Wittgenstein's Ladder
en.wikipedia.org
en.wikipedia.org
But after reading this Wikipedia page and then Googling it and then reading MollyRealized's ChatGPT explanation in a sibling comment...
...I have utterly no idea what the heck this is supposed to be.
If this is about using nonsense to explain something in philosophy, that seems awfully silly.
If 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.
If this is about achieving mystical realizations along the lines of zen koans, then OK but what has that got to do with Wittgenstein? And it seems like a Wikipedia article ought to mention this.
So I'm baffled. I think I need a ladder to help me understand this ladder? And understand why this was submitted to HN in the first place?
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...
Fantastically, our modern obsession with truth-tables when studying logic comes from exactly this misreading! (Which also lead to Wittgenstein quitting philosophy for years.)
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.
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.
> 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.
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.
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".
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.
> 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.
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...
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?
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.
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...
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.
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.
I guess they stopped making people read Kant for a while there... These were solved problems
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.
A more intuitive way for programmers to come at it may be this:
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.
That is my understanding anyway.
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. Whereas, training and taming are always outside pressures.
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". [4]
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 [https://en.wiktionary.org/wiki/%E1%BC%B0%CE%B4%CE%AD%CE%B1]).
[4] Just to get political for a second: this is also why "police training" and "military training" will only produce sociopathic, murderous, PTSD-stricken shells of a human being: an external force, the state, the tradition, sociopathic leaders, sociopathic societies, is obliterating any sense of internal learning, from empathic de-escalation to removal of the preconditions of violence altogether.
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.
The intermediate work is required to reach the goal, but not useful once there.
Like releasing a sex tape to get famous.
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"
I have kicked away
the ladder
which transcends
these propositions
and which
you were probably
climbing
to see the world aright
Forgive me
whereof one cannot speak
one must pass over
in silence.CHATGPT: Sure! Wittgenstein's ladder is a metaphor used by philosopher Ludwig Wittgenstein to explain how language and ideas work.
Imagine you want to get to the top of a tree. At first, you might use a ladder to climb up. But once you get to the top, you don't need the ladder anymore. You can throw it away or leave it behind.
In the same way, Wittgenstein argued that language is like a ladder. It's a tool we use to get to a certain point, but once we've reached that point, we don't need the language anymore. We can throw it away or leave it behind.
For example, imagine you're learning to count. You might use your fingers to help you count to five. But once you've learned how to count to five, you don't need to use your fingers anymore. You can count to ten, twenty, or even a hundred without needing to use your fingers.
Wittgenstein's ladder is a reminder that language is a tool we use to reach a certain goal, but it's not the goal itself. Once we've reached the goal, we don't need the language anymore.
ME: Why is this concept useful? Don't we always need language, simply to communicate with those around us?
CHATGPT: You're right that language is essential for communication, but Wittgenstein's ladder is more about the nature of language and how we use it to think and talk about the world around us.
The ladder metaphor is useful because it highlights the idea that language is not fixed and unchanging. Rather, it's a flexible tool that we can use in different ways to achieve different goals. Sometimes, we need to use language in a precise, technical way to communicate complex ideas, while other times we might use language more loosely and creatively to express our emotions or share stories.
Wittgenstein's ladder can also help us recognize when we're using language in a way that's no longer serving its original purpose. For example, if we're using technical jargon to communicate with someone who doesn't understand it, we might be climbing up the wrong ladder. We might need to switch to a different ladder (i.e., a different way of using language) that's more accessible and useful for the person we're communicating with.
Ultimately, the concept of Wittgenstein's ladder reminds us that language is a tool we can use in different ways to achieve different goals. By being aware of how we're using language and why, we can become more effective communicators and thinkers.
>My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)
It is his propositions (the propositions he lays out in the Tractatus - the book is structured as a list of propositions) that form the "ladder", not language itself.
I'm really not looking forward to people having dozens of hours of hallucination-filled conversations with ChatGPT and then thinking that they've learned something. (I've already seen it tell someone that "C++ is typically compiled to intermediate code and executed on a virtual machine, making it less performant than C".)
(Just read the Wikipedia page, c’mon.)
But to your point: it may not at all be accurate in terms of asking for a specific definition of a thing.
Is AI going to screw up semantics for us? Where we muddy the meaning of things like above?
That's probably an oversimplification and wrong in some way, happy for someone to correct me. But that was my takeaway from reading a ton of philosophy and eventually reading Wittgenstein and feeling "cured".
