Well, depends of what you mean by persist. As I said before, I don’ think that the cat or the table has an atta in the sense that it persists - this was my argument - and it doesn’t have a jiva either (just to be clear here).
Does it have any duration at all? Asking for Venerable @Vaddha 
Good one 
The question is: Is there really a liquid? My whole argumentation centers around the “it doesn’t exist-because-there-isn’t-something-to-be-found-in-the-first-place”-argumentation. That is what I find misleading.
So what persists? If nothing persists, what is being called real? Nothing.
See where I expanded it to include beings for whom the word ‘liquid’ is totally alien? For them I’d say they’d say ‘no, there is not really a liiiquuiiiddd’
I think what you’re asking is whether there is some fundamental common denominator that ALL beings would agree upon, right? And we’d call that common denominator what is real. But I’m putting forward the hypothesis that there doesn’t need to be some common denominator. There is nothing that ALL beings would agree upon in that simile. Hence it is all conventions all the way down 
And now to nod towards my friend @Jasudho, I’d say that all those beings are going to experience the situation however they are going to experience it based on causes and conditions.
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Yes, I can see that! But I could then go on explain what a liquid entails. And I could go on that water can freeze or evaporate. It was still a liquid at one point. It existed.
So then your position is that there is some preferred point of view and that this privileged POV is what is real and all those who do not experience it according to that POV are simply mistaken? You believe in a common denominator.
I can come up with more imaginative similes and thought experiments that might help undermine your position, but you seem a creative person so I’d encourage you to see if you can come up with them as well. That is if you are interested in having your position undermined
But the denominator is arbitrary. It’s not about the name we give things. It’s about the question if it has a referent in real life. A name is like a deixis. It points to something. And that something is not void of existence. That’s all I’m saying, really. It doesn’t have an etrnal, never-changing atta,jiva,soul but it has an -ness that we can refer to.
Yes, I understand your position. That it points to something is a good way of putting it. The problem is we can never pin down that something and find it and go aha!!! that is the something. You said the ‘liquid’ is the real referent in the simile above. And I’m encouraging you to keep exploring that. I think if you do you’re going to find that ‘liquid’ ain’t the ‘something’ you’re looking for
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Yes, I will do that. At this point of the discussion I sure wished I had paid more attention to my professor in philosophy class and the buddhist teachings and teacher I listened to.
I have to shoot off to work and will be able to reply tomorrow. 
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Hi,
Agree. Including the last line which I take to point to over-analysis of sheer experience rather than using experiences to skillfully attain liberation.
Philosophical musings about existence/non-existence are fundamentally not necessary for liberation, imo, based on the Buddha’s teachings on the Handful of Leaves (SN56.31) and the endless musings about why one was shot with an arrow, as in MN63.
All experiences are ultimately inscrutable, no?
But they’re real and exist in terms of: experiences, independent of our musings and speculations.
I mean denying experience is also an experience. So, existence in that sense and in this context.
Hi Yeshe, 
Agreed!
Causes and conditions is the only common denominator.
In this context, my use of “experience” is synonymous with this with the added aspect of consciousness, perception, and feelings in the human realm, (what we might conventionally call a “subjective” aspect of experiences ).
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Do you think it is necessary for liberation to understand the aggregates have no essence?
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Yes, if by “essence” we mean any sort of enduring, unchanging, soul/self/whatever.
At the same time, there is within causes and conditions some continuity. But that continuity imo is sometimes conflated with an on-going “essence” or self. DO teaches otherwise.
My point is that we can leave things there without trying to fill in the “mysterious gaps.”
True; but my general problem is that such expositions should lead to remarking the insufficiency of language to capture experience, not an ontological assertion that “Therefore nothing (actually) exists.”
There’s a difference between saying that and saying “It can not be said that something exists”. A difference of ontology & epistemology, don’t you agree?
The first one is a statement on existence, the other one a statement on our language and perceptions.
What about when the Teacher said that the Tathagata could not be found as true and actual in this very life? Was that an impermissible ontological assertion? I’m with you that language is inadequate, but I’m less clear that what has been said in this thread necessarily amounts to impermissible ontological assertions.
I think it’s an epistemological assertion, not an ontological one. He categorically doesn’t use an ontological qualifier such as “exist/ doesn’t exist” but something that implies perception - there is no tathagata that can be percieved.
See this quote:
or;
Even the choice of translating Dhamma here as phenomena rather than, say “ideas” or “concepts”.
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I don’t get your point. The conclusion of the Teacher was that because Anurādha had failed to find the Tathagata that it was inappropriate to claim the Tathagata as ‘true and actual’ in this very life.
The manner of search to find the Tathagata was to examine him in relation to the aggregates which were famously said by the Teacher to lack essence.
The conclusion was that the Tathagata is not ‘true and actual’, right? If we agree that for something to be said ‘to exist’ it must be ‘true and actual’, then the conclusion follows that the Tathagata does not exist, right?
Of course, you can say that ‘to exist’ doesn’t require something to be ‘true and actual’ in which case we’d be talking about conventional existence and not true existence, right? That would seem fair, but would only amount to which agreements we make with regard to definitions of words, right?
Maybe what you’re saying is that we can draw a distinction between saying ‘does not exist’ and ‘can’t be found to exist’ in the same way we can draw a distinction between ‘proven false’ versus ‘not proven true’?
If this ^^ is what you’re saying I would caution that adding ‘perception’ to the conversation can confuse. Illusions can be perceived for instance.
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The Buddha was quite clear that the self his opponents proposed didn’t exist, couldn’t exist, couldn’t be found. Thinking something is real is the basis of the self view.
But they’re real and exist in terms of: experiences, independent of our musings and speculations.
I mean denying experience is also an experience. So, existence in that sense and in this context.
How can they both be dependent and independent?
Solid, liquid and gas are concepts for a certain set for conditions. It’s just like milk, butter and ghee or baby, teenager and adult.