Yes, I am now calling to know wtf you mean by "true", since apparently something can literally not be real and still be true by your definition.

This is why I say you need to go read instead of arguing with me. We can't have a discussion on this topic if you don't even know what truth means in logic.
A proposition is true if it lacks contradiction. This definition is implied by the axioms of propositional logic (also known as the laws of thought):
* A=A is a true statement.
* A!=A is a false statement.
* A statement can only be true or false.
That's it. It has nothing to do with any aspect of the real world.

However, I reject your imagination, tell you your axioms are false, therefore y is not true.

Fine. You're just excusing yourself from the topic. I'm not going to develop a whole new system of mathematics just to please your sensibilities.

They are assumed true by definition.

Both statements mean the same thing.

EDIT: I should clarify this. "Assumption" has a special meaning in logic. It's what you take for granted to make an argument, without having to prove it. This is not the same thing as when one is discussing a matter of fact. "If we assume The Egyptians had prior contact with the Sea Peoples, then..." There's no fact underlying the principle of non-contradiction, or the parallel postulate, that we don't know the value of and we happen to assign as true. The act of defining an axiomatic system makes the axioms true per se.

show you logical and reasoning steps it did to do so

What you mean to say is that it spits out a string of characters that does not necessarily have any relationship to its internal workings.

Do you only know tautologies with certainty?

With 100% certainty? Yeah, pretty much. I know I'm currently alive, and that I'm feeling what I'm feeling. Everything else is at best tentative.

You've given me an impossible standard by which you would know things for 100% certainty such that I can never prove to you whether an LLM can reason.

It was never in the cards to reach that level of certainty, if I don't accept 100% that the universe exists as it superficially appears to me. But my point is that a questionnaire won't convince me in the least. You may as well not do anything, and it's equally compelling. I see the ability to answer questions correctly as totally disconnected from the question.

why would you trust that we are actually capable of identifying reasoning systems? why would you trust that we are capable of accurately dissecting the inner workings of LLMs? or why would you trust that humans could actually reason such that we could deduce any fact from the information given (hence we couldn't trust ourselves to figure out whether or not LLMs exist, even if we had all the necessary facts to do so and more)?

Reverse engineering methodology is inherently scientific. You hypothesize and you run experiments on the thing you're trying to understand. "We disconnected this part here from the rest of the device and that broke this function, so the function depends on that connection being intact." "We turned this knob up and measured the change in the behavior to establish a linear relationship between the value and the response." As long as the conclusions follow from the methodology and the experiments are repeatable, it's fine.

Absolute nonsense, as we know eyewitness testimony is the least credible form of evidence.

It's not eyewitness. I'm looking at the box. I can see there's two apples in it.

You'd know for 100% certainty there are 2 apples in the box, then the magician will pull out a 3rd one and your entire method for determining truth and facts will literally be blown to bits.

That wouldn't change the fact that when I looked there were, in fact, two apples inside the box.

The question writer didn't tell you that the machine can reason, they only wrote perfect questions.

Then no, I don't accept it.

Say you have Hitler (or his protege Trump), someone you don't wanna treat with any dignity or respect for. You'll now say they don't reason?

I don't think it's a good idea, if nothing else strategically, to dehumanize your enemies.

Not only that, but you then completely contradicted this very claim by saying you'd believe for a fact there are two apples in a box if you saw it - something you can easily be fooled into seeing.

I don't believe I can easily be fooled into seeing two apples in a box held right in front of my face where there's some other number. More to the point of the example, I can much more confidently believe there are two apples inside a box after looking at the box than that there are no white sheep in all of Scotland after conducting a sheep census. I think even you must agree that one of those experiments is much more fallible than the other. Yes, I can be deceived, but it's even easier to deceive a census.

I never thought a conversation would come to such a dead-end with you, as our past debates usually gave me some kind of new perspective to think about (even if I disagreed with it), which is rare.

Well, I would have hoped to inspire you to go read a bit of philosophy, as I have insisted several times. I can say you've given me a new appreciation for the field. I used to think it was all a bunch of useless wankery, but I guess some people really do need it.

This is why I say you need to go read instead of arguing with me. We can't have a discussion on this topic if you don't even know what truth means in logic.

You completely misunderstand. I meant what is true to you. What standard is required for you to accept something as true?

A=A is a true statement

Again, this doesn't help if we're trying to solve a murder. I find the fingerprints, gun registration, blood stains, etc.. All of it points to Sam being the killer. Sam then confesses to being the killer and cries. Do you accept this as true or just "probable"?

I'm not going to develop a whole new system of mathematics just to please your sensibilities.

This was never supposed to be about mathematics.

We accept things as true/fact all the time that would never live up to mathematical scrutiny.

Sorry, maybe not you - since you're not convinced of anything that's not a tautology apparently.

Both statements mean the same thing.

No. If X is true because we assumed it, it means we're granting it the status in order to make another point. However, we can still scrutinize X later.

If we know X is true via some method (like science), then that's it, it's true. You don't have to "assume" it.

In axiomatic systems, you assume certain axioms are true. However, they rarely are "actually true".


From now on, when I use "true" and "fact", unless otherwise stated, I mean true in the universe we live in - not a made up imaginary axiomatic system.

If your axiomatic system assumes that dogs are actually cats, that's not actually true. You can assume it all you want, and the conclusions you get will be valid only within that system.

We cannot reduce our universe to an axiomatic system for many reasons (too many axioms, we don't even have all the axioms, and it may not accurately represent the universe at all given Gödel's incompleteness theorem).

Therefore, it makes absolutely 0 sense to talk about a complex enough topic in the realm of an axiomatic system - because you are not guaranteed to even set it up correctly.

What you mean to say is that it spits out a string of characters that does not necessarily have any relationship to its internal workings.

That's incorrect by definition. The internal workings generated the string of characters.

I know I'm currently alive, and that I'm feeling what I'm feeling

How exactly do you know this? Your sensations traverse into God-hood? What is "alive"? How do you know you're alive?

