The Tractatus is about the limits of language/thought/the world (as a formal logical system), and the primary result of the argument in the Tractatus is that you can technically say nothing sensible about meaning or the world itself from within it, and the natural result of this is that the Tractatus is, itself, as an attempt to describe the world/language/thought itself, from a formal point of view, nonsense. Having said that, there are points of view outside of formal logic, where the Tractatus apparently and essentially all "philosophical" questions, which perhaps we can view now (from the ladder), although we cannot and probably should not say anything about them, as it is impossible. This is somewhere between the End of Philosophy and mystical gibberish, and while it sounds like that's an important distinction to make, by the rules of the game it is a nonsense distinction, so here we are.

Wittgenstein essentially rejected this view a decade later, so if he felt no obligation to abide by the paradoxical inconclusions of the Tractatus, neither should we. But it's a remarkable, frustrating little book in any case.

... >And understand why this was submitted to HN in the first place?

The implications of this to formal logical systems is enormous: Gödel's theorem is rubbished*, AI consciousness is impossible*, the meaning of the world lies outside of the world and so our lives have to be oriented at some technically nonexistent point beyond the horizon of reality to have any hope of escaping the absurdity of sensibleness.* After writing this in a WW1 POW camp he quit philosophy (because he had ended it) and became a (very bad) elementary school teacher and then spent several years designing a doorknob[1], as one does.

*one could argue

https://www.nybooks.com/online/2016/05/24/wittgensteins-hand...

> Gödel's theorem is rubbished

I am curious, could you elaborate a bit on this? If the Tractatus is about the inability to say something about a system from within the system, then isn't this basically what Gödel's theorem is about?

I'm curious too. Can we right-away accept the proposition that "A Sentence can refer to itself"?

If a sentence refers to 'this sentence', what does it in fact precisely refer to?

And what is the "it" that does the referring?

Maybe, a "sentence" can not refer to anything.

It is the person uttering the sentence that does the referring. But then of course when he or she says "this sentence" they would really mean, me, this person.

With the warning that I am not an expert, see my answer below. While there is obviously thematic overlap between the Tractatus and Gödel, Wittgenstein himself viewed Gödel's work as fundamentally nonsensical. Now why the "nonsense" of the Tractatus is ok, while the "nonsense" of Gödel is not, is admittedly not clear, and we are under no obligation to respect it, but that would be (early) Wittgenstein's opinion.

I studied Wittgenstein and the philosophy of AI/Computation for years. I don't see how any of those conclusions in your last paragraph follow from his work. (If anything, Godels incompleteness can be found as a trival result of Wittgenstein's arguments.)

Given sufficient axioms, I can make any theorem trivial.

First of all, I would be very interested to hear your thoughts and references on this subject, as I am no kind of expert in any of this.

Wittgenstein clearly did not feel the incompleteness theorem followed from his (or Russell's) work[1][2], this is generally considered to be an issue of Wittgenstein misunderstanding Gödel, but I think this isn't correct. From the POV of the Tractatus Wittgenstein, unprovable formal statements amount to "undecidable" conditions in the physical world, an absolute impossibility. These are, like Russell's paradox, language problems - we have not defined our terms clearly.

[1] https://wab.uib.no/agora/tools/alws/collection-6-issue-1-art...

[2] https://www.cantorsparadise.com/wittgenstein-didnt-absolutel...

The problems he elucidates in the Tractatus cuts an entire category deeper than just "language problems - we have not defined our terms clearly", but rather that the very project itself of finding the ultimate sound and complete formal description for reality is incoherent: not something we need to clarify before investigating further, but utter non-sense we were only curious about because we were confused: like asking what is the last digit of pi, or what is the most positive prime number. This is deeply related to German concept of Transcendental Illusion.

Wittgenstein had no interest in Godel, he felt he had long since done away with the whole idea of a sound and complete formal model for reality in the Tractatus, and yet another paradox in yet another attempt at this nonsensical project held no interest for him (obviously it was a bigger deal for everyone else, proving that such a paradox could always be found. Wittgenstein already knew this was a pointless goal).

