The infinite-regress trap

It is time to see exactly why a complete listing of a game's rules is impossible. There are several reasons:

  1. Game rules, like any rules, must be stated in some language, and all language is subject to interpretation. But the rules for interpreting any language would also have to be stated in some language, and these rules would likewise have to be interpreted. We are trapped in an infinite regress. Thus, the question "What are the rules?" can never be answered fully;

  2. Each individual player could have his or her own personal conception of a game which would differ (if only slightly) from all other players' versions, and each player's understanding of that game's rules could change over time. No finite list of rules could include an infinite number of possible variations.

  3. Since any two players could be playing the same game with different interpretations, there would have to be a set of meta-rules for reconciling these differences when they surface.

    Of course, these meta-rules are, in effect, the rules to another game and are therefore subject to the same interpretive variations as the rules of any other game. Again, we run into an infinite regression. There is no bottom line, no point when we can accurately say, "These are the ultimate meta-rules for settling disputes."

    Thus, the questions "How do we settle disputes about the rules themselves, about whether a player has violated a rule, and about the appropriate penalties for a rule violation?" can never have a final answer.

  4. Even if two players agree on certain rules and how to interpret them, disputes about what actually occurred (such as whether a ball landed on the back line or just beyond it) can still arise, and the players will need to abide by meta-rules in settling these disputes as well. These meta-rules, like those in #3 above, are also part of an infinite regression, so the question "How do we settle disputes about what really happened?" has no ultimate resolution either.

  5. Since there are various "levels" of rules, "higher" rules (such as a real-world crisis) might have to take precedence over "lower" rules (such as time constraints), there must be a set of meta-rules for determining when this is appropriate. As with the other meta-rules we've looked at, there is no "final" set for ending disputes, so the question, "When is it appropriate to suspend certain rules?" cannot be given a full answer.

  6. Since all games begin and end and may be interrupted by "outside" events (such as a TV ad), we must have a set of meta-rules for determining when the constraints apply and when they don't. Again, these meta-rules are susceptible to interpretation and dispute, leading to yet another unendable regression.

    "Simons" often take advantage of this fact by tricking players into thinking play hasn't begun and then saying something like "Before we start, say hi to your neighbor. Ah, I didn't say 'Simon says.'" Therefore, the question "When do the rules apply?" cannot be fully answered.

We can see now why it is impossible to spell out a complete set of rules for any game. Now we need to ask why we have no trouble playing a wide variety of games.

If we can't know all the rules,
how can we play any game at all?

Is it because participants rarely have to deal with "meta-rules" and so the infinite-regress problem almost never comes up?

To me, this is not a plausible explanation. There are simply too many occasions we can name—in virtually every game ever played—in which meta-rule questions arise. When a player accidentally rolls the dice off the table, argues a call, gives (or refuses to give) an opponent a handicap, calls for a do-over, takes a mulligan, asks for a director's ruling, warns an opponent about an unwise move, or encourages the other team to play faster, the players are facing situations that are not (and could not be) completely covered in the recorded rules. Meta-rules (and even meta-meta-rules) are an integral part of all rule-governed activities.

Is it because players don't take games seriously so it doesn't matter that they can't know all the rules?

Again, this doesn't work for me because it is clearly not true in all cases. Obviously, some players (myself included) care deeply about the game and the outcome.

Many of us are playing for high stakes—money, prestige, a trophy, pride, self-esteem, ego satisfaction, a feeling of control, etc. In fact, it's probably pretty rare for players to have no emotional involvement in the game they are playing. After all, why play unless the results "matter" in some important way?

My guess is that almost all games are taken very "seriously" by almost all players almost all of the time.

Is it because players mistakenly believe that there is a "bottom line," that the rules are clear, complete, and "final," and that somebody somewhere knows all of them?

This is getting closer to sounding right, but is still a half-truth at best. Having the misconception that a game's rules are solid and statable can provide a player with a sense of confidence in the "reality" of a game, but my realization that no one can know (let alone state) the rules of our doubles game has not dampened my enthusiasm for tennis one iota. In fact, my recognition that games, like languages, can exist only because of an unspoken, almost mystical, agreement among the participants actually enhances my appreciation of them.