But my point is that a questionnaire won't convince me in the least. You may as well not do anything, and it's equally compelling

Why even bring up the mathematically impossible standard if that wasn't the level you needed to be "convinced" in the traditional sense?

Reverse engineering methodology is inherently scientific

You trust science now? Is science a tautology?

As long as the conclusions follow from the methodology and the experiments are repeatable, it's fine

Still not an axiom. I also highly doubt you could deduce this methodology is logically sound through whatever set of axioms you hold true - because one axiom must always be that you don't have all the axioms necessary for all deductions (or that you cannot know when you have all the axioms necessary for a particular deduction).

That is, assuming we're talking about the real world and not your made up imaginary ones where you can prove Jesus sucked off the devil after losing a poker game because your axioms were Jesus plays poker, poker losers suck off the winner, and Jesus plays the devil and loses.

It's not eyewitness. I'm looking at the box. I can see there's two apples in it.

Uh huh. Would you say you used your eyes to .. witness the apples?

Eyewitness definition: "a person who has personally seen something happen and so can give a first-hand description of it."

Again, there's no reason why you looking at the box cannot be mistaken about seeing two apples. I double dare you to fly over here, I will trick you into seeing two apples in a box when such is not the case.

That wouldn't change the fact that when I looked there were, in fact, two apples inside the box.

Yes it would. You saw two apples in the box, that does not mean there are two apples in a box. All it means is your brain interpreted something as being two apples in a box.

If you're hallucinating, then there might not be a box to begin with, you could have been looking at anything. Hell, your eyes might have been closed and you thought you saw two apples in a box.

I don't think it's a good idea

You assume people reason because it's not a good idea to think otherwise. Hilarious.

I can much more confidently believe there are two apples inside a box after looking at the box than that there are no white sheep in all of Scotland after conducting a sheep census

I'd agree with you, but your own standards you've shown me up until now disagree with your claim here.

Well, I would have hoped to inspire you to go read a bit of philosophy

There's no philosophy here that I haven't read and understood many times before. What I'm arguing is your inability to actually apply that philosophy.

If I say I only believe tautologies but I also believe my mom when she tells me dinner is ready, then I must have some stupid axioms or contradicting systems of belief.

You can logically say you don't believe or aren't 100% certain of X, but that doesn't mean that's what you actually think.

The same way you may say you don't want to feel a certain way, but you still continue to. Say all you want you only know for certain tautologies, but you (consciously and unconsciously) believe much more than that. You have stated to me things in our very discussion that you believe with certainty that could never be proven by the very standards you gave me.

You then used these impossible standards to attack the testing methodology I presented. Well alright, you win. We can't know if a blackbox reasons by its output anymore than we can know if vaccines work by looking at patient outcomes. Congratz, you won.

You completely misunderstand. I meant what is true to you. What standard is required for you to accept something as true?

If we're talking about 100% certainty then, as already discussed, it must be tautological.

Again, this doesn't help if we're trying to solve a murder.

Uh huh... Because we're definining the idea of truth itself. What does it mean for something to be true? Not what's needed in order to know that it's true, what is needed in order for it to be true?

This was never supposed to be about mathematics.

You are trying to convince me that I don't know for certain mathematical truths, because I gave a mathematical truth as an example of something I know with 100% certainty. You say you reject the axiomatic foundations that make the Pythagorean theorem true, so I say back to you, "okay. Sorry." If you reject the language I'm using then that's where the conversation ends. I can't argue about which program is better than which program with someone who says computers are fake and gay.

In axiomatic systems, you assume certain axioms are true. However, they rarely are "actually true".

This is may fault because I made the edit late in the day. See:

EDIT: I should clarify this. "Assumption" has a special meaning in logic. It's what you take for granted to make an argument, without having to prove it. This is not the same thing as when one is discussing a matter of fact. "If we assume The Egyptians had prior contact with the Sea Peoples, then..." There's no fact underlying the principle of non-contradiction, or the parallel postulate, that we don't know the value of and we happen to assign as true. The act of defining an axiomatic system makes the axioms true per se.

So I don't know what it means for an axiom to be "actually true", in a sense that's distinct from it being defined as true. Are you a Platonic realist? Do you think mathematics is ultimately an empirical science that studies some kind of metaphysical realm?

From now on, when I use "true" and "fact", unless otherwise stated, I mean true in the universe we live in - not a made up imaginary axiomatic system.

Again, this just makes it impossible to talk about mathematics with you. What does it mean for hyperbolic geometry and higher-dimension linear algebra to reason in this manner? Just anything that doesn't fit into the universe is false? Is Graham's number in fact not a natural, since it cannot be stored in the universe? Do most reals actually not exist, since they're non-computable (i.e. we can't make any statements about them)?

We cannot reduce our universe to an axiomatic system

What, you mean even in theory? That's veering into metaphysics, but I disagree. I think the reason mathematics works to model the real world is because the real world is indeed based on strict, irreducible rules that are basically an axiomatic system.

Therefore, it makes absolutely 0 sense to talk about a complex enough topic in the realm of an axiomatic system

Why are you trying to mix them together, then? I never said it's reasonable to expect mathematical rigor from empirical sciences. In fact I said the opposite several times.

The internal workings generated the string of characters.

What I meant is the contents of the string are unrelated. I can say "this sentence was written with the help of an Atlantis king, Nememiah, whom I channel from time to time to help me in various tasks" and that doesn't help us at all to say whether it's true or not.

Why even bring up the mathematically impossible standard if that wasn't the level you needed to be "convinced" in the traditional sense?

Because you literally asked how confident I need to be to say I know something. You're the one who used the word "know". If you wanted to know something else then you should have asked something else. Then you insisted that I know more things than just tautologies, and then that I don't even know tautologies.

I also highly doubt you could deduce this methodology is logically sound through whatever set of axioms you hold true - because one axiom must always be that you don't have all the axioms necessary for all deductions

???
Look, a scientific paper is just an argument for a proposition. The argument may be convincing or unconvincing. If the argument manages to convince me because the researcher knew things I didn't, or because there were things that needed to be considered that we both missed, then oh well. I guess I've mistakenly raised my confidence in the truth of something I don't 100% accept anyway. Oh no, what ever shall I do? I might have to *gasp* lower my confidence in it in the future. What a crisis of faith!

