6 ms·

Bhartrhari's Paradox

61 points by surprisetalk 19d ago

goodmythical 25d ago
Are there actually things that cannot be named? Any such thing could easily be assigned some such "Phenomenon 8x306Q". If any two people agree to call it that and use that to succesfully discuss the thing, then that is a name for the thing. Otherwise nothing can be named. Is the cat in your house really a cat, or is it a Felis catus? How can we be certain that it's not a gato or a кот? If the cat in your house is indeed a кот, gato, Felis catus, and cat, then Phenomenon 8x306Q can certainly be Penomenon 8x306Q as much as it is "familial bonds strained by misdeeds" or whatever the things we're naming is.
- nofriend 25d ago
  The proof is simple: there are countably many names, but uncountably many real numbers. Hence, some real numbers must be unnameable.
  - goodmythical 23d ago
    Are there countably many names? Countably sayable, perhaps, but I don't recall seeing any limitation to word length in the spec. See: "Below is the full 189,819-lettered word for 'titin':" at https://cw39.com/wp-content/uploads/sites/10/2020/09/longest-word.pdf https://cw39.com/wp-content/uploads/sites/10/2020/09/longest... as an example. Surely if we can have a 189,819 lettered word we can have a million billion trillion lettered word or an uncountably lettered word. They'd be used in the same way as the really long numbers in that we'd give them some other handier name that collides when not given context. e.g. In spoken language pi/pie are often confused if the conversation does not already have a mathematical context and no one says 3.1415926535... conversationally just as no one uses the lenghtier version of chitin and no one would use the uncountably long name for some uncountably long number.
    - nofriend 23d ago
      names have to be finite in length. i think that's pretty obvious
      - goodmythical 22d ago
        I don't see how that's any more obvious than the suspicious claim that numbers can have only so many digits.
        nofriend 22d ago
        A number is not in the first place its digit sequence. A number like pi is in the first place the ratio of a circle's diameter and its circumference, and only incidentally a certain (infinite) decimal expansion. A name is in the first place something you say, hence the thing you say has to be (at least theoretically) sayable.
- dang 19d ago
  (This is an older subthread which I moved hither because a different submission happened to make it onto the frontpage)
snapcaster 19d ago
I'm open to the idea that some things are unnameable but would need an example :)
- loa_in_ 19d ago
  I'll write you as soon as I can
kranner 19d ago
The Herzbergers' paper: https://sci-hub.ru/10.1007/BF00202726 https://sci-hub.ru/10.1007/BF00202726
- rramadass 19d ago
  Thank You. Bhartrhari (https://en.wikipedia.org/wiki/Bhart%E1%B9%9Bhari https://en.wikipedia.org/wiki/Bhart%E1%B9%9Bhari) is a pretty difficult philosopher who seems to be enjoying a revival now due to the ascendancy of AI LLMs and the question of whether they can be considered as having "consciousness". His central idea (highly simplified) is that since Language is the only way we can name objects and discuss relations between them it is synonymous with "Reality" and "Consciousness". Sort of like how the properties of an object define that object (ADTs anyone?). One can imagine that the use of language by LLMs gives birth to appearance of both consciousness and reality as "emergent phenomena" in it. In his theory of "Sphota" he posits that "meaning bursts forth" (in consciousness) as an indivisible whole when a complete sentence/sentences is/are uttered (is this what happens when LLMs do reasoning and generate text within a "context window"?) Perhaps Epistemology and Ontology are just two sides of the same coin. Some resources for further study; 1) Bhartṛhari’s Linguistic Idealism - https://loc.closertotruth.com/theory/bhart-hari-s-linguistic-idealism https://loc.closertotruth.com/theory/bhart-hari-s-linguistic... 2) Bhartrhari on Language, Perception, and Consciousness - https://academic.oup.com/edited-volume/27982/chapter-abstract/211665674?redirectedFrom=fulltext https://academic.oup.com/edited-volume/27982/chapter-abstrac... 3) The Word And The World: India's Contribution To The Study Of Language by Bimal Krishna Matilal - https://archive.org/details/wordandtheworldindiascontributiontothestudyoflanguagebimalakrishnamatilal_202003_376_e https://archive.org/details/wordandtheworldindiascontributio... 4) Sabda: A Study of Bhartrhari's Philosophy of Language by Tandra Patnaik. This is particularly scholarly with the author comparing western authors (like Frege and Wittgenstein) model of language with Bhartrhari - https://test.dkprintworld.com/product/sabda/ https://test.dkprintworld.com/product/sabda/ 5) The Sphota Theory of Language by Harold Coward - https://www.mlbd.in/products/sphota-theory-of-language-harold-g-coward-9788120801813-8120801814?variant=49213095739678 https://www.mlbd.in/products/sphota-theory-of-language-harol... 6) Sphota - https://en.wikipedia.org/wiki/Spho%E1%B9%ADa https://en.wikipedia.org/wiki/Spho%E1%B9%ADa
GPerson 19d ago
If we assume the real numbers exist, then perhaps the paradox resolves because there are uncountably many reals and only countably many nameable things, but then perhaps the paradox does not resolve because we assume ZFC is true and we can well order the reals, hence name the first unnameable real.
- mark_something 19d ago
  The reals can be ordered, just use x < y. I think you mean that if ZFC is true, we could enumerate unnameable reals (choose one with the axiom of choice, remove it, choose another one, etc.), but you could not enumerate them all. But it is true that you could get a "first" unnameable real.
  - pdonis 19d ago
    > The reals can be ordered, just use x < y. That ordering is not a well-ordering, which is what the GP specified. A well ordering requires that every non-empty subset has a smallest element. That's not true for the reals ordered by x < y: for example, the set of all reals > 0 has no smallest element. No one has explicitly shown that the reals can be well ordered, but it's a consequence of the axiom of choice that every set can be well-ordered. So in ZFC there must be a well ordering of the reals, even though no one has found one. Issues like this are why not all mathematicians accept the axiom of choice.
    - simonh 19d ago
      Not a mathematician, so this question may be a bit thick. I see the problem with the set of reals > 0, but is it perhaps that in this case > 0 is the problem and for sets specified as >= 0 it's fine because 0 is a nameable real and the smallest element. Obviously you can't just exclude certain expressions arbitrarily though, so I don't know how you could justify that mathematically.
