March 10, 2010
Formal Logic in Law School?
Posted by Sarah Lawsky

I've been thinking about whether law students could benefit from a course in formal logic. Much of the course would be similar to an introductory formal logic course in a philosophy department.  The course would, for example, cover formal representations of logical arguments, including analyzing valid and invalid arguments. Students would do problem sets. A portion of the exam might involve proofs.

The course would also be directly related to the law, though, in at least two ways.  First, the course would draw examples of the principles we were studying from cases that interpreted statutes or contracts that explicitly draw on logical principles or implicitly rely (or misuse) them.   Second, the course would teach not only how to use logical arguments, but also when formal logic should not control.  (I expand on these possibilities after the jump.)

I don't doubt that "[t]he life of the law has not been logic. It has been experience." But immediately preceding these famous lines Holmes writes, "It is something to show that the consistency of a system requires a particular result" (though of course his main point is contained in the continuation of that sentence: "but it is not all"). And he does not say that logic is completely irrelevant, but rather that the law "cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics" (emphasis added).  

My guess is that law students could benefit from a very strong grounding in formal logic, combined with guidance in how to determine when to use more formal arguments and when and how to dismantle such arguments.  But I have never taught such a class, and I could well be wrong.  Does anyone have any experience teaching or taking such a course?  Does it seem like a good idea?

Imagine, for example, teaching the Tax Court case of O'Donnabhain v. Commissioner, 134 T.C. No. 4 (2010), which includes a debate about how formal logic should apply to the law. The case holds that medical expenses incurred for a sex-change operation are deductible. (More about the case here.) One issue is whether a sex-change operation is cosmetic surgery: Section 213 of the Tax Code permits taxpayers to deduct medical expenses above a certain amount, but explicitly forbids deductions for cosmetic surgery, which it defines as "any procedure which is directed at improving the patient's appearance and does not meaningfully promote the proper function of the body or prevent or treat illness or disease."

Judge Foley, dissenting and concurring, argues that a sex-change operation is cosmetic surgery even if it treats disease, because it does not also meaningfully promote the proper function of the body. That is, he argues that a procedure that is directed at improving a patient's appearance is cosmetic surgery unless it meaningfully promotes the proper function of the body and prevents or treats illness or disease.

In a concurring opinion, Judge Halpern explicitly invokes formal logic to explain why Judge Foley's interpretation "conflict[s]" with "the rules of logic and grammar." "In formal logic," Judge Halpern writes,

there is a set of rules, De Morgan’s laws, relating the logical operators "and' and "or" in terms of each other via negation. E.g., http://en.wikipedia.org/wiki/De_Morgan’s_laws. The rules are:

not (p or q) = (not p) and (not q)

not (p and q) = (not p) or (not q)

The first of the rules would appear to govern the disjunction in section 213(d)(9)(B), which is of the form "not (p or q)". Its equivalent is of the form "(not p) and (not q)"....The statute could be rewritten in the form

A procedure is cosmetic surgery if it (1) is directed at improving appearance and (2) does not meaningfully promote the proper function of the body and does not prevent or treat illness or disease. 

He then applies De Morgan's laws to conclude that (2) is true

only if the procedure neither meaningfully promotes the proper function of the body [p] nor prevents or treats illness or disease [q]. If one of the alternatives is true, however, then the expression is false and the test is flunked, so that the procedure is not cosmetic surgery.

Judge Foley is, however, unimpressed by the invocation of De Morgan's laws. "Congressional intent is not subservient to De Morgan's laws," he writes. The majority's opinion, and Judge Halpern's reading, is too broad, he claims, and does not respect Congress's intent to "limit[] deductions for procedures directed at improving appearance."  In other words, Judge Foley believes that formal logic should not control the interpretation of this statute.

Judge Foley did not invent the idea of disregarding a law of logic to adhere more closely to Congress's perceived intent. Drawing from Lawrence Solan's The Language of Judges, Judge Foley points to cases interpreting the phrase "without knowledge or consent," and quotes Solan as saying, "we have no way of telling whether the drafters of the statute intended that De Morgan's Rules apply or not." 

The class could read the line of cases to which Judge Foley refers as well as Solan's discussion of those cases.  We could note that Solan makes his comment about De Morgan's laws when discussing a particular forfeiture statute that is, he says, a good candidate for disregarding the distinction between "and" and "or" for three reasons: we usually think of "knowledge and consent" as a "single concept"; the categories of "knowledge" and "consent" are not exclusive of each other; and the outcome of construing a "complex and confusing statute" in a way consistent with De Morgan's law would be "extraordinarily harsh."  The class might conclude that none of those reasons applies to Section 213 or Judge Foley's proposed interpretation of that section, and that Judge Halpern thus might have the better side of this particular argument.

Judge Halpern is my colleague at GW Law School, but I have not discussed anything in this post with him, including the case itself.

The course might include material similar to that offered in courses such as the University of Chicago's Philosophy 30000, Elementary Logic

Eugene Volokh discusses how a Supreme Court case seems to run afoul of De Morgan's laws here.

James Grimmelmann gets the last word on De Morgan's law here.

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