I’ve always wanted to make a game where the rules are dynamic in a way, but better than that stupid game Flux. I’ve decided that the game would have to somehow rely on formal logic. Well, that lead me to an idea for a game whose rules are constant, but also based on formal logic. I call it Lenga (for Logic Jenga (I considered Longa, but that makes the game sound long, and nobody likes long games)). It is not a computer game (yet, mwahahaha!).
Each round starts with an empty paper. On each player’s turn, he can do zero or more derivations, followed by writing down a new axiom. A derivation can be:
- Show that another player’s axiom is in fact a theorem of the axioms written before it. At this point, the player who showed this gains a point, and the player who wrote that axiom is eliminated from the round.
- Derive a contradiction from the stated axioms. At this point, the round is over, and the player who derived this gains two points.
Play to ten or something. The game is over and everybody loses infinitely many points if people are being dicks and not writing anything interesting (for example, “an object X exists”, “an object Y exists”, …).
Note, by mentioning objects such as “sets” and “numbers”, you are importing that subfield of mathematics into your axiomatic system. At the very start of the round, anything goes, but if you say “a set X exists”, you are now working in ZF.