPT of uncountable infinity (_INFINITY). But we don't need to go there.

Paging "Dr. Conccepcione F. Orthogonáli to the main E-wing desk please, Dr. Othoganáli to the E-wing."

You don't have the luxury of any of that. Foundations, foundations, foundations = back to the QED of machinery and bits. You love invoking CONCEPT as if it's different from any other supranumeric axiom.

 

So that means, for example, a "trit" is just another axiomatic element being defined as a subset of bit. Indeed, you can define a trit componentally in terms of a bit. That means it's an axiom, not an ontological fundament. One trit is equivalent to log2 3 (about 1.58496) bits of information.

I disagree. A bit is no more fundamental than a trit -- both are arbitrary choices of n for a base-n unit. I can equally express bits in terms of trits as you can trits in terms of bits. To wit, one bit is equivalent to \( \log_{3}(2) \approx 0.630923 \) trits of information. We musn't mistake familiar with fundamental.

Same applies to an XOR gate. I'm not on board with that QED because an XOR gate is ontologically a contraption of 4 inverted OR gates (NAND gates). The OR gate is the ontological fundamental building block, which is in fact employing the "OR" axiom, or ADDITION operator. An XOR is simply a steroidal, mutually exclusive OR gate. The carry bit is an essential element of the TRUE-FALSE superposition and is being ferried to the next circuit to complete the addition (because a computer is an ADDING machine alone, and it ADDS via OR gates and inverters! — QED AF!).

Physically, one can make any boolean circuit out of just NAND gates or just NOR gates. So, is NOR more ontologically fundamental than OR? That's weird to suggest, as one needs an OR gate to build a NOR gate. But, if NOR is not fundamental, then neither is OR, as one cannot build arbitrary boolean circuits out of just OR gates.

How, then, should we define the ontological hierarchy of binary logic operations? Well, we can recognize that with two inputs, there are four possible combinations: FF, FT, TF, TT. Thus, there are \( 2^4 = 16 \) possible binary operations (which includes the familiar operations, such as AND, OR, etc.). Given two inputs, each of these operations has a distinct output. Indeed, this is how we define the operations, by their respective output to the set of four possible inputs. There is no other way in which we define the operations. Therefore, as binary logical operations, they are all fundamental. It makes no sense to say that OR is more or less fundamental than XOR.

That's the logic world. In the arithmetic world, there are no operations such as OR or XOR. The properties of the "+" operation depend on which model of arithmetic is in use. In the mod-12 model ("clock arithmetic"), "10 + 3 = 1" is a true statement. In boolean ring models (computer arithmetic), "1 + 1 = 0" is a true statement.

And when we compare the output of "+" in a boolean ring to the output of XOR in logic, we find that they can be mapped between each other:

A  B  A XOR B
F  F    F
F  T    T
T  F    T
T  T    F

A  B  A + B
0  0    0
0  1    1
1  0    1
1  1    0

Using the map 0 \( \to \) F and 1 \( \to \) T, we see that XOR and boolean "+" are compatible operations.

This is NOT the case for OR. If "+" were assigned to OR, then "1 + 1 = 1" would be true, but that breaks computer arithmetic, as you yourself showed in an earlier post. This is a dead-cold, non-negotiable, universal fact. No one, no matter how clever, will be able to find a loophole. It's utterly pointless and a waste of time to try. OR and "+" are not compatible.

 

As fun as conceptually burning everything down and rebuilding can be, we've got to leave something in the fire-proof box. And since logic is the very foundation on which everything reasonable stands, I say we spare having to re-invent propositional logic. And? Bits responding to other bits is how we're defining processing. I'm processing process.

I think I agree... but it may need to be "extended" to include some "entanglement" and carry-over elements. Like, 1 + 1 = 10 is also TRUE OR TRUE = FALSE-TRUE.. . It's 100% a fact that the most elementary computer is using OR gates and inverters as its foundation. The carry-bit is a load of OR gates and inverters carefully assembled to create a more powerful mutually exclusive "OR" in order to implement the carry-bit phenomenon.

Most definitely not! There are no numbers inside of a calculator. Open up a calculator and try to find a single number, I dare ya.