      - GPerson 19d ago
        A well ordering on a set is a total order such that all non empty subsets have a minimum element with respect to this order. The standard ordering of the reals is not a well ordering, but the axiom of choice is equivalent to the statement that all sets possess a well-ordering. A well-order of the reals would probably look pretty chaotic though.
curtisblaine 19d ago
How is it a paradox? Isn't this just a proof that there are many unnamed things, but no unnameable ones?
- WillAdams 19d ago
  Agreed. This is the stuff of magic and folklore, and neatly resolved by Ursula K. LeGuin in _A Wizard of Earthsea_.
- bwfan123 19d ago
  > Isn't this just a proof that there are many unnamed things, but no unnameable ones? Where is it a proof that there are many unnamed things ? I could only see it as an argument that there are no "unnameable" things.
  - curtisblaine 19d ago
    It depends how you define "named", but for example, not all the grain of sands you see on a beach are named (yes, they are named collectively, but not individually. If "collectively" is valid, then that's further proof that "unnameable" things can't exist, because they already have a collective name).
- arjie 19d ago
  Many ancient paradoxes are not really paradoxes. Zeno's ones are resolved today with infinite series. But this is a real one. Is it possible to describe an arbitrary real number? Almost all reals are not describable. But you cannot find a single such number. The 'paradox' is that the search itself is self-failing - a broken strategy. Of course, now we have the language of sets and functions between them and cardinalities and we resolve this for us in a way that is meaningful. But still now you know the 'existence' of this thing? Can't be described. It's interesting because of the property of creating with finite words universes of infiniteness.
- rramadass 19d ago
  See the original paper linked to here - https://news.ycombinator.com/item?id=49478566 https://news.ycombinator.com/item?id=49478566
gaoshan 19d ago
If you can't name it you can still describe it. But then by describing it you are committing it to a set of conditions this unnameable thing satisfies. But then if you go beyond a narrow interpretation of that paradox and accept that naming and describing are both accomplishing the same fundamental thing, that being committing a thing to a condition (like a name) or set of conditions (like a description), you do run into the same problem. Hmm, interesting. Now back to this E2E testing stuff I've been avoiding.
- bwfan123 19d ago
  Names are like variables in a function. you can name variables anything you want from a human understanding point of view (final cause), but the compiler doesnt care about that. The compiler only cares about the efficient cause of that variable in the sense of what it represents (stack/heap etc).
- deleted 19d ago
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- LanceH 19d ago
  In mathematics, there are infinitely many "computable" numbers. That is, numbers which can be describe using any mathematics available. Then there are far more "non computable" numbers, which can't be described by anything finite. I think there is some analogy to be made here.
cyanydeez 19d ago
Sounds akin to the complexity inherent in cellular automata. We know via the rules how to mutate successive generations, but backwards propagation, algorithmic simplification, etc may exist but not traceable from any given ruleset.
ngvrnd 19d ago
„Wovon man nicht sprechen kann, darüber muss man schweigen“ but if the thing can be interacted with, it can usually be mapped and defined and then named. But there will always be things which do not have names, at least in mathematics -- think of the real numbers.
- deleted 19d ago
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- abnry 19d ago
  I suppose if the number of nameable things is countable (because humans can only enumerate, and it is humans who name), then it trivially follows that some real numbers are unnameable. Which proves the existence of such entities. This reminds me of a YouTube video I watched this week titled "A counting argument for why mind comes before matter": https://youtu.be/AtduNjJV-6E?is=nBZ9ztZsyeoVhCj1 https://youtu.be/AtduNjJV-6E?is=nBZ9ztZsyeoVhCj1 The argument is something like the set of possible thoughts about physical objects is larger than the physical objects themselves. It feels similar in flavor to the idea of unameable objects. There's something special about a name. The name of the God of the Bible is special. Christians are to call upon _the name_ of the Lord. We pray, hallowed by _thy name_. It is somehow denotes the summary essence of the thing being named, even if it doesn't give specific details of its characteristics.
  - conmod278 19d ago
    The Beauty of Bézier Curves https://youtu.be/aVwxzDHniEw?si=tPPRId1y5L7U2_5L https://youtu.be/aVwxzDHniEw?si=tPPRId1y5L7U2_5L Name_I = a*lambda + b (1-lambda) lamda is a real number.
- bryanlarsen 19d ago
  "Unnameable" and "unnamed" are two different things, in my opinion. Are there real numbers that are unnameable or are those just unnamed? There are some that unnameable with my mathematical understanding, but that's not saying much.
  - 19d ago
b450 19d ago
counterargument: 1) let x be a thing 2) I name x "Jeff" 3) all things are nameable (from 1 and 2) another way to put this is that it's natural to take the paradox as a reductio.
- crimsonspy 19d ago
  Jeff jeff jeff, jeff jeff jeff jeff! Jeff? Jeff.
- amavect 19d ago
  You proved that definable implies nameable, and also unnameable implies undefinable. Obviously true. However, the idea of undefinable real numbers closely resembles a modern version of the paradox. No surjective function exists from definitions to real numbers. Really, the blurb about "seems impossible to verify this by giving positive instances" contains the tension between constructive math and non-constructive math. Does an unnameable (and undefinable) thing actually exist? If a tree falls in a forest, but no one can hear it, does it make a sound?
  - onraglanroad 19d ago
    > No surjective function exists from definitions to real numbers. I'm not really up on maths so this is possibly a stupid question, but can't any real number be written as an ASCII string, which is basically an integer number, so there is a direct mapping there? Or is it because the ASCII number wouldn't be in order that makes the difference? Or is it that you can't write that mapping as a mathematical function perhaps?
    - onraglanroad 19d ago
      Actually, and perhaps sadly, I asked an LLM and I understand now. But perhaps that's not such a bad thing that I can get answers to my foolish questions!
      - amavect 19d ago
thinkzilla 19d ago
c.f. the Berry paradox https://en.wikipedia.org/wiki/Berry_paradox https://en.wikipedia.org/wiki/Berry_paradox
