> By this logic, you can't even use the word "Aatma" without in every instance defining it down to the nines since you can't be sure at first, even in a context of two Indians talking to each other, that both of them understand it to mean exactly the same thing

You are just getting pedantic here. I am talking about official translations for scriptures/manuscripts. Do you agree that translations should strive for accuracy or not? I need you to clarify that first. Because if you believe there is no need to strive for accuracy then we can end the debate here as we are differing on the fundamentals itself. We can then agree to disagree.

If you believe that translations have to be as accurate as possible then yes. Definition of Aatma has to be defined down to the nines (by both yourself and the Poorva Paksha/opposite philosophy) before even proceeding with debates/discussions. What do you think we did for thousands of years researching on Vedanta if not for this exact thing?

The most famous incident that comes to my mind is from the "Madhva Vijaya" of Madhvacharya (he is the founder of Tattvavada school of Vedanta). This is set in the 13th century. Quoting from it [1] (Page 49):

"After successfully completing his first Southern Tour, Sri Madhva was passing through Kerala, en route to Udupi. In the course of the journey, he reached the banks of the river Payasvini & stayed there for some time. One day, there was a grand assembly of scholars in a temple on the banks of the holy river. Sri Madhva had just expounded a given Sookta in the Aitareya sakha of the Rig Veda as requested by a Veteran scholar of the locality (Verse 1, 2). Though the scholars admired his scholarship at heart, outwardly they said that it meant something else & gave their own meaning (Verse 3). Sri Madhva accepted their meaning & added that the Vedas carried three meaning & the Mahabharata had ten & each word of Vishnu Sahasranama a hundred meanings (verse 4). The pundits challenged him to give out those hundred meanings (verse 5). Sri Madhva readily accepted it but laid a condition that they should repeat the meanings after he had finished. (verse 6). They agree to do so. Sri Madhva then began with the first word “Vishwam” & went on expounding one meaning after another. (verse 7). As the exposition proceeded, the admiring scholars felt staggered, as they could no longer follow the grammatical intricacies, & much less keep them in their memory. Realizing their smallness, they begged him to stop & pleaded excuse for confronting him & sought his blessing (verses 8-10).

Sri Madhva’s stay in Kerala coincided with the annual Vidvat Sadas when Pandits received their usual Royal rewards of merit. Sri Acharya naturally availed the opportunity to meet the local luminaries & celebrities for discussion & expounding to them the correct interpretation of Vedic Texts (verse 11). Some of the pundits who participated in the debate with Sri Madhva in public, found it very difficult to answer his points (verse 12). The local pundits no more wanted a direct confrontation with him & earn a bad name for their entire region in case of
a defeat. They, therefore, engaged some outsider to contradict the Acharya’s derivation of the word pR^iNIyAt.h verse 14. Sri Acharya exposed the poor pandit’s inability in distinguishing the two roots pR^iNa dAne & prI~N. prINane and by himself explaining the grammatical difference between the two, won the reference of the whole assembly (verses 15, 16).

On another occasion during the period of Sri Acharya’s stay in Kerala, there arose a controversy over the meaning of the word “Apaalaa”. Sri Madhva explained that in the context it was used in the Veda, the word meant only “ a very young girl” ….. tAvadapAlA kIrtitA 'ati -taruNI ityayamUche) verse 17. But some Pandits were adamant in asserting that the word meant a leper. Sri Madhva said that a great scholar would soon arrive there & endorse his meanings & set at rest the controversy. So it happened. A great scholar did come & he
confirmed the view of the Acharya (verse 19). The Pundits of Kerala not only admired his profound scholarship but were also wonder struck at his prophetic vision (verse 20). In this way, making people rejoice by the magic of his ringing
voice & well reasoned arguments, Sri Madhva, shining like a pleasant full moon in the galaxy, completed his
Southern Tour with success & returned to Udupi (verse 21-23)."

> But it doesn't stop there! You have to make sure that every word used to define Aatma is also defined with unfailing precision. And every word in this meta-definition, and then every word in the meta-meta-definition, and so on. Unfortunately it's an infinite regress. So it turns out that by these absolutely exacting standards, all communication is impossible. But here we are, chatting away, no doubt misunderstanding each other in some crucial manner.

Yes we are and that is totally fine as the discussion won't be included in research papers/translations. There is no need to get so pedantic in regular conversations. It is perfectly fine to misinterpret or misunderstand. This becomes a problem only and only when you mistranslate a scripture and publish it for the masses without strictly defining each terminology and even mentioning the Philosophical school of Vedanta you are referring to. Because Aatma in Advaita is vastly different from Aatma in Tattvavada which is vastly different from Aatma in Jainisim. You can't just whip out a Sanskrit to English (or whatever language) dictionary and directly translate through that. This is the biggest problem I see "casual Pundits" do when it comes to interpretations/providing translations. I label them "casual Pundits" because they just blindly use the dictionary to explain Vedic verses/hymns, when in fact, that is the exact opposite of what is done in Vedanta. In Vedanta, every word has to have a reference to another Vedic scripture where that word is defined in detail. If no such direct reference is found, then the meaning of the word is derived by combining various verses where it is defined and then extracting the meaning out of it. It is a laborious process which requires mastery in all Vedic scriptures. Very few individuals actually achieved that mastery and hence became Jagadgurus founding Philosophical schools of Vedanta. If it was as easy as whipping out a Sanskrit-to-English dictionary and translating a verse, everyone of us can become PhDs.

Please first understand what Vedanta is and why it exists. Because Sanskrit is tightly coupled with Vedanta itself.

[1] (Page 49): https://anandsp1.files.wordpress.com/2010/08/madhwa-vijaya-g...