Perhaps, just perhaps I'm on board with "a number is an axiomatic conglomeration of bits". But I won't see a number apart from bits, and neither should you being a bit processor.

An abacus is a calculator. Most of them are not base-2, and none uses 0s and 1s -- they use stones or beads. Where are the numbers there? A traffic light is a state machine with three logical states. "IF RED, THEN STOP" and so on. So, if RED is a logic state, is it also a number?

The numbers in the abacus are the presence or absence of the stones or beads.

"IF RED, THEN STOP" is not an elementary proposition. It's "IF IT IS TRUE THAT IT IS RED, THEN STOP". Red is NOT the truth state itself — it is componental to it. RED is an axiom that can be mapped to either FALSE or TRUE. You can say, "If NOT RED, then STOP". IF INFINITY, then STOP. IF DOG, then STOP.

RED is in the space of defined axioms, which again, are not in the space of bits.

 

Nope. Lol. You're a brain, and you have no idea what your brain is doing.

Naturally, this is all speculation. I contend, however, that my speculations are better than yours.

Does Siri, with n⁹⁹⁹⁹⁹⁹⁹ yottabytes of Watson as a backend enable her to see or know the weather her faux-voice is reflecting (and which itself has no connection to the weather)?

Yes, of course! Siri's weather CONCEPT is probably not much like mine, but so what? My weather CONCEPT is almost certainly different than yours (and everyone else's). So, who has the "right" weather CONCEPT? It's an empty question. Fundamentally, Siri "knows" the weather much like I "know" the weather -- through sensors that update states that get associated with other states.

Just because I describe some of my sub-states as "feeling warm" doesn't make them any more real than Siri's line of code that says "IF TEMP > 70, SAY 'WARM'".

Nope, because no n-bit strings can know about those "thoughts" (another non-bit axiom) and you're just n-bit strings.

I'm NOT n-bit strings. I'm a set of states that evolve over time. I can represent those states with n-bit strings, but I'm not the strings.

This church doesn't exist though, because it doesn't know what anything is, including itself. As such, it is an indirect regional distributor for Kraft-Heinz, storing gaylord pallets of 55-gallon drums of Kool-Aid® in the basement next to Michelangelo's David-esque statues of Darwin and Hume.

Take a sip, it's tasty.

 

Relation shmlation! There are no RELATIONS between bits in a bit-processing machine!!

To a bit-processing machine, it's only the relations that matter, not the bits. The bits are just canvas, devoid of information; the relationships between the bits conveys information. Get that through your noodle before continuing!

NO one bit in Mario knows WTF any other bit means.

Again with meaning. Consider it this way: MARIO -- as a single, particular state of a set of bits -- doesn't "do anything". It's just there. An information processing machine, however, can do something with the information that's represented by MARIO. As an example, a CPU might read the MARIO bits from RAM and display it on a screen. As another example, my optical neurons might react to the light from the screen, causing a sh!t ton of other states in my brain to react, causing me to say "Hey, that's a picture of Mario".

No where in any of this is there any absolute sense of "meaning". It's just different configurations of state that some other configurations of state react to, causing other configurations of state to change. And so on.

Again, says the BRAIN who doesn't the difference or relationship between any one bit????

Someone comes into my room. The state of light in the room changes. My optical receptors react accordingly, triggering a whole bunch of sub-circuits in my brain. Some of these circuits work to match the pattern of light against a database of remembered faces. There's a match; the person coming into the room is my daughter. Another circuit reacts, and I smile.

My brain knows only the relationships between the "bits" (metaphorically, as there are no bits in my brain). It's these very changing relationships that account for my experience of the world, both internal and external. There's only relationships.

The "real" MARIO MUST BE INFINITE! Otherwise, there is NO first order definition of MARIO used to define any other Mario ever!!

WTF? MARIO is decidedly finite. We can easily count the bits needed to represent him. We can copy those bits at our leisure and call the copies other MARIOs, if we want. No infinity necessary.

Can you use bits to define INFINITY? No.

Yes, of course! My computer has at least seven programs that do just that! The Wikipedia entry on infinity uses a couple thousand bits to describe it pretty well.

Again, here is a brain "rolling its own axioms" with no permission. "CONCEPT" is invoking the concept of supra-bit "indivisible definition."

