The Common Law and the Forms of Reasoning by accinent


									   Jeffrey Downard
   Department of Philosophy
   Northern Arizona University

                            Induction, Error and the Common Law


    (Please note: the final draft will be made shorter condensing the background material

  in the first three sections. In addition, I will develop the argument in the last section)

   The aim of this paper is to examine how inductive forms of inference might be used

to decide cases in the common law tradition. What distinguishes the common law from

legislative or administrative law is that the common law develops primarily from

historical precedents set by past court decisions and not the acts of legislative or

administrative bodies. A remarkable feature of the common law is that it has the ability

to grow and develop on its own without the input of such a legislative or administrative

body. The question I will attempt to address is the following: how is it possible for

judges to use inductive forms of inference to correct errors made by prior courts?

   Genuine disputes about a legal issue typically arise when there is doubt about one of

three things. First, doubt can arise about the underlying facts in the case. The role of the

court when these disputes surface is to consider the evidence that is on each side and

determine what the facts are. In many respects, these questions are to be settled by the

trier of facts, which is often a jury. Second, doubt can arise about what the law is in a

given area or how the law applies to a particular issue. In many respects, these questions

are to be settled by trier of law, which is usually a judge. The role of the judge is to

consider the relevant precedents and determine what the rules and principles are that

cover the issue and how they apply to a particular case. Third, doubt can arise when a
new issue surfaces that is not covered by the existing law. When a court faces a case of

first impression, it must make a decision without the benefit of being able to rely on an

established set of precedents.

    The second question is the one that I will focus on in this paper. The second question

is primarily a concern of positive law: it is a matter of articulating the rules and

principles that are currently embodied in the settled core of precedents. The third

question is primarily a concern of normative law: it is a matter of deciding how new rules

and principles should be formulated in the unsettled periphery of the common law. The

strategy of this paper is to start by comparing the roles of hypothesis, induction and

deduction in developing an adequate answer to questions about the principles that are
embodied in a set of precedents. Part of the preliminary work for this project was

developed in a previously published paper. As such, I will start by summarizing the

results of this prior research.i What is new in this article is an attempt to focus on the role

of inductive inferences in correcting errors in past judgments by courts. In particular, I

propose to use Peirce’s account of the difference between quantitative and qualitative

inductive inference to examine the proper use of these two types of inductive inference in

legal reasoning about the common law.

1. Reasoning in the Common Law

    In The Problems of Jurisprudence, Richard Posner argues that logic does have a place

in legal reasoning, but that the place of logic is only in a fairly circumscribed area of law.1

Where a legal rule is both clear and well established and the circumstances of the case are

not in dispute, it is possible to reason using logic to a conclusion of law. For example,

the statutory law which makes it illegal to drive over 65 mph on a state highway is both

clear and well established. If a driver is caught driving 85 mph on a state highway, then it

iI have addressed these questions in a previous paper. See J. Downard “The Common Law and the
Forms of Reasoning,” International Journal for the Semiotics of Law,

is an easy logical inference to the conclusion that the driver has broken the law and must

pay the penalty.

   According to Posner, the kind of reasoning used by courts in these cut and dry cases is

what he calls syllogistic reasoning.2 As a paradigm of syllogistic reasoning, he considers

the following well known example:

   Major premise: All men are mortal

   Minor premise: Socrates is a man

   Conclusion: Socrates is mortal

In cut and dry cases, the given law serves as the major premise, the circumstances of the

person's action serve as the minor, and the conclusion that the law has been broken

follows with necessity from the syllogistic reasoning. So, taking the example of speeding

on state highways considered above, the law setting the speed limit and the relevant

penalties is the major premise, the circumstances in which the driver was caught driving

over the speed limit is the minor, and the conclusion is that the driver broke the law and

must pay a penalty. As Posner points out, what is attractive about the use of syllogistic

reasoning in the law is that the conclusions are objective and certain. Judges have little

discretion to impose their own values or beliefs when they reason in this way.

   The problem, according to Posner, is that deductive logic is often overused--

especially by formalists--in attempts to understand how legal decisions are made. While

there are a large number of cut and dry cases like the speeding example, it is a mistake to

ignore the fact that judges have the power to interpret the law where it is vague and even

to establish new rules of law where the old rules are incomplete or mistaken. The error of

the formalists is a misplaced confidence in our ability to derive conclusions from laws

using techniques of syllogistic reasoning. Syllogistic reasoning falls short of giving us a

comprehensive account of legal decision making because it is a mechanical form of

reasoning and can not introduce change into the law.3

    According to Posner, the method of interpretation is the primary way changes are

introduced into the law. In striking fashion, he asserts that the method of interpretation is

