Benjamin J

Karma: −33

Benjamin J 28 Jul 2022 21:07 UTC
1 point
0
in reply to: Anon User’s comment on: Choose one natural number
I can also change my definitions by the way. So I can define X = 3. I could literally edit the post above, although for the sake of consistency, I would not want to do that. But I define X = 3 now as far as this conversation is concerned, as I could have edited the post above.
If I did that, your “computation” of X := 1 would just be wrong, as X would be defined to be 3. That would be a contradiction as 1 is not equal to 3.😅
So that would show that you cannot compute X, as X has a value of 3. If it has a constant value, you cannot assign it another value, as that leads to a logical contradiction. I hard coded X=3 into the definition, so to speak, and I could do that in the post above, as it is not based on temporal logic but definitional logic. And of course that can be changed in time while still maintaining the order that the post above is the post, and your comment a comment.
It would then make more sense to go the route above to say I use variable [0] and define that. That would also be possible and valid, but it poses the same question, as we merely changed the variable. It does not really matter if you call it [0] or X, except for the purposes of definition.
I am not claiming everything can be defined, not even close to it. In fact math itself can prove there are undefinable real numbers, for example. So a lot of things are undefined. That is just life. Like uncomputational variables, which I use many in my brain, like [omega] which I can uncomputationally define to be anything I want. I could even define it to be an emoji🥨.
But then we are going beyond computation and definition into the realm of images and perception. Interesting.

Benjamin J 28 Jul 2022 20:47 UTC
1 point
0
in reply to: Anon User’s comment on: Choose one natural number
OK, but the variable name and mapping something to something is not the point here, as that is not a choice of a natural number.
It assumes that you can even computationally determine that there is ANY possible choice of concrete natural number for X.
That is not true. It is logically true that it could be there is not a possible choice of X, and you can choose for example to say it is equal to any of the variables A,B,C,D,AA,AB,AC,AAAAB,ABBBAABA,… or any other number of variables. It could also be meta variables, like meta variable [A] that can be assigned a variable for example AAAAB, or AAAAB. If I assign it the variable AA, [A]=AA, I now know I am talking about AA, which is a natural number of the set of natural numbers.
That did not get me close to actually choosing a natural number and defining X to be that natural number. Physically we could just be creating more variables, without actually defining X to be anything. That is logically perfectly valid, but does not really address the question posed in any way.
There is no computational choice of X, so what you are saying here is a variable. The question is what the variable 1 you are talking about here is. It could mean the pixels on the screen (the symbol 1 as it appears on my or your screen), it could in principle mean a variable symbolized by 1 that can take the value of a natural number.
It could also mean the natural number one, but based on what you said, that would just be my interpretation.
Based on what you said, it is not clear what definition you operate based on.
I am not talking about interpretations here. Well I am, evidently, but here we leave bivalent logic for sure.
There are always many many interpretations for anything. That is another rabbit hole to go down to. Very interesting for sure, but it doesn’t get us any closer to the semantic and epistemological question the post poses. Which is, what is X?
I can just define it to be a natural number 1, but that is not a computation, but a definition, as I define it as such.

Benjamin J 28 Jul 2022 20:24 UTC
1 point
0
in reply to: Anon User’s comment on: Choose one natural number
Yes, that is what the link in my post refers to.
However formalism is syntactic, I am talking about semantics here.
You can construct a formal language that way, but you can also not construct it that way.
In terms of bivalent logic, you can make a choice between constructive and non-constructive.
Because you can make the choice for non-constructive math, what I say is still true, as humans can do non-constructive math, as I just displayed to you. The truth of what I say is not dependent on whether someone else uses symbols like I do. It is related to the reality that we can and do reason in non-constructive ways. That is not a choice, so in that semantic sense non-constructive math is not a choice, as others will do it whether you like or not, and you can do it, whether you like or not.
It is true in constructive math you can construct everything. You can construct 1=2 if you define the symbol 2 to mean the natural number S(0). You can do that without a problem, formally speaking. So in terms of symbols, everything can mean everything just purely syntactically speaking.
I can define each finite set of symbols to mean any other finite set of symbols, purely from the rules of syntax.
Indeed you can literally do that, so all symbols mean the same per definition. I guess a computer does that in certain sense when it reads comments as that is just data that is not computed further (usually), meaning all symbols mean ( ).
Semantically what I say is still true. Of course syntactically you can define the set of symbols I said to mean Habeck would be the best Kanzler ever.
And maybe that would also be a good statement semantically speaking, but that is not what the post is about.