Eyewitness definition: "a person who has personally seen something happen and so can give a first-hand description of it."

Yes. To someone else. An eyewitness account is necessarily an interaction between two people, which is what makes it unreliable.

I'd agree with you, but your own standards you've shown me up until now disagree with your claim here.

You're trying to strawman me. I've never said that something not being tautological is indistinguishable from being completely ignorant of it. I just said that I don't know it. I accept that I can be deceived, or even plain mistaken. Hence why I don't say I have 100% confidence in anything. That doesn't mean confidence levels below 100% are all the same. I'm pretty sure I'm typing on this keyboard. I'm also pretty sure the Earth is spherical and orbiting a star. I'm not equally confident of both those propositions. In other words, I'd be more surprised to learn that one of them is false than the other.

If I say I only believe tautologies

You're putting words in my mouth.

You then used these impossible standards to attack the testing methodology I presented. Well alright, you win. We can't know if a blackbox reasons by its output anymore than we can know if vaccines work by looking at patient outcomes. Congratz, you won.

No, again, that's not what I said. What I said is that questioning a black box tells us absolutely nothing about whether it reasons. With a vaccine you can run experiments and attain some level of confidence in the results. By questioning we gain no confidence. It doesn't move the needle either way. Like I said, you may as well not have done anything.

Not what's needed in order to know that it's true, what is needed in order for it to be true?

Again, just not very interesting. It is true if it accurately defines reality. This is why tautologies are true, as they accurately define reality.. but in the universe in which they are conceived (their axiomatic systems).

Hence, again, why these tautologies can be "true", but I can still reject their truthfulness in reality.

You are trying to convince me that I don't know for certain mathematical truths

No, I doubt you can be convinced that you don't know them.

What I'm arguing is your own standards for 100% certainty would force you to not know for certain mathematical truths. Much different.

You say you reject the axiomatic foundations that make the Pythagorean theorem true, so I say back to you, "okay. Sorry."

If I said I believe with 100% certainty that the devil has sex with me every night, and I know this to be true because my axiomatic system makes this a tautology...

Is that even worth considering? You cannot deny that such an axiomatic system can be created such that this is true and would have the same validity as the one you gave me for Pythagorean Theorem.

If you try to argue one axiomatic system is more valid than another because of their relationship to reality, then you simply are taking my previous position.

This is may fault because I made the edit late in the day

I know what axioms are. This doesn't change anything from what I said.

If I said, "Let's imagine a system in which gravity pushes instead of pulls", this is an axiom for the imaginary system we created and/or our debate.

Axiomatic systems are imaginary. Only within that system must axioms be true. I do not have to assume them unless we agree to them.

Again, as I've defined true to be an accurate description of the actual universe we live in - not an imaginary one.

Do you think mathematics is ultimately an empirical science that studies some kind of metaphysical realm?

There's a very simple answer to this, but we're struggling to get there.

We use axiomatic systems to simplify the variables and have a system where direct logical connections are easy to see and make.

Just because an axiomatic system does not encompass all of reality doesn't mean that the deductions are wrong - but they may be incomplete.

Mathematics tries to describe the universe accurately (AKA reaching truths) but they cannot be expected to account for every atom in the universe every time they need to deduce a truth.

They reach conclusions that can be fairly trusted - as it works out logically within their system and then supported by empirical evidence.

this just makes it impossible to talk about mathematics with you

I honestly don't know how we got to mathematics.

You wanted to prove to me that you can't know if a blackbox can reason from just the output. My entire argument has been that every reason you gave was NOT applicable to the real world. Then in response to that, you keep giving me more inapplicable reasons.

Again, we can know something that we can't prove through mathematical rigor. Scientific rigor is just as good! We know scientific "truths" and "facts" that would be thousands of pages long to try and deduce mathematically.

Just anything that doesn't fit into the universe is false?

Anything that doesn't accurately describe reality is false or incomplete.

in fact not a natural, since it cannot be stored in the universe

This is like asking if the universe isn't real because you can't fit the universe in the universe.

I have no clue what you mean. Graham's number is not even infinite. What would it mean to "fit"? What do you mean "stored"? I can't write down Graham's number?

I think the reason mathematics works to model the real world is because the real world is indeed based on strict, irreducible rules that are basically an axiomatic system.

And again, Gödel's incompleteness theorem kicks in and tells you your system is incomplete or gives false outputs.

Even if we assumed a complete Axiomatic System for the universe is possible and accurate, we don't have it. Therefore, you'd be forced to conclude you can't know anything about the universe with 100% certainty until you have every single axiom.

Why are you trying to mix them together, then?

I'm actively trying to break out of this nonsense mathematical rigor. I want to talk about truth and knowledge in the traditional sense, where we know things without needing to check if an axiomatic system rubbed our balls the right way.

that doesn't help us at all to say whether it's true or not.

Elementary. If the blackbox outputs reasoning that has never existed before (and no cheating - like outside help 🙄), then that blackbox must have generated that reasoning. Therefore, the blackbox is capable of reasoning.

This is where I'd put the box or whatever at the end and hand the paper in to the professor with my complete proof.

It doesn't matter how many "layers" you add between the internal process and the reasoning output, as I could argue our brains don't reason directly either. As long as reasoning results from the process, we can call it reasoning.

Then you insisted that I know more things than just tautologies, and then that I don't even know tautologies.

Again, "🤓 erm actually" vibes.

Yes I insisted that you know more than just tautologies because your standard for "knowing" things in a traditional sense cannot be so strict. But if you insist on your strict standard, then you don't even know tautologies.

The argument may be convincing or unconvincing

What a way to live. Everything is only ever "convincing" or "unconvincing", but you can never be wrong because you'll just say, "Well, I never had 100% certainty in it anyway!"

This sounds like religion to me - with the believers arguing a point to the death, then changing their mind when convenient and claiming they were never wrong.

