I would tell the students that any compactly specified model has to rely on a certain amount of “common-sensical” interpretation on their part, such that they need to evaluate what “counts” as a legitimate application of the theory and what does not. I’d argue this by analogy to their daily lives where interpretation of this sort is constantly needed to make sense of basic statements. Abstractly, this arises due to reality having a lot of detail which needs to be dynamically interpreted by a large parallel model like their brain and can’t be handled by a very compact equation or statement, so they need to act as a “bridge” between the compact thing and actual experiments. (Indeed, this sort of interpretation is so ubiquitous that real students would almost never make this kind of mistake, at least not so blatantly) There’s also something to be said about how most of our evidence that a given world-model is true necessarily comes from the extended social web of other scientists, but I would focus on the more basic error of interpretation first.
I would tell the students that any compactly specified model has to rely on a certain amount of “common-sensical” interpretation on their part, such that they need to evaluate what “counts” as a legitimate application of the theory and what does not. I’d argue this by analogy to their daily lives where interpretation of this sort is constantly needed to make sense of basic statements. Abstractly, this arises due to reality having a lot of detail which needs to be dynamically interpreted by a large parallel model like their brain and can’t be handled by a very compact equation or statement, so they need to act as a “bridge” between the compact thing and actual experiments. (Indeed, this sort of interpretation is so ubiquitous that real students would almost never make this kind of mistake, at least not so blatantly) There’s also something to be said about how most of our evidence that a given world-model is true necessarily comes from the extended social web of other scientists, but I would focus on the more basic error of interpretation first.