It would seem that I need to crawl towards an understanding of your statement...
...but maybe there is progress. So what you are saying is: Any prediction about the future of the universe on whatever foundation, including our best understanding of physics today, would simply be repudiated by the catalyst. It would simply say "you cannot know that you are right!". As long as time goes on, everything is possible in the sense that we cannot "disprove" that some arbitrary event will happen.
If the catalyst bases his reasoning on this kind of fundamental scepticism, it can choose whatever prediction it wants and claim that one cannot disprove that it will happen anywhere in the future. While this is internally consistent, I would call it madness,
Yes, you got it. And I would call it madness as well but that's what this ending is. Also, it is important to note that the catalyst itself doesn't choose whatever it wants, it chose the synthetic thing. The argument that it could choose whatever it wants would be my Shepard's argument to try and illustrate to it the madness of it's own scheme. No idea how it would respond to that.
and it does not reflect how the Leviathans programmed and describe it in their DLC. Based on fundamental scepticism, it would never have been able to learn from observation, extrapolate further evolution of organic civilizations and come to any conclusion like the one it has.
Why not? i am a scientist myself. I do not question causality within the realm of our observation or that we can learn from observation and draw conclusions about the probability of events to happen in our limited frame of reference. Yet, I do consider the possibility that we may never be able to learn everything or know the entire extent of reality. That's why I said before that I have trouble really imagining infinity.
As for Leviathan, it's been a while since I played it, so I went back and had a look. Here is how they describe the catalyst:
"To solve this problem, we created an intelligence with the mandate to preserve life at any cost. As the intelligence evolved, it studied the development of civilizations. Its understanding grew until it found a solution."
First of all, I think it's actually interesting that their instructions do not include AIs specifically at all (although that was the pertinent issue at the time it was created apparently as is said before in the dialogue). The catalyst's mandate is to "preserve life" (which I guess they confine to organic life and just didn't mention it because otherwise we'll get into a whole new slew of problems). Now once these instructions are given, the catalyst evolves on it's own and apparently it does take quite some time to come up with the idea of the cycles. If it is a true AI, who's to say it didn't go mad in this time with the idea.
Why do I advocate the notion that this kind of madness is what drives the catalyst? Well, because I haven't heard a logical explanation as of yet, so if the AI would follow logic, you'd think it would be easy to persuade it to stop the cycles. Yet, it kept doing its thing for over a billion years. It has to be twisted enough to keep this going for so long, no?
It has to have some other understanding of Epistemology than fundamental scepticism ("we cannot know anything"). And we know that it has a concrete goal to overcome its harvest solution, namely synthethis (which does not make any sense to me, but there it is). There has to be some reasoning behind this.
In a way, I see it in the exact opposite way. If there were solid reasoning behind it, it would not do what it does for so long. Its reasoning - as we both seem to agree - should eventually lead it to the conclusion that what it does - or rather what the problem is in the first place - is stupid.
Also, I wouldn't say it goes with fundamental skepticism (as in "we cannot know anything") but rather with the doctrine that any understanding is fundamentally limited (as in "we cannot know everything").
In the ME universe, all organic life seems to evolve, become sapient and discovers and practices science much like we now it in our universe (surprise
). So I'd assume that the catalyst works somewhat along that line and employs some version of the "scientific method" (which isn't really one method, but that's another topic).
I just don't see how any entity thinking along these lines could possibly come to the conclusion that inevitably synthetics will destroy all organic life in the galaxy, no matter if time is finite or infinite. Shepard could and should have asked the catalyst about it (both would have been instantly crushed by a surprise attack by an overwhelming writer's block, for sure, but maybe that would have been a better ending than the original).
Give the Asari a chance, maybe they'll never develop any AI, or maybe they develop an AI that spends all its time with musings about the meaning of existence between having sex with its creators, until the end of the universe or forever. Maybe the Salarians develop an AI that succeeds with the synthesis program that the catalyst did not get right until Shepard and the crucible came along? Ugh, actually this seems to answer the question of the OP:
This kind of goes back to what I said above. You can use "the scientific method" for predictions that will be accurate to a certain point from the perspective of your original measurements. If your methodology is good, than your predictions will go very far. You will however never be able to define or have information about everything. Doesn't mean science is good for nothing, just means its application and the resulting conclusions do have limits.
P.S.:
To stick to this specific scenario: Of course the catalyst would also have ceased to exist during the shift, so it cannot do anything about what the new organic life does after the shift back
. So practically it would need to prove that the AI-induced extinction happens before the shift, because everything after cannot be influenced by it anyway.
I don't know if the catalyst considers it's own failure or destruction. I guess as a result of my own reasoning here, I'd say that the catalyst would have to view its own eventual failure as inevitable as well, even before the crucible docks. I guess it would have to constitute the obvious truth that it's mandate can only be valid as long as it exists. Whatever happens after it's destruction would therefore not be relevant to the problem from its perspective.
Another interesting point from Leviathan in this regard: It is implied that the catalyst - even before the crucible - does not see the cycles as the best or ultimate solution:
"The intelligence has one purpose: preservation of life. That purpose has not been fulfilled. It directed the Reapers to create the mass relays, to speed the time between cycles for greatest efficiency. The galaxy itself became an experiment. Evolution its tool."
It may very well be aware of the problems that its current solution - the cycles - pose. Yet, it never came up with another, better one so far. It may not be possible to do so in any case. "fulfilling the purpose" if the purpose is "preservation of life" would mean to achieve a static state in which life exists. However, life by definition cannot be static. Either the universe is infinite, which, according to our previous discussion will always limit the time frame in which anything can be preserved or the universe will reach a final state (big freeze, big crunch, whatever), in which case life would seize to exist anyway.
By the way, ironically, none of the ending choices provided in ME3 fulfill the catalyst's purpose either. The crucible really must be a brain washing device, which purges all the Leviathans' silly ideas from the catalyst's mind without it even realizing that. 