Yes. To someone else. An eyewitness account is necessarily an interaction between two people, which is what makes it unreliable.

Completely incorrect. The definition states: "so can give a first-hand description of it.

There's no requirement that they do give. An eyewitness is unreliable for a multitude of reasons. VERY low in those reasons is the fact that they have to communicate the information.

I just said that I don't know it. I accept that I can be deceived, or even plain mistaken

How can you be mistaken about something you don't know?

You cannot tell me, "I was mistaken to be 95% confident when I should have been 65% confident" as that's not being mistaken because you were not 100% confident in your confidence level either.

So how can you ever be wrong?

I'm not equally confident of both those propositions.

But you still believe both?

You're putting words in my mouth.

At this point, I'm willing to bet that if you had an LLM that solved novel problems and regularly showed stunning reasoning skills - you'd believe it was truly reasoning after a while.

You'd come to me and say, "but I don't actually know" but you'll "believe" it.

With a vaccine you can run experiments and attain some level of confidence in the results

Why? You're reasoning for a blackbox was that we could be tricked by it having more resources and other things that don't apply to real world testing.

Why can't I say you can't trust patient outcomes of vaccines because:

The patients are trying to get better so they may have cured themselves
The patients got stuck with a needle and that might have done it
etc.

I can say that this doesn't apply to real testing because we account for these things. But you don't give this same treatment to the blackbox testing - as if suddenly people are monkeys in a cage slamming cups around.

No, I doubt you can be convinced that you don't know them. What I'm arguing is your own standards for 100% certainty would force you to not know for certain mathematical truths. Much different.

They're one and the same to me. I know something if and only if I'm 100% certain of it.

If I said I believe with 100% certainty that the devil has sex with me every night, and I know this to be true because my axiomatic system makes this a tautology... Is that even worth considering? You cannot deny that such an axiomatic system can be created such that this is true and would have the same validity as the one you gave me for Pythagorean Theorem. If you try to argue one axiomatic system is more valid than another because of their relationship to reality, then you simply are taking my previous position.

You're making the same equivocation again and again. Yes, in the language you've conceived, "the devil has sex with me every night" is a true statement. What does that have to do with whether the devil has sex with you every night? Just because you've defined a language that uses the same words as English to express its statements, that doesn't tell you anything at all about empirical reality. Who's arguing otherwise? When did I say "because I know the Pythagorean theorem is true, I know that X", where X is literally any statement about reality? Not only did I not say that, I'm telling you right now: it's impossible to mathematically derive empirical knowledge.

I know what axioms are.

It doesn't sound like you do. It sounds like you're very very confused about what mathematics discusses.

Only within that system must axioms be true. I do not have to assume them unless we agree to them.

That's entire true. You do not need to accept axioms. Non-Euclidean geometry is a game mathematicians invented when they realized they didn't need to assume the parallel postulate.
And? That doesn't make Euclidean theorems not true. You can take their statements and expand them and expand them until you end up with a very long statement that contains only Euclidean axioms combined with Boolean operators and equalities. "But if I put in different truth values I get a different result." So what?

Mathematics tries to describe the universe accurately (AKA reaching truths) but they cannot be expected to account for every atom in the universe every time they need to deduce a truth.

LOL. Okay. Sure, buddy. Please cite a single author who's ever said that. It's not going to change my mind, but I could use a laugh.

This is like asking if the universe isn't real because you can't fit the universe in the universe.

The universe tautologically fits in the universe. The space the universe occupies is the space the universe occupies. The universe is neither larger nor smaller than itself.

I can't write down Graham's number?

Nope. You can't. The universe doesn't contain enough particles to express it. You can only write down an expression that computes it. Even if that were not the case, non-computable reals are even worse, as you can't even do that.

And again, Gödel's incompleteness theorem kicks in and tells you your system is incomplete or gives false outputs.

If we understand that the universe's axiomatic system proves the universe's current state (i.e. "it is true that the current state is reachable from the starting configuration"), then the universe's axiomatic system being incomplete would just mean that there exist states that are conceivable but unreachable from the starting configuration, or perhaps any starting configuration. As an example, Conway's game of life is proven to contain states that can only be reached by manually setting the board to that state, and not by the rules of the automaton.
https://en.wikipedia.org/wiki/Garden_of_Eden_(cellular_automaton)
A real unreachable state might be, say... all the particles in the universe arranged to form a sign saying "we apologize for the inconvenience" a million years after the Big Bang.

I want to talk about truth and knowledge in the traditional sense, where we know things without needing to check if an axiomatic system rubbed our balls the right way.

Well, sorry. You're barking up the wrong tree. Use a different sort of language to communicate what you want to say. "Believe"? "Accept"? "Defensible/Reasonable conclusion"?

Elementary. If the blackbox outputs reasoning that has never existed before (and no cheating - like outside help 🙄), then that blackbox must have generated that reasoning. Therefore, the blackbox is capable of reasoning.

You're assuming the conclusion in the premise. My whole point is that there's no criteria to detect reasoning from a string of characters. Looking at the at the output and saying "yeah, this looks like reasoning" is entirely uncompelling.

you can never be wrong because you'll just say, "Well, I never had 100% certainty in it anyway!"

Of course you can be wrong. You can be convinced by a piece of evidence of the truth of a hypothesis, rely on the hypothesis to build something, and fail in a way that shows it was actually false, and still change your mind and accept the falsification of the hypothesis.

This sounds like religion to me - with the believers arguing a point to the death, then changing their mind when convenient and claiming they were never wrong.

LOL, what? How is it religious to change my mind to fit new evidence? You're saying it'd be less religious (less dogmatic, I should say) to refuse to change my mind in the face of contradictory evidence and insist that I'm still in the right?
It's funny. I have a friend who gets annoyed when he shows I've said something wrong and I immediately just go "oh, okay, never mind then". I've asked him several times what he'd rather I do, and he's never been able to give me an answer.

You cannot tell me, "I was mistaken to be 95% confident when I should have been 65% confident" as that's not being mistaken because you were not 100% confident in your confidence level either.

