This kind of reasoning might make you feel emotionally uncertain, as it shakes up your assumptions of how the world or the mind works. It can me feel uncertain too (not sure why really, I feel maybe I am a bit wary of uphending other’s people thinking without being careful enough). This however is a rationality site, so I note this and do not budge to emotionality and would recommend addressing this in some compassionate way. Things like computer logic are largely independent of our emotions (largely in the sense if we program emotionally the program might not work, haha).
It might be like an earthquake. Thing is, clinging to certain views based on emotional reasons is not only not rational, clinging in general is a cause for dissatisfaction (like the Buddha called it, Dukkha).
The truth is, the world will shake us up. If not in a gentle way by reasoning or unconventional humans, then in more violent ways, by sickness and death.
But anyway here the less emotional part:
>Tarski only aplies to the whole concept of truth. For “things humans can prove” you can use enumeration + validy check.
I am not talking about things humans can prove computationally. That is the whole point, that humans are beyond computability. And yes you might say I talk about the whole truth, in so far as that is a meaningful concept, I am not talking about a certain set of true statements, like 1=1, 2=2, etc...
However human reasoning transcends the human brain, maybe that is the stuck thing that keeps you going back to this kind of logic.
Human reasoning is on your screen right here, it is not just in your brain. These are not just symbols. It is actually written by a human and is expression of human and transcendental reasoning, and it is linguistic reasoning. So the human reasoning is not just in the brain, it is literally on your screen. That cannot be comprehended in conventionalist terms or step-wise terms, but it evident as it is right here.
>I don’t think humans actually use continuum much when thinking: appearence of continuous space between words is just a failure of introspection, not a concequence of use of continuum—actual elements of human cognition are descrete. And real computers also exist in space—that’s one more reason to consider them.
Huh, it is here: ___________________________________________________________ that is a line continuum in thinking.
That is spacious continuum surrounded by linguistic reasoning: [ ].
I am not talking about “elements of human cognition”.
That is independent of what you think, as it can be perceived. You can perceive independent of verbal or image-based or conceptual thinking. Even if you perception is not comprehensible to you (which it is not really; even just what is related to it in terms of brain function is far too complex).
I am talking about the continuum of human cognition, which is beyond your personal mind; ie it expressed through my brain to get to your screen, but it is reasoning that is input to both your and my brain (as photons going from the screen to your retina and into your brain): ___________________________ __
See the small step at the end? That is “one element” of human cognition, a step within the continuum that is not really discrete in a conrete way: >>>[ ]<<<<<
If you want to be more concrete, you could take this ⚫ as a discrete element of human cognition. You are right these are discrete. But they are not in your brain but on your screen, or in the matrix of general geometry; like the geometry of the letters surrounding the box.
Can space be used? How? It is space. Space is not a “thing” to be utilized. That is not what space is. At best it is whitespace to be u t i l i z e d. But as you see that is just more space, it is not really a thing per se.
And this is not about introspection, it is about extraspection, as the words are on your screen, not inside your brain or just your individual mind. Extraspection is not “failure of introspection” it is literally what allows for the perception of the external world.
>No? “A more generalized notion” means all real computers are like your abstract computers and that is false.
Well, I can grant you that. A more abstractly generalized notion. It seems it is not definable in more of a broad generalized way, as I do not know how to “generalize” a literal real computer. It is there, not something I can generalize like a concept.
We do utilize a more abstract generalized notion to make sense of the programming and logic of computers though. It is more general in so far as it is the set of ALL computations² (computers just run a finite amount of computation based on the physical limits), and can run indefinitely (a computer stops running after its lifetime has finished). So that seems a meaningful notion in which it is more broad and general but I grant you it cannot quite be applied to a literal physical computer.
Those abstract computations transcend computers, as they can also manifest in the human brain, and they also transcend the human brain, as they can manifest in a computer, in someone else’s brain, etc...
²within a certain framework like a Turing machine, or a programming language, etc
Maybe—I can see how emotions may prevent human from accepting that humans are not special.
I am not talking about things humans can prove computationally.
