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Having slept on it, I think the confusion is perhaps brought about by our dropping of the word set . We have come to say "I'm going to buy a new television", but it should be a 'television set', as Jack's wireless was really a wireless set and prior to that a crystal set.
So strictly speaking, the thing you look at, - the object in the room, is a television set, but 'television' is now the medium we watch on it.
You wouldn't say it of course, but you could say " I saw a television programme on the screen of my television set" abbreviated to "I saw it on the television"
Am I right?