Science if properly understood is not an hypothesis to be tested but, taken as a whole, is the methodology applied within such individual tests of hypotheses.
Science is an activity, not a methodology. It's an activity that comes with a method, broadly defined, not a methodology. But, yes, the method makes the activity scientific but that doesn't make science a methodology. Rather, the methodology that each scientific field will have results from developing and improving on the scientific method, according to historical possibilities and the economic context. Methodology includes technological means, things like microscopes, and you don't want to be unable to do science till you get one, right? But just looking at nature doesn't make you a scientist so you need to use the proper method to become one.
let’s propose a definition and see whether it’s falsifiable: “Science is a methodology that results in well-tested theories that describe the observable world as well as possible given all the known facts”. Is it a testable hypothesis? Yes, I think it is! Not in one sitting but in all the instances of science, since they are science and there is no science-thing separable from them… testing falsifiable hypotheses with the scientific method does observably produce theories that successfully describe nature to the best of humans' current ability.
The things that need to be falsifiable if they want to avoid being vacuous are claims. Any claim. So, including the scientists' claims. To be scientific, scientists' claims, i.e. scientists' theories, i.e. general relativity, quantum physics, particle physics etc. have to be falsifiable, not science as a process. And theories put forward by scientists are usually falsifiable, although I don't know in the case of string theory for example.
Your definition is non-falsifiable because of the "as well as possible given all the known facts". According to your definition, Newton's theory was not falsifiable until it got falsified. Surely, it's more reasonable to say that Newton's theory has always been falsifiable, only scientists couldn't falsify it at the time and we had to wait for Einstein.
Maybe you could look at the claim that the scientific method is the most efficient/accurate/useful etc. method to use for describing/predicting/knowing the world. It seems to be falsifiable in theory but I'm not sure in practice. But it's also questionable in theory because of the term "world". What do you mean by "world"? I know pain whenever I'm in pain and science cannot beat that. But most scientists would have their own definition of pain so that science becomes the best way to investigate that while suggesting that pain as experienced subjectively by me somehow doesn't belong to the real world. So, I would put the claim a bit differently to make it falsifiable, at least in theory: The scientific method is the most effective method for representing the material world. But of course, this is acknnowledging that there are things that may not necessarily belong to the material world. But that's the challenge. To make your claim falsifiable you have to make it less fuzzy, which may result in leaving out essential things like subjective experience.
The scientific enterprise is itself its own test, but you have to recognize where the testing is done: in each and every scientific experiment. The category itself isn’t separably testable.
The "scientific enterprise" comes with the claim that science is the best way to know/predict/etc. the (material) world. So there's a claim and I think it's falsifiable although it may be be very difficult to do it even if the claim is wrong. But falsifiability only requires that you could realistically conceive of a way to show a claim to be false even if in practice you can't do it. Science in effect falsifies common-sense theories. Some common-sense claims would be very difficult to prove wrong to most of us but they are still falsifiable.
EB
