Friday, July 15, 2011

The Law: What's logic got to do with it?

One of my favorite daily reads is the Volokh conspiracy, a blog by a group of law professors. As one would expect, their arguments are exquisitely reasoned, honed by years of classroom teaching, academic writing, and litigation. Although they have a definite philosophical point of view (libertarian), these scholars apply the law with intellectual integrity, developing their arguments logically from existing law and precedent. However, I cannot help but wonder about the use of logic in law.

In formal logic, the starting point is an axiomatic system, a set of statements assumed as true (axioms) that defines a particular field. The rules of logic are then used to derive theorems within that field. The most famous example is the field of Euclidean geometry, which is built upon Euclid's axioms. When developing an axiomatic system, mathematicians want a system that is consistent, independent, and complete. For our purposes here, we can ignore independence and completeness. The crucial property is consistency: axioms within an axiomatic system should not contradict one another.

Legal analysis applies the rules of logic (for example, A implies B, B implies C, hence A implies C), but it does so outside of anything resembling an axiomatic system. Laws, statutes, and precedents vaguely resemble axioms in the sense that they are assumed to be true. But the legal system is rife with contradictions. When an axiomatic system is not consistent, it contains at least one statement that is simultaneously true and false, and from that statement one can derive an unlimited number of other statements that are simultaneously true and false. In law, one can reduce the inconsistencies by only considering those laws that are deemed relevant to a particular case. No matter which subset of laws one gets to work with, it is virtually impossible for it to be anywhere near a consistent axiomatic system. Formal logic seems doomed in legal reasoning.

In spite of their mutual resemblance, legal logic lives in a universe quite different from formal logic. Legal logic is about convincing others of the merits of a case. A legal argument is successful only if accepted by some authority, and this acceptance lasts only until a higher authority overturns it. With every decision, legal authorities help shape the nature of successful legal argument. This creates a legal logic that evolves over time and reflects the nature of the power of the state. The law is about power, not logic... Who knew?


  1. Law is mostly inductive reasoning (mostly analogies based on how people feel about past or hypothetically similar events).

    It's very rarely deductive though it often looks that way in application, e.g. you did X which violates law Y consequently you shall suffer penalty Z.

    But all that stuff from the violation and statute to the penalty applied actually rely on induction for the actual result. Who committed the crime (nun v. gang member)? Who was the victim (if any)? How many past offenses has the accused been convicted of? Is the accused remorseful? What do the sentencing guidelines say? What do we normally do in this kind of case? How do I feel about it right now when I'm making a decision as to guilt and punishment. Not deductive at all.

    (BTW I'm a lawyer, but I am not a philosopher so I may be using personalized definitions of the words herein)

  2. In 1978, I had to make the decision whether to go on studying mathematics after completing my bachelor's degree in math at Princeton, or to go to law school instead. In justifying my decision to go to law school, I said the following. It was tongue in cheek, but used humor to make a real point.

    In math, a proof reasons rigorously from its premises to it's conclusion. A good mathematician can achieve that rigor. A mediocre mathematician may be able to convince someone else that his conclusion is right, but he can't always prove it rigorously. But convincing is all a lawyer needs to do! I was a mediocre mathematician, so I should be a good lawyer.

    Thats pretty much the way it's worked out over the 30 years since I graduated from Harvard Law School.

  3. @Roy
    Actually, math looks a lot easier to me that law: in math, you know what the rules are. In the practice of law, you have to deal with irrational, self-interested, and fraudulent people. My hat's off to anyone who can do that and retain their sanity.

    Your observation is well taken, and it covers 90% of the practice of law. At the appellate level and above things seem different to me. When they are arguing about the rules and their interpretations, they seem to use deductive logic.

    I am mostly a jacuzzi philosopher myself. Perhaps my question about logic really should be broadened: the use of logic in philosophy. Things are worse there, of course, because there is no authority only peers.