My brain can roll its own axioms whenever it well pleases, thank you much. I dunno what a "supra-bit indivisible definition" is, though.

...and little do you know she's actually wanted in 50 states. Cue Robert Stack's voice: "IF YOU have any information concerning the whereabouts of the Tritone Killer, please contact the Unsolved Mysteries Hotline..."

I'm pretty sure she isn't, not yet anyway.

 

Also.... "Daughter," he says. You mean the parts and schematic to the T-8500 you brought over with you in the trunk of the time-deplacement equipment? Because that's the only thing that should be hearing a tri-tone in its "crib" FFS!

Yeah, it's weird to think about my daughter (and myself!) as a state machine. But then I realize that there are all kinds of state machines, and some of them are far more interesting (to this machine) than others, and it doesn't seem so weird, after all.

 

You don't have the luxury of any of that. Foundations, foundations, foundations = back to the QED of machinery and bits. You love invoking CONCEPT as if it's different from any other supranumeric axiom.

Eh? A hundred pages back or so, I defined CONCEPT from the axioms of STATE and PROCESS. A CONCEPT is just a set of associated states, nothing more. A state machine creates CONCEPTs by processing information. No numbers needed.

 

I disagree. A bit is no more fundamental than a trit -- both are arbitrary choices of n for a base-n unit. I can equally express bits in terms of trits as you can trits in terms of bits. To wit, one bit is equivalent to \( \log_{3}(2) \approx 0.630923 \) trits of information. We musn't mistake familiar with fundamental.

Physically, one can make any boolean circuit out of just NAND gates or just NOR gates. So, is NOR more ontologically fundamental than OR? That's weird to suggest, as one needs an OR gate to build a NOR gate. But, if NOR is not fundamental, then neither is OR, as one cannot build arbitrary boolean circuits out of just OR gates.

This is NOT the case for OR. If "+" were assigned to OR, then "1 + 1 = 1" would be true, but that breaks computer arithmetic, as you yourself showed in an earlier post. This is a dead-cold, non-negotiable, universal fact. No one, no matter how clever, will be able to find a loophole. It's utterly pointless and a waste of time to try. OR and "+" are not compatible.

It doesn't break the arithmetic: it "extends" it into undefined territory — that's what I'm proposing. An entanglement is false and true at the same time, and it's precisely what's happening here. It is 1 AND 0 because they are both necessary to continue the calculation of the string. IF not, how can we justify seeing strings of bits as having any connection? 010101110 only can be seen as legit because the far right 0 is connected to the next 1 to the left, etc. How do we connect them? Through the arithmetic of OR foundationals which yields superposition of true and false as manifested via a carry-bit.

Physically, one can make any boolean circuit out of just NAND gates or just NOR gates. So, is NOR more ontologically fundamental than OR? That's weird to suggest, as one needs an OR gate to build a NOR gate. But, if NOR is not fundamental, then neither is OR, as one cannot build arbitrary boolean circuits out of just OR gates.

One must see the inverter ontologically separate from the gate, because they exist functionally separate from each other axiom-wise. So yes, an OR gate is functionally more elemental because the NOR requires another element. The AND gate is composed of negated NANDS, and OR's can be made of negated NAND's, but the NAND's are componental. QED.

I disagree. A bit is no more fundamental than a trit -- both are arbitrary choices of n for a base-n unit. I can equally express bits in terms of trits as you can trits in terms of bits. To wit, one bit is equivalent to \( \log_{3}(2) \approx 0.630923 \) trits of information. We musn't mistake familiar with fundamental.

Again, ontological observation, though—because in the axiomatic world we can build ANYTHING. Where's the "trit" in the presence/absence element of the natural world? The natural world has a bit defined as a high or low voltage. A trit is...? Nowhere.

 

Eh? A hundred pages back or so, I defined CONCEPT from the axioms of STATE and PROCESS. A CONCEPT is just a set of associated states, nothing more. A state machine creates CONCEPTs by processing information. No numbers needed.

Must have slipped through, because I'm not on board. STATE and PROCESS are not elemental enough to be "SOMETHING" as in "dog" or "RED." A "dog"/noun can be in multiple states THROUGH process. E.g. the concept of a dog being put into a state of sleep via the process of tranquilization.

