Is deductive logic empirical? No. Is inductive logic also empirical? No. Is induction justified and, if so, is it just an extension of logic? Yes.
These are Stove’s conclusions as he takes Hume (and current-day relativists,such as Popper) to task and shows that, yes, induction is rational. He also shows that the common belief that ordinary logical is formal is a myth. Knowledge of the validness of certain arguements must come from intution, as Carnap argued, and Stove proves. He shows that certain forms of logical arguments do not always give valid conclusions, and that all arguments must be judged individually. In his words, “Cases Rule”.
This is another in a series of books that I think are largely unknown by most statisticians and probabilists, especially those who tend toward so-called pure mathematics. But this book, like those by Jaynes and Cox, argue the case for logical, as opposed to subjective, probability forcefully and conclusively. They deserve to be more widely read because, I believe, they have a great deal to say on the foundations of our field.
I have been playing the game of petanque for several years now. You may have seen its modified Italian form called bocce.
Both games are similar, but whereas in bocce the players use brightly colored lightweight, feminine wooden balls, petanque players use dark, heavy masculine balls of steel.
The game of petanque, like golf, looks deceptively simple: all that needs to be done is to get a ball as close as possible to a small wooden ball that is tossed from six to ten meters away.
Players are grouped into teams, each team throwing, rolling, tossing, or dropping their balls until at least one of them is closer to the small ball (called “the little one”, or cochonette) than any balls from the opposition team. Teams score one point for each of their balls that is closer to the cochonette than the nearest opponent’s ball. These, beyond one or two refinements, are the rules.
For two years I sat on a green bench in the southwest corner of Central Park where the old men play petanque, and I watched. One by one, these mostly French gentlemen would come to the throwing circle (a smallish area penciled into the ground to designate where to stand) and they would throw their balls, each time showing every appearance of great mental strain.
Almost invariably these balls would curve off, or bounce away, ending as far as one to two meters from their intended target. Some, and always by some miraculous path over twigs, roots, rocks, divots, and miscellaneous debris, would nestle right next to the little one. This was always a cause of great celebration on the part of the teammates of the lucky player. The player who made the throw invariably gave a subtle shrug, one that could equally well mean that he was aware of his luck, or that he knew all along that his skill was responsible for this throw’s perfection.
As a spectator I could see how each errant ball was misplayed. How could he have dropped it so close? My God! (Or, more precisely, Mon Dieu!) Did he not see that rock? How could he have thrown it so hard, when anybody could see that that shot called for the touch gentle?
I watched with a confident eye, certain that I could do this simple task. I went online and bought balls from Petanque America and showed up at the field the next week. The only thing that worried me was that I would become too good too fast, and so have to find a new place to play, somewhere where there were better players. I would, therefore, start slowly.
The men were happy to find a new victim, or, um, enthusiast. They let me play immediately. They even let me lead off. I stepped to the circle, knew to keep my feet on the ground, sized up the terrain, and let loose my ball. It soared through the air and rolled to the cochonette! It continued rolling past the cochonette, over a hill, across a tree trunk, and, as far as I know, is still rolling through the West side of Manhattan towards the Hudson river.
This was odd because I was certain I had only used a feather touch on the throw. It must be because the ground was too hard. My opponent put a ball about half a meter away. I came back to the circle, and this time I concentrated. Do not throw it too hard! I let the ball fall every so gently, and this time it lined up exactly with the little one. If it had only rolled more than the one meter it did, it would have been perfect.
The afternoon continued much the same. And so did the next week, and the week after that and so on. It was two months before I could make a throw that wasn’t acutely embarrassing. But did my teammates mind that I was helping them lose so many games?
To answer that, let me tell you that the best part of petanque is its sociability, its sense of camaraderie. So, no, they did not mind. They loved that I could perform one of the most valuable services that a player can perform: I made the other players feel better about themselves. No matter how badly another person played, once they watched me, they could always say, “At least I am not that bad.”
The game is very popular with spectators. Most who walk by our playing field stop to watch (games are played nearly every day of the year). These people give every appearance of enjoying our obvious eccentricities. Little kids like to pick up the balls and feel their solid heft. A few others try a toss.
But it’s the fifty-plus-year-old men who watch us that I can see have the same smug and not-so-secret grin that I had before I started playing. I can see their thoughts as they stand with their arms crossed. I can see their eyes roll with silent exasperation on every bad shot. I can see what they are thinking. They too believe that they can do this simple simple game better then we can.
Yes, I was exactly like these men were before I started to play. My smug grin is long gone. It has been replaced by a grimace of agony.
To explain the title: a carreau is the name of a perfect throw. It happens when you throw your ball and knock your opponent’s ball away, while yours stays in the same spot that your opponent’s ball occupied. Petanque is, as I have alluded, just as frustrating as golf, but it is free to play. You only have to buy a set of balls once: balls are about forty to eighty dollars. And you can play in just about any space. These qualities make it, in my opinion, a far superior game to golf.