Historical evidence shows Japan's claim groundless
The answer is definitely no. China holds an inchoate title over the Diaoyu Islands in accordance with international law. Voluminous historical materials show that China was the first country to discover, name and exercise administrative control over the Diaoyu Islands. For instance, the book Shun Feng Xiang Song (Voyage with a Tail Wind), published in 1403 during the reign of the Ming Emperor Yongle, already referred to the islands that Chinese voyagers had passed en route from Fujian to Ryukyu as the "Diaoyu Islet" and "Chikan Islet", which today are known as Diaoyu Island and Chiwei Islet. Chou Hai Tu Bian, or An Illustrated Compendium on Maritime Security, compiled by Hu Zongxian, the supreme commander of the southeast coastal defense of the Ming court, and geographer Zheng Ruozeng, marked the Diaoyu Islands as under the Ming court's coastal defense jurisdiction.
Even historical documents published by other countries recognize China's sovereignty over the Diaoyu Islands. The book Illustrated Outline of the Three Countries written by Japanese geologist Hayashi Shihei, was the earliest Japanese literature to mention the Diaoyu Islands, and the attached Map of the Three Provinces and 36 Islands of Ryukyu marked the Diaoyu Islands in the same color as the Chinese mainland. The Chronicle of Ryukyu also furnishes proof that British naval vessels had to obtain permission from the Chinese government before conducting surveys in waters off Ryukyu and Diaoyu islands in the 1840s. All these contradict Japan's claim that Diaoyu Islands were terra nullius.
Japan meanwhile denies that the Diaoyu Islands are geographically and historically affiliated to Taiwan. It says that it renounced Taiwan and the Penghu Islands that China had ceded to it under the unequal Treaty of Shimonoseki, however, the treaty did not mention the Diaoyu Islands. That is how Japan comes to the fallacy that the Diaoyu Islands were not ceded to Japan as islands appertaining or belonging to Taiwan, and claims instead they are part of the Nansei Islands. These arguments are untenable in the light of the historical evidence, as well as international treaties such as the Cairo Declaration and Potsdam Proclamation.
The San Francisco Peace Treaty cannot help justify Japan's sovereignty claim, either. Article 3 of the treaty gave the US sole power of administration over the Ryukyu Islands. In 1953, the US Civil Administration of the Ryukyu Islands issued the Civil Administration Proclamation No 27, which defined the geographical boundaries of the Nansei Islands as between 24 to 28 degrees north latitude and 122 to 133 degrees east longitude. However, the proclamation did not specify which islands were included, and without knowing the US actually included Diaoyu Islands within the boundaries, China did not lodge an immediate protest, but this can hardly indicate that China acquiesced in the islands being part of Ryukyus and that China did not consider the Diaoyu Islands as appertaining to the island of Taiwan.
It is widely known that the San Francisco Peace Treaty was signed between Japan and the allied powers, and China was never involved in the treaty. The US unilaterally included the Diaoyu Islands within the boundaries and returned the islands as part of the Ryukyus to Japan in 1972, and such an underhanded deal can by no means support Japan's sovereignty claim over the Diaoyu Islands.
The author is a researcher at the Hong Kong Institute of Asia-Pacific Studies, the Chinese University of Hong Kong.