Wittgenstein only ever published two works: the Tractatus, and the Philosophical Investigations. The "Remarks on the Foundations of Mathematics" are lectures notes from his students, which isn't to say they should be disregarded, but we should also keep in mind that they are on-the-spot comments transcribed by others.

Paper [1] is a great example of something that should send off BIG warning flags when reading this kind of stuff. It goes to great lengths to talk about how it is quoting Wittgenstein out of context (extra especially bad for lecture notes) and that the rest of what he had to say _in_ _that_ _very_ _paragraph_ just isn't relevant for their paper ("the last three sentences are omitted and will not be discussed in this paper"). Let's take a look at those omitted sentences (would be good to read the block quote in [1] immediately before, for context):

> ...If you assume that the proposition is true in the Russell sense, the same thing follows. Further: if the proposition is supposed to be false in some other than the Russell sense, then it does not contradict this for it to be proved in Russell's system. (What is called "losing" in chess may constitute winning in another game.)

Wittgenstein has no interest whatsoever in logical systems being sound and complete. He refuses even discuss this as a problem, making _constant_ reference to "true/false in the Russell system" and being _very_ clear in the strategically omitted sentences that the "proposition [can be] to be false in some other than the Russell sense", even compares it to chess, a game with arbitrary rules! Latter Wittgenstein believed we "play" a variety of different overlapping "language games", _none_ of which hold any kind of primacy: mathematics is just a "real" (or whatever) as poetry, they are just different games with completely different rules and different standards for correctness. (Briefly addressing a misreading in [2], that's also relevant for understanding this, for Wittgenstein the highest level of certainty is not analytic proof, for they are vacuous, but rather his standard for the highest level certainty is "I am certain that I have never been to the moon", while completely admitting the faint possibility that he is instantaneously transported there and back each time he blinks his eyes. For Wittgenstein, certainly is not impossibly of the opposite, but a claim made by a knower-of-things: staking your reputation as a "knower" on something being true).

The author's "Godelian" rebuttal mistakes the claim that "‘True in Russell’s system’ means, as was said: proved in Russell’s system" as Wittgenstein's assumption. It isn't. It's Russell's, and just one of the rules that comes along with playing this particular language game. Wittgenstein is saying: So what if we can show though some series of transformations that some proposition can be constructed that violates some other rules of truth and falsity? We already started this game with our definitions (the provable being definitionally true and opposite being provable being definitionally false _in_ _the_ _Russell_ _system_ ). This is very much so part of Russell's system, which Wittgenstein describes in detail in the previous seven sections of these lectures notes, which also get at best passing mention in this paper. Such Godel sentences are simply out of scope for what Russell's system is good at (Russell's language game about logic/mathematics), by the _very_ rules of the game. Russel hoped to describe the totality of the world with it so this was a problem for him, Wittgenstein always thought that whole goal was utter nonsense. Wittgenstein is not directly addressing Godel's theorems, he's just calling them irrelevant to this particular game ("the Russell system") which many people play, and he is teaching his students how to.

A language game not being sound and complete just doesn't matter to Wittgenstein. He proved the very idea of that was nonsense way back when he was a kid writing the Tractatus. Instead, they would have to claim it to a _bad_ or useless language game (or, better yet, come up with a better one that fulfills similar needs in our lives) to strike against it.

Link [1] above misses his point so entirely, the entire debate sketched out there just has nothing do with what he said, and that author is tying himself into knots trying to represent Wittgenstein's arguments with his symbolism. I can understand why Wittgenstein would get so frustrated he would stand with his back to everyone and read poetry... That selective quoting in this case is particularly egregious and not typical of philosophical scholarship, I wouldn't get discouraged. It looks like this author's primary focus is "to spell out a Wittgensteinian alternative to mathematical logic", so he _very_ much so has a horse in this race.

Cora Diamond and James Conant both have significant amounts of work on Wittgenstein and are both beyond excellent.

I hope this doesn't sound too mystical woo-woo to you, but its not about understanding concepts, its about understanding what happens after concepts. There is more to life than logic, and logic, while useful, should help one to understand that.

* * *

> how high school students need simplified versions

That's how I interpreted it.

One problem with 'ladders' (i.e. intentional use of simplified explanations) is that if someone is taught the simplification but never realises there's more to it, they can think they know how something works when in fact they don't, which could be worse than not knowing at all.