Zhyl 19d ago
The Way that can be walked is not the eternal Way. The name that can be named is not the eternal name. -- Lao Tzu, Tao Te Ching
Xcelerate 19d ago
Pretty sure ZFC proves such things exist (and that it also can’t pinpoint any individual instances of course). Now, whether syntactical “∃” in the formal language of set theory corresponds to the platonic existence of some “thing”, who knows.
lordnacho 19d ago
This reminds me of the 6 degrees of separation thing. People tell you that you can connect more or less everyone by 6 degrees. But what struck me was, for anyone you try this with, you know their names, so you've already restricted yourself in how far out someone can be.
svat 19d ago
Incidentally, it is a matter of some debate whether Bhartṛhari the philosopher and Bhartṛhari the poet are the same person or two (or more, in the case of the anthology of verses). Oral tradition holds them to be the same person, scholars have debated back and forth. I have a collection of the poems here: https://shreevatsa.net/bhartrhari/web/ https://shreevatsa.net/bhartrhari/web/ (will clean it up someday)
- rramadass 19d ago
  Nice. I have the A.N.D.Haksar, Purohit Gopinath translations of all the Satakas and Swami Madhavananda's translation of the "Vairagya Shatakam". Need to get the others ;-) Also see https://news.ycombinator.com/item?id=49486845 https://news.ycombinator.com/item?id=49486845
  - svat 18d ago
    I couldn't add the Haksar translation as it's still under copyright, but the site has the other two. Plan to add others like M. R. Kale's (https://github.com/shreevatsa/bhartrhari/issues/11 https://github.com/shreevatsa/bhartrhari/issues/11) — just need a chunk of time one of these weekends.
    - rramadass 18d ago
      One thing you might want to add after each author's name is which categories (viz. Niti, Shringara and Vairagya) they have translated. Due to excessive prudishness many have omitted the Shringara satakam which is quite silly (this is what makes him "Human"). I got the Haksar and Gopinath editions specifically because they include all three categories. A.N.D.Haksar in particular has translated many of the works in Sanskrit literature into easy English (including the Kama Sutra) and does not censor anything. Also i suggest that you add author names of all known translations of the work whether you have access to their actual text or not (due to copyright etc. reasons). That way your site can be a one-stop portal to Bhartrhari's Sataka-Trayam. PS: In case you don't already know of it; there is a much larger work in the Tamil language named Tirukkural which is also divided into three similar categories (viz. Aram, Porul and Kamam) the whole having a total of 1330 couplets (133 chapters of 10 couplets each). There are many English translations available of which the original Penguin edition titled "Kural" translated by P.S.Sundaram is pretty good and done in the original couplet style. For a more detailed study see the 2-vol translation with commentary by S.M.Diaz. Tirukkural - https://en.wikipedia.org/wiki/Kural https://en.wikipedia.org/wiki/Kural Tirukkural translations - https://en.wikipedia.org/wiki/Tirukkural_translations https://en.wikipedia.org/wiki/Tirukkural_translations
aabhay 19d ago
> There are some things that are unnameable Like what? Oh wait…
ogogmad 19d ago
This reminds me of how (I think) Zen koans are designed to make no sense at all. They are designed to teach you the limits of words and language and pure thinking.
- rramadass 18d ago
  > This reminds me of how (I think) Zen koans are designed to make no sense at all. True in a way. To understand how, note first the four stages of language given in my comment here - https://news.ycombinator.com/item?id=49491764 https://news.ycombinator.com/item?id=49491764 Zen koans don't have a meaning at the manifest (Vaikhari) and differentiated (Madhyama) stages. So you are forced to go back to the Intuitive/Holistic Meaning (Pashyanti) stage and thus realize "a burst of meaning" aka "a flash of insight" aka "Satori".
BiraIgnacio 19d ago
sounds like the paradox that _could_ illustrate Gödel's incompleteness theorems https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_th...
- rramadass 19d ago
  Russell's Paradox -> Hilbert's Program -> Godel's Theorems - https://news.ycombinator.com/item?id=49287595 https://news.ycombinator.com/item?id=49287595 Bhartrhari's Paradox can be said to be analogous to Russell's Paradox (though of course the latter is specific to mathematics/logic).
dredmorbius 19d ago
I see what you did there.
MrFiskarBengt 19d ago
"The Tao that can be told is not the eternal Tao"
hargup 19d ago
https://3quarksdaily.com/3quarksdaily/2014/03/boundaries-and-subtleties-the-mysterious-power-of-naming-in-human-cognition.html https://3quarksdaily.com/3quarksdaily/2014/03/boundaries-and... This is a beautiful article on the subject. To prove that there are unnamable concepts, he uses cantor's diagonal argument. There are countably infinite names. Any subset of these names is a concept, which is same as the powerset of the set of names, and through cantor's diagonal argument, there are uncountably infinite concepts, most which are not namable. Yes you can take a specific concept, and name it, but there are uncountably infinitely many, so even with infinite time, you cannot name them all.
- rramadass 19d ago
  Countable and Uncountable Infinities - https://philosophicaltreasures.com/countable-and-uncountable-infinities/ https://philosophicaltreasures.com/countable-and-uncountable...
- itemize123 18d ago
  i think there must be a scheme of naming that is uncountably infinite too.
  - deleted 18d ago
    [deleted]
whack 19d ago
Can't this also be used to justify things that are obviously nonsensical. Like for example: "I possess an immense undetectable sphere. How can I prove this? Well, any proof I offer you would by definition violate the undetectability of the sphere. So there's no way for me to prove it, I guess you'll just have to trust me bro."
- amavect 19d ago
  I love philosophy Calvinball, so I would counter by asserting that undetectable implies no possession, an immediate contradiction. Or go further and assert that undetectable implies nonexistence. We all possess an immense undetectable nonexistent sphere. No bounds on assumptions means I can make up anything to annoy the interlocutor. So, you're right. This shows why we should use formal math, so we can agree on the result yet bicker about the interpretation. Some folks point to Cantor's diagonalization theorem to show that some unnameable things exist, when the theorem doesn't say that at all.
raincom 19d ago
