What do I mean by a generalization? It happens when there is a set of objects. The set can be, for example, a group of people, animals of a certain species, a collection of inanimate objects. Let’s call the objects in the set “members” of the set. The generalization occurs when some members of the set possess a certain characteristic and the conclusion is drawn that all members of that set have the same characteristic.
Mathematicians would consider such a generalization a huge no-no.
Let’s take a simple mathematical example. Let the set of objects be the positive odd integers, that is 1, 3, 5, 7, and so forth. Now look at the 3, the 5, and the 7. Each of them is a prime number. You may recall a prime number is one that can be divided only by 1 and itself. Thus 7 is a prime because the only integers that divide it are 1 and 7. A silly generalization would be that all positive odd integers bigger than 1 are prime numbers. You don’t have to go much further to see how foolish this is. Nine is not a prime number since nine is divisible by three.
A less benign example goes something like this from an NBA lover. Hey, most of the players are Black. Blacks, meaning all Blacks, are natural athletes.
Nothing could be further from the truth. My guess is most Blacks are not athletic. I’ve known many and I would guess very few are athletically inclined. Including professionals such as doctors, lawyers, entrepreneurs, scientists, college professors, therapists, activists, musicians and just about any other job one could imagine.
Here are a few other generalizations you may have heard over the years.
Women don’t make good scientists.
Republicans don’t care about the poor.
Democrats hate businesses.
Businessmen and women are concerned only with making money.
College professors live in ivory towers and have no feeling for the real world.
Immigrants are criminals.
People on welfare are lazy and don’t want to work.
Everything Donald Trump says is stupid.
Everyone who flies an American flag is a Republican.
I hope you can look at every one of these examples and say, “Yeah, that’s a generalization. It may be true for some members of each set, but it sure isn’t always true.” And if a statement is not always true, it means a very important thing. It means the entire statement is false.
A generalization may be mostly true. An awful lot of what Donald Trump says is stupid. But not everything he says is. It’s important to question which statements are true and which are not. Otherwise, one is giving a gut reaction which eliminates the possibility of reasonable analysis, often to the detriment of good policy.
So, suppose Bill says to me, “I heard that guy over there is a Republican. You know he wants to eliminate Social Security, don’t you?” Bill says this because he’s aware of some Republicans who want to eliminate Social Security.
How should I respond?
How about, “I don’t know. Let’s talk to him and find out.”
It’s really important to understand a generalization is almost never true. So, when a person tries to ascribe an attribute to an entire class based on the observation of a few in the class, a typical politician’s trick, we must not fall for it. Instead, we should realize the only way to know is to look at every class member individually.
Do that and you’ll be acting like a mathematician!