-Introduction-
In this paper I intend to prove that the game ending does not follow from winning the game by escape velocity, and furthermore that it leads to contradiction. I also intend to show what contradictions arise from assuming that winning ends, or is in itself the act of ending the game. Finally I intend to show how winning the game without the game ending is the only logically consistent way of winning the game.
-Methodology-
For the purposes of this paper „winning“ refers to winning the game by reaching escape velocity. We will also define „is won“ as meaning that there exists at least one player having escape velocity. Furthermore „has been won“ means that a player has had escape velocity. „To end“ means here, being terminated.
-First thesis- The contradiction consisting in having escape velocity and a score of 0
If there is a player of Agora who has escape velocity, then there doesn’t exist a player that has escape velocity. Here I’m making the assumption that the rule is to be read logically, in which case you have „one or more specified players have achieved escape velocity“ and „all players’ scores are set to 0“ happening at the same time.‹1› This is obviously a contradiction, and not a logically consistent way of winning the game.
-Second thesis- The contradiction in achieving escape velocity followed by/being the game ending, without the score being reset
Next up for consideration is for the game: (a) to be won, followed by (b) being ended and finally (c) the scores being reset. If the game is won and then ended (or winning is ending the game), the scores cannot be reset. The scores being reset follows necessarily from winning the game, but can’t follow if the game has ended. Therefore it isn’t possible for the game to be won, end and then finally the score being reset. Nor is it possible for the game to be won and end at the same time, being followed by the score being reset.
A counter-argument would be saying that if you want to play a new game (here: after the game has ended), you would have to reset the score. But this obviously doesn’t work out for the simple reason that there would be no game for which you could reset the score if the game had ended.
For the same reason CFJ 3400 couldn’t have been judged TRUE, because it would then make a truth statement within the confines of the game itself about the game having been ended at a previous time, which would be a contradiction, because the game obviously hasn’t ended. This is therefore not a logically consistent way of winning the game.
-Third thesis- The contradiction in achieving escape velocity followed by the score being reset and the game ending thereafter
Next up for consideration is for the game: (a) to be won, followed by (b) the score being reset, followed by (c) the game ending. If the game is won, the score will be reset. If the score has been reset, the game isn’t won anymore, therefore there would be no reason to end the game. From this it seems plausible to conclude that the game being ended must follow from the game being won. This is the only logically consistent way of winning the game, it does not however, and cannot, follow that the game is ended because of winning the game in this manner, as has been shown.
-Conclusions-
It follows from the above that resetting the score must follow from winning the game, and that this is the only logically consistent way of winning the game. It has also been shown that ending the game cannot be, nor can it follow from winning the game. Because in the first case resetting the score cannot follow from winning the game, which would be a contradiction. In the second case ending the game would be pointless, because it wouldn’t be won anymore due to the score reset. It also follows that the game cannot judge the game to have ended within the confines of the game itself. It would seem then that ending the game transcends the possibilities of what can be done within the framework of the game itself.
-Citation-
‹1› Excerpts from R2419.
-Further reading-
‹1› Agora-business, February 2014 ‹2› Agora-discussion, February 2014