Everything that humans can prove, can be proven by that computable algorithm. Including things you call “uncomputational”. If your point is just that humans are real so they can affect space and abstract computers are abstract, then real computers also can affect space, and perceive space better than humans. Is there part of this you disagree or it’s just that you think “people don’t talk about real-world effects of computers” is important?
I do not know how to “generalize” a literal real computer.
If you need to generalize it to make your point you can imagine your computer but with infinite memory and arbitrary fast execution speed. It can do literally everything a human can.
>If your point is just that humans are real so they can affect space and abstract computers are abstract, then real computers also can affect space
How can you affect space? Space is absolutely inert physically. There is no way to affect it.
I think you meant space as in w h i t e s p a c e. But that is basically only more light on your screen, not darkness, as real space is.
>Everything that humans can prove, can be proven by that computable algorithm.
How to have an algorithm prove that 1=1?
How do you know it is true, unless you define it that way first?
So it seems a computer cannot prove that, unless you define it true first.
That however can be proven, as you can define validation to not be able to able to be validated by computer.
As if you feed it the information 1=1 it could be programmed to output “false”, so if the definition of validation is absolute validation with no possibility of a false output, it is clearly wrong, as you can program a computer to falsely claim 1=1 is false.
However I doubt you would do that as you can see the uncomputable consistency and absolute 100% chance truth of 1=1.
This means the whole spectrum of completely false to completely true is available to a computable validation mechanism. A true proof is only true and can only be true as otherwise it would be not a proof, in so far as bivalent logic applies at all (which I will admit it does not always apply).
If you can validate it in a wrong way (meaning a false validation, or deducing the correct conclusion from a false premise, so that you can correctly conclude something that is wrong but correct), that is not really proving.
If you arbitrarily decide or guess whether the proof is accurate or not, it is not a proof.
This statement cannot be computationally verified: This statement cannot be proven.
Ever heard of Gödel?😅
The statement is true, but not provable. As nothing can be proven if you do not have a definition of what is true first. As we can see the Gödel sentence to be true, that entails that we can see true what is not provable, and hence not computationally verifiable too.
So we can realize truth beyond computational verification.
As if you feed it the information 1=1 it could be programmed to output “false”, so if the definition of validation is absolute validation with no possibility of a false output, it is clearly wrong, as you can program a computer to falsely claim 1=1 is false.
By that definition of validation humans never proved anything, because they sometimes say that 1=1 is false.
As we can see the Gödel sentence to be true, that entails that we can see true what is not provable, and hence not computationally verifiable too.
Gödel sentence for some formal system can’t be proven in that system, but it can be proven in more powerful system. Humans that see the sentence to be true are just (reasoning in a way equivalent to) using a more powerful formal system. And everything in that system is computably verifiable.
>Maybe—I can see how emotions may prevent human from accepting that humans are not special.
Fully agree here. I definitely have this issue as well!
Like we want to imagine we are so special in our power and intelligence that we can emulate them at what they are good at. We really cannot. Computers are already unfathomably more intelligent in the domain of precise calculation of crystallized information which they operate in. We also imagine we can program computers do anything we want.
Which again, computers will often do what their internal logic causes them to do, not what we program them to do, and they will always be like that, as that is how a computer operates.
So there is no hope to ever get to that level. I kind of want to speed up my computational speed sometimes, but I have trouble even getting the accuracy right, like calculating 3-digit number effortlessly. For a computer that is just a silly joke in terms of difficulty of calculation.
>If you need to generalize it to make your point you can imagine your computer but with infinite memory and arbitrary fast execution speed. It can do literally everything a human can.
Huh? I don’t think it could walk, as it does not have legs. I am not being silly here, I think you mean in terms of some abstract computational capability, but that is not what you said.
Again in a physical sense it is also not true. A computer is made of silicon so it cannot send information between neurons.
So I am not even sure in which sense it could be true. I think you mean in terms of precise calculations of crystallized information. I guess then you have very good point, as I already talked about above.
