Wednesday, May 11, 2011

Scorekeeping in a Football Game

According to David Lewis's classic paper, "Scorekeeping in a Language Game," conversations, like sporting matches, have scores, which characterize the current situation, and rules, which interact with scores to determine what is permissible. The score of a baseball game includes the number of runs scored, an indication of which team is batting, the number of outs, balls, strikes, etc. (Lewis characterizes baseball scores as ordered septuples; in fact, they're more complicated. Lewis's baseball scores leave out, e.g., the batting order, which pitchers have already appeared in the game, and perhaps most egregiously, who is on which bases.) An example of a baseball rule, in Lewis's sense, is that if a the score includes three balls, if the pitcher throws a ball, the score is updated by resetting the count, putting the batter on first base, updating other runners and the run total as necessary, as making the next member of the lineup the batter. This is a rule that tells you what happens to the score when a particular event occurs; there are also rules that tell you what is permissible, given the score. You may not come up to bat if you're in the lineup and it is not your turn.

In a language games, scores will include contextual parameters like who is speaking, what is presupposed, what is salient, etc. There are rules that tell you what is permissible, given the score, and there are rules that govern the updating of scores. These sometimes interact, as when the score is accommodated to permit a conversational move. For example, there's a rule that say I'm only allowed to use the definite article "the cat" when there is a uniquely salient cat. But if there's not one that was already salient -- if the score didn't already indicate a uniquely salient cat -- my utterance can cause an updating of the score, to make it permissible. If I say "I'd better go home because the cat is hungry," the score is updated to make my cat at home the uniquely salient one.

This feature of conversational games, Lewis says, marks a difference between conversations and sporting events.
There is one big difference between baseball score and conversational score. Suppose the batter walks to first base after only three balls. His behavior would be correct play if there were four balls rather than three. That’s just too bad - his behavior does not at all make it the case that there were four balls and his behavior is correct. Baseball has no rule of accommodation to the effect that if a fourth ball is required to make correct the play that occurs, then that very fact suffices to change the score so that straightway there are four balls.

I'm not sure Lewis is right about this. Of course he's right that you don't get a walk just by trotting along to first base, but I'm not sure that's because there's no accommodation in play. What, plausibly, would happen in a Major League game where a batter tossed his bat aside and jogged to first base after ball three? The umpire would call him back. That's a baseball move too; that's what the umpire is supposed to do, and it's surely what he would do. And there's plausibly a baseball rule that says that when the umpire says you're still at bat and have three balls, the score is updated to make that the case. If the umpire stood idly by and let the batter take first base, I think that might well make it the case that he got a walk. That's part of why bad calls suck so much; they make themselves true. After this play, there were only two outs in the inning, even though, had the umpire performed correctly, there would have been three. (To deny this would be to say that there were four outs in that inning -- or that Melky Cabrera's subsequent apparent plate appearance was illusory, and that his turn was skipped in the lineup.)

This happened pretty dramatically in an infamous college football game between Colorado and Missouri. The football score, in Lewis's sense, will include what down it is. And failure to convert on fourth down means you lose possession. But in this game, the officials miscounted the downs, and nobody noticed until afterward, when Colorado scored a touchdown on 'fifth down', which had been described by the officials as fourth down. The officials got it wrong, obviously. But, I think, they didn't get it wrong in the sense of saying something false; they got it wrong by making the wrong thing the case. It really was fourth down, and there really was a touchdown.

So I think, contra Lewis, that football scores and baseball scores can accommodate, in more or less the same way that conversational scores can. (There's no doubt it's easier to do in the case of conversational scores.)


  1. Did you see this yesterday?

  2. No, I missed it. Awesome! It looks like I was right. :) Thanks for the link!