If 'it' is unnameable, there is no way to circumscribe or even describe what 'it' is. Even to show that what it refers to is an empty set, we need its description. If we use concepts like intention and extension, we can sketch out four scenarios: extension, no intension (yes, we can point out things, which we can't describe) extension, intension (we point out, and we describe) no extension, intension (Yes, we can imagine and describe things vividly, but no referent in the world. Here, one can say these things exist in a Platonic world, but not the world we live in; this is where numbers, sets, ideas can exist. Neo-Platonism in Philosophy of Mathematics) no extension, no intension (this paradox falls in this area).
kazinator 19d ago
The claim is false. There is not a thing that cannot be given a name. If it is a thing, it can be given a name. You take that thing into the discourse and say, "let this thing be X", and now it has a name. What cannot be given a name cannot be discussed in any way; it is completely vague, undefined or ephemeral. The inability to name it is not what is at the core of not being able to pin it down; it is a byproduct or corollary.
- Smaug123 19d ago
  You didn't name the object when you said "let this thing be X"; you actually had already identified that "thing", and that process of identification was the process of naming it. You then defined some syntax ("X") and said that it was a name. But there are things for which you can't even say "let 'this thing' be…". For example, ZF proves that there are uncountably many reals. There are only countably many names, so there must be unnameable reals. You can talk about "generic" reals (you can say "let x be a real" and do all sorts of interesting things with a generic x), but there are specific reals you will never be able to name specifically enough to distinguish them from their uncountably-many brethren. That doesn't make them "vague, undefined or ephemeral"! They're just so numerous that you can't describe the distinctions between them. (Even hardcore constructivists usually accept enough Choice to prove the reals uncountable, although https://arxiv.org/abs/2404.01256 https://arxiv.org/abs/2404.01256 made headlines when it was shown not to be necessarily true.)
  - itemize123 18d ago
    naming schemes can produce uncountably inf names
    - deleted 16d ago
      [deleted]
  - kazinator 18d ago
    > that process of identification was the process of naming it. No, it wasn't. Entities can be identified without being named, by relationships to other entities and class and such. That identification requires words. Not all denotational words and phrases constitute names.
Drophouse 19d ago
This is basically why art exists — painting, music, and poetry can point at things without having to name them. Language traps itself; other forms don't.
- rramadass 18d ago
  What you say is valid only when you restrict yourself to Western definitions/conceptions of language/linguistics i.e. study of Phonetics/Morphemes/Syntax/Semantics/etc. In Bhartrhari's Philosophy (and other Hindu philosophies) "Language" has a much broader definition which can encompass Art/Dance/Music/Painting/etc. Any medium of communication which can bring forth a "burst of meaning" (called Sphota) in one's consciousness is a language. Natural Spoken language based on Sound (aka Sabda in Sanskrit) is considered the most fundamental since you can have languages without a written script/symbols/diagrams. In Hindu philosophy, a "Language" is said to have four stages, only the last of which is the gross manifestation in the physical world; 1) Para - This is the latent undifferentiated potential which exists in everybody. 2) Pashyanti - This stage is where intuitive holistic meaning (of what you want to convey) exists. 3) Madhyama - This stage is where you have differentiated the thought/intention into an object and the means of representation for its communication. 4) Vaikhari - In spoken language, this is the manifest stage where you utter sentences according to established syntax/semantics to convey meaning. Note that the first three stages are internal and only the last is the medium of expression in the physical world. It should now be obvious that the last can be any medium (eg. Dance/Painting/Music/Written-Language/Sign-Language/etc.) as long as the receiver "gets" the intended meaning. PS: See also this comment of mine for further resources - https://news.ycombinator.com/item?id=49486845 https://news.ycombinator.com/item?id=49486845
__rito__ 18d ago
Bhartrihari was a king, philosopher, and poet. Scholars argue whether they were the same person or not, but I don't care, as scholars also argue about if Socrates really existed or not. He wrote 300 verses in Sanskrit. And they are on three different topics: sensuality and pleasure, policy and ethics, and finally renunciation. In Shringar Shatakam (100 verses on sensual pleasures), he writes: “Casting aside envy, considering the matter carefully, let the noble ones tell us, with due propriety: Which ought one to frequent — the slopes of the mountains, or the buttocks of women whose smiles are stirred by Love?” and “Why all this elaborate, pointless talk? There are only two things worth attending to in this world: the fresh, wine-intoxicated youth of beautiful women, heavy with their breasts - or the forest.” But in the final book, he realizes the folly of the senses, and writes: “Sensual objects will inevitably leave us, even after remaining with us for a long time. What difference is there between losing them and voluntarily abandoning them? When they depart against our will, they cause unbearable anguish; but when we ourselves abandon them, they produce the infinite happiness of inner tranquility.” Amazing character.
- svat 18d ago
  The third verse you quoted (https://shreevatsa.net/bhartrhari/web/K157.html https://shreevatsa.net/bhartrhari/web/K157.html) has a nice translation into English verse by Ryder: A REASON FOR RENUNCIATION Possessions leave us at the end, However long they stay; Then why not cast aside, my friend, What leaves us anyway? And if they leave against our will, The heart takes time in mending; If given willingly, they fill That heart with joy unending. The other two you quoted (https://shreevatsa.net/bhartrhari/web/K084.html https://shreevatsa.net/bhartrhari/web/K084.html https://shreevatsa.net/bhartrhari/web/K085.html https://shreevatsa.net/bhartrhari/web/K085.html) have also been translated, though IMO not as successfully.
- TFNA 17d ago
  No one argues about whether Socrates really existed. He is attested by multiple writers of the time. The debate is solely about how much the Socrates of Plato's dialogues represents the views of the historical figure.
typerist 17d ago
It's very easy to give examples. Often when someone coins a word, they are giving a name to something that previously had no name. Therefore the thing is an example of something that did not have a name prior to the coining.

