The Drake Equation (Formal Fallacies, Part 1)

Frank Drake

In February, I completed a 25-part series on red herrings, a category of argumentative fallacies that are intended to distract from the argument, rather than address it directly. That's only one category of argumentative fallacy. In this series, we'll look at formal fallacies. Formal fallacies are errors in basic logic. You don't even need to understand the argument to know that it is fallacious. Let's start with the appeal to probability.

Appeal to Probability

If I play the lottery long enough, I'm bound to win, and I can live on the prize comfortably for the rest of my life! Yes, it's possible that if you play the lottery, you'll win. Somebody has to. The logical fallacy here is to confuse the possibility of winning with the inevitability of winning. Of course, that doesn't follow.

In our study of cognitive bias (also available in compiled form here), we learned that numerous biases result from the misapplication or misunderstanding of probability in a given situation. Examples include the base rate effect, the gambler's fallacy, the hindsight bias, the ludic fallacy, and overall neglect of probability. Use the tag cloud to the right to learn more about each. We are, as a species, generally bad at estimating probability, especially when it affects us personally.

Various arguments about the Drake equation can fall into this trap. The Drake equation, developed by astrophysicist Frank Drake in 1961, provides a set of guidelines for estimating the number of potential alien civilizations that might exist in the Milky Way galaxy. Here's the formula:

in which:

N = the number of civilizations in our galaxy with which communication might be possible;
R* = the average rate of star formation per year in our galaxy
fp = the fraction of those stars that have planets
ne = the average number of planets that can potentially support life per star that has planets
fℓ = the fraction of the above that actually go on to develop life at some point
fi = the fraction of the above that actually go on to develop intelligent life
fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L = the length of time for which such civilizations release detectable signals into space

There are various arguments about the Drake equation. Some argue for additional terms in the equation, others point out that the value of many of the equation's terms are fundamentally unknown. There's a reasonable argument to be made that "N" has to be a fairly low number, on the simple grounds that we have not yet detected any extraterrestrial civilizations. Depending on the assumed values of the terms in the equation, you can derive conclusions that range from the idea that we're alone in the galaxy (see the Fermi Paradox) to an estimate that there may be as many as 182 million alien civilizations awaiting our discovery (or their discovery of us).

From a fallacies basis, however, the problem comes when people argue that the vast number of stars makes it certain that alien civilizations exist. As much as I'd personally prefer to believe this, the logic here is fallacious. Probable — even highly probable — doesn't translate to certainty.

That's not an argument against the Drake equation per se, but merely a problem with an extreme conclusion drawn from it. The Drake equation was never intended to be science, but rather a way to stimulate dialogue on the question of alien civilizations.

Fallacies (a New Series in the Manner of Cognitive Biases) - Part 1

As a follow-up to my series on cognitive biases, here’s the start of a new one: a description of classical fallacies. For the purposes of this discussion, a fallacy is an opinion or position based on invalid reasoning. The conclusion itself may not be wrong, but the argument offered in support of it is wrong.

“He plays a doctor on TV; he endorses this medical product; therefore, the medical product is good” is fallacious not because the medical product being touted is necessarily not good, but because it’s ad verecundiam, an appeal to an authority outside the authority’s area of expertise. If the same authority made a statement about the profession of acting, however, it wouldn’t be ad verecundiam because the actor presumably has standing on the subject.

Just because the actor has standing, however, doesn’t constitute a final proof that the proposition is true. At most, it counts as an evidence point — but it’s a logically valid one.

For the list of fallacies, I’m starting with the list on Wikipedia. There’s another extensive list at The Nizkor Project.  The examples and discussion are my own.

Fallacies come in two basic flavors.

Formal fallacies, as the name suggests, are errors of form: regardless of the contents of the argument, or the truth of any of the statements, the argument is invalid on its face.  An appeal to probability is one such fallacy: the idea that if something could happen, it necessarily will happen.

There are subsets of formal fallacies. Propositional fallacies are structural errors in logic.  “It’s raining or it’s Tuesday; it’s not raining, therefore it’s Tuesday” is a propositional fallacy (affirming a disjunct). It may not be raining, but that doesn’t make it Tuesday.

Syllogistic fallacies also fall into the category of formal fallacies. “Some cats are black; some black things are televisions; therefore some cats are televisions” involves an illicit treatment of the minor term (you can’t assume that the set of televisions and the set of cats have common members because they share a particular color).

Informal fallacies are not fallacious because of their structure, but usually because of their content. Ad verecundiam and its kissing cousin ad hominem both use a personal characteristic to prove or disprove a proposition without establishing that the personal characteristic in question actually determines whether the conclusion is true or false.

I learned a lot doing the cognitive biases series, and I hope to learn a lot on this project as well. If you’ve seen any great examples of any of these fallacies, please let me know.