Yesterday, the question became a deadly one, after a Hong Kong man died in the latest round of a dispute which is proving a grave embarrassment to the governments of Tokyo, Taipei and Peking.
The tragedy occurred yesterday afternoon when a cargo ship, the Kien Hwa No 2, arrived in the sea close to the islands following a four-day voyage from Hong Kong. As well as several dozen journalists, the vessel carried members of a group of Hong Kong Chinese with a mission to carry out. This was the demolition of a small beacon which had been erected two months earlier by a group of Japanese right-wingers. To the Hong Kong protesters, the islands are unquestionably the Diaoyus, and they belong to China - a claim made with equal vehemence by Japan (Senkakus) and Taiwan (Tiaoyutais).
To prove their point, and despite the presence of 20 patrol boats and helicopters of the Japanese coastguard, some of the protesters launched dinghies from which they jumped into the rough sea. By 2pm, in spite of attempts at resuscitation by doctors, the expedition's leader, David Chan, was dead.
A consular officer from the British embassy in Tokyo is today making the 1,200-mile journey to a hospital in Japan's southern Okinawa prefecture to visit another member of Mr Chan's party who narrowly escaped death; the protesters' ship was last night sailing away from the Tiaoyutai-Senkaku- Diaoyus. But the tragedy will only fuel a struggle that has been smouldering for 25 years and which the governments in the region hoped to forget.
Both Tokyo and Peking find themselves in the unaccustomed position of being bounced into taking a stand on the islands by nationalists within and outside their own countries. Despite a bitter wartime history, and occasional explosions of vituperative rhetoric from Peking, the two sides had agreed to shelve the question.
But the issue was forced in July by the construction of the small lighthouse by the Japan Youth Federation, an unsavoury right-wing group which has links with organised crime.
The act provoked immediate protests from Taiwan and China, which has hinted darkly of "connivance and protection from certain Japanese quarters". Tokyo maintains, rather unconvincingly, that there is nothing that it can do: the islands are privately owned and no offence has been committed under Japanese law.
But while the diplomatic exchanges continued, the dispute stirred up a rare burst of pan- Chinese outrage. In Taipei and Hong Kong, there have been furious demonstrations against the lighthouse. This is alarming enough in Tokyo, but it is also causing anxiety in China. Independent nationalist movements of whatever type are alarming to Peking, especially when they issue from Taiwan which still claims it is the "true" China.
On Wednesday, the Japanese and Chinese foreign ministers met in New York for an inconclusive meeting which appeared to have calmed the situation. The question is whether this calm can survive the death of Mr Chan.