Benjamin J 28 Jul 2022 19:50 UTC
1 point
0
in reply to: GuySrinivasan’s comment on: Choose one natural number
No, I do not think it is wrong.
It says it enables to associate a program with each proof in Zermelo-Fraenkel set theory. You can also, in principle associate a program to each value of the busy beaver function, or even uncountably many of them (for example for each value of the BB function a complex-valued function that based of the square of the value of the BB function as a constant in each of the complex-valued functions of each value). Even though you cannot compute the values of the busy beaver function.
That means you can associate programs to uncomputable functions, like the function of definition.
I can also associate a program to X = ?; for example rand(60). That however assumes that the natural number in question is a constant, which as I said above does not logically follow from the instruction of choosing one natural number. You can logically instruct something, and do something different. That is not a contradiction in terms of logic.
But as I said above that program would not compute X, it would merely be associated to X, which is a different notion. For example I can associate the BB function to X, but that does not make X computable, and indeed the opposite follows, as X could have the values of the BB function, which is proven to not be computable. So X could be not computable, and as it could be not computable, it is uncomputable in this context, as the question is if you can compute X without first defining it, which you cannot. Once you defined X=3, you can of course program a computer to deduce X=3, but that happens after the definition, and is not the definition of X in this context (which was asked to be done by a person) but a computational replication of an earlier definition, which is still a definition but not a choice, or even the acknowledgement that there is a choice between choice and no choice (meaning just saying X=Y which is a bit of a non-choice in this context but still valid).
You can find programs for axioms, like if have the axiom S(0)=1 I can find a program that display s(0)=1 on my screen. That is just not a definition, it is a replication or association. I can even find a program that displays 0=1 and is correct about that if I define 0 to mean the natural number 0 the symbol 1 to mean the natural number 0. All of these things are possible and valid, although a bit wild syntactically.

Benjamin J 28 Jul 2022 19:24 UTC
1 point
0
in reply to: Dagon’s comment on: Choose one natural number
>But I think there’s a reference problem when you say humans can do “it”. Humans can’t actually solve any of these problems
You got me here. Problem can be a “trick” term in this regard, as this is a very simple definition. I am just calling it problem to lure people into a computational logic to see for themselves that it makes no sense and is not how they address the question or instruction.🙂
In fact definition is also not necessarily the right term.
Internally I did uncomputationally deduce that X=1, because it is the first natural number and X can be 1, and hence X is 1 in this particular context of me actually writing this text. Of course one could deduce something else, but it is what I deduced.
Only afterwards did I define X=1, as I recognized in principle I could have deduced something else if my natural numbers were sorted differently, but I deduced based on logical order not geometric order.
>I don’t know how much exploration have been done about whether definitions are computable, and whether a theoretical Turing machine can define problems that it can’t solve.
They are not always (in bivalent logic), as that is contradictory (for example I can self-referentially state: “This definition is not computable and X=1”, which is a valid definition, and true by definition, as you can define something to not be computable, even though it is already not computable as a definition is not a computation (for example I could define that the busy beaver function is “really really really not computable”, even though it is already proven it is not computable).
You can define the busy beaver function, but you cannot compute it. The abstract set of Turing machines and their computations define the busy beaver function, but it cannot be computed by a Turing machine. That was proven by contradiction, as you can verify on the internet.
I guess in polyvalent logic you can through all terms together as you have infinite options what the terms can mean. Also a bit of a pitfall, as I think in general polyvalent logic might be be more valid, as it applies in more situations, but in mathematical reasoning bivalent logic is used for good reasons (like if 0s might or might not be 1 your numbers system becomes pretty complex pretty quickly).
>I also object to the sloppy title—“choose one” has a pretty open meaning, and “one” is an absolutely valid choice. It was performed by my brain (or by the section of the universe that computes my thinking, if you prefer), so it was done computationally
Choose one has a well defined meaning. You take one number of the set of all natural numbers, and put it on the right side of the equation. It is open, as the set of natural numbers is infinite.
That is inherent to the process, not sloppy in any way. I would say it is a bit sloppy to suggest otherwise but whatever, I think my term “problem” was also sloppy, so maybe let’s say instruction😉.
You said “one” is an absolutely valid choice, I unfortunately have to say it is literally not a valid choice as it a string not a natural number. It seems you just converted what I said into a string and outputted it back to me. That is a valid computation, it is however not a valid definition for X.
It seems just internally restated your assumption that your brain performs definitions computationally. The question is if that is true?
I would say per definition it is not true as definition and computation have a different semantic meaning, and are also different terms syntactically as definition!=computation. It might be point out the obvious, but although it is obvious we are not always conscious of it. We are not always conscious of any definitions which is maybe because definitions are not that important. Even just in math there is undefinability like the undefinable real numbers which make up almost all of the real numbers. Let alone outside of math.
Of course syntactically you can mix up definition and computation somewhat arbitrarily as you can define “definition”=”computation”=”undefined”=”ojfg99″=”krümpeldefinatorisator”=”????!??!”. That is just a matter of syntax then, and that gets absurdly complex if you produce many complex definitions which might be different than earlier definitions. Hence maybe sometimes the long time it can take to wash all of that away to start with clearer definitions.
Unquestionably if you are not an absolute lover of math it might be a bit boring to talk about definitions, and I am only partially fond of math as bivalent logic and well-defined numbers are only of so much interest to me. That is emojis for the people that want hearts on the other hand: 💚💛🧡❤💜🖤🤎 Also computer are cool haha.🖱👾💻

