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Games in the Philosophical Investigations and Meaning in Game-Theoretical Semantics

..."There is a game of guessing thoughts." We guess them because we cannot see them, or hear them, or feel them. They are "hidden" from us. But - "The future is hidden from us." To the player, private games are simply played. "Our mistake is to look for an explanation where we ought to look at what happens as a 'proto-phenomenon'." When the private game becomes a public game, as in "guessing thoughts", we can see that the "thoughts" are hidden only until we win the game by guessing them correctly, or until we are told them. The meteorologist does not say that tomorrow's weather is presently suspended in an inaccessible state, even though he might be persuaded to say that it is hidden from him.

Using the concept of games, Wittgenstein wants not only to demystify language-use; he also intends to demystify thought.

"Our clear and simple language-games are not preparatory studies for a future regularization of language - as it were first approximations, ignoring friction and air-resistance." Instead the concept of language-games is a metaphor, or model, for the real phenomena of language. Karl Deutsch lists four basic functions of models.

The organizing function, a feature of metaphor in general, is manifested in the new relations we discover. "Scientific" metaphors, or models, serve the additional functions of prediction (the anticipation of unobserved relations) and measurement. Last is the heuristic function, pointing beyond the model to relations not evident in the direct analogy. How is the "language-game" used as concept, metaphor, or model?

Language-games enable us to see language in a new light. We are led to see language-use as an activity. In studying language we should look at the "proto-phenomenon", the instance where "this language-game is played". There is a multiplicity of uses for language, yet the model suggests that there are particular relations between instances of language-use. The model gives us ways of distinguishing invalid or superfluous uses.

The model establishes a relation between names and things named. It clarifies the role of components or features in language-activities: "What looks as if it had to exist, is part of the language".

The concept of language-games brings out possible forms of rules in language. And it shows that we need not have rules for all aspects of the activity.

And it shows what understanding a word can mean. Understanding a word in the context of a language-game means being able to play with it. How do we "get at" an understanding of a sentence? If by analysis, in what way do we "break up" the components? What part-whole relations should we strive for? The model shows that these are arbitrary. Meaning is use, not hidden structure. From the concept of meaning as use in language-games we get the idea of a family of meanings.
 		Language-Games


detail, ludwig wittgenstein
"four philosophers", collection of the artist

1977

Wittgenstein, one of the most influential and charismatic philosophers of the 20th century, came to believe that the meaning of words and expressions emerged as they were used in ordinary speech, reflecting a sort of game between the speakers.

This was not a very philosophical thing to say, and although Wittgenstein had a huge cult following, philosophers didn't know what to do with his ideas. Jaakko Hintikka, my professor at Stanford, decided to try a literal approach, using the mathematical theory of games. Shown here are excerpts from my term paper for Hintikka's course.

 ...Mathematical games are patterns of conflict characterized by information sets, choices, and outcomes. A game will have opponents who, for simplicity, will usually be assumed omniscient, and who are guided or limited in their actions be explicit rules. The paradigm for a "mathematical" game will be embodied in these rules; the unknown elements differentiating individual instances of play are the choices made by the opponents.

Hintikka has applied game theory to the semantics of quantifiers in formal and natural languages; furthermore, he has asserted that the resulting interpretation corresponds to the language-games of Wittgenstein.

A game program emerges from Hintikka's association of quantifiers with verification. To him, "Everybody loves somebody sometime" has a game associated with it, a potential game of seeking and finding (or producing) wherein lies its meaning and our knowledge of its truth or falsity. The forms of life may circumscribe our domain of individuals; the rules or paradigms corresponding to the particular quantifier expressions will guide and limit our actions (including linguistic manipulations); our opponent is Nature; verification of a sentence consists in its reduction, through a search over the given domain, to a true atomic sentence.

...Hintikka makes passing mention of the "games of exploring the world". What are they? How do we build up substantive knowledge?

One way is by observation and induction. This need not be an active search and will probably not be a well-defined and circumscribed activity. We simply notice things when we have the opportunity, and we revise our beliefs (our notions of truth) concurrently.

In acquiring knowledge, one does not judge what is formally called truth; rather, one assigns credibility. In Hintikka's terminology this is indicated without psychological connotations by the undecidability of quantification. Indeed, substantive knowledge about the world can usually be communicated by quantifier sentences, and when it is, agreement or belief will be at issue rather than formal truth.

But can we see the activity of accumulating knowledge as a game? The buildup of knowledge is an unstructured activity which may develop sporadically throughout life, and in which one may take sometimes an active and sometimes a passive role. Such an activity fits in very nicely with the children's games which we found to dominate Wittgenstein's discussion. It fits in even more nicely with the notion of a two-person game against Nature, for the very reason that it depends largely on chance. When the opportunity arises, and I observe something new about the world, Nature has moved. When I take the initiative, looking at something deliberately,"Myself" has moved.

This way of looking at learning-games enriches Wittgenstein's notion. These games are not yet competitive, nor do they necessarily admit of an outcome, but they show a relation between game-players and the world which was not brought out in the Philosophical Investigations.