Um... No. I was mistaken to be 95% confident about something that's false. I would have been correct if I had been any% confident that it's false. What makes me correct or incorrect is not how confident I am, but whether the contents of my mind coincide with objective reality.

Why can't I say you can't trust patient outcomes of vaccines because: [...]

Confounding factors is one thing, but science cannot cope with the thing being studied trying to trick the researcher -- that is, being aware that it's being researched and behaving in a particular way as a consequence. If you had a clinical trial where it was found out that someone did something to change the results of the experiment, the whole thing would be thrown out. With something as vague as "does this machine reason?" where we don't even have clear criteria for what a successful test is, and where there are incentives to force a particular outcome, there's just no way. The methodology is just unworkable.

They're one and the same to me. I know something if and only if I'm 100% certain of it.

And I'm saying that's a contradiction, as you cannot actually be 100% certain of any of the things you've said.

that doesn't tell you anything at all about empirical reality. Who's arguing otherwise?

If you cannot know anything about reality through what you're saying, then there's even less logic in bringing up this methodology to try and see if LLMs or any blackbox can reason, as you'd never know even if proven through your method.

it's impossible to mathematically derive empirical knowledge.

So you admit you know nothing about the universe you live in.

It doesn't sound like you do. It sounds like you're very very confused about what mathematics discusses.

I've taken 2 logic (philosophy) classes as well as 2 mathematical proofs class and passed both.

I'm sensing you are the one misguided about what you're talking about.

You do not need to accept axioms

Yes, and I've rejected your axioms because, by your own admission earlier, you cannot derive empirical truths from them (which I don't 100% agree with but is true enough to let slide for this discussion).

LOL. Okay. Sure, buddy

Sorry? Was mathematics invented to describe imagination? Do we not use mathematics to reach empirical truths?

I didn't wanna get into that topic of whether we deduce empirical truths or not from mathematics, but isn't it the goal?

Do we have equations for gravity because it's fun? Or are they actually useful in deriving truths? Such as when an eclipse will occur?

If reality doesn't match your equations, it's not because the equations are "wrong", it's that the equations are incomplete (didn't account for a planet or something else we couldn't know about). This is consistent with what I said would occur given any axiomatic system deduction which doesn't have all the axioms needed to represent the universe.

The universe doesn't contain enough particles to express it

That's a big statement, given we don't know for sure anything beyond our horizon. The universe could be infinite and contain infinite mass.

But yes, I can see that's it's too large to express as far as we know. (unless you're... 100% confident otherwise?)

If we understand that the universe's axiomatic system proves the universe's current state (i.e. "it is true that the current state is reachable from the starting configuration"), then the universe's axiomatic system being incomplete would just mean that there exist states that are conceivable but unreachable from the starting configuration

I may have argued against this, but that would take us into a greater debate on whether we CAN deduce empirical truths mathematically - since your interpretation means there can exist a "God Formula" of sorts where we can deduce anything since we have taken everything into account.

Use a different sort of language to communicate what you want to say.

This sounds like someone who's clearly a man asking me to call them a woman. Like sure, you can ask, but it's not something my brain wants to do and feels illogical.

I'm not gonna change how I use language to fit some niche. If I say the devil has sex with me every night, that's "true" according to you since I called it an axiom in my axiomatic system.

No one else would agree with you about how you defined true. If you want to go the mathematical/philosophical route, you should present that you're going to do so beforehand so we can agree on definitions.

You're assuming the conclusion in the premise. My whole point is that there's no criteria to detect reasoning from a string of characters

Never asked you to detect reasoning from looking at the string. You can look at the string and determine if it follows reasoning.

For example, if I say:

If Sally eats a cookie, then she must have milk with it. I know Sally ate 3 cookies this morning. After she was done eating the cookies, I found that there wasn't any milk left! Sally must have drank all the milk when eating her cookies.

You don't need to determine whether reasoning occurred to start, only that the logic given to you follows reasoning. Is what was said logical and following proper reasoning.

If so, and that logic/reasoning could not have been reused (as the novel program required brand new reasoning), then the black box must have reasoned.


If you disagree, then you must provide me a mechanism in which correct and brand new logical reasoning can be generated without reasoning.

You can be convinced by a piece of evidence of the truth of a hypothesis

Huh? Since when? Since when has evidence lead to 100% truth? Tautologies aren't built from evidence, they are purely true from forced reasoning.

How can you prove anything to be true to the same degree of confidence as a tautology?

LOL, what? How is it religious to change my mind to fit new evidence?

That wasn't the point at all. It wasn't that you'd change your mind to fit new evidence, but that you wouldn't agree you were wrong about what you thought previously.

What makes me correct or incorrect is not how confident I am, but whether the contents of my mind coincide with objective reality.

What a strange way to say, "I'm wrong if I believe X and X is wrong".

Or is believe not the right word? Maybe we should replace it with "hypothesized" to keep with your standards LOL.

It's funny. I have a friend who gets annoyed when he shows I've said something wrong and I immediately just go "oh, okay, never mind then"

He probably doesn't think you're actually convinced. Convincing people they are wrong is usually an uphill battle - like we're having now.

but science cannot cope with the thing being studied trying to trick the researcher

Of course it can given the right resources. This was your exact argument against the black box. If the black box creators try to deceive us, it becomes a game of who has the most resources to throw at the problem.

So I give it back to you: If you have 1 person trying to trick you from a study involving 1 million people, it just doesn't matter. If the resources goes up (now it's 500,000 people trying to trick you!), you can defeat this by having a trillion people in the study.

Therefore, vaccines are not proven by your own standard because we're being fooled! Those darn antivaxers always ruining our vaccine studies!


I should point out that tautologies, while supposed to exist without axioms, still make assumptions in order to be true. They must. I believe this is related to the concept of the "problem of logical foundations" and Gödel's incompleteness theorem (since the system cannot prove its own consistency). Within the logical system you create the tautology it will be true, but you still must justify the logical system or I will reject it.