Benjamin J 28 Jul 2022 18:27 UTC
−9 points
0
in reply to: gwern’s comment on: Choose one natural number
Have you heard of ad hominem? If that is what is called rationality and upvoted on this platform, than there is truly no hope for fruitful conversation on it. Unfortunately this attitude if you continue to uphold is certain to lead to a lot of problems and dissatisfaction for you and others.
What do you think it does to schizo that is not like me and might be genuinely schizophrenic (I did say that I am but technically I got another diagnosis which I think was more accurate) and psychotic and gets verbally attacked with an ad hominem like this? They might start to lash out at others or harm themselves.
Well done, pat yourself on the back.
>distinctive wordsalad
This is about mathematical proof and mathematical definition.
What you are saying is toxic word salad. It is irrational words, which are also literally toxic if engaged in, which I do not, as I keep my distance from such insults.
1=1 is proven to be true.
1=8 is not true, be definition.
That is not word salad, you are being an extremely impolite and contra-rational (as ad-hominem is one of the most irrational fallacies one could think of) and contra-humanistic by creating an ad hominem of a severe diagnosed condition of all things.
I rarely say this, but you and everyone that upvoted this comment should rethink what they are doing, and frankly it would make sense to be ashamed of what you just said.
Feel free to delete your comment if you think it was not appropriate.

Benjamin J 28 Jul 2022 13:32 UTC
1 point
0
in reply to: Signer’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
>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.

Benjamin J 28 Jul 2022 13:18 UTC
1 point
0
in reply to: Signer’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
>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.