That set of qualities (being wrong but certain they're right) reminds me of the 'midwit' meme.

Wittgenstein tries to explain how language works, how it represents the world. One consequence of his theory is that language cannot represent that relationship itself. (At one point, he compares this limitation to the way that an eye necessarily can't see itself.) Well, if you believe that, what's the point of writing the Tractatus? So the ladder metaphor is supposed to suggest that contemplating the Tractatus might lead the reader to grasp the nature of language, even as they ultimately realize that a book can't really depict that straightforwardly.

One source which I've found very accessible on this topic is Bryan Magee's interviews of John Searle: https://www.youtube.com/watch?v=qrmPq8pzG9Q&list=PLB72977AF4...

Hold up. You can see your eye just fine by looking in a mirror. Where's the problem?

I think parent comment meant that one can’t use the eye to see itself directly without using any intermediaries like mirror or photograph.

Obviously, but why isn't the use of an intermediary allowed in this metaphor?

It's allowed, but once you've used a mirror to understand your eye, you don't need the mirror anymore.

Technically it’s entirely possible given sufficient gravitational bending.

The eye can't see inside of itself. The metaphor breaks down though, because the inside of an eye are in principle _seeable_ (mirrors and microscopes etc), while the "nature of language" or whatever, is in principle _unspeakable_ , no so much as a coherent thing to ask after.

Well, you are not really seeing an eye in a mirror, you are just seeing a representation of it. The medium cannot depict all the dimensions and details of the object, so again you are able to see depictions, representations, and simplifications of it, but never truly be able to grasp the object itself.

Right, it's a three dimensional object projected onto a two dimensional surface and your knowledge about it, from looking into the mirror, is merely superficial. What's to say our world isn't a five dimensional space projected onto four dimensions? What can language say about anything, everything, and the universe when great amounts of it is hidden from us?

Sure you can say that everything I see is technically a representation in my head. But there is very much a shared reality, a domain of objects and state of affairs for which we both agree about the presence or absence of the same representations. There's a difference between a value and our measurement of a value. If every multimeter we touch to a battery reads 5.9v, its possible the battery is actually 6v and every single multimeter was coincidentally wrong. However from the inside the situation is indistinguishable from a 5.9v battery. We may as well accept the reality of our perception and its representations as the real thing per se, because even if it is delusion we are still stuck playing by its rules as if it were real.

I am "really" seeing an eye in the mirror in the sense that I'm seeing the same thing other people would call an eye, and thus it exists in the shared domain. To have a shared domain of objects and facts is to have a common ground. There is no "object itself" for us to reach out and grasp outside of our mutual perception of objects. We might all be in a computer simulation. Doesn't matter. The conversational/perceptual reality is reality.

Even better, you absolutely see things in your eye. They're called "floaters". Your brain learns to mostly ignore them.

And if you develop cataracts, your vision tends to "yellow", and you'll be seeing more and more of the lens of your eye, as it becomes less transparent. Cataract surgery (= replacing natural lens with plastic lens) can lead to the operated eye seeing "bright" and un-operated one "yellow".

Thanks, that's actually a much better explanation than the one on wikipedia

Exactly this, but even more so. Wittgenstein believed the purpose of philosophy is to "prevent the bewitchment of our senses by means of language". Throwing the ladder away is important, else the reader might mistakenly interpret the tractatus as being the ultimate systemization of reality, rather than a critique of all such projects.

Fantastically, our modern obsession with truth-tables when studying logic comes from exactly this misreading! (Which also lead to Wittgenstein quitting philosophy for years.)

Wittgenstein was initially received by Bertrand Russell, and by the various positivists of the time as a possible intellectual giant who could champion their various projects. But he sews the seeds in the end of the Tractatus of the criticisms that would be developed more fully in his Philosophical Investigations, which is sometimes read as a repudiation of his own earlier work.

I don't think he intended with his ladder metaphor to fully repudiate the Tractatus, I think the purpose of the Tractatus evolved over the course of him writing it. Otherwise the second half of his philosophical career would have just been an endorsement of the Tractatus rather than retrospective criticisms of it.