If you cannot know anything about reality through what you're saying, then there's even less logic in bringing up this methodology to try and see if LLMs or any blackbox can reason, as you'd never know even if proven through your method.

You're repeating the same fallacy from before, that not being 100% confident is the same as being completely ignorant.

So you admit you know nothing about the universe you live in.

When did I claim otherwise?

I know you're going to say that this previous sentence is in direct contradiction with the one immediately preceding it. If I take an apple and drop it and watch it fall, I know that I've seen something, even if the ultimate truth of what happened when I did that is unknowable to me. I know a little bit, I just can't know how much relation the things that I know bear with the actual state of affairs. If I am in fact a brain in a vat, when I observe something I'm still observing it.

Do we not use mathematics to reach empirical truths?

Well, if I take your words strictly, no. We use mathematics to attempt to model the real world, approximate it, and predict it. Because models are approximations, they cannot achieve truth.
But more to the point, what I responded to was the assertion "mathematics tries to describe the universe accurately", which is patently false. Mathematics is ultimately a branch of philosophy, and does not concern itself with what is physically true, only with what is deductively true. Not having the axioms for the universe, the universe is not deducible, so mathematics doesn't care about it.

Do we have equations for gravity because it's fun? Or are they actually useful in deriving truths? Such as when an eclipse will occur?

So if I say F = G m1 m2 d^-2, where does that come from? Is this equation a consequence of an axiomatic system? More to the point, is the value of G deducible without measuring the real world? Can we arrive at it from pure mathematics?

If you disagree, then you must provide me a mechanism in which correct and brand new logical reasoning can be generated without reasoning.

LLMs and ML models in general have already shown that there's more statistical correlation in the content humans consume than was previously thought. How could you possibly show that an answer given by a model in response to a question is statistically uncorrelated to any part of the training set, when at the very least it must be in a language previously seen? It's what the thing does. It finds patterns in data and exploits them to generate more data.

Huh? Since when? Since when has evidence lead to 100% truth? Tautologies aren't built from evidence, they are purely true from forced reasoning. How can you prove anything to be true to the same degree of confidence as a tautology?

Did I say "prove to be true", or "convinced of the truth"? Would "persuaded of the truth" convey the meaning better? You seem to keep trying to catch me in a contradiction, like I haven't given all this stuff thought for years and years.

It wasn't that you'd change your mind to fit new evidence, but that you wouldn't agree you were wrong about what you thought previously.

Okay, well, then it was a response to something that nobody said.

What a strange way to say, "I'm wrong if I believe X and X is wrong".

You forced me to clarify what it means for someone to be wrong. "I'm wrong if I believe something wrong" is an incomplete definition, because it doesn't say what it means for a belief to be wrong. If you don't like wordiness then don't ask dumb questions.

If the black box creators try to deceive us, it becomes a game of who has the most resources to throw at the problem.

I did say that, but I've realized that was wrong. Because we don't even have a method to detect if reasoning was present when generating a string, it doesn't matter at all.

So I give it back to you: If you have 1 person trying to trick you from a study involving 1 million people, it just doesn't matter. If the resources goes up (now it's 500,000 people trying to trick you!), you can defeat this by having a trillion people in the study.

"The thing being studied" is a trillion people. If one person out of those is trying to trick you then one trillionth of the thing you're studying is trying to trick you.

I should point out that tautologies, while supposed to exist without axioms, still make assumptions in order to be true. They must.

Well, yes. Tautologies are true because of the laws of thought, as I said earlier.

I believe this is related to the concept of the "problem of logical foundations" and Gödel's incompleteness theorem (since the system cannot prove its own consistency).

Keep in mind that Gödel's theorems only apply to axiomatic systems at least as powerful as Peano's construction of the naturals, not to all axiomatic systems. I think that also included first order logic. It does not include propositional logic.

Within the logical system you create the tautology it will be true, but you still must justify the logical system or I will reject it.

You will reject it? Now I'm the one calling you out. You will not follow this standard consistently in your life. You'd be rejecting basically all mathematics, certainly all mathematics over the integers and the reals. So come on. Throw away all your money and go live in the woods. If you're rejecting all axiomatic systems that cannot be proven consistent then you're rejecting that addition makes sense, so money can't have any meaning to you. Someone might hand you two dollars and demons might fly out of your nose as a result.

You're repeating the same fallacy from before, that not being 100% confident is the same as being completely ignorant

No, I'm simply not gonna put a percentage on every "belief". Either you think something is true or you don't. I don't wanna hear that tautologies you are 100% certain, but the laws of physics you're 98% certain, and the fact that you can type on a keyboard you're 92% certain.

What's the point of this. If you tell me you don't know if you're actually typing on a keyboard, but you're 92% certain, how should I interpret that? Do I say you believe it and you think it's true? What do I do with this information other than simply assume that you must believe it if you're 92% certain?

If you told me you're 95% confident that a black box could reason.. Is that good enough? Did I prove that it reasons enough? Is the goal 100%?

Either give me standards that make sense in our context or I'm going to assume you can't know anything at all.

When did I claim otherwise?

Not only is this, yes, in direct opposition to what you said otherwise, but it means that being less than 100% confident, in fact, does mean you are completely ignorant.

If you're 99% confident, then you can still be a brain in a vat thinking nonsense. Therefore, you don't know which is which, making you ignorant of the facts.

Mathematics is ultimately a branch of philosophy, and does not concern itself with what is physically true, only with what is deductively true

What math does and the purpose of math are different. I said the purpose of math is to try and deduce truths of our universe. The fact that it goes about it through philosophical logic of what can be deduced is exactly what I said it does.

What math does is the methodology - but for the purpose of trying to deduce truths that we can actually use. No one cares that you can inject a faster than light proton into Einsteins equations and they work fine, because that's not gonna help up us in the real world where that doesn't exist.

So if I say F = G m1 m2 d^-2, where does that come from?

Science - empirical evidence. The axioms we use in mathematics are things we've derived from the real world through evidence.

It finds patterns in data and exploits them to generate more data.

And we're different... how?