Benjamin J 28 Jul 2022 13:02 UTC
1 point
0
in reply to: gjm’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
>This is just flatly false. Of course blindly executing the code is one thing a literal computer can do when faced with it, but there are others
I am talking about a programmable computer. And I said the program is meant to be executed. It does NOT lead to an endless loop, as it can be halted or left or transcended uncomputationally. That is the whole point of the argument. The brand new internal computer system you use to execute it can be halted uncomputationally.
That is really an important information, otherwise this is rather confusing right there, it might get someone rather confused if you miss that crucial point.
If you ignore the instruction that the program is to be executed the demonstration does not work, and the whole reasoning around it does not work either, as it is in the context of that instruction.
>The OP promised, in so many words, “a clearly structured argument”, but it does not contain a clearly structured argument.
This is unfortunately 100% true. The commentary I hope is somewhat clearly structured (hence bolding etc), but the post itself is not an argument. It is meant as a demonstration.
Meaning it is meant to demonstrate something that is already the case. It is meant to be valid and true, not to be “convincing”. There is not need to convince anyone of this, and attempting to do so will just lead to tie my head up in knots and possibly others too😅.
I edited my post appropriately, my bad. Thank a lot for pointing it out!
Again just for clarity you can execute and halt the following loop by reading it:
START: START COMMENT This kind of loop cannot be left computationally-deterministically but it can be left or halted deterministically-uncomputably or chaotically-randomly². END COMMENT GOTO START
Maybe that is a much better demonstration? As it leaves the whole meta and trans-computational stuff aside.
²which is not computationally either (not talking about classical chaos or pseudo-randomness here, as that can be computed in principle—although not in practice, but uncomputational chaos, whether deterministic or stochstically-deterministically, meaning with a quantifiable probability or in an i n d e t e r m i n s t i c way that is not stochastically quantifiable)
I think the difference between computational loop and uncomputational loop can be explained by a computational loop being at the very least a loop between two states. An uncomputational loop is just a loop going around and back to a single state.
As for a program you need at least two states (For example S start and E end).
The mere state “loop” is not a program, it is just a loop. O
♾
An instruction can be open ended: S start. That is not a computer program. It cannot be computed, as it is open-ended. You cannot tell a computer just start, and do nothing else. That is just a start of some kind, not a computer program, haha. Maybe in this case the start into a new future of clear reasoning about uncomputability, who knows?
It seems to me in many ways illustrations would be more useful for this than words. As in a certain way, it seems the structure becomes more clear by way of illustration than verbal elucidation. So again, also thanks for giving me some reason that maybe the structure can be made clearer!
I feel I am a bit too serious about this. I used to think computers will solve a lot of my problems too and even perhaps digitally revive me after I am dead😅. They do solve MANY problems, but not as many as I thought.
I think this past belief still haunts me a bit, so that I take this whole thing more heavily than it needs to be. Computers work great. My brain works, at least somewhat okayishly, enough to write this to you. Heavy is heavy illness or heavy conflict. Not really this kind of question or conversation🙏.
I believe that insight will at some point gain more popularity in AI culture, as it just becomes clear that computers do not fulfill all of our expectations, and that there are some false assumptions about what the brain and the mind are going around (Penrose addresses those things quite well lately, as he now tends to leave aside the OR stuff more that seems a bit questionable).

Benjamin J 28 Jul 2022 11:56 UTC
−4 points
−5
in reply to: gjm’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
>This is just flatly false. Of course blindly executing the code is one thing a literal computer can do when faced with it, but there are others, such as translating it into directly-machine-executable instructions, or checking it for certain classes of bugs, or counting the words in it, or executing it while watching for easily-spotted infinite loops.
I said the program is to be executed! If you say I choose to not execute it and choose to process it in other ways, then the argument doesn’t work.
But a computer cannot do that, it cannot decline being programmed, unless it is computer that has programming functionality disabled (which obviously is not the kind of computer I am talking about). A functioning computer simply executes a program if you give it and execute it.
That is why the reasoning is valid, I executed the program and validated it (obviously it is easy to validate, as it is just a simple START: GOTO START loop). Of course if you have a high level computer that just does not permit programming by an end user, the argument does not work, as the program is not being executed. But is simple to just access a new low level computer internally which can be easily programmed, which is what I did. Maybe that should be part of the instruction. Because it is true we have a lot of internal quasi-computations going on already. I say quasi, because I notice how tricky it can be to actually build a precisely functioning computer inside of your mind, a lot of our computations are very fuzzy and could be wrong potentially (I tried adding simple 3-digit numbers and it is surprisingly tricky).
The program is not merely be executed of course, as it not about blindly executing; as that would not be very fruitful, it is about mindfully doing so.
It is a simple GOTO loop. The comment is a comment is not part of the program!
You can also attempt to execute the comment as a START GOTO START loop (you can basically ignore the text apart from This loop cannot be left computationally; which is logically true, as the computation is just a START GOTO START loop which cannot be left computationally if executed correctly), but that leads to an inconsistency if the text in-between is processed. You can correctly spot the inconsistency and exit the loop and thus execute the instruction (which is not a program) correctly. A computer cannot, as that is not part of the program, but the commentary (obviously, as it says START comment, and this comment here is outside the program in the post, in the comment section, just to remind you). It is not part of the program described in the post and to be executed by reading.
Seems easy enough to understand. It seems you are doing meta-computation or unrelated computations, which as I said is not part of the program described which is crucial for the reasoning to make sense.
You cannot compile the comment correctly, as it is not a computational instruction. It is a comment, and such the only way for the compiler to treat it correctly is to discard it.
The point of my argument is to look at assumptions and see if they are true, not to assume some assumptions are true and inductively conclude from that they are true. It might be the assumptions we have are false.
If you want to execute the program correctly, first delete the comment, and then run the program.
Of course if you want to understand the program you can read the comment. That is what a comment is for, as you know but it seems I have to point out with all the complex commentary😉. But you cannot understand this program without running it, as it is a program that runs by reading it.
>The fact that human beings looking at the code don’t blindly execute it tells you nothing about whether human beings are computational.
That is true. It seems you tried to blindly execute the comment, but you cannot do that either, as it is not a program, but the comment to explain the program (which is a simple loop, but exists in a context; same way that a simple loop exists in a context in a larger program, or even a computer that is only running a simple loop exists in a larger context; if you can imagine a simple computer that does nothing but run a START GOTO START or however that is translated into machine code—I don’t really know those 01111011 numbers).
>The OP promised, in so many words, “a clearly structured argument”, but it does not contain a clearly structured argument.
If you ignore the main point which is that the program is a program to be executed and the comment is a comment, then it is not an argument but a jumble of words. But that is not what I said! The program can be executed and then elucidations makes sense.😃
However unfortunately I did make a bit of a blunder here, and it does make you 100% correct here. This is not an argument!
I corrected it by editing my post. My bad.
It is not meant to “convince” but to be true and valid. Being “convincing” is not good enough. So more like a proof, although as it is a program to be executed it is something different than an ordinary proof. I guess a demonstration that leads to a certain true conclusion in a deterministic way (as the loop is not an endless loop uncomputationally, the program can be executed and successfully halted uncomputationally!).
But you probably cannot correctly understand this program unless you loosen your 99.99999% assumption that a human brain works solely computationally, as it leads to a logical inconsistency which might leady you to slip up and read a comment as a program as you get into meta-computational loops in your own brain (which BTW a functional computer would never do unless it is massively malfunctioning, oopsie my internal computer malfunctions, as I make this mistake sometimes it seems😅🤨🙄😑).

