Is impermance provable?

In Buddhism, not all things are impermanent, such as the enlightenment & Nirvana during the lifetime of a fully enlightened mind, which are permanent.

His release, being founded on truth, does not fluctuate, for whatever is deceptive is false; Nirvana — the undeceptive — is true. MN 140

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Sariputta, there are certain recluses and brahmans whose doctrine and view is this: 'As long as this good man is still young, a black-haired young man endowed with the blessing of youth, in the prime of life, so long is he perfect in his lucid wisdom. But when this good man is old, aged, burdened with years, advanced in life, and come to the last stage, being eighty, ninety or a hundred years old, then the lucidity of his wisdom is lost.' But it should not be regarded so. I am now old, aged, burdened with years, advanced in life, and come to the last stage: my years have turned eighty. Now suppose that I had four disciples with a hundred years' lifespan, perfect in mindfulness, retentiveness, memory and lucidity of wisdom. Just as a skilled archer, trained, practiced and tested, could easily shoot a light arrow across the shadow of a palm tree, suppose that they were even to that extent perfect in mindfulness, retentiveness, memory and lucidity of wisdom. Suppose that they continuously asked me about the four foundations of mindfulness and that I answered them when asked and that they remembered each answer of mine and never asked a subsidiary question or paused except to eat, drink, consume food, taste, urinate, defecate and rest in order to remove sleepiness and tiredness. Still the Tathagata's exposition of the Dhamma, his explanations of factors of the Dhamma, and his replies to questions would not yet come to an end, but meanwhile those four disciples of mine with their hundred years' lifespan would have died at the end of those hundred years. Sariputta, even if you have to carry me about on a bed, still there will be no change in the lucidity of the Tathagata's wisdom. MN 12

The above being said, the enlightenment of a Buddha does end at the termination of life, therefore it is, ultimately, impermanent.

And the Blessed One addressed the bhikkhus, saying: "Behold now, bhikkhus, I exhort you: All compounded things are subject to vanish. Strive with earnestness!" This was the last word of the Tathagata. DN 16

Impermanence is experienced when it happens not in memory. Impermanence is contemplated by being aware of when phenomena has ended. If you were to be aware of memory then when that memory ends and one is aware of it then that is the contemplation of impermanence.

One doesn't contemplate impermanence of intellectual or conceptual entities. They don't really have any concrete beginning or end.

A little bit about science, proofs and buddhism bellow.

"Check out my reasoning and tell me where it's flawed."

1) To know that nothing stays the same you have to have a reliable, permanent memory.
2) If memory is impermanent, then it cannot be used to measure change.
3) If you cannot measure change then you can't know if anything is impermanent.
4) Impermanence is impossible to prove.

Domain and definitions

"to know", "the same", "reliable", "permanent" and "memory", all of these terms can be, individually, subject of many books. The same goes for "impermanent", "measure" and "change".

As they are, they can be very ambiguous, hard to understand their meanings and hard to understand how they relate. For example, does "permanent memory" mean inability to forget? Does "reliable memory" mean what is remembered is always precise and "the same"?

Playing this little game, if these questions are answered with "yes", then the requisites you posited seem to refer to some sort of ability not found in humans and animals, since we forget and our memory faculty is not reliable and does not work like reliable "data retrieval" mechanisms (which always "results" in the "same data"). Therefore, one can argue that if we don't have this sort of faculty, then what can we "know"?

And the really tricky part in the first and third propositions is the "to know" part: it imports the massive topic of epistemology into the problem. Pandora box opens with questions such as "what is knowledge?", and goes through "well, how do you know that our memories are unreliable and we forget?" (to which a witty person could reply: "I'm sorry, what are we talking about, again?").

At this point, you are in philosophical grounds and might feel like venturing into the nature of knowledge and what is possible to know, exploring the dungeons of theories of knowledge.

One might also age and die in this dungeon, ironically witnessing and suffering a lot of changes oneself, and still feeling uncertain of whether things are impermanent.

Science, Inferences and Proofs

Or, perhaps you might not want to philosophically penetrate every corner here and die without an answer. Then, some corners must be given up.

"to know" seems too philosophical, and perhaps you want to be scientific in some way. Interestingly, in science, "knowledge" is, roughly speaking, just something accepted, shared and rooted in what is public, accessible, reproducible -- or simply, "empirical". All that is needed is two observers agreeing on their descriptions of what they observe.

