Did Japanese military and political leaders during WW2 realistically believe that they could conquer and hold China, hold most of South East Asia, and defeat the U.S in the Pacific? If so, what was their reasoning?

Outside of China/Korea occupied territory was under control of independent governments under something called the greater eastern co prosperity sphere. Officially this was a economic grouping of countries against western imperialism in practise it was a way of dominating east asia and slaving these countries economies to Japan's benefit. Japanese aim was to secure resources not living space.

At least within Korea and Taiwan (which were imperial colonies, not puppet states as Japan employed elsewhere), there was more colonization of Japanese settlers, integration of the native people into Japanese society (e.g., being required to use Japanese names, being taught in school to be good imperial citizens and subjects), and even taking moves to incorporate the territory into the empire proper, although the war would end before that happened.

There were significant differences in the way that natives and Japanese were treated and their opportunities in life, although the gap was closed somewhat over time. It was certainly a Yamato First colonization, but not as barefaced in its exploitation as that of European powers often was; in fact, many elderly Taiwanese look rosily on the period, partially because of the relatively better treatment of Taiwan to other occupied/colonized areas, partially because of the despotic rule of the KMT following the end of the Chinese Civil War.

While there was plenty of exploitation of Taiwan's natural resources, it's unlikely conditions would've been better under any other government. The Japanese government undertook a number of public works that are still in use today--much of Taiwan's railway network was developed during the colonial period, as was much of the educational system. The top school in Taiwan, National Taiwan University, was the first and only Imperial University established on the island (Taihoku Teikoku Daigaku, Taipei Imperial University; Seoul University likewise was an Imperial University established outside Japan.); the Presidential Building in downtown Taipei was originally the Governor's Mansion during colonial rule (fun fact: the building is shaped like a giant 日 character, the "ni" in "nihon")

To bring it back around, when Japan took control of Taiwan in 1895, the Qing dynasty had mostly only allowed settlement on the flatlands on the western coast of the island--the land apportioned for Han settlers was segregated from that of the mountains, reserved for the native peoples (this line would be extended further and further into native territory). While they had begun the process of modernization, they had not fully developed or exercised sovereignty over the whole of the island. I do not actually know if Japan had specific intentions in taking Korea and Taiwan beyond the obvious economic and strategic reasons, so I won't speculate, but keep in mind that these takings occurred in the context of East Asian politics at the time, and Japan's conflict with the Qing; not a mere desire for those territories exclusively.

/r/AskHistorians Thread Parent