But then, the computer cannot do this: 💻💡
As THIS💡 is the light produced by the screen you are seeing when reading this, not a computation. It is not produced by the computer either, but by the screen the computer is connected to.
I feel an issue here is emotion:
This kind of reasoning might make you feel emotionally uncertain, as it shakes up your assumptions of how the world or the mind works. It can me feel uncertain too (not sure why really, I feel maybe I am a bit wary of uphending other’s people thinking without being careful enough). This however is a rationality site, so I note this and do not budge to emotionality and would recommend addressing this in some compassionate way. Things like computer logic are largely independent of our emotions (largely in the sense if we program emotionally the program might not work, haha).
It might be like an earthquake. Thing is, clinging to certain views based on emotional reasons is not only not rational, clinging in general is a cause for dissatisfaction (like the Buddha called it, Dukkha).
The truth is, the world will shake us up. If not in a gentle way by reasoning or unconventional humans, then in more violent ways, by sickness and death.
But anyway here the less emotional part:
>Tarski only aplies to the whole concept of truth. For “things humans can prove” you can use enumeration + validy check.
I am not talking about things humans can prove computationally. That is the whole point, that humans are beyond computability. And yes you might say I talk about the whole truth, in so far as that is a meaningful concept, I am not talking about a certain set of true statements, like 1=1, 2=2, etc...
However human reasoning transcends the human brain, maybe that is the stuck thing that keeps you going back to this kind of logic.
Human reasoning is on your screen right here, it is not just in your brain. These are not just symbols. It is actually written by a human and is expression of human and transcendental reasoning, and it is linguistic reasoning. So the human reasoning is not just in the brain, it is literally on your screen. That cannot be comprehended in conventionalist terms or step-wise terms, but it evident as it is right here.
>I don’t think humans actually use continuum much when thinking: appearence of continuous space between words is just a failure of introspection, not a concequence of use of continuum—actual elements of human cognition are descrete. And real computers also exist in space—that’s one more reason to consider them.
Huh, it is here: ___________________________________________________________ that is a line continuum in thinking.
That is spacious continuum surrounded by linguistic reasoning: [ ].
I am not talking about “elements of human cognition”.
That is independent of what you think, as it can be perceived. You can perceive independent of verbal or image-based or conceptual thinking. Even if you perception is not comprehensible to you (which it is not really; even just what is related to it in terms of brain function is far too complex).
I am talking about the continuum of human cognition, which is beyond your personal mind; ie it expressed through my brain to get to your screen, but it is reasoning that is input to both your and my brain (as photons going from the screen to your retina and into your brain): ___________________________ __
See the small step at the end? That is “one element” of human cognition, a step within the continuum that is not really discrete in a conrete way: >>>[ ]<<<<<
If you want to be more concrete, you could take this ⚫ as a discrete element of human cognition. You are right these are discrete. But they are not in your brain but on your screen, or in the matrix of general geometry; like the geometry of the letters surrounding the box.
Can space be used? How? It is space. Space is not a “thing” to be utilized. That is not what space is. At best it is whitespace to be u t i l i z e d. But as you see that is just more space, it is not really a thing per se.
And this is not about introspection, it is about extraspection, as the words are on your screen, not inside your brain or just your individual mind. Extraspection is not “failure of introspection” it is literally what allows for the perception of the external world.
>No? “A more generalized notion” means all real computers are like your abstract computers and that is false.
Well, I can grant you that. A more abstractly generalized notion. It seems it is not definable in more of a broad generalized way, as I do not know how to “generalize” a literal real computer. It is there, not something I can generalize like a concept.
We do utilize a more abstract generalized notion to make sense of the programming and logic of computers though. It is more general in so far as it is the set of ALL computations² (computers just run a finite amount of computation based on the physical limits), and can run indefinitely (a computer stops running after its lifetime has finished). So that seems a meaningful notion in which it is more broad and general but I grant you it cannot quite be applied to a literal physical computer.
Those abstract computations transcend computers, as they can also manifest in the human brain, and they also transcend the human brain, as they can manifest in a computer, in someone else’s brain, etc...
