Objection!

Erratum on Sun, 10/3/21, 8:01 PM UTC: On some browsers, the embedded player may suffer from jittering. We believe this is now fixed, but if you are experiencing this, please use the YouTube link instead. This is not part of the puzzle.

Erratum on Sun, 10/3/21, 9:56 PM UTC: The last dialogue of Argument 1 should say: "Egg and mushroom soup has two sets of double letters, the G and the O. Isn't that wonderful?" with "two sets of double letters" in orange.

The many-headed giant loves to argue with itself. What needs to happen for the heads to reach common ground?

The video versions of each argument are provided only for convenience. Any differences with the interactive versions are not part of the puzzle.