61 points by surprisetalk 19d ago

Are there actually things that cannot be named? Any such thing could easily be assigned some such "Phenomenon 8x306Q". If any two people agree to call it that and use that to succesfully discuss the thing, then that is a name for the thing. Otherwise nothing can be named. Is the cat in your house really a cat, or is it a Felis catus? How can we be certain that it's not a gato or a кот? If the cat in your house is indeed a кот, gato, Felis catus, and cat, then Phenomenon 8x306Q can certainly be Penomenon 8x306Q as much as it is "familial bonds strained by misdeeds" or whatever the things we're naming is.

nofriend 25d ago
The proof is simple: there are countably many names, but uncountably many real numbers. Hence, some real numbers must be unnameable.
- goodmythical 23d ago
  Are there countably many names? Countably sayable, perhaps, but I don't recall seeing any limitation to word length in the spec. See: "Below is the full 189,819-lettered word for 'titin':" at https://cw39.com/wp-content/uploads/sites/10/2020/09/longest-word.pdf https://cw39.com/wp-content/uploads/sites/10/2020/09/longest... as an example. Surely if we can have a 189,819 lettered word we can have a million billion trillion lettered word or an uncountably lettered word. They'd be used in the same way as the really long numbers in that we'd give them some other handier name that collides when not given context. e.g. In spoken language pi/pie are often confused if the conversation does not already have a mathematical context and no one says 3.1415926535... conversationally just as no one uses the lenghtier version of chitin and no one would use the uncountably long name for some uncountably long number.
  - nofriend 23d ago
    names have to be finite in length. i think that's pretty obvious
    - goodmythical 22d ago
      I don't see how that's any more obvious than the suspicious claim that numbers can have only so many digits.
      - nofriend 22d ago
        A number is not in the first place its digit sequence. A number like pi is in the first place the ratio of a circle's diameter and its circumference, and only incidentally a certain (infinite) decimal expansion. A name is in the first place something you say, hence the thing you say has to be (at least theoretically) sayable.
dang 19d ago
(This is an older subthread which I moved hither because a different submission happened to make it onto the frontpage)

snapcaster 19d ago

I'm open to the idea that some things are unnameable but would need an example :)

loa_in_ 19d ago
I'll write you as soon as I can

kranner 19d ago

The Herzbergers' paper: https://sci-hub.ru/10.1007/BF00202726 https://sci-hub.ru/10.1007/BF00202726

rramadass 19d ago
Thank You. Bhartrhari (https://en.wikipedia.org/wiki/Bhart%E1%B9%9Bhari https://en.wikipedia.org/wiki/Bhart%E1%B9%9Bhari) is a pretty difficult philosopher who seems to be enjoying a revival now due to the ascendancy of AI LLMs and the question of whether they can be considered as having "consciousness". His central idea (highly simplified) is that since Language is the only way we can name objects and discuss relations between them it is synonymous with "Reality" and "Consciousness". Sort of like how the properties of an object define that object (ADTs anyone?). One can imagine that the use of language by LLMs gives birth to appearance of both consciousness and reality as "emergent phenomena" in it. In his theory of "Sphota" he posits that "meaning bursts forth" (in consciousness) as an indivisible whole when a complete sentence/sentences is/are uttered (is this what happens when LLMs do reasoning and generate text within a "context window"?) Perhaps Epistemology and Ontology are just two sides of the same coin. Some resources for further study; 1) Bhartṛhari’s Linguistic Idealism - https://loc.closertotruth.com/theory/bhart-hari-s-linguistic-idealism https://loc.closertotruth.com/theory/bhart-hari-s-linguistic... 2) Bhartrhari on Language, Perception, and Consciousness - https://academic.oup.com/edited-volume/27982/chapter-abstract/211665674?redirectedFrom=fulltext https://academic.oup.com/edited-volume/27982/chapter-abstrac... 3) The Word And The World: India's Contribution To The Study Of Language by Bimal Krishna Matilal - https://archive.org/details/wordandtheworldindiascontributiontothestudyoflanguagebimalakrishnamatilal_202003_376_e https://archive.org/details/wordandtheworldindiascontributio... 4) Sabda: A Study of Bhartrhari's Philosophy of Language by Tandra Patnaik. This is particularly scholarly with the author comparing western authors (like Frege and Wittgenstein) model of language with Bhartrhari - https://test.dkprintworld.com/product/sabda/ https://test.dkprintworld.com/product/sabda/ 5) The Sphota Theory of Language by Harold Coward - https://www.mlbd.in/products/sphota-theory-of-language-harold-g-coward-9788120801813-8120801814?variant=49213095739678 https://www.mlbd.in/products/sphota-theory-of-language-harol... 6) Sphota - https://en.wikipedia.org/wiki/Spho%E1%B9%ADa https://en.wikipedia.org/wiki/Spho%E1%B9%ADa

GPerson 19d ago

If we assume the real numbers exist, then perhaps the paradox resolves because there are uncountably many reals and only countably many nameable things, but then perhaps the paradox does not resolve because we assume ZFC is true and we can well order the reals, hence name the first unnameable real.

mark_something 19d ago
The reals can be ordered, just use x < y. I think you mean that if ZFC is true, we could enumerate unnameable reals (choose one with the axiom of choice, remove it, choose another one, etc.), but you could not enumerate them all. But it is true that you could get a "first" unnameable real.
- pdonis 19d ago
  > The reals can be ordered, just use x < y. That ordering is not a well-ordering, which is what the GP specified. A well ordering requires that every non-empty subset has a smallest element. That's not true for the reals ordered by x < y: for example, the set of all reals > 0 has no smallest element. No one has explicitly shown that the reals can be well ordered, but it's a consequence of the axiom of choice that every set can be well-ordered. So in ZFC there must be a well ordering of the reals, even though no one has found one. Issues like this are why not all mathematicians accept the axiom of choice.
  - simonh 19d ago
    Not a mathematician, so this question may be a bit thick. I see the problem with the set of reals > 0, but is it perhaps that in this case > 0 is the problem and for sets specified as >= 0 it's fine because 0 is a nameable real and the smallest element. Obviously you can't just exclude certain expressions arbitrarily though, so I don't know how you could justify that mathematically.
    - GPerson 19d ago
      A well ordering on a set is a total order such that all non empty subsets have a minimum element with respect to this order. The standard ordering of the reals is not a well ordering, but the axiom of choice is equivalent to the statement that all sets possess a well-ordering. A well-order of the reals would probably look pretty chaotic though.

curtisblaine 19d ago

How is it a paradox? Isn't this just a proof that there are many unnamed things, but no unnameable ones?

