Bhartrhari's Paradox(futilitycloset.com) |
Bhartrhari's Paradox(futilitycloset.com) |
Like what?
Oh wait…
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.
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.
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 debate is solely about how much the Socrates of Plato's dialogues represents the views of the historical figure.
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 ;-)
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.
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.
There are some that unnameable with my mathematical understanding, but that's not saying much.
On the other hand, given any real number, I can name it. I'll run out of unique names, since no injective function exists from real numbers to names.
So, some unnamed real numbers will always remain (non-constructively), I can make real numbers that escape a naming scheme (constructively), and no unnameable real numbers exist.
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
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.
https://youtu.be/aVwxzDHniEw?si=tPPRId1y5L7U2_5L
Name_I = a*lambda + b (1-lambda)
lamda is a real number.
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.
This is the stuff of magic and folklore, and neatly resolved by Ursula K. LeGuin in _A Wizard of Earthsea_.
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.
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.
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).
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
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.
I think there is some analogy to be made here.
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.
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 made headlines when it was shown not to be necessarily true.)
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.
https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_th...
Bhartrhari's Paradox can be said to be analogous to Russell's Paradox (though of course the latter is specific to mathematics/logic).
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.
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.
The name that can be named is not the eternal name.
-- Lao Tzu, Tao Te Ching
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
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".
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.
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?
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?
For that matter, the paradox is self-resolving. By labeling the entities it is concerned with as "unnameable things", it has named them. As a collection, entities not otherwise named can be simply referred to as "Bhartrhari's things".
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.
Bhartrhari (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...
2) Bhartrhari on Language, Perception, and Consciousness - 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/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/
5) The Sphota Theory of Language by Harold Coward - https://www.mlbd.in/products/sphota-theory-of-language-harol...
6) Sphota - https://en.wikipedia.org/wiki/Spho%E1%B9%ADa
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
Tirukkural translations - https://en.wikipedia.org/wiki/Tirukkural_translations
Assigning a symbol? But who said that the set of symbols must be countable?
More than that: there is no way to build one (assuming the word "build" means some concrete construction), because it's consistent with ZF that the reals admit no well-ordering. Indeed, you can use forcing to construct a model of R in which there is an infinite but Dedekind-finite subset of R; and you can't well-order such a set, because a well-ordering would turn it into an ordinal, and any Dedekind-finite ordinal is finite. You must use some sort of choice principle to construct a well-ordering. (Of course, it's consistent that they can be well-ordered, too, as you say; or e.g. under the hypothesis V=L, where there's even a canonical well-ordering given by the lexicographic well-ordering L comes with.)
An unknowable name isn't a very good name, IMHO.
But perhaps that's not such a bad thing that I can get answers to my foolish questions!