Benjamin J 28 Jul 2022 6:31 UTC
1 point
0
in reply to: gjm’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
>You didn’t say to blindly execute it. But you did (unless I misunderstood, in which case please do correct me) repeatedly imply that being “computational” implies blindly executing it.
No, in fact I said you can execute it computationally and transcend it by understanding meta-computation (you can run a computation and still think of it as something you are not “in” or engaged in, but that implies you are beyond computations as you can transcend them) or how something can be computational in one dimension, and non-computational in another dimension (like the +1 computation of 1,2,3,4,5,6… being created into towers of the size of the busy beaver function), something I call computational-orthogonally-uncomputational.
I see the issue of thinking you “should” run the program, but that is more a psychological thing, I did not say that, and did not really mean that either, it would be better if you feel inspired by this text to re-evaluate your assumptions🙂.
If you are computational like a literal computer, it does imply blindly executing it. That what a computer would do, just execute the loop. Unless you assume computer spirit, which is a bit of a rabbit hole. Although to be fair I would not disregard it, it just does not affect much about how computers function, as they function as they are programmed if they work well. I would more likely to say sp1r1t as that sounds more like something a computer would say haha. Well actually in a way I am this computer (referencing your computer), as I am manifesting to you through this text on your screen so to speak 0101011111000 haha). But that only works as there is another human somewhere else that is sending this you via internet. I have no way to intelligently talk to you otherwise. Except maybe through spooky means like spooky errors, but again, a bit of a rabbit hole isn’t it.
In any case you literally are not solely computational already, let alone a literal computer (apart from when you assume that role by executing the instruction as if you were a computer). That is my whole point. You won’t execute it blindly because you are not a computer, let alone a simple one (although we do have computational functions which we can utilize).
At the very least, executing it will make you feel interested in the rest of the text or perhaps insecure or confused, which is the start of not being blind about it and reading the context or loosening your assumptions a little. You will probably not get into a trance of reading it for hours. Let alone until you cease functioning physically or are shut off like a good computer would.