WillAdams 19d ago
Agreed. This is the stuff of magic and folklore, and neatly resolved by Ursula K. LeGuin in _A Wizard of Earthsea_.
bwfan123 19d ago
> Isn't this just a proof that there are many unnamed things, but no unnameable ones? Where is it a proof that there are many unnamed things ? I could only see it as an argument that there are no "unnameable" things.
- curtisblaine 19d ago
  It depends how you define "named", but for example, not all the grain of sands you see on a beach are named (yes, they are named collectively, but not individually. If "collectively" is valid, then that's further proof that "unnameable" things can't exist, because they already have a collective name).
arjie 19d ago
Many ancient paradoxes are not really paradoxes. Zeno's ones are resolved today with infinite series. But this is a real one. Is it possible to describe an arbitrary real number? Almost all reals are not describable. But you cannot find a single such number. The 'paradox' is that the search itself is self-failing - a broken strategy. Of course, now we have the language of sets and functions between them and cardinalities and we resolve this for us in a way that is meaningful. But still now you know the 'existence' of this thing? Can't be described. It's interesting because of the property of creating with finite words universes of infiniteness.
rramadass 19d ago
See the original paper linked to here - https://news.ycombinator.com/item?id=49478566 https://news.ycombinator.com/item?id=49478566

gaoshan 19d ago

If you can't name it you can still describe it. But then by describing it you are committing it to a set of conditions this unnameable thing satisfies. But then if you go beyond a narrow interpretation of that paradox and accept that naming and describing are both accomplishing the same fundamental thing, that being committing a thing to a condition (like a name) or set of conditions (like a description), you do run into the same problem. Hmm, interesting. Now back to this E2E testing stuff I've been avoiding.

bwfan123 19d ago
Names are like variables in a function. you can name variables anything you want from a human understanding point of view (final cause), but the compiler doesnt care about that. The compiler only cares about the efficient cause of that variable in the sense of what it represents (stack/heap etc).
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LanceH 19d ago
In mathematics, there are infinitely many "computable" numbers. That is, numbers which can be describe using any mathematics available. Then there are far more "non computable" numbers, which can't be described by anything finite. I think there is some analogy to be made here.

cyanydeez 19d ago

Sounds akin to the complexity inherent in cellular automata. We know via the rules how to mutate successive generations, but backwards propagation, algorithmic simplification, etc may exist but not traceable from any given ruleset.

ngvrnd 19d ago

„Wovon man nicht sprechen kann, darüber muss man schweigen“ but if the thing can be interacted with, it can usually be mapped and defined and then named. But there will always be things which do not have names, at least in mathematics -- think of the real numbers.

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abnry 19d ago
I suppose if the number of nameable things is countable (because humans can only enumerate, and it is humans who name), then it trivially follows that some real numbers are unnameable. Which proves the existence of such entities. This reminds me of a YouTube video I watched this week titled "A counting argument for why mind comes before matter": https://youtu.be/AtduNjJV-6E?is=nBZ9ztZsyeoVhCj1 https://youtu.be/AtduNjJV-6E?is=nBZ9ztZsyeoVhCj1 The argument is something like the set of possible thoughts about physical objects is larger than the physical objects themselves. It feels similar in flavor to the idea of unameable objects. There's something special about a name. The name of the God of the Bible is special. Christians are to call upon _the name_ of the Lord. We pray, hallowed by _thy name_. It is somehow denotes the summary essence of the thing being named, even if it doesn't give specific details of its characteristics.
- conmod278 19d ago
  The Beauty of Bézier Curves https://youtu.be/aVwxzDHniEw?si=tPPRId1y5L7U2_5L https://youtu.be/aVwxzDHniEw?si=tPPRId1y5L7U2_5L Name_I = a*lambda + b (1-lambda) lamda is a real number.
bryanlarsen 19d ago
"Unnameable" and "unnamed" are two different things, in my opinion. Are there real numbers that are unnameable or are those just unnamed? There are some that unnameable with my mathematical understanding, but that's not saying much.
- 19d ago

b450 19d ago

counterargument: 1) let x be a thing 2) I name x "Jeff" 3) all things are nameable (from 1 and 2) another way to put this is that it's natural to take the paradox as a reductio.

crimsonspy 19d ago
Jeff jeff jeff, jeff jeff jeff jeff! Jeff? Jeff.
amavect 19d ago
You proved that definable implies nameable, and also unnameable implies undefinable. Obviously true. However, the idea of undefinable real numbers closely resembles a modern version of the paradox. No surjective function exists from definitions to real numbers. Really, the blurb about "seems impossible to verify this by giving positive instances" contains the tension between constructive math and non-constructive math. Does an unnameable (and undefinable) thing actually exist? If a tree falls in a forest, but no one can hear it, does it make a sound?
- onraglanroad 19d ago
  > No surjective function exists from definitions to real numbers. I'm not really up on maths so this is possibly a stupid question, but can't any real number be written as an ASCII string, which is basically an integer number, so there is a direct mapping there? Or is it because the ASCII number wouldn't be in order that makes the difference? Or is it that you can't write that mapping as a mathematical function perhaps?
  - onraglanroad 19d ago
    Actually, and perhaps sadly, I asked an LLM and I understand now. But perhaps that's not such a bad thing that I can get answers to my foolish questions!
    - amavect 19d ago

thinkzilla 19d ago

c.f. the Berry paradox https://en.wikipedia.org/wiki/Berry_paradox https://en.wikipedia.org/wiki/Berry_paradox