"not a method of logic."4 Posner seems to be committed to the view that only syllogistic

reasoning and the basic principles of noncontradiction and identity are properly thought

of as methods of logical reasoning. This claim denotes a certain presumption about what

counts as a method of logic. In the upcoming sections of the paper, I will suggest that this

presumption includes an overly narrow view of the kinds of reasonings that count as
methods of logic. I want to examine a conjecture that various forms of experimental

reasoning can be used in the law, where the paradigm of experimental reasoning is taken

from scientific inquiry. I will suggest that the kinds of reasonings used by scientists can

be reduced to three forms of inference: making hypotheses, testing by induction, and

drawing conclusions by deduction. Furthermore, I will suggest that none of these forms

of inference is reducible to the other two. Posner is sceptical of our ability to use the

method of experimental reasoning in law: "The methods by which scientific knowledge

is created and, if not verified, at least temporarily supported . . . are by and large not

available to law, not yet anyway." He adds the rejoinder at the end because he thinks that

certain empirical sciences, such as economics and psychology, may someday be brought

more fully into the study of law.

    Much of the time, questions of positive law and questions of normative law are

intertwined in a tangled and complex fashion. Nevertheless, what I will try to do here is

to keep the two kinds of questions separate. The reason for this is that my larger research

project is to compare the types of reasoning that are employed by courts when they

address questions of positive law to the types of reasoning that are used by courts to

address questions of normative law. As a lead-in to this comparison, consider the
position that Oliver Wendell Holmes takes:

        It is the merit of the common law that it decides the case first and

        determines the principle afterwards. Looking at the forms of logic it might

        be inferred that when you have a minor premise and a conclusion, there

        must be a major, which you are also prepared then and there to assert. ... It

        is only after a series of determinations on the same subject matter that it

        becomes necessary to "reconcile the cases," as it is called, that is, by a true

        induction to state the principle which has until then been obscurely felt.

        And this statement is often modified more than once by new decisions
        before the abstracted general rule takes its final shape. A well-settled

        doctrine embodies the work of many minds, and has been tested in form as

        well as substance by trained critics whose practical interest it is to resist it

        at every step.5

There are some important observations that Holmes makes in this passage. First of all, he

notes that the common law often proceeds by deciding the particular case first and then

later determining the principle. This observation is akin to a point we have mentioned

earlier, namely that cases of first impression are decided as questions of normative law

and such decisions often lead to the start of a new line of precedents. Second, he

observes that the rules and principles of the common law are articulated on the basis of a

number of individual cases. Third, he notes that the reasoning of a court can be explained

in terms of the logical forms that it employs. As a negative claim, he states that the

reasoning of a court in a case of first impression does not have the logical form of a first

order syllogism. Positively, he states that the kind of reasoning which is employed in the

articulation of a legal rule is induction.6

    What is needed at this point is a clear discussion of the major types of reasoning
which mignt be employed by a court. Once we have this, we will then be in a position to

understand and evaluate each of the claims that Holmes makes in this passage. In the

next section, I will outline a Peircean account of the three major types of reasoning.

Although there is much dispute among philosophers about the basic forms of reasoning, I

think it is reasonable to rely on a Peircean account here because it arguably is the most

complete. Opponents to this account generally attempt to collapse one or another form of

reasoning into a type which they claim is more basic. Because the Peircean account is

comprehensive, we will not run an undue risk of failing to distinguish one type of

reasoning from another. As such, I believe it is good place to start.

2. The Basic Forms of Reasoning

   According to a Peircean account, all reasoning is either deduction, induction or

hypothesis. These three types of reasonings constitute an exhaustive classification.

Within these three main classes of reasonings there are various species, but for our

purposes it will be sufficient to give a general explanation of the three main classes.

What we will try to do in this section is consider the salient features that distinguish one

class of reasoning from another. Once we have distinguished the three major types of

reasoning, we will be able in later sections to consider how the different types of

reasoning are used in the common law.

   Before working through each of main types of reasoning, we should consider a few

background points common to all three classes that are important on the Peircean

account. First of all, the fundamental unit of an act of reasoning is an argument. It is true

that terms and propositions are the constituent parts of arguments, but neither of these is

the fundamental unit of reasoning. This is because both terms and propositions are

defined on the basis of the role that they have in arguments. We can state the point in

another way that may be more familiar to some, although it will be putting the matter
roughly. The linguistic analogues of terms, propositions and arguments are words,

sentences, and paragraphs respectively. From the perspective of a logician who is trying

to classify reasonings, the fundamental unit is a paragraph and not a sentence or term.

This is because a paragraph contains the whole of a reasoning, while the terms and

propositions contained in the paragraph are only parts of the larger reasoning.

   A second background point should help to explain why the first is true. An argument

consists in a certain kind of relationship between a set of premises and a conclusion.

