Newt Gingrich And The Fallacy Of Inversion

Caption: No, the word "if" is not misspelled. Click on the image credit link and then hover your mouse cursor over the cartoon to see the clever hidden message.


Image credit: xkcd

It's not every day that a prominent American politician gives us an unambiguous example of logical fallacy. No, that's actually not true. It's a rare day when an American politician doesn't provide an example. What's unusual is that xkcd provides a good illustration on the same day.

Yesterday, President Obama had this to say about the tragic death of Trayvon Martin, a young African American who was killed by an armed "neighborhood watch" participant in Florida:

"When I think about this boy, I think about my own kids," Obama said in the Rose Garden. "I think every parent in America should be able to understand why it is absolutely imperative that we investigate every aspect of this. And that everybody pull together."
...
"My main message is to the parents of Trayvon Martin. You know, if I had a son, he'd look like Trayvon," Obama said. "All of us as Americans are going to take this with the seriousness it deserves."

Obama: 'If I had a son, he'd look like Trayvon'

Which was to say that he saw a resemblance to his own children, and so the thought of the young man being killed for no good reason hit him especially hard. I'll simplify this thought to an easily parsed sentence for reasons that will become clear a bit later:

This boy resembles my own children, so I feel sympathy for him and his family.

This seems to have offended Newt Gingrich. He had this to say, according to Politico:

“It’s not a question of who that young man looked like. Any young American of any ethnic background should be safe, period. We should all be horrified no matter what the ethnic background," Gingrich said. "Is the President suggesting that if it had been a white who had been shot that would be ok because it didn’t look like him?"

Newt calls Obama's Trayvon Martin comments 'disgraceful'

Anyone who hadn't slept through his introductory philosophy course would have been able to answer Gingrich with something like this:

No, that's the fallacy of inversion.

The logical inverse of my characterization of the President's statement is this:

If someone doesn't look like me or my kids, then I won't feel sympathy for him or his family.

This is an elementary fallacy of logic, as this website explains:

The fallacy of the inverse states that if a first even[t] implies a second event, then the opposite of the first even[t] occurring will cause the opposite of the second even[t] occurring. You must be careful of this flawed thinking and actively train your mind to oppose it.

Ultimately, the fallacy of the inverse is our minds confusing the notion of cause and effect.

The Fallacy Of The Inverse

Which is something politicians get away with doing pretty often. Wikipedia describes the fallacy this way:

Denying the antecedent, sometimes also called inverse error, is a formal fallacy, committed by reasoning in the form:

If P, then Q.
Not P.
Therefore, not Q.

Arguments of this form are invalid. Informally, this means that arguments of this form do not give good reason to establish their conclusions, even if their premises are true.

Wikipedia: Denying The Antecedent

Both articles provide good examples of why this is true. I think to really understand why Gingrich is wrong, though, all you have to do is be a human being. People who resemble people we love will tend to evoke more compassion in us than those who don't. Most of us understand that, when it's not convenient for us not to, at least.

The case of Trayvon Martin's death has been another one of those events that spawn far too much of what I call Molestus hoc, ergo propter hoc reasoning, meaning "this annoys me, therefore it's the cause". Whether it's racism, or kids wearing those hoodies, everyone seems to have an opinion about this. Newt Gingrich sees persecuted white people. What I see is another person who should not have had access to a firearm in that circumstance foolishly causing the death of an innocent person. The difference between me and these other people is that I know it's possible that I'm wrong, despite the reasonable-sounding nature of my hypothesis.

I'm not going to rush to judgment on this matter, as I think no one should. We all have our opinions, and just because something looks like something we're familiar with doesn't mean that it's caused by the same thing. Nor should we, as Newt Gingrich has done, forget the basic rules of logic we should all have learned in high school.