Logical game

In the con­text of Value Align­ment The­ory, a ‘log­i­cal’ game is one that we are, for pur­poses of thought ex­per­i­ment, treat­ing as hav­ing only the math­e­mat­i­cal struc­ture of the game as usu­ally un­der­stood. In real-world chess, you can po­ten­tially bribe the op­pos­ing player, drug them, shoot them, or re­ar­range the board when they’re not look­ing. In log­i­cal chess, we con­sider the en­tire uni­verse to have shrunken to the size of the chess board plus two Carte­sian play­ers, and we imag­ine that the con­ven­tional rules of chess are the ab­solute and un­alter­able laws of physics.

Thus, real-world chess is a rich do­main, and log­i­cal chess is not. In fact, since ev­ery­thing in the real uni­verse is con­stantly in­ter­act­ing (e.g., a peb­ble thrown on the Earth ex­erts a grav­i­ta­tional in­fluence on the Moon), to con­sider a con­cep­tual ex­am­ple of some­thing that is definitely, in­dis­putably a nar­row do­main, we must gen­er­ally re­sort to imag­in­ing log­i­cal (not real-world) Tic-Tac-Toe.

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