Definitions are a powerful tool. In mathematics, we can precisely define classes of object (numbers, algebraic structures, topological spaces, etc.) and then learn things about them by logically manipulating the definition. Writing down a formal definition is the only way we can actually get at a class of non-physical objects and do stuff with it. This the thing I've seen students struggle the most with in learning maths - they will start out trying to prove a result without considering the definitions of the objects it mentions, and they get nowhere at all because they have nothing to work with but a vague intuition and some examples.
Definitions need to be exclusive to be useful. The smaller the class of objects you're talking about, the more truths will hold in general for all objects in the class. If you talk about finite two-player perfect-information zero-sum games, you can make some pretty strong statements, which are very useful if you're working in that context.
It's important to bear in mind that theorems are completely meaningless if not all their conditions are satisfied - if you try to apply them where your assumptions don't hold, bad things can happen.
And it's important to bear in mind that a definition does not say anything about how things should be. It's not a prescription. It doesn't say that what lies outside is not worthy of consideration.
@doougle: @ElectronDance @raphkoster Raph, these discussions have POLITICAL consequences. Like what games get recognized at IGF, etc.
So there's a tension here. For POLITICAL purposes, definitions should be as inclusive as possible. Everyone should just make cool stuff and not care whether it fits some restriction, and festivals like IGF should be broad and accepting of all of this. But for useful technical discussions, we need to be clear and precise about what we're talking about by using exclusive definitions. When people confuse the two there's a problem.
I kind of wish "game" wasn't the general term for interactive software art. Maybe we kind of need a new term for rule-driven consequentially-interactive maybe-competitive games, because they're an interesting class of object and it's worth discussing them, and it would be nice if we could reason about them without having to make exceptions for Proteus every time.