 

Yeah, it's weird to think about my daughter (and myself!) as a state machine. But then I realize that there are all kinds of state machines, and some of them are far more interesting (to this machine) than others, and it doesn't seem so weird, after all.

We'll get there, but the difference between a T-9000 and you and your daughter is here:

And that is entirely not a function of bits or chemicals without a metanatural component, because the guy on the gurney ain't experiencing anything, and watson couldn't care less about the laughter in this discussion.

 

I think I agree... but it may need to be "extended" to include some "entanglement" and carry-over elements. Like, 1 + 1 = 10 is also TRUE OR TRUE = FALSE-TRUE.. .

Remember, it's not "1 + 1 = 10", it's actually "01 + 01 = 10". The extra characters is what "carry-over" implies, not entanglement.

It's 100% a fact that the most elementary computer is using OR gates and inverters as its foundation. The carry-bit is a load of OR gates and inverters carefully assembled to create a more powerful mutually exclusive "OR" in order to implement the carry-bit phenomenon.

100% not true. In the abstract world of logic and math, the NOR operation is just an inverted OR operation. But physical logic gates are made from transistors, and a NOR gate is not an inverted OR gate. So, even if you build a computer purely out of NOR gates, you're not using OR gates to make the NOR gates.

On top of that, actual computers are built with NAND gates, not NOR gates. Due to the transistors used in each type of gate, NAND gates have several manufacturing advantages over NOR gates (most significantly, surface area).

In an ALU, the carry-bit is an AND gate. The actual sum is performed by XOR. This isn't a theoretical idea; I designed and built ALUs as part of a computer architecture class. You really should let go of this idea that OR is somehow primal. I love OR, it's a great operation (my favorite answer to "Beer or wine?" is "yes"). But it doesn't hold any fundamental truth, and you can't use OR in place of "+".

"IF RED, THEN STOP" is not an elementary proposition. It's "IF IT IS TRUE THAT IT IS RED, THEN STOP".

Huh? "IF A THEN B" is most certainly an elementary proposition. The truth value of the proposition depends on the truth values of A and B, being false only when A is false and B is true. This is precisely why we use it in programming conditional statements: STOP should only be true when RED is true.

Red is NOT the truth state itself — it is componental to it. RED is an axiom that can be mapped to either FALSE or TRUE.

What?! RED is not an axiom, it is a symbol representing a logical state that can be either TRUE or FALSE. Same with a bit! In fact, in a programming language we would likely declare RED as a boolean variable (whose value is stored in one bit).

 

Remember, it's not "1 + 1 = 10", it's actually "01 + 01 = 10". The extra characters is what "carry-over" implies, not entanglement.

Consider this tabula rasa for a moment. The base concept we're dealing with here is "TRUE + TRUE = FALSE."

It implies, "If I have a voltage OR I have another voltage" I have NO VOLTAGE. That makes NO sense, and is patently conceptually insane. So that is NOT true in observational reality. What's true in reality is, "I have a voltage, OR I have another voltage which would ordinarily equal 'having a voltage,' but because I cannot augment the definition of voltage to contain "more" voltage for truth-state purposes (as in the case of infinity not getting "more" of itself and changing the fact that it is infinity), I must start a new computation sequence in order to represent the full string of logic states to make up the sequential continuum of this n-bit string. Therefore, it is "FALSE" that I have "MORE VOLTAGE here," but TRUE that we are spawning a new column to do more computing." If this isn't true, there is NO legal right to make "ANY SENSE" out concatenating 0's and 1's to create new value. They are tied together, emulsified by this principle.

We are in the business here of rolling new architecture to describe the VERY unintuitive elements of reality like entanglement and nonlocation. We are trying to get at relationships in nature that involve untapped definitions and overlaps. So I would say "be open to seeing this in a very new light where the moon can disappear just by looking at it." lol

100% not true. In the abstract world of logic and math, the NOR operation is just an inverted OR operation. But physical logic gates are made from transistors, and a NOR gate is not an inverted OR gate. So, even if you build a computer purely out of NOR gates, you're not using OR gates to make the NOR gates.

And W to the T to the F, and boy does this ever prove my point: this makes zero sense that the "abstract world of logic" is not reflecting the reality of the ontology and hardware — or you couldn't make BOOLEAN-based circuits!!

