I forget exactly where I heard this, who said, or who it was about. All I remember about the pithy little saying I am about to express (rather than continuing to allude to it) is the laughs that it caused. I was driving along listening to some show about politics when one of the commentators suggested that some member of the government was ‘often wrong but never in doubt’.
Once my laughter faded – a process that took some time as that gem struck my funny bone – I began to reflect not only on the truth that was being conveyed but also why it worked that way. So many of our most prominent citizens, from all professions, seem to not understand just what logic is all about.
The examples are so numerous that I’ve begun to filter them out to the point where I can’t even cite a specific one. But the scenario is quite clear. A media figure cites a study that, perhaps, mildly suggests that item A and item B are correlated and runs with it to suggest that A causes B. A politician takes the words of another politician out of context, twists and turns them this way and that, and ends by constructing something with exactly the opposite meaning. This typically occurs in its most egregious form when there are big stakes on the line, the kind that engender large emotions, but it isn’t confined to that.
The effect is quite clear but, what about the cause? Now, if I am not careful, I’ll end up doing exactly what I am criticizing – drawing sweeping generalizations supported by a paucity of data but a lot of belief. So let me say simply that I think that what causes wrong conclusions walking hand-in-hand with little or no doubt is that it is uncomfortable to deal with the doubt.
Each time we try to make an inductive argument we are dealing, whether formally or not, with statistical data and probabilistic inferences. As Harry Gensler points out
Deductive reasoning is an all or nothing undertaking. Everything is locked down, certain, and the outcomes are never in doubt. The rules for proceeding from premises are established and have no room for negotiation. The application can be in error but sufficient effort always results in valid reasoning. The only open question is the soundness of the argument, which hinges on whether the premises are true.
In contrast with deductive arguments, inductive ones generally get murkier as data are added. Certainly a sufficient number of observations are needed to grasp a pattern, but too many observations begin to undermine it. In addition, patterns are simple when they involve one or two variables but as the number of considerations grow so too do the number of combinations, each with its own rule. Inductive arguments always take the form of statistical syllogisms that works most cleanly the less we know. These arguments may not be reliable (the analog to sound) but they can be quite strong (the analog to valid) if the probabilities we assign to the premises are high. This is most easily done if we don’t have a host of additional factors making exceptions here and there.
Gensler provides a nice example of this point using college football and I want to give him full credit for a good teaching device. That said, I will present its flavor only after having switched to professional football.
Suppose we know, having analyzed the total plays called by the Pittsburgh Steelers, that 80% of the time they throw the ball deep on a second and short yardage situation when they are at least 30 yards from their own end zone. Suppose, also that we see during this Sunday’s divisional playoff game between them and the Denver Broncos, that the Steelers have 2nd-and-3 down with the ball on Denver’s 47-yard line. We can reason thus:
- The Steelers throw the ball deep 80% of the time with second and short yardage when they are not backed up their goal
- The Steelers have the ball on Denver’s 47-yard line with a 2nd-and-3 down
- There is an 80% chance the Steelers will throw deep
This seems simple enough, but Gensler often adds to this form the additional line that reads ‘This is all we know’. At first glance this may seem to be superfluous but as the next example shows, saying that we want to limit our facts may actually beneficial.
Suppose we know, again from the sample of plays, that the Steelers run 70% of the time when they are ahead by at least 10 points. Now if we knew nothing about down and distance but knew that they were winning 20-3, we might reason
- The Steelers run the ball 70% of the time when they have at least a 10-point lead
- The Steelers are leading Denver by the score 20-3
- That is all we know
- There is a 70% chance the Steelers will run the ball
So far so good! But now consider that the score is 20-3 and that they have the ball on Denver’s 47-yard line in a short-yardage second down. What should we conclude? Do they run or pass. Perhaps they should just punt. Now layer in additional considerations like the time left in the game, weather conditions, and critical injuries and the situation really gets complicated.
And this is exactly why I think that there is such a correlation between certainty and intellectual short-sightedness. It is easier and more comforting to focus on a single aspect of a complex scenario, find a pattern and merciless apply it. The result is a logic ostrich, with its head in the sand, comforted that it can’t see the messy possibilities. Socrates was right – the only wisdom is in knowing that one is not wise (although it is possible that an ostrich is still better looking than Socrates).