Zhyl 19d ago

The Way that can be walked is not the eternal Way. The name that can be named is not the eternal name. -- Lao Tzu, Tao Te Ching

Xcelerate 19d ago

Pretty sure ZFC proves such things exist (and that it also can’t pinpoint any individual instances of course). Now, whether syntactical “∃” in the formal language of set theory corresponds to the platonic existence of some “thing”, who knows.

lordnacho 19d ago

This reminds me of the 6 degrees of separation thing. People tell you that you can connect more or less everyone by 6 degrees. But what struck me was, for anyone you try this with, you know their names, so you've already restricted yourself in how far out someone can be.

svat 19d ago

Incidentally, it is a matter of some debate whether Bhartṛhari the philosopher and Bhartṛhari the poet are the same person or two (or more, in the case of the anthology of verses). Oral tradition holds them to be the same person, scholars have debated back and forth. I have a collection of the poems here: https://shreevatsa.net/bhartrhari/web/ https://shreevatsa.net/bhartrhari/web/ (will clean it up someday)

rramadass 19d ago
Nice. I have the A.N.D.Haksar, Purohit Gopinath translations of all the Satakas and Swami Madhavananda's translation of the "Vairagya Shatakam". Need to get the others ;-) Also see https://news.ycombinator.com/item?id=49486845 https://news.ycombinator.com/item?id=49486845
- svat 18d ago
  I couldn't add the Haksar translation as it's still under copyright, but the site has the other two. Plan to add others like M. R. Kale's (https://github.com/shreevatsa/bhartrhari/issues/11 https://github.com/shreevatsa/bhartrhari/issues/11) — just need a chunk of time one of these weekends.
  - rramadass 18d ago
    One thing you might want to add after each author's name is which categories (viz. Niti, Shringara and Vairagya) they have translated. Due to excessive prudishness many have omitted the Shringara satakam which is quite silly (this is what makes him "Human"). I got the Haksar and Gopinath editions specifically because they include all three categories. A.N.D.Haksar in particular has translated many of the works in Sanskrit literature into easy English (including the Kama Sutra) and does not censor anything. Also i suggest that you add author names of all known translations of the work whether you have access to their actual text or not (due to copyright etc. reasons). That way your site can be a one-stop portal to Bhartrhari's Sataka-Trayam. PS: In case you don't already know of it; there is a much larger work in the Tamil language named Tirukkural which is also divided into three similar categories (viz. Aram, Porul and Kamam) the whole having a total of 1330 couplets (133 chapters of 10 couplets each). There are many English translations available of which the original Penguin edition titled "Kural" translated by P.S.Sundaram is pretty good and done in the original couplet style. For a more detailed study see the 2-vol translation with commentary by S.M.Diaz. Tirukkural - https://en.wikipedia.org/wiki/Kural https://en.wikipedia.org/wiki/Kural Tirukkural translations - https://en.wikipedia.org/wiki/Tirukkural_translations https://en.wikipedia.org/wiki/Tirukkural_translations

aabhay 19d ago

> There are some things that are unnameable Like what? Oh wait…

ogogmad 19d ago

This reminds me of how (I think) Zen koans are designed to make no sense at all. They are designed to teach you the limits of words and language and pure thinking.

rramadass 18d ago
> This reminds me of how (I think) Zen koans are designed to make no sense at all. True in a way. To understand how, note first the four stages of language given in my comment here - https://news.ycombinator.com/item?id=49491764 https://news.ycombinator.com/item?id=49491764 Zen koans don't have a meaning at the manifest (Vaikhari) and differentiated (Madhyama) stages. So you are forced to go back to the Intuitive/Holistic Meaning (Pashyanti) stage and thus realize "a burst of meaning" aka "a flash of insight" aka "Satori".

BiraIgnacio 19d ago

sounds like the paradox that _could_ illustrate Gödel's incompleteness theorems https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_th...

rramadass 19d ago
Russell's Paradox -> Hilbert's Program -> Godel's Theorems - https://news.ycombinator.com/item?id=49287595 https://news.ycombinator.com/item?id=49287595 Bhartrhari's Paradox can be said to be analogous to Russell's Paradox (though of course the latter is specific to mathematics/logic).

dredmorbius 19d ago

I see what you did there.

MrFiskarBengt 19d ago

"The Tao that can be told is not the eternal Tao"

hargup 19d ago

https://3quarksdaily.com/3quarksdaily/2014/03/boundaries-and-subtleties-the-mysterious-power-of-naming-in-human-cognition.html https://3quarksdaily.com/3quarksdaily/2014/03/boundaries-and... This is a beautiful article on the subject. To prove that there are unnamable concepts, he uses cantor's diagonal argument. There are countably infinite names. Any subset of these names is a concept, which is same as the powerset of the set of names, and through cantor's diagonal argument, there are uncountably infinite concepts, most which are not namable. Yes you can take a specific concept, and name it, but there are uncountably infinitely many, so even with infinite time, you cannot name them all.

rramadass 19d ago
Countable and Uncountable Infinities - https://philosophicaltreasures.com/countable-and-uncountable-infinities/ https://philosophicaltreasures.com/countable-and-uncountable...
itemize123 18d ago
i think there must be a scheme of naming that is uncountably infinite too.
- deleted 18d ago
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whack 19d ago

Can't this also be used to justify things that are obviously nonsensical. Like for example: "I possess an immense undetectable sphere. How can I prove this? Well, any proof I offer you would by definition violate the undetectability of the sphere. So there's no way for me to prove it, I guess you'll just have to trust me bro."

amavect 19d ago
I love philosophy Calvinball, so I would counter by asserting that undetectable implies no possession, an immediate contradiction. Or go further and assert that undetectable implies nonexistence. We all possess an immense undetectable nonexistent sphere. No bounds on assumptions means I can make up anything to annoy the interlocutor. So, you're right. This shows why we should use formal math, so we can agree on the result yet bicker about the interpretation. Some folks point to Cantor's diagonalization theorem to show that some unnameable things exist, when the theorem doesn't say that at all.