Benjamin J 28 Jul 2022 5:46 UTC
1 point
0
in reply to: Signer’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
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

Benjamin J 27 Jul 2022 10:23 UTC
0 points
−1
in reply to: Signer’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
>You can check that every proof you enumerate consist of only valid steps. That check can be performed computationally. Every such proof would prove true statement.
It cannot. Truth cannot even always be defined, let alone computed (Tarski’s undefinability theorem). Of course you cannot compute something if it cannot even be defined; a computation needs defined states and defined outputs to be a computation as understood in computer science. That is a proven fact, it is not my opinion.
“Tarski’s theorem, on the other hand, is not directly about mathematics but about the inherent limitations of any formal language sufficiently expressive to be of real interest. Such languages are necessarily capable of enough self-reference for the diagonal lemma to apply to them. The broader philosophical import of Tarski’s theorem is more strikingly evident.
An interpreted language is strongly-semantically-self-representational exactly when the language contains predicates and function symbols defining all the semantic concepts specific to the language. Hence the required functions include the “semantic valuation function” mapping a formula A to its truth value ||A||, and the “semantic denotation function” mapping a term t to the object it denotes. Tarski’s theorem then generalizes as follows: No sufficiently powerful language is strongly-semantically-self-representational.”
>Reasoning about continuum can be done in discrete steps. Human reasoning doesn’t use continuum in any way fundamentally different from how neural networks use floats.
I am not talking about reasoning about continuum as a representation, in which regard you are correct I can refer to continuum or real numbers as a symbol and reason about that. But that is just not the kind of reasoning I am talking about. I can add two such functions correctly like sin(x)+sin(x)=2*sin(x).
It is not the kind of of reasoning I am talking about as I am reasoning about the continuum itself, not the representation you have of it (or the computer has of it), so I am talking about this: [ ], or maybe this ________.
Depending if you mean something more tangible, or more intangible, both which are valid, although the real numbers seem more like the latter, as they are one-dimensional.
Talking as it appears on your screen, not as my reasoning and text with whitespaces is represented in the computer which is another question.
You maybe have an interesting point here in that while we can reason about continuum, it is more striking we reason within continuum. As you see the space around the letters, you will notice it is continuous. There are no steps there. My reasoning right here, even as it appears on your screen, happens within that and it can even enter the c o n t i n u u m to create more c o n t i n u u m.
One might say the continuum I am reasoning within (or shall I say, we, as you are also know in the process of understanding) is the box this comment appears in—as far as the written language as it appears goes -, or even more broadly, the space in front of my and your computer screen where the pixels end in the depth dimension; where the written words are. And ultimately outer space, which we are both floating within✨.
>But okay, abstract computers. So you are saying that humans work differently from some abstract computer. This is true in a sense. Why is this interesting, again?
Because abstract computers are a more generalized notion that physical computers, as we use abstract computational logic to program and even construct physical computers (I guess in theory there could maybe be “other” computers that are not like that, that maybe do not need to be programmed, or are programmed in a way that does not rely on certain concepts like binary logic or binary data; but then you are stretching the definition—I can just define the whole universe as a “computer”, that doesn’t tell me anything except that I arbitrarily choose to define it that way).
So it implies that it is even more true humans work differently than real computers, and real computers cannot replace real humans, not even just in terms of reasoning, let alone perception, feeling, consciousness which are all more than just reasoning.
At least abstract computer logic DOES work in the human brain. I will not deny that, although it is often more like quasi-computational, as it is approximate and sometimes might be wrongly applied (like literal mathematical mistakes) and computations that are frequently wrong in a practical sense are not <💻⚙computations>, which we expect to actually work, like a computer works, but more like elementary school child doing math.
However real computer logic does not work in the brain, as it uses physical logic gates, silicon materials, etc.. It is also very precise logic that can add or even multiplicate extremely long numbers with nearly 100% accuracy. So there it is even more clear and undeniable a human is not a computational in that sense as it far far far more inaccurate.

Benjamin J 27 Jul 2022 7:33 UTC
1 point
0
in reply to: Signer’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
>you can prove everything humans know about BB by computably deterministically enumerating proofs
This is an oopsie right here. Of course you can enumerate proofs, but if you enumerate wrong proofs along with right proofs, where is the truth in that? You would have to distinguish true from false, and no finite set of technical symbols or states can decide between computable and uncomputable, as abstractly a computation could generate all finite sets of abstract symbols or states (no matter if they correspond to truth or not).
>By that definition computers are also not operating computationally.
Very well observed in a technical sense. That is why I am first and foremost talking about abstract computability. In a sense that term might not be the best, as it is indeed not that related to real life computers.
I thought of using the term “definable, infinitely regularizable” or something akin to it for computability and “process-wise irregularizable but deterministic” for deterministic uncomputability.
>these steps also could be performed by computer.
I am not talking about steps here, but about continuum. The real numbers for example are not step-wise, they are continuous and contain uncomputable and undefinable sections in a technical sense (you can google that).

