Why is Formal Logic under Game Theory?

Subsuming Formal Logic under Game Theory

“Game Theory and Formal Logic” Royalty free image by DALLE-3 and Victor Morgante

Game Theory is painted as a theory adjunct to Formal Logic, however my conception of Coherent Cooperative Games sees all of Formal Logic under Game Theory.

When I first asked GPT to draw me an image for this article, this is what I got:

“Coherence and Cooperation” Royalty free image by DALLE-3 and Victor Morgante

This paints a much better image of how formal logic works.

When a theory of formal logic in one person’s mind (or in that of an AI) is the same interpretation as that within another person’s mind, a coherent exchange is possible such that interchanged tokens (theorems) mean the same thing to sender and receiver.

That theories, and their theorems, may be seen as tokens in a game may be surprising to the uninitiated, however the models and structures formed in your mind when you apply model theory to a formal theory are simply that…in your mind.

Just as when we consider quantum mechanics and the position of a photon unknow until it has an observer, and when we consider the question as to whether logic and mathematics is a man-made invention or something that exists in the ether, coming to be known as quantum space or fields, without you as the observer, interpreter and token constructor, manipulator and sharer, formal logic need not exist as neither would you.

So formal logic must sit under game theory. There is no choice.

As a one-person game, you can construct your own theory, write your own theorems, and test their validity to the theory, all on your own. No other players are required. You can map your theory to the real-world and test it to see if you can formulate a proof, within your theory.

As a multi-player game, there is no theory without coherence…that is useful for idea or concept exchange, or coherent discourse, merely contention and discussion and disagreement as to interpretation or banter as to the proper interpretation, or sharing of a proof or new theorem or technique to achieve a result.

And when you picture yourself doing that when you consider formal logic, then you know it is a game, and that you are part of it.

Even the process of understanding or learning formal logic is a game.

Until such time as your conception of formal logic matches that being taught to you, or where you discredit, misinterpret, argue or challenge a theory or the conception of logic, the model of formal logic formed in your mind (its rules, if you will) are those very tokens that you later exchange when you write theorems down on a piece of paper, or form conceptions that meet with your logic in your own mind.

Whether they ideas or concepts, or the formal written symbols of logic, I call these The Atoms of Knowledge, and where knowledge is meaning of data in context. Because theorems are one thing, their theory another, but the data they operate over a different thing altogether.

Your active moulding of models in your mind, or where an AI does the same, is a process.

If its a process, then you think.

If you think, you are, and so are a very real part of the game of logic.

Lewis Carroll wrote a book of the same name may years ago, “The Game of Logic” (1886), and it is fitting.

I have been writing about Coherent Cooperative Games for a little while now, but it seems I am not alone. An internet search of the AI researcher Joscha Bach and Coherence will return something similar. Bach says, for instance, that machines that think like a human must first master coherence and playing games (at start of video and [here]).

Making the link to the Unification of Game Theory, Information/Communication Theory and Formal Logic, is the next step, as any such structure that can be formed in the brain, and as is coherent to another person/AI, may be represented in one form or another as a structure that can be expressed formally or as bits-and-bytes within a computer, whatever the fidelity and whatever the clock-speed of the universe.

So Formal Logic sits under Game Theory.

Thanks for reading. As time permits, I will write more on the unification of Game Theory, Information/Communication Theory and Formal Logic.

===Further Reading===

1. Coherent Cooperative Games — As I describe them;
2. The Genesis of Coherent Cooperative Games;
3. Coherent Cooperative Games — Described;
4. Coherent Cooperative Games and the Law;
5. Formal Logic — And Coherent Cooperative Games;

….and…

1. All of Logic is a Game;
2. What is Formal Logic;
3. Applied Use of Ehrenfeucht Fraisse Games;
4. What is a Graph Database;

…and…

1. The Atoms of Knowledge;
2. The Richmond Architecture;

…and where it all started:

1. Morphing Conceptual Models.

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