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There is a historical account of the Buddha saying this about shared experience:
MN77:33.1: Furthermore, I have explained to my disciples a practice that they use to understand the minds of other beings and individuals, having comprehended them with their own mind.
Although this sounds simple, it isn't. Under the sway of greed, hate, and delusion, such comprehension escapes us.
MN77:32.4: And many of my disciples meditate on that having attained perfection and consummation of insight.
Fractured by greed, hate and delusion, we gravitate towards those who share that greed, hate and delusion. And then we argue with others:
MN77:4.2: Now at that time, Sakuludāyī was sitting together with a large assembly of wanderers making an uproar, a dreadful racket. They engaged in all kinds of unworthy talk, such as talk about kings, bandits, and ministers; talk about armies, threats, and wars; talk about food, drink, clothes, and beds; talk about garlands and fragrances; talk about family, vehicles, villages, towns, cities, and countries; talk about women and heroes; street talk and well talk; talk about the departed; motley talk; tales of land and sea; and talk about being reborn in this or that state of existence.
Perhaps it is better to see clearly what is ignored by many:
MN77:36.2: Suppose there was a lake that was transparent, clear, and unclouded. A person with good eyesight standing on the bank would see the mussel shells, gravel and pebbles, and schools of fish swimming about or staying still. They’d think: ‘This lake is transparent, clear, and unclouded. And here are the mussel shells, gravel and pebbles, and schools of fish swimming about or staying still.’
MN77:36.3: In the same way, I have explained to my disciples a practice that they use to realize the undefiled freedom of heart and freedom by wisdom in this very life. And they live having realized it with their own insight due to the ending of defilements.
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Mental appearances can be shared but it is not your mental appearance nor it is someone else's.
famous Buddhist Yogacaraist Vasubandhu "uses the example of mass hallucinations (in Buddhist hell) to defend against those who would doubt that mental appearances can be shared".
What you call as mass hallucination is not a hallucination. Mind leads future. Hell is raised in the minds before it is seen through direct experience. This is applicable for diseases as well. All diseases first germinate in the mind then it spreads for real. How this happens is a different question?
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If I understand your question correctly, check out Mipham Rinpoche's Beacon of Certainty topic 6, along with its commentary.
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There is a famous allegory in Mahayana Buddhism relating three different beings' experience of the very same cup of liquid. The first being is a God, the second is a human, and the third is a hungry ghost. To the God, the cup full of liquid is experienced as a golden chalice full of the most wonderful crystal clear ambrosia giving off a mesmerizing scent. To the human being it is a rather ordinary cup of water. To the hungry ghost it's a revolting and ugly basin full of blood and pus.
Then the Buddhist student is asked to consider what is the truth of this object? Is it a chalice of amazing elixir? Just a cup of water? A vile concoction of mucus and phlegm? And what is it to an ant? An ocean? Is it something else? All of these things at the same time? How about to other humans? To other gods? To other beings? Could it be that there are countless experiences of the same "thing" all related to the karma of the beings experiencing it?
A western philosophical student might wonder what is the qualia of this object? How can different beings experience such different qualia of the same underlying object? Is it "the same" underlying object?? If so, how can it have different qualia? If it is not the same, then what is it? Can anything at all be objectively measured and understood and experienced the same by all beings that might encounter it? By some subsets but not others?
"As a side note, I know this is very similar to the Problem of Other Minds in modern social science where scholars and philosophers invented a term "intersubjectivity" defined here to objectify the existence of certain social common "thought communities" one unavoidably belongs to explain why people can share their private intrinsically different experiences."
I think that is a very poor set of definitions. From all I can tell, it sounds like "intersubjectivity" is merely another word for "convention."
But I think this community-wise intersubjectivity is just like the sound of a chorus which can be entirely reduced to the superposition of individual sounds, thus seems not a necessary concept.
Ah, this is rejected by Mahayana buddhism (and I think Thervada too) as can easily be seen in the allegory of the chariot by Chandrakirti. This can be found also in this sutta.
Or does Buddhism never have an answer for such question as it belongs to papañca (conception proliferation) and thus effectively reject true possibility of exact mental appearances sharing?
What do you mean by "exact" here? I would challenge you to find even one set "thing" in this world or any other in which all beings immediately agree or have a universal objective experience that does not differ in any significant way. Name one such universal qualia that is permanent and fixed. Can you?
I'm not sure if these allegories help answer your questions, but your questions aren't very specific. Rather they seem to allude to a whole host of ideas that are not well defined and mixing western philosophical words/ideas - that are themselves ill-defined - with Buddhist ideas that may/may not be defined according to your usage. Anyway, I hope it is helpful.
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I took the time to read through the 20 Verses — interesting read — and then I returned to this question, and I have to say that the first thing that sprang up in my mind was and old, old joke:
Doubtless they are all seeing the same 'external (non-mental) object', but their inclinations draw them to interpret it in different ways.
But to the point... Mental appearances are publicly shareable because mental appearances are intrinsically public, not private. Or put more precisely, if I were to put (say) a tomato on the table between us, there are three factors involved in our perception of it:
The first is a given that lies a bit beyond our comprehension; the second is personal, private, and unsharable; the third is collective, passed down to us from each other and our ancestors. I mean, if you happen to be red-green colorblind what you 'see' when you look at that tomato is not much like what I 'see', and what each of us 'sees' doesn't capture the true nature of the tomato in all its real-world glory. But we both know it's a tomato — we have that concept fixing the landscape between us — and we will agree to it with barely a thought.
There's a psychology experiment where the experimenter will flash color words at people in various colors (e.g., flash the word 'green' in letters that are sometimes green, sometimes blue, sometimes red...). Ask the subjects what color the word 'was', they will most likely tell you what color the word 'said', not the color the 'saw'; the invocation of the linguistic concept overrides the sensory perception entirely.
Dream states are driven by concepts: we might see a chipmunk in a dream and 'know' it is our best friend, because the concept of our best friend arose and (somehow) invoked our private image of a chipmunk. Hallucinations are concepts that are mis-triggered: we experience something and it brings up the concept of 'hair' or 'the moon' so that we swear we have seen those. People in hell realms interpret everything they see as disgusting and offensive, because their consciousness has been warped into that pattern, and because they share common concepts of what things are offensive and disgusting they share their warped perceptions among themselves.
We share concepts because concepts have been passed down to us. When we apply them rightly they bind our consciousnesses together; when we apply them wrongly we sow confusion, doubt, and misery.