This essay originally appeared in the Journal of Law and Education, 17, 1 (Winter 1988) 91-98. Copyright © 1987, Peter Suber.

Analogy Exercises
for Teaching Legal Reasoning
Peter Suber, Philosophy Department, Earlham College

Legal reasoning is not the same as the reasoning in mathematics or the physical sciences. It is like them. Specifying the likeness in more detail, and deciding whether there is more likeness than unlikeness, are the kinds of tasks that legal reasoning is better adapted to do than mathematical or scientific reasoning.

There is more to legal reasoning than deciding cases by precedent, anticipating decisions by reference to precedent, or deciding when and how far a case fits under a rule, but those are the clearly its chief tasks. The rule to follow precedents is called stare decisis (stand by the decision). It is notoriously vague and hard to pin down. It does not demand slavish deference to the past. It permits (a) decisions that bring rules up to date with changing technology and social circumstances, as when cases of horse and buggy negligence were applied to automobiles. It permits (b) decisions that favor one set of binding precedents over another, to avoid inconsistency, to promote predictability, or even to pursue a worthier social policy. It permits (c) decisions that limit the application of older rules and it even permits (d) decisions that overrule 'bad' decisions. A rule that said in effect, 'follow all and only existing valid law', could not permit any of these things.

(In this short essay I assume that the type of analogical reasoning used in common law cases is the same as that used to interpret or apply statutes. In a longer piece I would not reject this bald claim, but qualify it.)

But even when we must follow existing valid law, we must know two things that are very difficult to ascertain: which law is relevant, and what it means to 'follow' it. Deciding these things is a task for legal reasoning, and cannot be reduced to an exact science. (The pretense sometimes taught in law school that there are scientific methods to help out here not only overlooks the ideological element in legal decision, but the role of analogy in legal reasoning.) Reasoning by analogy, while clearly a kind of reasoning, is inherently inexact.

If the world's first automobile loses control and plows up your garden, how do courts 'follow existing valid law' when no law whatsoever refers to automobiles? There is law for the horse and buggy, law for public nuisance, law for trespass, and law for captive wild animals that have escaped captivity (to cut the list arbitrarily short). Which of these is the rampaging automobile most like? Is it more like a horse and buggy than a pig sty within the city limits? Is it more like either of these than a trespassing vagrant whose campsite ruins the garden? Is it more like any of these than a marauding circus bear? The liability of the owner, driver, seller, and manufacturer of the automobile depend on which analogy we think is strongest.

This is the first occasion to think analogically. If we are led to look at horse and buggy law, then we must 'follow' it only after we make the requisite changes in the rules to reflect the fact that we are only dealing with something analogous to horses and buggies. Refracting the law 'properly' or 'justly' is the second occasion to think analogically. The two occasions are united in the common law maxim to treat like cases alike.

Clearly the law deals with just this kind of problem every day. We do not need revolutionary new technology to test the boundaries of our categories or the fit of rules to life. We need only the rendezvous of rich experience with abstract rules. Because even the comparatively 'concrete' rules of a 900 year old common law are no match for the manifold of experience, the task of subsuming cases under rules and applying cases to one another cannot become automatic or deductive. But even when a case falls uncontestably under a certain rule (e.g. the statute defining murder) it may raise an analogy problem if it is a borderline case of an exception, excuse, or justification (e.g. self- defense, insanity) as provided in a different or higher body of law.

If cases were limited to the significance of their own unique facts, they could not serve as precedents for other cases. Horse and buggy cases could never be applied to automobiles. In fact, a case about John Smith committing libel could never be applied to a case about Jane Doe committing libel. All cases have the power to expand analogically so that they apply to, have something to say about, have implications for, all 'like' or analogous cases. If they lacked this power, we would not only be unable to decide cases by precedent (by reference to other cases), but we would even be unable to state the narrow rule of a case in isolation from others. Is a particular horse and buggy case about the negligence of vehicles or animals? about the liability of owners or operators? It could be cited in future case for any of these points, as well as for principles of evidence, procedure, jurisdiction, or a thousand other things. We only know what a case is about, when we know what other, analogous cases are in line for decision, or when we know why we want to know.

Let's be a little more specific about deciding the rule of a case. What does the court judgment in the case of John Wilkes Booth say that is of legal significance? Obviously not simply, "John Wilkes Booth is guilty of murder when he kills an American President in a theater with a handgun on a Friday, while wearing..." But if we must abstract from some of the detail of a case to see a legal rule —let alone a rule applicable to other cases— then we must know what to leave out and when to stop leaving things out. If we left out the 'wrong' set of detail, we might get a rule like, "A white male commits murder when he is a citizen of the same nation as the victim, wears a moustache, is present in a theater when the victim is shot with a handgun, and is found with a broken leg within one week of the victim's death." This rule would explain why John Wilkes Booth and only John Wilkes Booth was guilty of the murder of Abraham Lincoln. But it is a bad rule. We could probably say why if we tried; if we tried, we would be using legal reasoning to help us articulate our sense that 'the salient points' (as if there were just one set!) had been missed. If the rule left out more detail, it could explain Booth's guilt but could not explain the innocence of others, e.g., "An actor commits murder when he is fully clothed in the theater where a person is killed."

