Sloppy Thinking Is Always Wrong

Not too long ago I was at dinner with a forensic dentist, a forensic mathematician, and a forensic biologist. One member of the group mentioned that his wife was terrified to go camping because she feared abduction by UFOs. Being a pack of know-it-alls, we all had a good snicker at her absent expense.

The biologist piped up at this point:

While her fear sounds silly, it's very likely that there's life on other planets, and somewhat likely that there's intelligent life. So, therefore-

The forensic mathematician put his head in his hands and interrupted with a groan.

You have no idea how offensive that statement is to me. How can you say you know anything about the probability of finding life on other planets without knowing something about the frequency of life on other planets? And how can you determine this frequency of life on other planets without actually visiting them or somehow performing an experiment to test these planets for life? Unless, of course, you are trying to tell me that you're from another planet?

The mathematician's rebuke is harsh but fair. People carelessly assign probabilistic statements to events without any information other than their own wishes that something be true.

When we say something is "likely" we are in fact making a numerical judgment that the chances are greater than 50%. When we say that something is very likely, we make the statement that the chances are even greater than our estimate of "likely".

The fact that we refuse to be precise in our estimate does not excuse us from reaching a conclusion without any supporting information.

Someone might rejoinder that there's a chance our fuzzy-headed biologist might just be correct in his statement. Unfortunately, he's no more correct than the stopped clock that's right twice a day. "Correct" in this case is based on luck instead of knowledge.