As johnecheck points out, in a certain level of abstraction, the main way of defining a country is whether other countries consider you a country or not. Even when other countries do consider you a country, what the borders are exactly might not be clearly recognized.

Since countries are political divisions, I'd also argue that this is the main and most important definition.

BTW, even "continents" suffer from this where in the US, Europe and Asia they are defined differently.