For instance, "Le garçon mange la viande" means "the boy is eating the meat", why does it also mean "the boy is eating meat"? (No article in the English translation..) When does this apply, and when doesn't it?

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Well, I'd translate "the boy is eating meat" by "Le garçon mange de la viande". In this context 'de la' means an unknown amount, pretty much like the English sentence. Just saying "'mange la viande" indicates the subject is eating a particular piece of meat.