> We use words as tools to get things done; and to get things done, we improvise, making use of whatever materials are ready to hand. If you want to whack a piece of sheet metal to bend it, and don’t know or care what the “right” tool is (if there even is one), you might take a quick look around the garage, grab a large screwdriver at the “wrong” end, and hit the target with its hard rubber handle. A hand tool may have one or two standard uses; some less common but pretty obvious ones; and unusual, creative ones. But these are not clearly distinct categories of usage.
> Words go the same way. Almost any word can be used to mean almost anything, in some context. You could play this as a challenge game… How about “The eggplant is a straw hat, and the spinach is yelling about politics”?
> We’re in the kitchen of a vegetarian restaurant. A table’s entrees are ready, and the server who took the order is explaining to the one who will deliver the meal which diner gets which dish. One customer’s flamboyant straw hat is a salient, unambiguously identifying feature; you can see it all the way across the room. The other probably needs to turn up a hearing aid; you can hear their opinions about cultural appropriation all the way across the room.
https://www.accesstoinsight.org/tipitaka/mn/mn.022.than.html
1] Nāgārjuna, Nietzsche, and Rorty’s Strange Looping Trick
Philosophers have lots of tools and tricks up their sleeves. They, of course, can use formal argumentation, they can employ all sorts of thought experiments to elicit various intuitions, they can lay out examples, dilemmas, dialectics, and do a whole host of other things. But I want to talk about one particular trick that only a select few philosophers have employed. This trick involves wrapping everything up in a philosophical system only to have that system knock itself down by its own internal means, and doing all in order to produce some sort of anti-philosophical result. I’ve come to call this the “looping” trick, and it’s one of the most philosophically curious things that I’ve ever stumbled upon.
[1] : https://absoluteirony.wordpress.com/2014/09/17/nagarjuna-nie...
This seems similar to a ladder of physical competence, but applied to philosophical reasoning. It's not clear to me that there is a there there outside of math, physics, (and increasingly computation) where you have to physically practice the calculations to arrive at the conclusions, whereas I don't think philosophy has an analogous objective competence. Ironically, some mysticisms like meditation (and perhaps even prayer) may even have a higher bar because they are a physically transformative competence akin to practicing music, whereas attaching yourself to an academic and fundamentally political consensus doesn't have the same honest signals or investment.
The issue there is that while meditating leads to "something" happening for sure, almost nobody is going to stop to check if it's the right "something" and the teacher can't look inside your mind. So you might just have a mental breakdown then decide that's proof you're "enlightened".
(Was going to quote David Chapman here but someone already did in this thread. But I mean, it's how most cults or New Agey religious groups start.)
Conspicuously, there is no honorary enlightenment either.
I’m not completely in agreement with this philosophy if indeed my interpretation holds water.
A related concept to this interpretation is Eno’s oblique strategies deck or random word decks.
Basically to include extensive caveats and exceptions in the first explanation is to risk overwhelming the novice.
I think that's what this is. Sort of just moving from a high level understanding to a lower level one. Is there more to it?
This is more of a sabotage mission, where the examples are meant to convince of their own inadequacy (and the inadequacy of rigid logical thought).
Full disclosure, I'm not a fan of Wittgenstein at all (I wish he were less studied in universities), and I think his Tractatus is nonsense (though not because I'm climbing his ladder) and an abject failure.
† Which is a real thing, but I'm not sure if it's completely correct to use here.
[1] https://plato.stanford.edu/entries/causation-metaphysics/
The lead editor of the SEP is a big Frege guy, and unfortunately, the site is extremely biased on anything tangentially related to Frege, and unfortunately this is one of those areas.
This is a very dubious claim, and you'd probably never hear the end of it if you claimed this in a graduate philosophy course at any reputable university. (There's probably some arguments to be made here, but still.) Of course, Wittgenstein later changed his course, but he was instrumental in popularizing logical positivism in its early days, unwittingly or not. The Tractatus was like contraband.
Once you understand some "model" it does not matter what are the words you gave to the components of the whole and the relations between them. You would create such a model out of colored wires. You could attach a note to each wire giving it a name. But the name does not really matter, the connections between the wires are an accurate presentation of reality. Once you have such a wire-model you can throw out the words.
His thoughts on group classification are the most crisp refutation of classic logic I've ever heard, far better than Godel. Godel worked inside the system, Wittgenstein challenged it from the outside.
I have been contemplating the use theory of meaning recently, and it’s direct implications for generative language models.