Ancient Greek and Roman lawyers recognized that pith and wit could overcome logical rigor in the courtrooms of their day. For example, Socrates was convicted and executed, not because his prosecutors proved that he did what they alleged with irrefutable logic, but because their rhetoric convinced the jury to make one decision instead of another.¹ Rather than run from rhetoric in search of truth, ancient lawyers used rhetoric to aid the truth in coming out. Cicero, for example, wrote a few books on the use of rhetoric in courtrooms. Perhaps they understood that rhetoric often beats logic, even in a fair fight.

One reason rhetoric is so powerful is that logic is so dadgum hard. Denying the antecedent has been recognized as a logical fallacy for perhaps 2,300 years. Aristotle gave an example of its twin sister, affirming the consequent, way back in his Sophistical Refutations in the late 4th century B.C.E. I am not aware of a “classic” example of denying the antecedent, but they are easy and fun to come up with. For example:

1. If it is a basketball, it is round.
2. A baseball is not a basketball.
3. Therefore, a baseball is not round.

On the other hand, a piano is not a basketball, and a piano is, in fact, not round. Sticking the piano into the syllogism in the place of the baseball makes it look like the syllogism works:

1. If it is a basketball, it is round.
2. A piano is not a basketball.
3. Therefore, a piano is not round.

And that’s the trouble with logical fallacies: they tell you nothing about the conclusion. They make it neither more likely nor less likely that the conclusion is true.

Still, this particular fallacy has some staying power. Perhaps that is because its other two sisters—affirming the antecedent and denying the consequent—are logically valid. If the thing in my hands is a basketball, it must be round. Because the piano in my room is not round, it cannot be a basketball.

Denying the antecedent is a common mistake. People make it all the time. Even federal judges in published opinions affecting the lives and livelihoods of hundreds of people. In fact, I found an example in a recent Fifth Circuit opinion, DISH Network Corp. v. NLRB. The facts are remarkably complicated, but the bedrock syllogism on which the decision is built goes something like this:

1. If the attrition rate at the union shops was 116 percent, then the offer to phase out QPC was substantial evidence that the parties were not at an impasse.
2. The attrition rate at the union shops was not 116 percent.²
3. Therefore, the offer to phase out QPC was not substantial evidence that the parties were not at an impasse.

(Slip Op. at 8–9.) Or, to put it in the same terms as the first syllogism:

1. Definitions
   1. Let the “basketball” signify that the attrition rate at union shops is 116 percent.
   2. Let the “baseball” signify that the attrition rate at union shops is not 116 percent.
   3. Let “being round” signify that there is substantial evidence that the parties were not at an impasse.
2. If it is a basketball, it is round.
3. A baseball is not a basketball.
4. Therefore, a baseball is not round.

It may or may not be actually true that the parties were at an impasse. Perhaps what I have called a baseball is in fact a piano. That’s the problem with invalid syllogisms—they look smart but they tell you nothing.

Rhetoric, on the other hand, particularly pith and wit, can be very satisfying to read. And the court gets high marks on for that. The opinion is full of quotable soundbite phrases like:

• “The Board’s no-impasse finding flunks these standards.” (Slip Op. at 7.)
• “The ALJ erred, and the Board doubled down. Two wrongs can’t make the Board right.” (Slip Op. at 9.)
• “We recognize that the NLRB, in particular, struggles with this rule.” (Slip Op. at 14.)

Pith and wit are more exciting to read and, on some level, convincing. But they should not be confused for logical rigor.

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Footnotes:

n.1: Despite his (disingenuous?) thrashing of rhetoric as an empty art in Plato’s Gorgias, Socrates really could have used it at his trial. His trademark socratic method may be a great educational tool, but it’s pretty terrible at convincing anybody to do anything.

n.2: The opinion never states what the attrition rate at the union shops actually was, and this is a second problem. Although the court refers to the attrition rate at union shops as the “relevant data” and assures us (the people it’s trying to convince) that the “relevant data . . . supported DISH,” the court never discloses the relevant data. One footnote concedes that the “correct attrition rates,” whatever they may have been, were “described . . . as ‘high’.” (Slip Op. at 9 n.3.) Another paragraph refers to “an attrition rate of 30.5%,” but the court dismissed that as “simply not what the Board or the ALJ said.” (Slip Op. at 14–15.) So it’s not clear what the actual attrition rate was.

Perhaps the court avoided showing the “correct attrition rates” because it wanted to avoid the paradox of Zeno’s grain of millet. The court seems to agree that an attrition rate of 116 percent would be high enough. Its refusal to confront the 30.5-percent rate suggests that 30.5 percent may be high enough, but it’s not conclusive. What about the 86 percent that a prior court in the same case found at one of the union shops? Kinard v. DISH Network, 228 F. Supp. 3d 771, 782 (N.D. Tex. 2017). The truth is: we don’t know what attrition rate would have been high enough for the court to perceive the union’s offer to phase out QPC as substantial evidence that the parties were not at an impasse and further negotiations might be fruitful.