Ontologically and logically, there are two separate functions being married here in a NOR gate.

In the case of a NOR gate, the transistor setup is identical to an OR as its foundational structure, except that the output is connected to the collector of both transistors and the emitter of each transistor is connected to ground. If either one of the transistors is on, current from the Vcc will be short-circuited to ground, bypassing the output. As a result, the output will be HIGH only when both inputs are LOW. If either input is HIGH or both inputs are HIGH, the output will be LOW. Therefore, in hardware, and ontologically, the NOR is a modulation of the OR fundamental functionality by subsequent modulation (inversion) of its output. QED.

In an ALU, the carry-bit is an AND gate. The actual sum is performed by XOR.

Both of which are foundationally and conceptually comprised of OR gates or NOR (OR gate with modulated output) gates as shown.

On top of that, actual computers are built with NAND gates, not NOR gates. Due to the transistors used in each type of gate, NAND gates have several manufacturing advantages over NOR gates (most significantly, surface area).

But that's irrelevant to the ontology, because modern sophisticated implementations are abstractions and shortcuts that are not where the simple truth building blocks are found. I'm talking about THE most base of computational hardware, 1940 style, which is where the ontology is found that is implementing the boolean reality.

In an ALU, the carry-bit is an AND gate. The actual sum is performed by XOR. This isn't a theoretical idea; I designed and built ALUs as part of a computer architecture class. You really should let go of this idea that OR is somehow primal. I love OR, it's a great operation (my favorite answer to "Beer or wine?" is "yes"). But it doesn't hold any fundamental truth, and you can't use OR in place of "+".

I'm not letting go of it one second. It is the foundational axiom upon which every logic operation is built, and I just showed that earlier. NAND and NOR is built on OR or inverting its output.

Also, when we use OR in most language use — like the beer or wine — what we are REALLY using is XOR. People should say, "Beer xor wine?" And XOR, as shown, is mutually exclusive, modulated OR.

Huh? "IF A THEN B" is most certainly an elementary proposition. The truth value of the proposition depends on the truth values of A and B, being false only when A is false and B is true. This is precisely why we use it in programming conditional statements: STOP should only be true when RED is true.

Again, you're not seeing at the zoomed-in ontological level! "IF A THEN B" to a MACHINE is equivalent to:

"IF 10101010 = TRUE THEN 110101001," which is either a new stored state or the prompting of a new set of instructions.

You are a brain according to you. You don't know what A and B are beyond the bits. This keeps proving my point. You only know if things are on and off and are routing voltages based on switches and inverters. Symbols are abstractions that DO NOT EXIST in the brain that is a bit processor per your QED!

There is ZERO alpha component to the ALPHANUMERIC phrase in a computer. It is ALL NUMERIC, ALL bits. You keep showing partiality to clumps of bits and calling them "symbols" and "axioms" and "concepts" No. can. do.

What?! RED is not an axiom, it is a symbol representing a logical state that can be either TRUE or FALSE. Same with a bit! In fact, in a programming language we would likely declare RED as a boolean variable (whose value is stored in one bit).

There's your magic wand again. Lol.

Your desire to make "symbols" and axioms out of bits is the equivalent of 400 bits of Mario's cartoon head spawning a pixelated "thought bubble" that "refers" to 210 bits of his arm as separate concepts. At no time is there any emulsifying agent to bits that you are referencing either IN the head, IN the arm, or ANY connection to them.

This is literally the impasse here.

Axioms and symbols are NOT bits in the same way INFINITY is NOT a number, NOR is it a bit. This is the divide I'm showing in that graphic. I don't care how many bits you have, at no time does a computer "know" any one bit or "group" of bits as representing anything, anywhere at anytime! Why are you drawing "conceptual distinctions between:

100101010101011000111010101010

and

111001010011010100110001010100

????

Top is RED, bottom is JOE BIDEN. You don't know what either are, and you claim you can bracket them and "conceptualize them" because one group happens to be stored on an network drive, and the other is stored on a flash drive, but you Harry Potter them together in this discourse by saying "CONCEPT" and "AXIOM"!!

<insert 9000 exclamation points here in 400 fonts>