In this path, you are effectively sacrificing all the philosophical problems of knowledge in order to move on, on a hopefully more manageable ground. By making this sacrifice, you will also be forced to change your propositions that refer to "knowledge". Likely, the best you can do is talk about what is observed.

"Memory" is very problematic as well (do you really want to talk about whether there's knowledge or not for a being with imprecise memory such as humans? This puts you right back into philosophy asking what knowledge is...).

But I see other problems with your reasoning too, if you want to explore this in the domain of science.

The first problem are the inferences. Taking your propositions as they are for illustration, to undertake this project it will be clear you need to rigorously justify things like: how properties of memory affect possibility of knowledge (p.1), how they affect ability of measurement (p.2), how this ability relates to knowledge (p.3), and how the impossibility of measuring a property entails impossibility of proving same property (p.4).

For example, in p.1, if "to know" is simply what is agreed by two or more people, then how does a unrelated change in memory affects knowledge? According to the answer, your reasoning and formulations must be revised.

The second problem is "proof". And what is a proof? In mathematics and logic they are roughly structures drawn from rules of inference and axioms. In journalism, it's how journalists and media refer to scientific work. And in science (to the surprised of journalists) it's not advised to use it: "evidence" and "arguments" are commonly used in contexts of findings and theories, since as a matter of principle, "proofs" must be subject to refutation.

So, to insist on irrefutable proofs, you must sacrifice science. And to insist on science, you must sacrifice proofs. The same goes, roughly, for what is "possible" or "impossible" (p.4).

Reality and Buddhism

If you turned around from the philosophy dungeon trying to answer this question and preferred to stick with reality, at this point, I believe you concluded that the nature of knowledge won't help you decide if impermanence is experienced or not.

Also -- and if I was convincing enough so far -- I hope you have concluded that elaborating a proof that impermanence can't be proved is a futile exercise.

What is left, then, is a job much easier. To establish whether something is impermanent or not:

1. start with an observation.
2. If any alteration is perceived, then Q.E.D.

I think perhaps that a permanent perfect memory isn't necessary. Even if all you have is a fake memory, all you need is for it to be telling you that there was a past moment that is different from the present.

First, I think you don't "prove" theories: instead you you "test" them.

For example there's a theory of Gravity (sometimes called Newton's Law of Gravity) -- it's not that you can prove that, exactly, it's that you can test that, by dropping things.

Similarly I think you're expected to test the theory of Impermanence -- does the theory match your experience, your observations?

Second, IMO the doctrine isn't that "anything" or that "everything" is impermanent: it's more specific, for example it says that "feelings" are impermanent, or that sankharas are impermanent.

Third, to address the logic you asked about -- IMO even an impermanent memory is sufficient to measure change. For example any thermometer is impermanent (will break eventually) but can measure change of temperature. Any human being is impermanent (will die eventually) but can observe and experience change (change in the seasons, in their surroundings, in their thoughts and feelings, and breath, and anything else you care to mention).

I guess you might want to argue that some things are relatively long-lived and seem permanent -- perhaps your family, a mountain, the sky -- if so I might reply that reason or science (even if not personal memory) suggests that these things too are impermanent for various reasons; and, more importantly, our awareness or "consciousness" of them is impermanent or ever-changing.

I think that Buddhism isn't trying to make statements about "the world" -- it isn't physics or geology, nor is it philosophy or pure logic -- it's applied logic, and it's trying to make statements about our experience of the world.

Consider dukkha, for example, you're not going to measure that with a thermometer, it's not a property of the physical world (the world of physics), it's a property of our experience of the world (perhaps our clinging).

Ditto other important components of Buddhism: view, wisdom, clinging, and so on.

My answer is that Awakened One knows it by experience. For example if you experience world is a dream then will you not agree that all things are impermanent? Yes you will.

Some Truths are better explained by the Awakened One only because he has experienced those Truths.We can only believe in the Awakened One. We believe in him because he brings goodness and happiness in our lives just by believing him. Therefore there must be faith in the Awakened One. Remove all your doubts and believe in the Awakened One.

Is impermance provable?

Of course. Through the practice of Insight meditation the mark of impermanence becomes visible. It can be seen in all conditioned phenomena, e.g. the breath. Try to observe the in/out-breath and you will see impermanence on a gross level..