The tractatus isn't like the blue and brown notebooks, where we just grabbed random notes of his after he died and published them for future generations to study. It's an intentional published work. He means everything he says in it the moment it is published.

He _definitely_ evolves the view presented throughout the course of the tractatus, but this is intentional, walking the reader up the ladder, the last step of which is throwing the ladder (the tractatus) away.

The relation between early and late Wittgenstein more complex than outright repudiation. Immediately after the tractatus he thought he solved the problems of philosophy, and later came to realize simply destroying the positivist project was not ask there was the problem of philosophy.

On Russell, hilariously, he would organize readings of the tractatus with the Vienna circle. Wittgenstein would be so furious with their interpretation he would sit the room with his back to them and talk Indian poetry aloud.

So it's the third of GPs options:

> achieving mystical realizations along the lines of zen koans

Except that there's really nothing mystical about zen koans, if mystical is meant in a derogatory way as vague mumbo-jumbo. Zen koans are trying to do the same thing as Wittgenstein is (according to the parent - I haven't read him): lead the thinker to recognise the limitations of language, and in particular its inability to fully express ideas about its own limitations. The response "mu" unasks the question, indicates that the concept has been understood but the question itself seen as nonsensical.

That's my understanding anyway. I haven't practised Rinzai Zen, the one that emphasises koans, but only Soto Zen, which mostly eschews philosophising in favour of just sitting quietly.

>lead the thinker to recognise the limitations of language, and in particular its inability to fully express ideas about its own limitations

Right, I think that's a good way of putting it. He even writes in the Tractatus about how we can see with our eye, but we can't "see" the limits of our visual field. (Edit: I see now that GP mentioned this, which I missed while skimming.)

I think Wittgenstein would have credited those higher meanings with significance and not divided them as mumbo jumbo. In a way you're supposed to apprehend that those things that mean the most are not the things that language is capable of representing.

If I can respond to Wittgenstein here:

> he compares this limitation to the way that an eye necessarily can't see itself

On the contrary, language is both perception and action. And it is also a self replicator: language -> model or brain -> language. I think that's why LLMs are so great - they rely on this medium that is both receptive and emissive, unlike other modalities.

> this is about how e.g. high school students need simplified versions of how an electron works (a point) before college students learn the reality (a cloud), then it seems banal

Why is it banal? Just because you already understand it? It's an important idea that comes up all over education, and isn't often explicitly mentioned.

>If this is about achieving mystical realizations along the lines of zen koans, then OK but what has that got to do with Wittgenstein?

The Tractatus Logico-Philosophicus is, in my view, a mystical text. Its use of mathematical-like notation and arguments make it seem like something akin to Russell and Whitehead's Principia Mathematica, or Language, Truth, and Logic, but it is really quite different, with totally different aims and methods. It is not aiming to prove or instill in the reader any kind of propositional knowledge, despite its format. The statements at either end of the text (1. and 6.) are often quite obscure in their meaning. The point is, in my view, to induce the reader to change his mindset, and to discard his previous philosophical beliefs, rather than to acquire new ones.

It's very much intended to be a tearing down of such projects "from the inside". Back in the day, philosophers _actually_ _believed_ they could write down a series of proposition that fully and completely described reality. They even thought they were discovering the fundamental nature of reality with whatever new symbolic logic notation they came up with that week.

I guess they stopped making people read Kant for a while there... These were solved problems

Closest to koans, but more practical, less of a blind leap.

The intermediate work is required to reach the goal, but not useful once there.

Like releasing a sex tape to get famous.

Perhaps Foucault could make things a little bit more clearer, which as philosophy goes, the clear is always muddier, muddled with more questions: "I don't say the things I say because they are what I think, I say them as a way to make sure they no longer are what I think. [...] To be really certain that from now on, outside of me, they are going to live or die in such a way that I will not have to recognize myself in them." [1]

One other thing, pertaining to philosophers and learning, is to account for the distinction between "learning" and "training" or even "taming". Learning is something which comes from inside, Plato would call it anamnesis [2], a kind of remembering of innate knowledge, having Socrates show that a slave already knew mathematics in the dialogue Meno.