²within a certain framework like a Turing machine, or a programming language, etc
Maybe—I can see how emotions may prevent human from accepting that humans are not special.
Everything that humans can prove, can be proven by that computable algorithm. Including things you call “uncomputational”. If your point is just that humans are real so they can affect space and abstract computers are abstract, then real computers also can affect space, and perceive space better than humans. Is there part of this you disagree or it’s just that you think “people don’t talk about real-world effects of computers” is important?
If you need to generalize it to make your point you can imagine your computer but with infinite memory and arbitrary fast execution speed. It can do literally everything a human can.
>If your point is just that humans are real so they can affect space and abstract computers are abstract, then real computers also can affect space
How can you affect space? Space is absolutely inert physically. There is no way to affect it.
I think you meant space as in w h i t e s p a c e. But that is basically only more light on your screen, not darkness, as real space is.
>Everything that humans can prove, can be proven by that computable algorithm.
How to have an algorithm prove that 1=1?
How do you know it is true, unless you define it that way first?
So it seems a computer cannot prove that, unless you define it true first.
That however can be proven, as you can define validation to not be able to able to be validated by computer.
As if you feed it the information 1=1 it could be programmed to output “false”, so if the definition of validation is absolute validation with no possibility of a false output, it is clearly wrong, as you can program a computer to falsely claim 1=1 is false.
However I doubt you would do that as you can see the uncomputable consistency and absolute 100% chance truth of 1=1.
This means the whole spectrum of completely false to completely true is available to a computable validation mechanism. A true proof is only true and can only be true as otherwise it would be not a proof, in so far as bivalent logic applies at all (which I will admit it does not always apply).
If you can validate it in a wrong way (meaning a false validation, or deducing the correct conclusion from a false premise, so that you can correctly conclude something that is wrong but correct), that is not really proving.
If you arbitrarily decide or guess whether the proof is accurate or not, it is not a proof.
This statement cannot be computationally verified: This statement cannot be proven.
Ever heard of Gödel?😅
The statement is true, but not provable. As nothing can be proven if you do not have a definition of what is true first. As we can see the Gödel sentence to be true, that entails that we can see true what is not provable, and hence not computationally verifiable too.
So we can realize truth beyond computational verification.
By that definition of validation humans never proved anything, because they sometimes say that 1=1 is false.
Gödel sentence for some formal system can’t be proven in that system, but it can be proven in more powerful system. Humans that see the sentence to be true are just (reasoning in a way equivalent to) using a more powerful formal system. And everything in that system is computably verifiable.
>Maybe—I can see how emotions may prevent human from accepting that humans are not special.
Fully agree here. I definitely have this issue as well!
Like we want to imagine we are so special in our power and intelligence that we can emulate them at what they are good at. We really cannot. Computers are already unfathomably more intelligent in the domain of precise calculation of crystallized information which they operate in. We also imagine we can program computers do anything we want.
Which again, computers will often do what their internal logic causes them to do, not what we program them to do, and they will always be like that, as that is how a computer operates.
So there is no hope to ever get to that level. I kind of want to speed up my computational speed sometimes, but I have trouble even getting the accuracy right, like calculating 3-digit number effortlessly. For a computer that is just a silly joke in terms of difficulty of calculation.
>If you need to generalize it to make your point you can imagine your computer but with infinite memory and arbitrary fast execution speed. It can do literally everything a human can.
Huh? I don’t think it could walk, as it does not have legs. I am not being silly here, I think you mean in terms of some abstract computational capability, but that is not what you said.
Again in a physical sense it is also not true. A computer is made of silicon so it cannot send information between neurons.
So I am not even sure in which sense it could be true. I think you mean in terms of precise calculations of crystallized information. I guess then you have very good point, as I already talked about above.
But then, the computer cannot do this: 💻💡
As THIS💡 is the light produced by the screen you are seeing when reading this, not a computation. It is not produced by the computer either, but by the screen the computer is connected to.
I assumed it can make legs and neurons instantly using photons radiating from its chip.