(Puzzle the fourth.)
Knowing that he cannot hope to win the Battle of the Marks over the chessboard, royalchicken issue the following challenge to T1000 (and anyone else who'll solve it).
Royalchicken says that there are two identical twins, let's call them Akribis and Lathemenos, who behave in an odd way. Akribis has a perfect understanding, and always tells the truth. This means that he believes all true statements to be true, and false ones to be false, and he always tells the truth. Lathemenos believes all true statements to be false, and false ones to be true, but he always tells what he would consider a lie. For example, when asked Is 9*7 = 63?, they would give identical responses-Yes. Akribis would think he was telling the truth, Lathemenos would consider his response a lie. My question is whether a series of yes-or-no queries can be devised to tell which is Akribis and which is Lathemenos, and if so, specify this series of questions.
Enjoy. Also, upon further reflection, I note that certain philosophical questions could arise, so there are some answers that are better thn others (hint).