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Bhartrhari's Paradox

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Re: Bhartrhari's Paradox

#61

Post by amavect »

ithkuil wrote: post #59
amavect wrote: post #36

Earlier quoted context omitted.

No surjective function exists from names to real numbers (diagonalization). With any naming scheme, some unnamed real numbers always remain. 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 (const…

What does "naming" mean? Assigning a symbol? But who said that the set of symbols must be countable?

My hidden assumption: I said the set of names must be countable! I assumed you would know that naming means assigning a finite string (in the Ithkuil writing system of course). and don't nitpick further or else I'll have to write a proof in Agda or Rocq lol

Re: Bhartrhari's Paradox

#62

Post by rramadass »

kranner wrote: post #9

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

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

Re: Bhartrhari's Paradox

#63

Post by rramadass »

svat wrote: post #38

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/ (will clean it up someday)

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

Re: Bhartrhari's Paradox

#64

Post by kazinator »

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.

Re: Bhartrhari's Paradox

#65

Post by kranner »

rramadass wrote: post #62
kranner wrote: post #9

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

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…

Excellent resources, thank you. Discussions of Sphotavāda are limited to the non-English Indosphere, largely, but the word itself is also used in high register Hindi to appreciate an unexpected but brilliant off-hand remark. Sort of like the English expression of calling something inspired; it both appreciates the speaker while taking away from their absolute agency.

Re: Bhartrhari's Paradox

#67

Post by Smaug123 »

kazinator wrote: post #64

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…

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.)

Re: Bhartrhari's Paradox

#68

Post by conmod278 »

abnry wrote: post #26
ngvrnd wrote: post #18

„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.

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 somethi…

The Beauty of Bézier Curves

https://youtu.be/aVwxzDHniEw?si=tPPRId1y5L7U2_5L

Name_I = a*lambda + b (1-lambda)

lamda is a real number.

Re: Bhartrhari's Paradox

#69

Post by rramadass »

BiraIgnacio wrote: post #44

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

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).

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