This is one of the reasons why Plato hated sophists, or if he could, despised the self-help literature of today: help, knowledge, learning can only come from inside [3]. This is also why Plato would say "machine learning" is a misnomer, the machine doesn't learn from an inside, but it is forced by us, the outside, to learn, even in unsupervised learning, it's actually "machine training".

Hence why Wittgenstein and Kierkegaard (and even Heidegger) advise against thinking that one can learn to be from someone else: authenticity is a process, not a fact.

[1] From minute 14, but the whole interview is interesting, https://www.youtube.com/watch?v=qzoOhhh4aJg

[2] https://en.wikipedia.org/wiki/Anamnesis_(philosophy)

[3] An example of this in micro would be a transistor (or a voltage-gated ion channel): once they establish their form, being able to switch states between 0 and 1, suddenly they have access to an entire new realm, the truth table, which was always there, somewhere (Plato would call this ἰδέα, form, idea [4]).

[4] https://en.wiktionary.org/wiki/%E1%BC%B0%CE%B4%CE%AD%CE%B1

So from mathematical logic we know that if you take a simple statement you can have a formal statement equivalent to it[0]. For example, 'not all frogs are green', or 'quadrupeds are four-legged animals'. For the logical form there is a mathematical procedure that let's you verify its meaning (reduction in lambda-calculus, or equivalently a proof tree). However, these statements are not very interesting![1]

So what are 'interesting statements'? That would be something that has some deeper meaning, philosophical ideas (let's call them 'general ideas'). If we wanted to use the same approach, we would need to encode all the necessary concepts through predicates or compose them in logic functions or formula fragments. Of course, to arrive at a concept such as 'philosophy' the endeavor would be enormous. Even if you managed to do it, would your encoding be recognized as 'philosophy' by everyone else?

Instead, we communicate with these general statements that requires that you reduce them to simpler statement that actually mean something. Let's take 'the early bird gets the worm'. You need to take some examples to think 'what does it mean in this situation'? You can try to falsify and work with it like a hypothesis. You get some understanding from that process and not from the statement itself. Can it be called the meaning of the statement? Not really, because there is no way to associate to a simple mathematical process, it depends on each individual's mental process. And given that, how can you be sure of what exactly is the idea that you're communicating?

If you understand these general ideas, and that you cannot communicate them except to people that already understood them, these statements are meaningless in a certain sense [2].

You can say that "but we communicate about these things all the time". But how well? There's a an anecdote due to Lucian about two people talking to each others without really understanding anything, so he went to them and asked "doesn't it seem to you that one is trying to milk a billygoat and the other is handing him a colander?".

[0] you just need to provide a precise definition for all terms and associate a predicate for each property of interest. It's a slog to do but it's something that is done, for example in engineering when you need some safety properties.

[1] That was identified as the inanity of mathematics; you can only prove tautologies. In a way what you can salvage from this procedure is that some statements are meaningful, whereas some are not (e.g. Russel's paradox)

[2] A concept that helps is Quine's "indeterminacy of translation"

Wittgenstein's Tractatus is about "playing" philosophy, using its rule, until we prove that what has been said since the beginning is pure non-sense.

Think about proving that a problem cannot be solved in maths.

The problem with Wittgenstein is that his terms are very specific and their meaning is very precise. When one reads “nonsensical” in that sentence one tends to think “ah, so they are stupid” whereas he likely means “they do not represent the world” (no-sense: without reference), which for Wittgenstein is true because language is unable to grasp “the thing itself” (the “state of affairs, in his terminology).

That is my understanding anyway.

Yeesh. Not a single good explanation here.

The only reason the "point" version of electrons is a valid "step" on the ladder to the "cloud" version of electrons, is it's plausible. You are capable of fully believing it before recognizing it as bullshit once you use it as a foundation to learn the next step.

Such intermediary steps aren't easy to create. The best ones come from history, from time periods where we had an outdated but plausible theory (point to cloud electrons, flat earth to round earth, etc.)

The "step" is a flat surface you can stand on. Ever try to learn some math concept from wikipedia? It's impossible, right? To understand X you must understand Y, and to understand Y you must understand X. You break this cycle by telling the learner "Don't look into Y, it's already a solved problem, just trust me". Then they can focus on X and fully learn it without being distracted.