An Introduction to the Game Theoretic Semantics view of Scientific Theory

What is a scientific theory?  In an abstract sense, a scientific theory is a group of statements about the world.  For instance the Special Theory of Relativity has, “The speed of light in a vacuum is invariant,” as a core statement, among others, about the world.  This statement is scientific because, in part, it is meant to hold in a ‘law-like’ fashion: it holds across time, space and observer.

The Popperian view is that we have scientific theories and we test those theories with experiments.  This means that given a scientific theory, a set of scientific statements about phenomena, we can deductively generate predictions.  These predictions are further statements about the world.  If our experiments yield results that run counter to what the theory predicts — the experiments generate statements that contradict the predictions, the theory did not hold across time, space or observer — then the theory eventually becomes falsified.  Else the theory may be considered ‘true’ (or at least not falsified) and it lives to fight another day.

The game theoretic semantics (GTS) view is that truth is the existence of a winning strategy in a game.  In terms of the philosophy of science, this means that our theories are strategic games (of imperfect information) played between ourselves and Nature.  Each statement of a theory is a description of a certain way the world is, or could be.  An experiment is a certain set of moves — a strategy for setting up the world in a certain way — that yields predicted situations according to the statements of the theory.  If our theory is true and an experiment is run, then this means that there is no way for Nature to do anything other than yield the predicted situation.  Said slightly differently: truth of a scientific theory is knowing a guaranteed strategy for obtaining a predicted Natural outcome by performing experiments.  If the strategy is executed and the predicted situations do not obtain, then this means that Nature has found a way around our theory, our strategy.  Hence there is no guaranteed strategy for obtaining those predictions and the theory is not true.

An example:

Take Galileo’s famous experiment of dropping masses off the Tower of Pisa.  Galileo’s theory was that objects of different mass fall at equal rates, opposing the older Aristotelian view that objects of greater mass fall faster.

According to the Popperian view Galileo inferred from his theory that if he dropped the two balls of different mass off the tower at the same time, they would hit the ground at the same time.  When he executed the experiment, the balls did hit the ground at the same time, falsifying the Aristotelian theory and lending support to his theory.

The GTS view is that dropping balls of unequal mass off a tower is a strategic game setup.  This experimental game setup is an instance of a strategy to force Nature to act in a certain way, namely to have the masses hit at the same time or not.  According to Galilean theory, when we are playing this game with Nature, Nature has no choice other than to force the two masses to hit the ground at the same time.  According to Aristotelian theory, when playing this game, Nature will force the more massive ball to hit the ground first.  History has shown that every time this game is played, the two masses hit the ground at the same time.  This means that there is a strategy to force Nature to act in the same way every time, that there is a ‘winning strategy’ for obtaining this outcome in this game with Nature.  Hence the Galilean theory is true: it got a win over the Aristotelian theory.

Why you might want to consider doing things the GTS way:

GTS handles scientific practice in a relatively straightforward way.  Theories compete against Nature for results and against each other for explanatory power.  Everything is handled by the same underlying logic-game structure.

GTS is a powerful system.  It has application to  game theory, computer science, decision theory, communication and more.

If you are sympathetic to a Wittgensteinian language game view of the world, GTS is in the language game tradition.

More on GTS:

http://plato.stanford.edu/entries/logic-games/
https://en.wikipedia.org/wiki/Game_semantics

Posted in game theory, logic, philosophy, science. Tagged with , , , , .
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