What is Archaeology?

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I am told that over in the UK there was a feature this morning on BBC Breakfast, repeated about hourly, about how well thought of detectorists are by archaeologists. The programme features among other things Central Yorkshire Metal detecting club (wot, no webpage?) members in a nice line on a suspected civil war site. They are hunting artefacts on it in co-operation with the Yorkshire Museum - who says more and more are becoming "responsible" and reporting their finds. Michael Lewis appears on the programme to say the usual PAS stuff. What annoyed my correspondent however was that both the presenters in the studio and the woman on the outside broadcast repeatedly called the artefact hunters "amateur archaeologists" (at least 5 times and the programme was repeated). Who is telling them that artefact hunting is amateur archaeology? Is big game shooting (or pheasant shooting) amateur ecology? Is collecting costume 'Barbie' dolls amateur ethnology? More to the point when (if at all) should we consider artefact hunting and collecting amateur archaeology, and when can it not be? Or perhaps to turn the question round, when is archaeology merely artefact hunting?

I am just waiting for the day when a British developer, told he should finance an expensive rescue excavation, refuses but instead offers to allow the archaeologists to run all the soil dug out through a water-sieving plant (like in gravel quarries) to get the artefacts out, and I would like to see the public debate why not. I suspect if the British public is fed any more of this 'we only want the (gold and silver) artefacts' and 'artefact hunters are archaeologists too' nonsense, the archaeologists will not get a lot of public sympathy.

What is archaeology according to British archaeologists? Why are they keeping it a secret from the British public with its largest public 'outreach' presenting it as something completely different?

UPDATE: See now here (link to BBC video).
Vignette: the official scheme has got it wrong, thank goodness for Time Team which talks the archie talk much better.