Bhartrhari's Paradox

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.

sounds like the paradox that _could_ illustrate Gödel's incompleteness theorems

https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_th...

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.

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."

„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.

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.

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)

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.

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

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.

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

I see what you did there.

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

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

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.

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

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

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.

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.

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.

> There are some things that are unnameable

Like what?

Oh wait…