Earlier quoted context omitted.
Take the simplest problem of searching over a continuous range between zero and one exhaustively. Let the value you search for be 0.1. By a diagnolization argument we can realize that even a search carried on for an infinite amount of time and granted an infinite amount of space would not terminate. After all, to find 0.1 you need to make it past 0.01. But to reach that you have to reach 0.001. And so on. Let abstrac…
You are talking about game theory without any precise definition of "abstraction", which it seems like one can define it to be whatever one wants it to be. One abstraction that is very useful is linear algebra which is an abstraction without errors. Same goes for category theory. Grothendiecks work wasn't about tolerating errors in abstractions either. Simple abstractions like generic containers are also not about ig…
You're claiming that if someone points out that abstractions with error - which are literally impossible to avoid - are useful despite the error, then they're just pretending to know things. But anyone complaining about abstractions having error as a basis for abstraction being wrong is fundamentally missing the point of abstraction.
We need abstraction. It isn't illogical to tolerate the error. It is suicide to not tolerate the error, because you won't terminate - which means you can't react. Haven't you ever wondered why people aren't purely rational? Why we think fast, not just slow, but also fast? These questions have answers. You can look at the foundations of learning in terms of graphs and see why it has to be so. I'm sorry it goes over your head, but it is fascinating regardless of whether or not others understand it. And I think it is worth sharing, because it is fundamental truth.
This is formally provable, but to put that another way - I don't care if you want to be wrong; good for you, saving yourself some time. Enjoy your day.