Reasonings can be classified according to the types of relationships that are found to exist

between premises and conclusion. Accordingly, a sentence is important in the

classification of reasonings in virtue of its role as premise or conclusion and the kinds of
relationships which it bears to other sentences in the paragraph.

   The third point is that logical principles teach us how we ought to think and not how

we in fact do think. Because the principles of logic are normative in character, they can

serve as guides for the self control of our reasonings.

   Having mentioned these preliminary points, let us review three very simple arguments

that Peirce offers as examples of the three main classes of reasonings. He asks us to

consider a case in which a sack of beans is sitting in a barn, next to which sits a small pile

of beans--all of which are white.7

Deduction proceeds from the rule and the case to the result:

   Rule.--All the beans from this bag are white.

   Case.--These beans are from this bag.

   Result.--These beans are white.

Hypothesis proceeds from the rule and the result to the case:

   Rule.--All the beans from this bag are white.

   Result.--These beans are white.

   Case.--These beans are from this bag.

Induction proceeds from the case and the result to the rule:

   Case.--These beans are from this bag.

   Result.--These beans are white.

   Rule.--All the beans from this bag are white.

It is worth noting that the different reasonings about this simple case each start from a

different set a premises. In the example of a deductive reasoning, much more is known in

the set of premises. As a result, the conclusion which is drawn follows from the premises

necessarily: if all of the beans in the bag are white, and these beans are from the bag, then

these beans must be white. The logical necessity which is contained in the reasoning is

not difficult to establish, however, because the conclusion really tells us nothing more

about the case than was already contained in the premises. The principles of deductive

logic allow us to rearrange the representations contained in the premises soas to preserve

any truth contained in the premises, but they do not allow us to say anything new about

the objects themselves. The structure of this type of reasoning should be familiar to

anyone who has taken a course in formal logic because such courses usually limit

themselves to the study of deductive logic.

   In the example of a reasoning by hypothesis, it is clear that much less about the

situation is given in the premises. From the scant amount of information that is provided

in the premises, a highly informative hypothesis is drawn. The conclusion that these

beans are from the bag does not follow necessarily from the premises contained in the

sample argument. For example, the beans might have come from many different sources
besides the bag that they are sitting next to: someone might have placed them there on

purpose; they might have been spilled before the bag of beans was ever brought to the

barn; or a stray bird might even have carried them into the barn from a field. What is

asserted in the abductive reasoning is that the hypothesis that the beans are from the bag

is a good conjecture, meaning that it is worth pursuing in further inquiry.

   At times Peirce calls this type of inference abduction, retroduction, presumption and

hypothesis.8 For the sake of clarity in our terminology, I will call the inference which is

used to arrive at the new explanation an abduction, and I will call the explanation that is

formed as the conclusion of an abductive argument a hypothesis.

   We should note that abduction, as a type of reasoning, begins when something out of
the expected course of events happens that calls for an explanation. Our expectations are

fixed, of course, by the explanations and theories that are currently accepted by the

community of inquirers. An observed fact is surprising when it falls outside of the course

of events that were expected on the basis of accepted theory. When confronted with a

surprising observation, a new explanation is called for to account for its occurrence.

   Given the two initial points that have been made about abduction--that it is called for

when a surprising observation is made, and that a new hypothesis is formed to explain the

surprising observation--it should be clear that abduction is a fundamentally different type

of inference from deduction. As we have said earlier, deduction adds nothing new to the

conclusion that was not already contained in the premises. Abduction, however, is

ampliative in that new content is introduced in the reasoning. Further, it is ampliative in

the sense that a new idea is introduced in the conclusion that was not contained in the


   According to Peirce, there are two basic conditions that an abduction must meet in

order for it to be a valid abductive reasoning. First, the hypothesis must allow for the

anticipation or prediction of the unexpected event that was observed. The unexpected

event must be deducible in a demonstration from the hypothesis. Since the hypothesis
contains new content, new predictions must be deducible from the hypothesis. Second,

the new predictions that are made on the basis of the hypothesis must be testable by


   In the example of an inductive reasoning, the inference moves from premises which

state that a small sample of beans are all white to a conclusion that all the beans in the

bag are white. Like abduction, induction is also ampliative in that new content is

introduced in the reasoning. However, it is not the case that a new idea is introduced in

the conclusion. Instead, "(i)nduction is where we generalize from a number of cases of

which something is true, and infer that the same thing is true of the whole class. Or,

where we find a certain thing to be true of a certain proportion of cases and infer that it is
true of the same proportion of the whole class."9

   Inductive reasonings come in different forms. In a quantitative induction, the

proportion of certain occurrences in a sample is generalized to the whole class. For

example, if a sample of 100 beans were taken from a large bag and 48 were white and 52

were black, and then another hundred were taken in a second sample and 53 were white

and 47 were black, it could be inferred that the proportion of beans in the bag was about

half white and half black. In a qualitative induction, on the other hand, the characters of a

particular thing are generalized to characters known to be common and peculiar to a

certain type. An example Peirce gives is a case in which a man has the dress, expression

and countenance of a Catholic priest. The hypothesis that the man is in fact a priest may

be tested by comparing other features of the man to the many characters which are

common and peculiar to Catholic priests.

