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Published online by Cambridge University Press: 24 December 2009
THE GAME
Consider a little language game that is played as follows.
There are three players, called the Master, the Slave, and the Kibitzer. It would change nothing to have more than one slave, or more than one kibitzer, but let us put aside the complications that arise if a slave must serve two masters. (They say it can't be done.)
There is a certain set of strings of symbols, called the set of sentences. A player may at any time make the move of saying any sentence to any other player within earshot.
There is a certain function that assigns to any sentence Φ, at any pair 〈t, w〉 of a time t during the game and a suitable possible world w, a value 1 or 0 called the truth value of Φ at t at w. (We leave off the ‘at w’ when w is the actual world.) Φ is called true or false at t at w according as the truth value is 1 or 0.
There is another function that assigns to any such pair 〈t, w〉 a set of worlds called the sphere of permissibility at t at w. Worlds in this set are said to be permissible at t at w.
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