Countable and Uncountable Infinities - https://philosophicaltreasures.com/countable-and-uncountable...

i think there must be a scheme of naming that is uncountably infinite too.

The third verse you quoted (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.

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.

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

"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.

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

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.

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.

Agreed.

This is the stuff of magic and folklore, and neatly resolved by Ursula K. LeGuin in _A Wizard of Earthsea_.

See the original paper linked to here - https://news.ycombinator.com/item?id=49478566

> 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.

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.

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

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 made headlines when it was shown not to be necessarily true.)

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.

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).

Thank You.

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

I'll write you as soon as I can

Russell's Paradox -> Hilbert's Program -> Godel's Theorems - 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).

(This is an older subthread which I moved hither because a different submission happened to make it onto the frontpage)

The proof is simple: there are countably many names, but uncountably many real numbers. Hence, some real numbers must be unnameable.

> 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

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".

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?

Jeff jeff jeff, jeff jeff jeff jeff! Jeff? Jeff.

The problem with such sleight of hand counterargument is that you haven't even defined what "a thing" is nor "all things" are in this world. And such discussions will just come back to set theory, ZFC, axiom of choice and real numbers.

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.