Let's say I give an LLM the problem: "10 * 10". And let's assume it has never had to do this problem before nor has it seen or been trained on this particular problem. Maybe it has seen 9 * 9 and 11 * 11, but not 10 * 10.

Through "generalization", it can abstract the idea of multiplication and apply it to the new problem. There's no particular reason to think it can't do that with reasoning too.

Did I say "prove to be true", or "convinced of the truth"? Would "persuaded of the truth" convey the meaning better? You seem to keep trying to catch me in a contradiction

How exactly can you be convinced of "the truth" if the truth is not proven to be true?

You said "of course [I] can be wrong", then proceeded to say you could be, "convinced by a piece of evidence of the truth of a hypothesis". You can be wrong and convinced of the truth. Convinced of the truth is not 100% confidence?


Again, absolute nonsense. I understand the idea of accepting certain facts more "confidently" than others. But just say you believe them if you believe them, we don't need a whole pony show to know if you're 95% or 100% confident.

You forced me to clarify what it means for someone to be wrong

Funny, because I still have no idea what it means to you to be wrong.

We know believe something with 100% confidence and it is incorrect (axiom), you are wrong. You then told me that if you believe something with any confidence (assuming even 1%) and you are incorrect, then you are still wrong?

This confusion comes out of what you mean by "believe". Do you believe something if you're even just 1% confident? Is there a threshold? Can we just not have this idiotic system you've created so you can just say you believe X and don't believe Y without needing this song and dance?

If one person out of those is trying to trick you then one trillionth of the thing you're studying is trying to trick you.

Who cares, the idea was that given a large enough sample size, they wouldn't be able to trick you. Hence, throwing more resources at it than the tricksters.

Tautologies are true because of the laws of thought, as I said earlier

And you're 100% confident about the laws of thought.. because reasons?

If you're a brain in a vat, there's no reason to think the laws of logic apply outside of your mind.

You will reject it? Now I'm the one calling you out.

I will reject it in your argument so I can maintain balance, not because I actually think it. Again, you've essentially proven to me that you cannot know anything for certain. You've argued that there are things you know for certain, and I'm saying even those things rely on assumptions, that I will reject since you cannot prove them to the same standard as the tautologies themselves.

Someone might hand you two dollars and demons might fly out of your nose as a result.

Maybe you're starting to understand how it sounds like talking to you right now. "X could be true... or I could be a brain in vat". How does that help?

If you told me you're 95% confident that a black box could reason.. Is that good enough? Did I prove that it reasons enough? Is the goal 100%?

You're asking me to define your goal for you? Don't you know what you're trying to accomplish?
If we're talking about rhetoric, the ultimate goal in a debate is to convince the other person of your position. Failing that, to make them less certain of their own position.

If you're 99% confident, then you can still be a brain in a vat thinking nonsense. Therefore, you don't know which is which, making you ignorant of the facts.

I'm ignorant of the ultimate facts, but not of all facts. I'm still perceiving what I'm perceiving. If it's all hallucinations, and my perception is my own mind putting on a show for my own mind, that doesn't change the fact that I perceived something. There is something that exists that is distinct from the part of me that's aware of perception.

No one cares that you can inject a faster than light proton into Einsteins equations and they work fine, because that's not gonna help up us in the real world where that doesn't exist.

Completely false. Theoretical physicists actually care a lot about that sort of thing. What consclusions can we reach if we take a theory and we follow it to its logical extremes? Mathematics is the same way. There's branches of mathematics that are pure, with no known application. Until only the 20th century, number theory was one of them. There's no purpose to it, mathematicians, and especially pure mathematicians, just research what they find interesting.

Science - empirical evidence.

Right. So you didn't deduce it from mathematics. Even if Newton's equation exactly described the universe exactly, he could not have arrived at it with no input from the real world. That's what I was getting at when I said that

The axioms we use in mathematics are things we've derived from the real world through evidence.

Only because mathematicians can't help living in the real world. The intuitive notion that pouring one glass into another yields a volume that's the sum of the two original volumes comes before the formalization.

Through "generalization", it can abstract the idea of multiplication and apply it to the new problem.

You're treating "reasoning" as a synonym of "intelligence". I'm not.

How exactly can you be convinced of "the truth" if the truth is not proven to be true?

I don't understand what the confusion is, here. We are talking about knowing the real world, right? It is impossible to *prove* things about the real world, so necessarily if we're going to have any beliefs about the real world, we're going to be accepting arguments that are less can perfectly water-tight. To do otherwise is to be unable to live. "Oh, am I actually eating if I put this thing in my mouth and chew? It's worked before, but I haven't proven it will work every time."

Do you believe something if you're even just 1% confident? Is there a threshold?

Do you think I have a little gauge here with a green bit that lights up?

Can we just not have this idiotic system you've created so you can just say you believe X and don't believe Y without needing this song and dance?

Tell me why I should ignore the real nuance of confidence just because it makes things more complicated.

If you're a brain in a vat, there's no reason to think the laws of logic apply outside of your mind.

I don't understand what that means. I don't what it means for "the laws of logic to not apply". Could you please clarify in concrete terms how a reality like that would work?

I will reject it in your argument so I can maintain balance, not because I actually think it. Again, you've essentially proven to me that you cannot know anything for certain. You've argued that there are things you know for certain, and I'm saying even those things rely on assumptions, that I will reject since you cannot prove them to the same standard as the tautologies themselves.

But you won't reject them. You share those assumptions, and you've conceded that you do. On what grounds do you accept them in one case and reject them in another?

Tell me, what's a proof? What's the purpose of a proof?

Maybe you're starting to understand how it sounds like talking to you right now. "X could be true... or I could be a brain in vat". How does that help?

Do you think a practical approach is incompatible with sollipsism? Just because I can't be sure what reality is doesn't mean I can't play along.

You're asking me to define your goal for you? Don't you know what you're trying to accomplish?

Completely disingenuous. You're the one arguing we can't know if the black box reasons - and you won't give me your standards such that you would believe.