   Taken together, these three types of inferences each have a place in the experimental

method. The first stage of experimentation is to arrive at a conjecture or explanatory

hypothesis to account for a surprising phenomenon.10 The second stage is to deduce the

consequences or predictions that follow from the hypothesis.11 The third stage is to test

by induction how far the predictions accord with our experience.12

   The basic question that we will try to address is whether or not issues of common law

can be settled by the experimental method of reasoning. In particular, we will examine

how inductive forms of inference can be used to correct errors made by courts in their

prior interpretation of the positive law and how they can be used to answer questions of

normative law. The assumption I am working on is that the two basic types of questions

that one might ask about the law—positive questions about what the law is and normative

questions about what the law ought to be—should be answered somewhat differently.

3. Other Methods for Settling Legal Issues

   At this initial stage of our investigation, we should acknowledge that the experimental

method is not the only way in which common law issues could be settled. In fact, a quick

glance at the hierarchical structure of the court system itself suggests that other methods

may be used. Questions of positive and normative law are decided in a trial by the judge.

Since the power of the court resides in this single person, it seems that the judge is rather

free to settle these legal issues on the basis of his own preferences and biases. A plaintiff

or defendant who disagrees with the ruling of a judge on a question of law has no way to

make the judge change his mind. In Peirce's terms, a judge could settle questions using

the method of tenacity: the judge could simply choose the answer which he likes best and

try to hold on to it in the face of the disagreement of others.13

   In some cases, an issue of law can be appealed to a higher court and reconsidered by

another judge. The method of authority settles issues by submitting them to a body which

has the power to decide for others. When a legal authority has reached a decision, it is

made public so that others can be educated in the law and taught to obey, and it can be

enforced by an executive body. One of the most striking features of the common law is

that issues of law can be appealed up through the levels to the highest court of appeals or

supreme court. Once an issue has been decided by a supreme court, then the issued has

for practical purposes been settled.

   As a side point I would like to note that this puts the supreme court in an unusual

position. As the final arbiters on questions of law, they have no other authority to appeal

to; as a result they must use another method to settle issues of law such as the method of


   The final alternative to the experimental method which Peirce considers is that of the

a priori method. This method of settling an issue chooses the answer which is most

"agreeable to reason."14 Although few judges explicitly say in an opinion that their
decision on a question of positive or normative law was agreeable to reason, some judges

do settle these issues by appeal to general requirements of justice and principles of

morality. Where the underlying requirements of justice and moral principles are

conceived as requirements of reason, their use in settling issues of law would conform to

the a priori method.

   In saying this, I do not mean to imply that any appeal to an underlying moral principle

to settle doubt about a legal issue would conform to the a priori method. Rather, this

move simply pushes the question back a step. The relevant question then becomes how

issues concerning moral principles are settled: by tenacity, appeal to authority, the a

priori method, or by the experimental method. Since the purpose of this paper is to

consider which forms of legal reasoning can be used to settle issues of law, I will try to

resist the temptation to push the question back to the territory of moral principles; instead,

I will attempt to address the questions within the realm of the law itself.

   Peirce argues that the method of tenacity, the method of authority, and the a priori

method offer the only three alternatives to the experimental method. I will not review the

argument which he gives for this conclusion, but I will say that the three methods are

supposed to constitute an exhaustive list of the possible material grounds for settling

opinions.15 Only the experimental method offers a way of settling issues that does not

rely on material grounds.

   We are now ready to consider which of the four methods for settling opinions are

used to settle issues of law. There are three questions that are wrapped up in this matter

and we should be careful to distinguish each. The first question, and the one which I

intend to focus attention on, is which of the methods can in fact be used settle legal

issues. In particular, I consider whether the experimental method can be used to settle

legal issues. This question arises because the best method for settling legal issues may

be one which can't in fact be employed in real world situations--there may be practical or
conceptual roadblocks to the use of the best possible method. The second question is

how issues of law should be settled. This question is explicitly normative and asks us to

pick the method that is best for settling legal issues. It is my hope that in the process of

addressing the first question an answer to the second will emerge. The third question,

and one which I will not try answer, is which of the methods are actually used to settle

issues in the common law, and if more than one is used, which is used most often. This

question is one of social psychology and is outside of the scope of this paper.

