The Rules of Logic and the Rules of Inference

Lawyers make formal arguments in court and elsewhere. A formal argument needs to be consistent with formal logic, and it needs to begin with a base of knowledge and build from there, using the rules of logic or the rules of inference.

So, in order to think like a lawyer, you need to know how to think. Surprising, eh? This article does not provide a deliberate introduction to formal logic, but it does point out some of the basic fallacies that can plague argument or hide the perfidy of sophists.

The rules of inference, drawn from all the sciences—all the ways in which we know things—are the customary or consensus-accepted methodological conventions that tell us whether it is permissible to draw a factual inference based on a certain quantity or quality of data. For example, statisticians and econometricians have a highly developed set of rules of inference that they use in their work. These rules can seem arbitrary, but they have been accepted by consensus as a useful basis for discourse.

We must recall that it is a social choice whether the legal process, or any other decision-making process, will simply accept these rules of inference. (The rules of logic are pretty, well, irrefutable.) For example, as you know, we have standards of proof in law for certain things; in the U.S., conviction of a crime requires proof beyond a reasonable doubt. This is a higher standard than that which we might use in our daily lives for determining whether someone is a criminal.

 But it does not show how, or even show directly that, smoking causes cancer. Correlative relationships are “circumstantial” evidence, which we sometimes disdain, but circumstantial evidence can still be useful in reasoned arguments. You may have seen a television or film courtroom drama in which a lawyer discounts evidence that is merely “circumstantial,” but the truth is that circumstantial evidence is often a good, if not irrefutable, basis for inference. Much of what we know is based on circumstantial evidence.

In fact, a statistician might ask what this “beyond a reasonable doubt” standard of proof means—how would you quantify this level of probability? The often-used convention of statistical significance states that if there is less than (choose one) a 5% or 10% possibility that an observed correlation is just random chance, it will be deemed “statistically significant.” If analysis shows that the correlation is stronger than the selected level of statistical significance, does this mean that the correlation has been proven “beyond a reasonable doubt?” Aren’t statisticians the consummate “reasonable people?”

Most of us would answer that we seldom can reduce evidence of a crime to statistical measurements—there are multiple pieces of evidence, each with different significance or weight. Even if we could measure the probability of crime statistically, we might feel uncomfortable doing so. But the response to this discomfort is to ask whether the discretion retained by not specifying a quantitative threshold is consistent with the idea of the rule of law, which is defined as the absence, or at least the minimization, of human discretion.