Rightness and Popularity are independent of one another

Lately I've been thinking about the old adage "What is popular is not always right, and what is right is not always popular," which is true I think. 

The problem I have with it is that it doesn't give you any clues about whether or not you are right. Some may think, indeed evidently some do think, that unpopularity is itself a sign of rightness. Which doesn't follow at all, as I will endeavor to show by and by.

Some may also understand the adage to mean "stand up for what you believe in, irrespective of popularity." Again, this is unhelpful. What you believe may be wrong. How do you tell?

An extreme version of this adage I read in an article about the Westboro Baptist Church. "If you are doing all the right things the world will hate you. The world hates us. So, we must be doing something right."

This is a very simple argument as far as its logical components go: we have two premises and a conclusion, and I can tell you straightaway the argument is invalid. But let's prove it. (What follows will seem awfully pedestrian to anyone who's ever taken a 100-level Logic course).

First let's remove the content. It's irrelevant anyway. Because once we reveal that the logical structure is bad, the argument will be bad no matter what content we replace it with. 

We'll replace "You are doing the right things" with "A", and "The world hates you" with "B". Then replace them in each occurrence in the argument . We're left with:

If A then B.

B

Therefore A

Logicians among you will recognize the formal fallacy immediately. To reveal it to the rest of us, all we have to is find suitable replacement sentences for A and B. So let's use the legendary thoroughbred Seabiscuit. Who we all acknowledge is a horse, I hope.

Let A= Seabiscuit is a cat, and B = Seabiscuit is a mammal. 

Now we have "if Seabiscuit is a cat, then Seabiscuit is a mammal." It may seem odd to say, but this is True. If he were a cat, he'd be a mammal.

We also have "Seabiscuit is a mammal" this is true, too. Horses are mammals.

And the conclusion "Seabiscuit is a cat." Which we all know is false.

Now the definition of a valid argument is that if all the premises are true, the conclusion must be true, and yet here we have two true premises and a false conclusion. This is an invalid argument structure. Which means both our dreamed-up argument and the one from the WBC are invalid. And it would still be invalid if all the sentences were true: if Barnaby is a Cat, he is a mammal. Barnaby is a mammal, therefore he is a Cat. All of that is true, but the argument is still invalid, because the conditional arrow flows in one direction (from being a cat to being a mammal), not in the other. He is not a cat due to being a mammal, he's a mammal due to being a cat.

So, rightness is independent of popularity, or indeed hatred. Which is why I think the old adage is true. What is popular is not always right. But what is popular is not always wrong, either. And since popularity and rightness are independent of one another, we must look for other, more accurate criteria.