Benjamin J 27 Jul 2022 6:58 UTC
1 point
0
in reply to: Signer’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
>I mean you didn’t present logical argument for “human brain works uncomputationally”.
That might be true, in so far as it is already the case. There is no argument to be made, I only point out what is already true.
The human brain cannot be conceived to work solely computationally as this statement is starting to be understood to be true based on conclusive bivalent deterministic reasoning.
True → It is true.
False → It “can be conceived?”, but it cannot be conceived to work that way if it really really does not work that way. If you consider that it might or might not, you have two options with no way to deterministically, logically choose between them. So conclusively, deterministically only the true option remains, as even the false option is inconsistent in bivalent, deterministic logic, which is what is being assumed here in this particular context (which doesn’t negate that other logic is valid in other contexts). But there is no general way to compute inconsistency, it becomes evident in another way.
This is not really an argument, it is just a simple stating of bivalent truth.
It is not mean to persuade, but to point out the truth that is already the case.
Being, yes there is uncomputable deterministic reasoning. Which doesn’t mean there is not also a lot of quasi-computational reasoning happening, or indeterministic reasoning, and even indeterminate but non-probabilistic reasoning (->??? Knightian Uncertainty or one might call it Knightian indeterminacy, stochastically unquantifiable indeterminacy).

Benjamin J 27 Jul 2022 6:51 UTC
1 point
0
in reply to: gjm’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
>Analysing a program rather than blindly executing it is not “ignoring logic”. And even actually ignoring logic does not imply not being computational “underneath”.
Blindly executing? Where did I say to blindly execute it? I did not once state this, or imply this in the text.
In fact I stated the opposite: And read comments or elucidations to understand what it is about.
Which means not blindly, but with the semantic meaning of the text in mind.
If you ignore logic and semantics, that is operating blindly as far as this post is concerned.
>I’m sorry to be increasingly blunt, but I do not think you are thinking clearly about this stuff at all,
No, it’s OK. However logically and semantically, what you think about whether I think clearly has no implications whether I actually do.
I have not persuaded myself of anything. This post is meant to yield understanding, not to be persuasive to myself, or others. Truth is true, regardless if it persuasive. If I correctly calculate the 8988343th digit of pi, me stating it might not be persuasive as they might not know whether it is correct but it is still true.

Benjamin J 26 Jul 2022 22:44 UTC
1 point
0
in reply to: Signer’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
Busy beavers have no correlation with the environment, except in the word which to be fair is interesting and inspiring as it is a cool animal, but ultimately does not logically relate much to the function itself.
It is good you acknowledge indeterminism. There we are getting somewhere interesting!
However a computation as defined normally is operating deterministically. That is what we consider a correctly functioning computation to be.
So the subject of indeterminism is very interesting, but it itself shows you that you are not operating computationally. Also something I have pointed out numerous times.
People like to refer to heuristics or probabilistic computing which is indeed not deterministic but can still operate within a computational space (also if it is computational itself does depend on the definitions), but it also does not suffice, as humans can understand things that are neither probabilistic / heuristic nor deterministic.
This statement is true and not probabilistic but not determinate.
Or even neither deterministic nor indeterminate, like space, as it is beyond nameability, so the word indeterminate itself becomes i nd ete rm ina a a a tee eee ee e and infested by space👽.

Benjamin J 26 Jul 2022 22:18 UTC
1 point
0
in reply to: gjm’s comment on: The incomputability of the human brain
>In any case, your attempted paradox—“This true (in bivalent logic) statement cannot be processed by the human brain”—doesn’t even work. What I mean is that if I say it’s false but can be processed, there’s nothing paradoxical there at all.
I somewhat agree. As you said you can just process it and probabilistically or empirically find out if you can process it is or not.
The statement was not precise enough:
“This true (in bivalent logic) statement cannot be deterministically processed by the human brain, but can still seen and determined to be unambiguously true by something beyond it (meaning needing no empirical confirmation).”
I was meaning to imply that, but I did not SAY that. So you are very right that it is only true in so far as that is implicitly understood, or explicitly stated.
If it is consider it could be false, you have two options, the TRUE and FALSE option with no logical option of deciding between them (regardless of your assumptions, both are logically possible a priori). But then you cannot logically decide it is false, because you would then arbitrarily reject the possibility it is true, but arbitrary rejection is not logical, it is probabilistic or assumptive, or based on free will (but again free will is free, it is not based on bivalent logic, so the truth value of the statement is independent of that).
So you get into an undecidable contradiction here logically that can only be resolved if the statement is true.

