The author isn’t committed to any claims about what animals can or cannot do. The argument concerns whether showing that animals can signal proves they have language — the author believes it doesn’t. But the author might believe that animals can entertain abstract ideas. That doesn’t undermine the argument. What matters is whether showing animals can signal can prove animals have language.

Not necessary, because this confuses sufficient and necessary conditions. The author believes that if an animal can’t refer to concrete objects or abstract ideas, then they don’t have language. But there can be many other requirements for language. So if an animal doesn’t have language, this doesn’t have to be due to lack of ability to refer to abstract ideas. Also, being able to “entertain abstract ideas” is different from being able to use signals to refer to abstract ideas.

Not necessary, because what matters is that showing animals can signal DOES NOT PROVE that they have the ability to use sounds or gestures to refer to objects/ideas. Even if animals actually are referring to objects/ideas when they signal, it’s still the case that the mere fact of showing that they signal would not prove that they’re referring to objects/ideas.

Necessary, because if it were not true — if a system of sounds/gestures CAN be a language even if it doesn’t refer to objects/ideas — then the potential lack of reference to objects/ideas would not be a reason to think that animals might not have language. If (D) weren’t true, showing animals can signal MIGHT be able to prove they have language, because language doesn’t require that those signals refer to objects/ideas.

Not necessary, becaue the author doesn’t have to believe there exist any animals that have language. In any case, the author’s assumed requirement is just that the system of sounds/gestures be able to refer to objects OR ideas. This doesn’t imply the author thinks a language requires the system to refer to BOTH objects AND ideas.