raincom 19d ago

If 'it' is unnameable, there is no way to circumscribe or even describe what 'it' is. Even to show that what it refers to is an empty set, we need its description. If we use concepts like intention and extension, we can sketch out four scenarios: extension, no intension (yes, we can point out things, which we can't describe) extension, intension (we point out, and we describe) no extension, intension (Yes, we can imagine and describe things vividly, but no referent in the world. Here, one can say these things exist in a Platonic world, but not the world we live in; this is where numbers, sets, ideas can exist. Neo-Platonism in Philosophy of Mathematics) no extension, no intension (this paradox falls in this area).

kazinator 19d ago

The claim is false. There is not a thing that cannot be given a name. If it is a thing, it can be given a name. You take that thing into the discourse and say, "let this thing be X", and now it has a name. What cannot be given a name cannot be discussed in any way; it is completely vague, undefined or ephemeral. The inability to name it is not what is at the core of not being able to pin it down; it is a byproduct or corollary.

Smaug123 19d ago
You didn't name the object when you said "let this thing be X"; you actually had already identified that "thing", and that process of identification was the process of naming it. You then defined some syntax ("X") and said that it was a name. But there are things for which you can't even say "let 'this thing' be…". For example, ZF proves that there are uncountably many reals. There are only countably many names, so there must be unnameable reals. You can talk about "generic" reals (you can say "let x be a real" and do all sorts of interesting things with a generic x), but there are specific reals you will never be able to name specifically enough to distinguish them from their uncountably-many brethren. That doesn't make them "vague, undefined or ephemeral"! They're just so numerous that you can't describe the distinctions between them. (Even hardcore constructivists usually accept enough Choice to prove the reals uncountable, although https://arxiv.org/abs/2404.01256 https://arxiv.org/abs/2404.01256 made headlines when it was shown not to be necessarily true.)
- itemize123 18d ago
  naming schemes can produce uncountably inf names
  - deleted 16d ago
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- kazinator 18d ago
  > that process of identification was the process of naming it. No, it wasn't. Entities can be identified without being named, by relationships to other entities and class and such. That identification requires words. Not all denotational words and phrases constitute names.

Drophouse 19d ago

This is basically why art exists — painting, music, and poetry can point at things without having to name them. Language traps itself; other forms don't.

rramadass 18d ago
What you say is valid only when you restrict yourself to Western definitions/conceptions of language/linguistics i.e. study of Phonetics/Morphemes/Syntax/Semantics/etc. In Bhartrhari's Philosophy (and other Hindu philosophies) "Language" has a much broader definition which can encompass Art/Dance/Music/Painting/etc. Any medium of communication which can bring forth a "burst of meaning" (called Sphota) in one's consciousness is a language. Natural Spoken language based on Sound (aka Sabda in Sanskrit) is considered the most fundamental since you can have languages without a written script/symbols/diagrams. In Hindu philosophy, a "Language" is said to have four stages, only the last of which is the gross manifestation in the physical world; 1) Para - This is the latent undifferentiated potential which exists in everybody. 2) Pashyanti - This stage is where intuitive holistic meaning (of what you want to convey) exists. 3) Madhyama - This stage is where you have differentiated the thought/intention into an object and the means of representation for its communication. 4) Vaikhari - In spoken language, this is the manifest stage where you utter sentences according to established syntax/semantics to convey meaning. Note that the first three stages are internal and only the last is the medium of expression in the physical world. It should now be obvious that the last can be any medium (eg. Dance/Painting/Music/Written-Language/Sign-Language/etc.) as long as the receiver "gets" the intended meaning. PS: See also this comment of mine for further resources - https://news.ycombinator.com/item?id=49486845 https://news.ycombinator.com/item?id=49486845

__rito__ 18d ago

Bhartrihari was a king, philosopher, and poet. Scholars argue whether they were the same person or not, but I don't care, as scholars also argue about if Socrates really existed or not. He wrote 300 verses in Sanskrit. And they are on three different topics: sensuality and pleasure, policy and ethics, and finally renunciation. In Shringar Shatakam (100 verses on sensual pleasures), he writes: “Casting aside envy, considering the matter carefully, let the noble ones tell us, with due propriety: Which ought one to frequent — the slopes of the mountains, or the buttocks of women whose smiles are stirred by Love?” and “Why all this elaborate, pointless talk? There are only two things worth attending to in this world: the fresh, wine-intoxicated youth of beautiful women, heavy with their breasts - or the forest.” But in the final book, he realizes the folly of the senses, and writes: “Sensual objects will inevitably leave us, even after remaining with us for a long time. What difference is there between losing them and voluntarily abandoning them? When they depart against our will, they cause unbearable anguish; but when we ourselves abandon them, they produce the infinite happiness of inner tranquility.” Amazing character.

svat 18d ago
The third verse you quoted (https://shreevatsa.net/bhartrhari/web/K157.html https://shreevatsa.net/bhartrhari/web/K157.html) has a nice translation into English verse by Ryder: A REASON FOR RENUNCIATION Possessions leave us at the end, However long they stay; Then why not cast aside, my friend, What leaves us anyway? And if they leave against our will, The heart takes time in mending; If given willingly, they fill That heart with joy unending. The other two you quoted (https://shreevatsa.net/bhartrhari/web/K084.html https://shreevatsa.net/bhartrhari/web/K084.html https://shreevatsa.net/bhartrhari/web/K085.html https://shreevatsa.net/bhartrhari/web/K085.html) have also been translated, though IMO not as successfully.
TFNA 17d ago
No one argues about whether Socrates really existed. He is attested by multiple writers of the time. The debate is solely about how much the Socrates of Plato's dialogues represents the views of the historical figure.

typerist 17d ago

It's very easy to give examples. Often when someone coins a word, they are giving a name to something that previously had no name. Therefore the thing is an example of something that did not have a name prior to the coining.