my conditions:
saftey
1, yes send it back if: the work was stollen from a country, and that country is now stable and seccure enough to return it to
2, no, keep it in the UK if: the country poses a risk to the work = no, keep it safe in the UK
justification/examples - work originating in middle eastern countries that do not have stable goverments and have a recent history of destroying monuments/imagary not assosiated with X belief/political movement, may be best preseved in the UK, rather than back in its country of origin. Until the country is stable again.
if condition 1 of saftey is met, then:
cultural relivance to the UK
1, yes send it back if: if the work has developed no significant cultural relevance to the UK since arriving, and has just been sat in museums/galleries
2, no, keep it in the UK if: if the work has greater cultural relivance to the UK beyond just being taken from its country or origin to show, for example it became cultural symbol
justification/examples - the kohinoor diamond has developed its own significance within the UK, as a part of our royal families crown jewels, and should be kept. Had it just sat in a museum and played no function or gained no further significance after arriving, it should be sent back
If conditions 1+2 are met, then:
what was the origin of its departure from its country of origin
1, yes send it back if: it was stolen or looted during war-time.
2, no, keep it in the UK if: it was a gift from another culture, or part of a trade/deal
justification/examples - Stealing/looting is obviously morrally wrong. Gifts are much more subjective and hard to make judgements on retrospectivly. The dynamics of historical gifts or deals are highly debatable, especially to what extent extortion, or power-dynamics played into them. Given that its rarely possible to unanimously agree on the nature of a gift, the susspicion of immorality is not alone enough to warrent returning artifacts
if conditions 1+2+3 are met, then:
what is the current relationship like between the UK and the artifacts country or origin
1, yes send it back if: there is a good relationship between the two countries, and any british artifacts held by the other country are also exchanged
2, no keep it in the UK if: there is a problematic relationship, threats, or violent/political issues between the two countries, or if the other country holds british artifacts which it is not willing to relinquish
if all conditions are met then send the work back to its country of origin
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based on those conditions, given the example of the loot taken from the summer palace in China - yes I would send it back. I don't see any reason beyond selfishness/racism/nationalism/blind patriotism to keep it in the UK. I also don't see a moral justification in selling it back, as that would seem to me like a historical version of stealing someones car and demanding a ransom for its return.