4. Positive Law

   In the first part of Holmes' famous essay, the "Path of the Law," he argues that in

order for one to determine what the positive law is in some area of the common law, one

must take the perspective of an attorney who is trying to predict the decisions of a court.16

"When we study law," according to Holmes:

       we are not studying a mystery but a well known profession. We are

       studying what we shall want in order to appear before judges, or to advise
       people in such a way as to keep them out of court. . . . The object of our

        study, then, is prediction, the prediction of the incidence of the public

        force through the instrumentality of the courts. . . . Far the most

        important and pretty nearly the whole meaning of every new effort of legal

        thought is to make these prophecies more precise, and to generalize them

        into a thoroughly connected system.17

    The first task of an attorney who wants to predict the future decisions of a court is to

trace back the trail of precedents. In gathering together a set of precedents, an attorney

must distinguish and set aside cases that are not relevant to the issue at hand and assemble
the set of cases that are on point.

    There is an assumption contained in this method that is significant, although it may

seem rather obvious. The assumption is that the precedents set by a line of cases contain

a guiding principle or set of principles. The reason why this assumption is needed can be

readily seen: to the extent that the future decisions of courts are taken to be predictable

on the basis of past decisions, then there must be principles which are used by courts in

the past and will continue to be used in the future. If no such principles were employed

by courts to decide cases in the past, then it is highly unlikely that the future decisions of

courts would conform to the established precedents.

    Legal principles may be used quite explicitly by courts to make their decisions. When

a court has a fairly clear understanding of the principles that they are using, then they

often try to set them down in the reasoning for the case. Many times, however, a court

will only implicitly employ a principle to make its decision. Upon reflection, a judge may

have only a vague sense of the principle that was used; nevertheless, a judge in these

circumstances may still be able to use an implicit principle quite capably.

    One of the driving insights in Holmes' position is that the judge who tries to articulate

the principles contained in a line of precedents (so that he can use the principle to decide
a case) is in roughly the same position as the lawyer who is trying to articulate the

principles in order to predict the future decisions of a court. Both the judge and the

lawyer must examine the line of precedents in order to articulate and clarify the principles

that were at work in the past decisions of the courts. Neither may simply rely on the

explicit statements that are made by some courts to explain the principles that they were


    The reason for this is twofold. First, in some cases the explicit statements of a court

may be at least partially wrong about the principles that were used to decide a case. A

judge's understanding of his or her own reasoning may be vague and somewhat confused.

It has been noted by more than one keen observer that courts sometimes decide particular
cases correctly even where many of their acts of reasoning were mistaken. This kind of

remark may seem presumptuous on the part of the keen observers, but consider that

judges are usually intimately familiar with the context and details of the precedents; and

let us note that it is one thing to be able to have a feel for and be able to use a principle in

one's decisions, while it quite another thing to be able to fully articulate the principles

which are being used.     Karl Llewellyn makes a related point in the Bramble Bush:

         Every case lays down a rule, the rule of the case. The express ratio

         decidendi is prima facie the rule of the case, since it is the ground upon

         which the court chose to rest its decision. But a later court can reexamine

         the case and can invoke the canon that no judge has power to decide what

         is not before him, can, through the examination of the facts or of the

         procedural issue, narrow the picture of what was actually before the court

         and can hold that the ruling made requires to be understood as thus


Second, any given case may contain only a partial statement of the principles that underlie
a series of precedents. Only by examining all of the relevant precedents together is it

possible to fully piece together all of the related parts and principles which govern a set of


    Holmes rejects the use of the method of authority to settle issues of positive law when

he says: "It is only after a series of determinations on the same subject matter that it

becomes necessary to 'reconcile the cases,' as it is called, that is, by a true induction to

state the principle which has until then been obscurely felt."19 Instead of simply

appealing to the past statements by courts and relying on their authority, an attorney or

judge must examine the line of precedents and use inductive reasoning to articulate the

underlying principles.
    On this point, I want to argue that Holmes is right to think that we must use

experimental reasonings such as induction in order to articulate the principles of law. At

the same time, I want to show that he has made a common mistake about the precise

nature of the experimental reasonings that are being used. I believe that Holmes has

conflated two different kinds of reasonings: abduction and induction. With due

diligence, we should be able to make clear how the two different kinds of reasonings can

be used in the common law.

    According to Peirce, the first step in the process of experimental reasoning is to

formulate a hypothesis to explain some surprising observation. The kinds of surprising

facts which we are confronted with in the positive law include situations where there is a

line of precedents which appears to contain a certain amount of regularity. If no attempt

has yet been made to articulate the principle which underlies the regularity, then a

hypothesis is made as a first conjecture. If, as is often the case, a principle has already

been formulated to account for the regularity, then doubt occurs when new cases are

decided which do not quite square with the accepted principle. In this situation, a new

hypothesis is formulated to reconcile the cases, and it is hoped that the new hypothesis

will turn out to be a better explanation than the accepted principle.

