I do question the effectiveness (and accuracy) of this exercise, but its learning objectives I think are quite apt.
I do question the effectiveness (and accuracy) of this exercise, but its learning objectives I think are quite apt.
> and correctly taxonomising those propositions
The correct taxonomy for a proposition is true/false and proven/unproven.
I can not even fathom a mathematical model where distinguishing a "law" from a "fact" is meaningful.
And the idea of defining a "fact" as something empirically demonstrated is just ridiculous, I totally reject it.
Put another way, decidability is a large area of mathematical research.
What does ZF(C) have to do with decidability? Decidability is a question in any sufficiently complex system (Gödel's first theorem). And exactly this distinction is what I made for the taxonomy of propositions, you can group them into true and false and also into provable and unprovable. What would be a fact and what would be a law?
Regardless of that, in neither case the empiricism the site uses to define a fact would play any role.