# All of logic is a game

## Game Theory, Communications Theory and Formal Logic

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The central thesis of my research is that formal logic may be considered under game theory and communications theory under what I call a Coherent Cooperative Game of Formal Logic.

The metatheory is that a Coherent Cooperative Game of Formal Logic (CCGFL) adequately describes the machinations that people engage in when engaging with the game of formal logic.

A CCGFL is a game where each move that player makes is a move where the other players win and where you only play a CCGFL if you play such that the other players win.

It is normal to think of a game, e.g. a zero-sum game, where there are winners and losers, however if a theory of formal logic is to be engaged with at all, it must be such that each player wins when using that formal theory to communicate among players in a logical fashion if not otherwise playing a zero-sum game. For instance, a formal theory may well be consistent, complete, compact etc, but well formed theorems (as plays in the CCGFL) are only useful under a CCGFL where each player has an interpretation of the theory (beyond and including the standard interpretation of the theory) such that the theory is consistent, complete, compact etc in their mind. I.e. Theorems of a theory under formal logic are tokens in a communication between players and where a CCGFL is played when each player has a common understanding of the theory under interpretation and where a set of well formed theorems that lead to either consistency or contradiction of the theory have the same interpretation to each player.

Formal logic is a game, because if any one player has a different interpretation of a formal theory to every other player then they effectively play such that no other player wins. Players, individually, however may win in their own interpretation (as when playing an Ehrenfeucht Fraisse Game unbeknownst to other players) . An effective coalition of players is formed for each instance of a CCGFL that includes all players, as when within a group of people speaking the same language and where each person understands what the other person is saying. Formal logic narrows the communication to a shared interpretation under a CCGFL, and if when a player chooses to have a different interpretation…