    After a worthy hypothesis is formulated, it can then be tested against other decisions

of the courts. From the hypothesis, it should be possible to deduce other consequences

which can be used to predict how courts will decide similar cases in the future. The

obvious way to test the hypothesis is then to compare the predictions that are deduced

from the principle to the future decisions of the courts.20

    As is often the case with any kind of hypothesis, the first formulation may turn out to

be inadequate, or to put it in other terms, the hypothesis may fail some of the tests. This

does not show that the hypothesis was not a good first conjecture, however, because the

purpose of the hypothesis was to provide a provisional starting point to start the
investigation. Where the hypothesis fails the tests of experience, modifications must be

made by the use of another abductive reasoning. According to Holmes, the first statement

of a legal principle "is often modified more than once by new decisions before the

abstracted general rule takes its final shape."21

    In carrying out the process of formulating and testing a hypothesis, a judge or attorney

does not work alone; instead, the process takes place through the joint efforts of many

judges, attorneys, and lay observers. In Holmes words, "A well-settled doctrine embodies

the work of many minds, and has been tested in form as well as substance by trained

critics whose practical interest it is to resist it at every step."22 When a hypothesis is

found that can meet a number of such tests, the principle which is contained in the

hypothesis can be generalized by induction from the limited number of sample cases to

the whole class of legal decisions about the issue.

    If it is correct to think that inductive reasonings can be used to articulate legal

principles, then we should look more closely to see which kinds of inductions can be

used. In the empirical sciences such as biology and chemistry, it is common to use

quantitative inductions to specify the mathematical frequency of some phenomena. As an

example from the history of biology, consider a hypothetical case from Mendel's study of
the heredity of characters such as flower color in plants. If Mendel had examined a

sample of flowers in which he noted a ratio of 1/2 pink flowers and 1/2 white in a certain

species of pea, he could have inferred by induction that the same ratio would hold for the

rest all populations of that species of plant. While quantitative induction is used

frequently and works well in empirical sciences such as biology, we do not see attorneys

and judges making mathematically precise inductive inferences in the study of the law.

   It can be argued that quantitative induction is used to articulate legal principles but

that the relative frequency of the principles is always 1. I do not know what to think

about this claim. To a certain extent it does make some sense. This is because there

seems to be a tendency among attorneys and judges who examine a sample set of
precedents to require that any principle which is articulated cover all of the cases in a

series of precedents. Where a principle does not bring all of the cases into conformity,

attorneys and judges can either discard the principle and attempt to formulate another, or

they can take another look at the precedents and try to find cases which are inconsistent

with the others. Where neither of these is possible, they can simply say that the series of

precedents is not fully developed and more time is needed in order for the cases to

become orderly. While it may be true that judges and attorneys can do this, it is not clear

at this point why they would require every legal principle to have such uniformity.

   A second type of inductive reasoning which might be used to settle issues of positive

law is qualitative induction. This type of reasoning is similar to what is commonly called

reasoning by analogy. Since common law courts often find themselves in the position of

having to analogize cases that are similar but not identical, it is reasonable to suppose that

qualitative induction plays an important role in their reasonings. Peirce characterizes this

type of reasoning in the following way:

       So long as the class sampled consists of units, and the ratio in question is a

       ratio between counts of occurrences, induction is a comparatively simple
       affair. But suppose we wish to test the hypothesis that a man is a Catholic

       priest, that is, has all the characters that are common to Catholic priests

       and peculiar to them. Now characters are not units, nor do they consist of

       units, nor can they be counted, in such a sense that one count is right and

       every other count wrong. Characters have to be estimated according to

       their significance. The consequence is that there will be a certain element

       of guess-work in such an induction; so that I call it an abductory


   Following this line of thought, suppose that we have examined a series of precedents
and formulated a hypothesis about the principles which are employed by the courts to

decide the cases. If we want to test the hypothesis by comparing it to a new case that has

just been decided, then we must make certain comparisons. We must, for example,

compare the legally relevant circumstances of the case at hand to the circumstances of

precedents. In doing so, it is likely that the cases will have some characteristics in

common and others that are not shared. We cannot simply quantify the characteristics

that are common between the cases because the characteristics are not discreet units.

Some characteristics of the circumstances are more important to the use of the principle

while others are less important, so the use of the induction requires us to put a certain

weight on each of the characteristics.

   So far we have taken a look at the use of abduction to formulate a hypothesis about

the principles that are employed in a series of precedents. As a legal hypothesis, it seems

to meet the two conditions that are required of any valid hypothesis. First, predictions

can be deduced from the hypothesis about the future decisions of courts in a proscribed

area of law. Second, the predictions can be tested by certain kinds of inductions: it

appears that quantitative inductions can't be used to give mathematically precise

predictions of future cases, but it may be the case that they can be used to formulate

uniform predictions; and it appears that qualitative inductions can be used to analogize a

case to a series of precedents.

