Both Taiwan and China rely on the argument that Japan took the islands from the Qing, Japan agreed to return the islands after WWII, Japan should return the islands to us, as the successors of the Qing dynasty. To say that Taiwan might have a claim but China does not is not logical, unless you think that the PRC is not the proper successor to the Qing dynasty (and you'd be objecting to the handovers of Macau and Hong Kong to the PRC).
China thinks they have more than a Ming dynasty map, including Japanese maps that claimed them to be Chinese territory, as well as a letter from the Japanese foreign minister in 1884 indicating that the islands had Chinese names, and that China and its newspapers were protesting Japanese activity on the islands, and believing that China will protest if they annex the islands in 1885. Requests to formally annex the islands were denied until they had beaten China in 1895. China believes these facts indicate that they falsely claim that the islands were considered unclaimed lands in 1895.
The Ihlen declaration by the Norwegian foreign ministry was found to be binding in a dispute between Norway and Denmark over the sovereignty of Eastern Greenland, so statements by foreign ministers can be used as evidence in sovereignty disputes:
http://en.wikipedia.org/wiki/Ihlen_Declaration
I think China has an easier case of proving that the land was not terra nullius compared to Japan's case in proving that they were terra nullius in 1895, especially if we have the Japanese foreign minister saying China will protest if we take the islands in 1884 and 1885, with them taking the islands only after they had beaten China in 1895, and subsequently signing a treaty that says China will give them Taiwan and its surrounding islands.
The Eastern Greenland case shows how difficult it is to prove that land becomes terra nullius after it has been previously claimed, even without any exercise of power:
http://www.worldcourts.com/pcij/eng/decisions/1933.04.05_greenland.htm
I'm not objecting to either the PRC and/or the RoC being the successor of the Qing only that it's not clear that in relation to islands that are most proximate to the RoC (and who were the legitimate government when islands were ceded back to China after WW2) that control should go to the PRC (assuming that Japan is illegitimately controlling the islands). Because again, while both countries may say otherwise, and while the international community turns a blind eye to it, the PRC has no legal authority within Taiwan and its possessions. Am I wrong? Can the Mainland create law that has binding effect within Taiwan?
Thanks for the information! These are the types of arguments I wish people would make more often.