Taiwan is formally the Republic of China. Its government used to be the government of China as a whole until forced to retreat to Taiwan by the communists, during the civil war.

In fact, formally they still claim the whole of China since that's the constitution of the Republic of China, founded in 1912.

You'll note the portrait of Sun Yat-sen, first President in 1912 in the Taiwanese Parliament. And obviously the flag.

Based on this I believe that 'independence' means writing this off and declaring that Taiwan is not China but an independent "Republic of Taiwan" only.