   Taken together, these three inferences constitute a method of experimental reasoning

about the principles of positive law. If it is true that judges and attorneys can reason

experimentally about the law in this way, then I believe something philosophically

interesting follows as a corollary. In order to make out this point, we must take a closer

look at the legal principles that are articulated through the use of the method.

   The principles of law that are articulated on the basis of a series of precedents can and

often are used by judges to decide the cases the come into their courts. When a judge
uses a principle of law to decide a case before him, the judge uses the principle as a guide

for how the case ought to be decided. If the principle is used correctly in the reasoning of

the judge, then it will serve to decide the case properly.

   It is always possible that a judge will fail to use the legal principle in the right way.

And it is also true that a judge can ignore any and all legal principles and decide a case in

another way; a judge could, for example, act out of personal spite and decide a case

against a party based solely on personal interests. Where the bias of a judge is egregious,

a party can seek a mistrial and have a new trial before a different judge. But where the

bias is more subtle, such options are not available. This point is worth making for the

following reason. A street-wise attorney who is trying to predict a future decision of a

particular judge may take note of past tendencies of the judge to resort to personal

interests as reasons for the decisions of the court. Judges are in a different position,

however, because they should strive to extricate uses of personal biases in the rulings of

courts that have preceded them. By doing this, it is possible to keep the personal biases

of judges who decided past cases from infecting the articulation of legal principles.

   Because legal principles determine how cases should be decided and not how they in

fact are, they are normative principles. A philosophical interesting point about this fact is
that the legal principles of the common law--as normative principles--can be articulated

using experimental reasonings. It is well known that empiricist philosophers such as

David Hume have argued that we can reason only about matters of fact. Well, if legal

principles are normative rules, and rules of law can be articulated using experimental

reasonings such as abduction, induction and deduction, then there is at least a certain

tension with Hume's arguments. It is true that the legal principles we are talking about

are principles of positive law and as, such, are the currently accepted principles contained

in a body of legal precedent. So the experimental reasonings are used as part of an

inquiry into what the law actually is and not what it should be. Nevertheless, it is an

inquiry into the principles which are used by courts in their reasonings about how cases
should be decided.

   Before leaving our discussion of the positive law, I would like to make another

attempt at the problem we encountered earlier in our discussion of the use of quantitative

induction. We noted the peculiar feature that judges who strive to articulate the

principles of positive law do not try to specify a certain mathematical proportion in a

hypothesis about a legal principle. This is peculiar given the fact that a series of

precedents may split in the way in which they decide a particular issue. For example, 2/3

of the courts may decide a particular issue one way, while the other 1/3 may decide the

same issue another way. This is especially typical in questions of state law where the

courts of different states serve as only persuasive precedents for one another.

   I think we can come to some understanding of why judges refrain from forming

hypotheses that contain mathematical proportions if we keep in mind that the legal

principles which are being articulated are inherently normative in character. The very

purpose of having normative principles is to guide the conduct of the subjects within a

state and to guide the conduct of courts in the resolution of disputes. Judges refrain from

formulating principles of law that contain mathematical proportions because such

principles do not meet the purposes law. It does not make sense to say that a person
should guide her conduct using a legal principle where that principle is of the form: do

act X 2/3 of the time and do act Y 1/3 of the time. A principle containing a mathematical

ratio would not serve well as a guide for conduct because it does not say when to do act X

and when to do act Y. Such a principle would create uncertainty in the minds of people

about how others would act on the basis of the law.

   This is one significant difference between laws of nature and legal principles.

Because laws of nature are used to explain and predict the behavior of natural objects,

laws that contain mathematical proportions may be the most accurate kind of natural laws

that a theory can have about a certain kind of phenomena. Legal principles, on the other

hand, have to serve a dual purpose. On the one hand, subjects of the law must use
representations of the law as a guide for their conduct and judges must use them to guide

their decision making. On the other hand, legal principles are used by attorneys to

explain and predict the future decisions of courts.

5. Conclusion

   In this paper I have tried to suggest that experimental reasonings can be used to

decide issues in the common law. I have tried to compare the kinds of reasonings that

can be used to answer questions of positive law to the kinds of reasonings that can be

used to answer questions of normative law. Through this comparison a striking point has

emerged. On the one hand, it seems that questions of positive law can be addressed using

all three forms of inference: abduction, deduction and induction. I have argued

elsewhere that questions about what the law normatively should be in cases of first

impression can be addressed using only abduction and deduction.