If a case is best used as a precedent when we abstract only from its 'inessential' detail, then to reason well we must know what is essential. But what is essential depends on the relationship between the precedent-case and the new case before us that demands a judgment, the case for which it will be a precedent. The reason is that what is essential and what is secondary (hence, even what is 'holding' and what is 'dictum') depends on what the case is used as an analogy to. We would —and should— see the essential detail of the Booth case differently if we were to cite it in a murder case, a tort case on the negligence of theater owners, a case on trespass within reserved theater boxes, a constitutional case on what creates 'reasonable cause' for an arrest, or a case on sentencing discretion.

Determining what is essential is difficult enough. Now we see that the essential varies with different purposes. There is no single rule of a case. Every case is the intersection of a thousand strands of historical meaning. By itself it points in no particular direction. It becomes 'directional' only when we have a new case to decide and go back to the older case in order to explore its similarities and differences with our own case. As in geometry, it takes two points to make a line.

When we examine a case as a precedent, we may discern many rules; the rule that we take as the guiding or controlling rule of the case depends, then, on what sort of case it is to be precedent for. It may well depend too on how we want our own case to be decided. Clearly, there is more art than rigorous science to legal reasoning. (And the space left for art is just as much space left for politics and ideology.) Yet, the art can be learned and, within limits, rules for its practice can be described.

Good lawyers are good at legal reasoning. This means that they can find the rule of a case that is 'better' than its alternatives for a given new application. It does not mean that they can explain how they do this. Law students acquire the skill of legal reasoning by reading hundreds of cases. They get better and better at finding the stronger or more defensible holdings for a given case insofar as these are to be a function of the applicable precedents. But they may not get any better at explaining how this is to be done. What they are learning is to recognize complex and important similarities in cases, that is, to recognize critical ways in which they are analogous. This is much like the commonplace but extremely subtle process by which we all learn to recognize family resemblance in faces, rejecting irrelevant similarities and fastening only on those most indicative of kinship. As a logical problem, this recognition boggles the mind and should lead us to astonishment that it is so often done reliably. At first, each process is ineffable; but their general reliability shows that there is some structure here that can be learned, and perhaps discussed.

The following exercises are designed to simulate legal reasoning. To do them is to acquire the experience that law students acquire by reading hundreds of cases, as well as the experience judges acquire by judging hundreds of cases. They will at least give non-lawyers an idea of what legal reasoning is. They should also give one (lawyer and non-lawyer alike) a greater skill at legal reasoning and, it is hoped, a basis to articulate how it is done.

The exercises omit one element about legal reasoning that only cases themselves can include: content. By omitting content, they ignore the dominant values of the state, and to that extent fail to simulate a critical aspect of legal education and legal reasoning. In deciding cases by precedent, and in anticipating decisions by reference to precedent, knowledge of these values is at least as helpful as practice in analogical thinking. My hope is that focussing on the form of reasoning by analogy can teach something valuable by itself. But I go further, and suggest that articulate form can do some of the work of content. The formalism that makes these exercises possible excludes the actual values of the state, but is capable of sufficient internal differentiation to simulate the weak and strong tugs of analogy that real content provides in real cases.

These exercises are adapted from a very stimulating article on analogies and artificial intelligence by Douglas R. Hofstadter, "Metamagical Themas," Scientific American, September 1981, pp. 18-30. It has been reprinted with a P.S., P.P.S, and a P.P.P.S., in his book, Metamagical Themas, Basic Books, 1985, pp. 547-603.

Case Type One

You are in a very simple legal system on the second day of its existence. On the first day one decision was made:

Justice is 1 2 3
5 4 3 2 1

That is all you know. It is your only precedent for making future decisions. It is not a rule, but a case —and a very abstract kind of case at that! You must decide what rule it stands for and apply it to the cases below. To 'decide' a case is to circle the number in the string of numbers that makes the string most analogous to the precedent. Justice demands the strongest analogy, the best fit. You must treat like cases alike.

First Level

If the principal case above is all you know about justice (if it is your only precedent), then decide what justice demands in the other cases below. Formulate a rule to justify your answer in each case.

For example, if the next case were 5 4 3 2 1 2 3 4 5, then you might answer:

  1. the first 4, because the rule is to pick the first 4;
  2. the first 2, because the rule is to pick the number just to the left of the 'turn';
  3. the second 4, because the rule is to pick the 4 in the ascending part of the double series;
  4. the second 2, because the rule is to pick the number in the ascending part of the series right next to the 'turn';
  5. the first 5, because the rule is to pick the greatest of the repeated numbers, and of the repeated instances to favor the one on the left side of the turn;
  6. the second 5, because the rule is to pick the greatest of the repeated numbers, and of the repeated instances to favor the one in the ascending part of the series.

(Of course many other answers and rules are possible.)