Benjamin J 26 Jul 2022 21:55 UTC
1 point
−1
in reply to: gjm’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
>It reads the text of a program written in your language with “START:” and “GOTO START” and so forth.
Those are the program and will put thet program into a loop. If you write a different program, you did not follow my instructions, but wrote your OWN program, which maybe is a meta-computational-program.
Of course meta-computational-program can be correct in some ways. I did not dispute that. But it is a different level. I am talking about base level computation here, as there is no meta-computation without a base level (which is why a lot of software is utter rubbish nowadays, it is written as if there is no base level to take into account).
>As it executes it, it monitors the internal state of the execution and looks to see if the program ever gets into the exact same state that it has recently been in.
That sounds a bit like solving the halting problem? That halting problem is proven to be not solvable by computers in general. Hence why I said KIND of loop. I guess any specific loop can be exited by computation that just is a bit error prone, or does not quite follow the program given (maybe because the high level programming language gets not well translated into a low level programming language; what I am talking about here is most basic assembler logic, it is not anything complex in terms of the computational logic given, although of course maybe complex in terms of computational & uncomputational logic already operating in our minds.
>So no, it is not really really really true that “this kind of loop cannot be left computationally”. I just showed you one way in which it might be left computationally. No magic is required.
Meta-computationally, as you said your program ignores the START and GOTO START program instructions and does something else. That is a program that meta-ignores and meta-computes something. That is not what I am talking about on the base level (the comment is something different, but not meant to be processed by computer). So unfortunately you are “not even wrong”. You are talking about meta-computation and meta-ignoring, while I am talking about base-level computation.
START [this program will not halt computationally, but does halt uncomputationally] (END if non-computational logic is applied) GOTO START
Maybe this is clearer? You can execute it as you can function as a simple computer, and realize the comment is true. I don’t see the issue. There is computational halting, but this statement is a looping program so it won’t halt computationally. So the only other option left IS that is halts uncomputationally (who says uncomputational processes can’t halt? like you might run a busy beaver a few steps, like people already did and then halt; you could get the same states via computation, but that doesn’t make the busy beaver a computational process), or that you ignore logic.
If you ignore logic, that might be good to meditate and in that way is a good idea to be fair, but it doesn’t directly help to correctly program a computer or draw correct conclusions about uncomputability.
Again, the logic is rather simple, it is just that for some reason we do not like logic sometimes, I guess because we are trans-rational and trans-logical beings. That is being human I suppose. Thanks God. We do not want to ignore feelings and emotions and wild ideas and playing with language in favor of mere logic. But still logic has its place.
I would like functioning software, but people insist that their computers should “understand” their spagetti code that is barely logical and produces constant errors.

Benjamin J 26 Jul 2022 21:30 UTC
1 point
0
in reply to: Signer’s comment on: Can someone show the error in my reasoning here that seems to show something about the limits of AI?
I guess it is a definitional issue too.
That is maybe why in some way, I might have just no chance getting through to many people.
If you define “uncomputational processes” in your mind as = computational, or you say 1=1.000000001, which is 100% false in mathematics, what can I do?
If you define “false”=true and “true”=false in your mind, and maybe sometimes the reverse, it seems conversation about true and false becomes basically impossible.
The fact of the matter is we can PROVE certain abstract functions to be uncomputational. Where does the human system get its information on that from? It cannot be random, as it is a deterministic function. It cannot be from the environment, as it is utterly unrelated to anything practical. It cannot be computational, as no finite series of states can make you draw any abstract conclusions about if they come from something computable or uncomputable. So where does it come from?
I guess the computationalist answer is, busy beavers don’t really exist, but they DO as an abstract function. And abstract functions CAN effect our brains when we think about them. Obviously!
So how exactly can you explain that humans can reason about uncomputability? How does that enter our brain, if it does not already exists there?
They do not “actually” but just randomly arrive at those ideas? Monkey typewriter that came up with the strings uncomputable and busy beaver?
They magically get the ideas about uncomputability and the correct results based on that (ie they only do computations, but they magically do them in an invalid manner to still get the right result or the right idea, like the busy beaver being uncomputable and a certain BB being above 100^100^100^100?).