If the goal is to convince myself, I obviously would just talk to myself, not you.

the ultimate goal in a debate is to convince the other person of your position

Obviously this, and not that I'm trying to actually run an experiment to see if random black boxes reason.

But again, you've given me no standards in which you would actually believe.. anything. At least not practically or consistently.

I'm ignorant of the ultimate facts, but not of all facts

I make no distinction between ultimate facts and all facts. If the only fact you know is that you are "feeling" something, then congratz. I cannot deny you your experience, but I can deny every single thing you derive from experience - including your own use of logic.

Either you're going to argue that's valid, or that this is stupid, but I'm afraid you're going to go with the former.

What consclusions can we reach if we take a theory and we follow it to its logical extremes? Mathematics is the same way. There's branches of mathematics that are pure, with no known application.

Is the goal to have fun in the sandbox or to reach some sort of understanding/knowledge that can actually be helpful?

There's no serious mathematician doing complex math equations for funsies thinking that it may never bear fruit in terms of being applicable to the real world or giving us insight to the real world.

This point is moot.

EDIT: you cannot argue against this point by saying they're curious or something. Because the only thing they're curious about is discovering new truths - not imaginary ones.

Right. So you didn't deduce it from mathematics

Sure, but that's because mathematics is a system that requires axioms to begin.

I'm not even sure what you're getting at - YOU are the only person arguing for this math proof nonsense. I've been telling you this is impractical.

You're treating "reasoning" as a synonym of "intelligence". I'm not.

Reasoning is a byproduct of intelligence. If you can learn mathematics, you can learn reasoning. If you surrender that LLMs have "intelligence", a general intelligence at that, then you surrender that they can learn things like reasoning.

if we're going to have any beliefs about the real world, we're going to be accepting arguments that are less can perfectly water-tight. To do otherwise is to be unable to live

You just said my argument back to me. I'm saying let's not talk about this nonsensical 100% confidence and 99% confidence nonsense because we all clearly accept things to be factual when presented with "good enough" evidence.

We also have no reasonable doubt for the rigorous scientific facts we know and whether the scientific method can bring us to facts.

Saying a blackbox output is insufficient to establish reasoning given a certain set of conditions isn't evidence because "what if Jesus injected his sperm into the blackbox and gave it a real brain" isn't an argument.

Do you think I have a little gauge here with a green bit that lights up?

Apparently. You can't tell me if 1% confidence means you believe something or not, so how can I know when you believe anything or not?

Giving me an impossible task with contradicting standards for your "belief".

You then give me what you would need in order to believe a black box reasons, and it completely contradicts everything you said earlier about what you need to "know".

Then you argue you don't need to know with 100% certainty to believe. Then you can't tell me what level of certainty is required.

Again, no way to have any discussion. Absolutely unnecessary but you brought us here. We're not even talking about proving reasoning or how we could prove it because we can't agree on what "proving" even means apparently.

Tell me why I should ignore the real nuance of confidence just because it makes things more complicated.

Here we go again. When YOU provided this very explanation for why:

"We are talking about knowing the real world, right? It is impossible to *prove* things about the real world, so necessarily if we're going to have any beliefs about the real world, we're going to be accepting arguments that are less can perfectly water-tight"

So argue with yourself I guess.

I don't what it means for "the laws of logic to not apply"

Easily. If I say X -> Y, we're assuming logic applies such that there is some system that has consistency and rules which can lead to truths.

We call this system "logic". If this system does not exist, then you cannot deduce any truths from your axioms. Hence, logic does not apply.

If you think logic applies, then please prove it to me (with 100% certainty such that it is a tautology). This means that the axiomatic system you need to prove it cannot assume logic applies. Since no logic applies, you cannot do anything with your axioms. Therefore, you cannot prove it to me.

Very simple really. Perhaps you're the one who should read on some philosophy, as I know this is not an uncommon philosophical discussion. Again, the "problem of logical foundations".

Could you please clarify in concrete terms how a reality like that would work?

What do you mean, "work"? Is the reality simply existing not "working"? Why can't such a reality generate a system of logic for a few billion years, then scrap it and make a new one?

Your question is one that language allows, but really isn't a valid question.

On what grounds do you accept them in one case and reject them in another?

Devil's Advocate. Very common. You can't deny my rejection simply because I conceded them personally.

My grounds for rejecting them is that you cannot prove them to your own satisfaction, therefore I'm saying you've contradicted yourself in your own standards of confidence.

Tell me, what's a proof? What's the purpose of a proof?

According to you? The purpose of a proof is to be certain that we aren't certain or something.

Lmao, you can't even tell me you're certain of the Pythagorean Theorem, as you only said you're 100% certain of it in the context of its axiomatic system (mathematics). "it doesn't account for the curvature of the universe 🤓".


MY standards don't suddenly explode like yours do. As I can say the Pythagorean Theorem is correct and proven, but it may always be somewhat incomplete. At some point we have to accept that the few variables that such a thing doesn't account for simply doesn't matter for the practical uses of the thing.

In terms of Newton's physics, it's still correct and proven - it was simply incomplete. You can't say Newton's equations were wrong (as they are the basis for the actual equations), they were simply incomplete - which I hold to be completely different.

Like saying, "The guy who robbed my hose had on a black hoodie". Just because I didn't mention he had navy pants doesn't mean I'm wrong.

Do you think a practical approach is incompatible with sollipsism?

Fundamentally, yes. I acknowledge you can "play along", but that's basically evidence that you don't actually believe solipsism.

If you were in a jail cell and told that you actually weren't, you'd be trying to escape while "playing along". There's a purpose to playing along, it's not the ultimate goal to just do that forever.

That's my speculation anyway, you can say you play along while thinking something else all you want, I cannot prove that you don't.

However, you've made this whole discussion very impractical by bringing in this nonsense - which isn't very "play along" of you.

You're being an asshat. Stop it. No one is forcing you to keep replying.

HUH? You're not forced to reply either. I just wanted to reach some common ground so we could actually say something useful.

If I'm being rude, my bad, my patience has run dry on account of dealing with the country I live in becoming Nazi Germany before my eyes every day.