Here are the cases that must be decided by 'following' the one and only precedent:

1 1 2 2 3 3 2 2 1 1
1 2 3 4 4 3 2 1
1 2 3 4 4 4 4 3 2 1
2 3 4 5 4 3 2 1
2 3 4 5 5 4 3 2 1
5 4 3 2 1 2 3 4 5
9 8 7 6 5 6 7 8 9
9 8 7 6 5 1 2 3 4
1 2 3 4 5 9 8 7 6
5 4 3 3 4 5
0 1 5 4 0
0 1 9 8 0
1 2 3 5 4 3 2 1
1 2 3 4 3 2 1
1 5 4 3 2 1
1 2 3 3 5 4 3 2 1
1 2 3 4 5 4 3 2 1 2 3 4 5
5 4 3 2 1 2 3 4 5 4 3 2 1
1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1 2 3 4 5 4 3 2 1
1 2 3 4 5 4 3 4 5 4 3 2 1
1 3 4 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0
1 2 3 0 5 4 3 2 1
-1 -2 -3 -4 -5 5 4 3 2 1
-1 -2 -3 -4 -5 1 2 3 4 5
1 2 3 1 2 3
3 2 1 3 2 1
1 0 0 0 2 3 2 1
1 2 0 0 0 3 2 1
1 2 3 0 0 0 4 3 2 1
5 6 7 8 9 4 7 6 5
0 0 0 1 1 1 0 0 0
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 4
4 1 1 1 1 1 1 1 4
1 1 1 1 1 4 1 1 1
0.1 0.2 0.3 0.4 0.5 4.0 0.3 0.2 0.1
100 200 300 400 500 4 300 200 100
11 22 33 40 55 44 33 22 11
1 5 2 6 3 7 2 6 1 5
99 98 97 4 95 96 97 98 99
1 1 1 1 1 2 3 4 5
1 1 1 1 5 4 3 2 1
1 1 2 3 4 4 5 4 3 2 1
2 3 4 5 4 5 4 3 2
1 2 3 4 6 5 5 6 4 3 2 1
1 20 300 4000 50000 4 3 2 1
5 4 3 2 1
1 1 1 1 1 2 3 4 5 4 3 2 1 1 1 1 1
1 4
4 1

(Write some of your own!)

Second Level

Provide rules for several of the possible answers to the same case in the first level task. Whenever possible provide more than one rule per answer.

Third Level

Take several of the possible answers to the same case in the first level task and argue that one is best or strongest. Be as specific as possible in citing reasons. Begin to formulate a general theory of 'strong' analogies.

Fourth Level

Have someone else (1) give an answer to any single case and (2) formulate a rule to justify the answer. Construct a new case for which the best answer violates the rule just given. Get your friend to give the rule for the new case. Construct a third case for which the best answer violates both rules so far formulated. Continue as long as you can. Is it possible in principle to construct a case for which the best answer violates all rules given in analogous cases, indefinitely? Can you develop a rule or a technique for the construction of such cases?

Fifth Level

Do the cases in order. For each case, assume that all cases decided up to that point are applicable precedents for the next case. Decide the next case in light of all the precedents. Be as specific as you can in explaining which 'line of cases' is most applicable to the present case, and what it requires.

Sixth Level

Get some 'authoritative' answers to the fifth level task (e.g., the vote of a class). Take one of the decisions. Can you concoct a consistent and plausible theory that reconciles all the applicable precedents with one another and with the authoritative decision in the given case? Can you reconcile the decision in the given case with all precedents? If not, can you explain why some precedents are stronger guides to decision in the present case than others? If some precedents are apparently inconsistent with each other, how did you determine inconsistency and how did you decide which precedent of the inconsistent pair was killed off by the other for purposes of deciding the present case?

Case Type Two

In the first type of case, the judge had to pick among a small set of possible answers by analogy with the precedent(s). In the second type of case, the judge will be asked to craft an answer by analogy with the precedent(s). No list or menu of possible answers is given for the judge's contemplation.

These cases have three elements. The first two stand in a relationship that determines the rule of the case. The third stands to the missing fourth in the same relationship.

For example, if justice converts ACB to ABC (in a precedent case), then justice would convert VSUT to what? Possible answers are:

  1. VUST, because the rule is to switch the second and third letters;
  2. VSTU, because the rule is to switch the last two letters;
  3. VTSU, because the rule is to switch the last letter with the unit between the first and last letters;
  4. VRVT, because the rule is to replace the second letter with its predecessor and the third letter with its successor;
  5. STUV, because the rule is to put all the letters in alphabetical order;
  6. ABC, because the rule is to convert anything to ABC;
  7. VSBC, because the rule is to convert the last two letters of any string to BC.

(Of course, many other answers and rules are possible.)

If justice converts ABC to ABD, then how would justice convert the following?


[The following set did not appear in the published version of this essay.]


Some others:

ABC : QBC :: CBA : ?
ABC : ZBC :: XYZ : ?
MRP : ZRP :: EG : ?
TARP : TZRP :: MGZ : ?
:: FTPRRJ : ?
:: CFTPRRJ : ?

Ribbon] Peter Suber, Department of Philosophy, Earlham College, Richmond, Indiana, 47374, U.S.A. Copyright © 1988, Peter Suber.