Although my attitude may be idiosyncratic, I seriously doubt that anyone else's enjoyment of a game (or willingness or ability to play it) would be diminished by realizing that we can't list all its rules.

"It's only a game"

I believe we can go on playing games wholeheartedly even when we are aware of the incompleteness of their rules. Why? Because, on a gut level, we cannot distinguish between something fanciful—like a movie or a joke or a dream or a game—and something "real."

Games feel like any life-event, so we can get immersed in them even though we may know intellectually that they are artificial constructions. Therefore, it makes no difference to us (emotionally) that a list of rules governing them cannot be completed, just as we can be profoundly affected by a joke or piece of fiction or nightmare that is not logical or realistic or "complete."

We can suspend disbelief and rationality (even when some part of our brain is telling us it's only a story or it's only a dream) and respond deeply to creations of the imagination—our own or others'.

We can do this because we have the wonderful (and perhaps unique) capacity to operate on the "as if" level; we can play a game as if we know all its rules, as if there is an ultimate set of meta-rules, as if all potential disputes can be settled. We can imagine a game in the abstract and in a vacuum and can project that Platonic ideal onto the one that must be played in the world of social and political reality.

In other words, we can operate on (at least) two distinct levels of cognition at once. We can play any game as if it had an autonomous existence, even though we know perfectly well that the players create the game each time they agree to play and that any player at any time can destroy the game by quitting, by arguing, by stalling, or by any number of other spoilsport tactics.

Similarly, we can play any game as if it is important (and genuinely feel that it is), even though we know that it is not very high on our list of life priorities. We can play any game as if it transcended our culture, even though we recognize that players can have "unfair" (dis)advantages as a result of their upbringing. We can play any game as if it transcended morality (so we might intentionally and unashamedly foul or fool an opponent) even though we know that players can cheat or violate the rules in inappropriate ways.

Suspension of disbelief

Without this ability to operate in the conditional universe of "Suppose . . ." and "What if . . .," game-playing would be impossible, as would drama and fiction and, I suspect, language itself. We must be able to behave as if a game were not "merely" play, even though we are fully aware it is nothing else.

Like an actor, we must be able to take on a role but never give up our sense of self. We must be "in" the game to enjoy it but never so far in that we forget who we are. It is a delicate balance that is fraught with danger, which is perhaps why so many people (especially adults) shy away from games.

Non-human gameplayers?

It is also, I believe, one more reason that computers (at least as they are today) will never play a game in the same sense that humans do. Computers have no conditional, no ability to create temporary self-delusions, no play mode, no sense of "as if." To a computer (we must assume), a chess move is just another calculation, no different from finding the square root of pi.

To a human, a chess move is (usually) part of a carefully designed pretense, a system of orchestrated assumptions, an artificial structure that can bring stimulation, competition, camaraderie, fun, and a variety of other good feelings. In general, the chess-playing human voluntarily accepts a particular challenge that involves a specific goal and specific constraints and which s/he can abandon at any time. The chess-playing computer, on the other hand, does not choose to start and cannot stop on its own. The human is aware of the voluntary and "non-serious," conditional nature of the activity, but the machine is not (and probably can never be).

What about animals? Does any non-human creature have the ability to suppose, to imagine something that doesn't exist except as an agreement among participants? If not, they will never play a game as we do. They will either take it too seriously or not seriously enough and, therefore, like any spoilsport, undermine the enjoyment of the game for any human participants or observers (as was the case with the water-polo-playing dolphins).

But even if animals (or computers) could think in the conditional, they still might not be able to play games as we do. They would also have to be able to trust other players to function in basically the same way. To play a game (or use a system) meaningfully without knowing all the rules requires the faith that others understand the game/system as you do or at least will behave in ways that seem consistent with such an understanding. Without that faith, a player would inevitably end up being the spoilsport.

"Unwritten Rules" by Stephen Sniderman2 | 3 | 4 | 5 | 6 | 7

The Life of Games
No. 1 (October 1999)
©1999 Kadon Enterprises, Inc.