   The source of this divergence in the kinds of reasonings that can be used to answer

these different questions seems to be the normative character of the legal principles

themselves. Because legal principles can only be used by judges through their
representations of the principles in their legal reasonings, the principles cannot control the

reasoning of judges until the principles are formulated as a rule. In a case of first

impression, a judge does not have a legal principle that is adequate to decide the case.

     It should be noted that the same normative character of legal principles also gave rise

to the point that quantitative inductions can't be used to articulate legal principles of

positive law with mathematically precise ratios. This reason for this is that the purpose of

having legal principles is to guide the conduct of people who are subject to the laws as

well as judges and juries who must decide disputes about the law. Principles containing

mathematical ratios are not articulated because such principles would not be terribly

useful in the guidance of conduct.
     Here, at the end of this paper, I want to note that there is a further question we should

ask: given that experimental reasonings can be used to answer questions in the common

law, should experimental reasonings then be used to decide these issues? It is my hope

that something of an answer to this question has emerged along the way. It is my belief

that if legal questions can be answered experimentally, then they should. For as Peirce

has persuasively argued, only the experimental method offers a distinction between a

right and a wrong way.

    Richard Posner, The Problems of Jurisprudence (Cambridge: Harvard University

     Press, 1990).
    Posner, The Problems of Jurisprudence , 38-42.
    Posner, The Problems of Jurisprudence , 41.
    Posner, The Problems of Jurisprudence , 41-2.
    O.W. Holmes, "Codes, and the Arrangement of Law," American Law Review, 5 (1870),

    Posner strives to adopt a kind of Holmesian pragmatism towards legal reasoning. He

     considers the possibility that induction can be used in the method of interpretation but
     seems to have practical worries about the possibility. R. Posner, The Problems of

      Jurisprudence , 61-70.
     C.S. Peirce, "Deduction, Induction, and Hypothesis," in Charles S. Peirce: Essays in

      the Philosophy of Science, ed. Vincent Thomas (New York: Liberal Arts Press,

      1957), 126-144.
     Other philosophers use the phrase 'inference to the best explanation' in order to classify

      reasonings in a manner that is similar to what Peirce means by abduction. However,

      we should be careful not to equate the two. This is because some of the arguments

      that are labeled inference to the best explanation are actually a complex argument on
      the Peircean account. These complex arguments are composed in part of abductive

      reasonings and in part of inductive reasonings and Peirce is insistent upon keeping the

      distinction between these two clear.
     Peirce, "Deduction, Induction and Hypothesis," 129.
     C.S. Peirce, Collected Papers of Charles Sanders Peirce, 8 vols., ed. Charles

      Hartshorne, Paul Weiss and Arthur Burks (Cambridge, Massachusetts: Harvard

      University Press, 1958), 5:602. See Misak, Truth and the End of Inquiry (Oxford:

      Oxford University Press, 1991), 94.
     Peirce, MS 841, 44.
     Peirce, Collected Papers of Charles Sanders Peirce, 2:755.
     C.S. Peirce, "The Fixation of Belief," in Philosophical Writings of Peirce, ed. J.

      Buchler (New York: Dover Publications, Inc., 1955), 5-22.
     Peirce, "The Fixation of Belief," 15.
     For an historical reading of Peirce's argument for this conclusion, see Richard Smyth,

      "Why Be Logical," Transactions of the Charles S. Peirce Society, 24 (1988), 441-68.
     For an historical account of the relations between Peirce's and Holmes' thought, see

      Frederic, R. Kellogg, "Holmes, Pragmatism, and the Deconstruction of
      Utilitarianism," Transactions of the Charles S. Peirce Society, 23 (1987), 99-120.

     O.W. Holmes, "The Path of the Law" appeared in the Harvard Law Review (1896-7),

      456. Reprinted in G.C. Christie, Jurisprudence (St Paul: West, 1973), 648-63.
     O.W. Holmes,The Bramble Bush (Dobbs Ferry, N.Y.: Oceana Publications, 1960), 6.
     Holmes, "Codes, and the Arrangement of Law," 4.
     Another way to test the hypothesis is to compare it to other past decisions of the courts.

      In doing this, however, there may be a temptation to compare the hypothesis to

      precedents which were used to formulate the hypothesis. This temptation must be

      avoided because such comparisons would not constitute any real test, the reason being
      that the sample would be fixed. Therefore, the only past cases which should be used

      to test a hypothesis about a legal principle are the cases which were not consulted in

      the formation of the hypothesis.
     Holmes, "Codes, and the Arrangement of Law," 4.
     Holmes, "Codes, and the Arrangement of Law," 4.
     C.S. Peirce, "Abduction and Induction," in Philosophical Writings of Peirce, ed. J.

      Buchler (New York: Dover Publications, Inc., 1955), 152.


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