Do you have a cite that the ambiguity was intended to reduce the chance the Japanese would surrender? I don't know the history well.
I have the impression that, given the US's knowledge of its own military superiority, it would never have accepted anything besides total surrender and occupation. (This is not just vindictive; cease fires and truces are less effective for ensuring the enemy doesn't rise later.) Therefore, if the declaration was vague, this if anything would have been to encourage getting the Japanese to the bargaining table.
Wikipedia seems consistent with this:
> A major aspect relating to the Potsdam Declaration was that it was intended to be ambiguous. It is not clear from the document itself whether a Japanese government was to remain under Allied occupation or whether the occupation would be run by a foreign military government. In the same manner, it was not clear whether after the end of the occupation Japan was to include any territory other than the four main Japanese islands...This ambiguity was intentional on the part of the U.S. government in order to allow the Allies a free hand in running the affairs of Japan afterwards.
One can certainly criticize the US for not accepting conditional/partial surrender as a way to avoid unnecessary deaths, but the ambiguity of the declaration doesn't seem like the issue.
If fairly clearly shows that they were not listening to the requests made in the Szilard petition, which is what I am claiming. They did not publicly offer the terms of surrender or wait for a refusal.
For others, here are the relevant excerpts from the Szilard petition, which is quite short and worth reading in full:
> We feel, however, that such attacks on Japan could not be justified, at least not unless the terms which will be imposed after the war on Japan were made public in detail and Japan were given an opportunity to surrender....If such public announcement gave assurance to the Japanese that they could look forward to a life devoted to peaceful pursuits in their homeland and if Japan still refused to surrender our nation might then, in certain circumstances, find itself forced to resort to the use of atomic bombs....we, the undersigned, respectfully petition: first, that you exercise your power as Commander-in-Chief, to rule that the United States shall not resort to the use of atomic bombs in this war unless the terms which will be imposed upon Japan have been made public in detail and Japan knowing these terms has refused to surrender; ...
This is not the case, the petition was to prevent the US from dropping a bomb unless Japan had been given the terms of surrender and refused them. This did not happen, and thus the situation can't be boiled down to "nuke or invasion" as there was a third option was not tried. I'm not making any further arguments, my positions on them are extreme and I don't want to try to convince others of them.