Probability and Uncertainty in Law

Philosopher contemplating sunset -- or, possibly, dinner.

The law needs a satisfactory mechanism for ascertaining whether or not instances of the types of spatio-temporal states that are said (by the law) to be necessary are in fact present. Whether or not U.S. law as it now stands has a satisfactory mechanism of this sort is unclear: quite literally, no one really knowsif there is an adequate proof mechanism -- because no one really knows how to test how well (or how poorly) the existing proof mechanism works. (Nonetheless, most of us have our suspcions -- one way or another.)

Notes

for

Konstanz 2003 International Summer School Lectures on

Probability and Uncertainty in Law

Introduction

Two Types of Uncertainty in Law

Uncertainty is a pervasive feature of law and legal systems. For example, uncertainty attends the interpretation of many or all legal norms. Legal systems, however, are also forced to grapple with a different kind of uncertainty. The law^{^[1]} frequently (and perhaps always) conditions the application of legal norms on the occurrence or non-occurrence of certain kinds of spatio-temporal events or conditions. The law conditions its own use in this way even though the occurrence or non-occurrence of instances of the kinds of spatio-temporal states that the law prescribes is always or almost always necessarily uncertain to some extent. Consequently, the phenomenon of factual uncertainty confronts the law at every step.

Factual uncertainty -- uncertainty of propositions or hypotheses about states of the world -- has been a prominent topic and problem for a very long time. Factual uncertainty has presumably always interested specialists in the law of evidence and proof. Factual uncertainty has been a major topic of philosophical discussion for millennia: the topic was of interest, for example, to Aristotle; [2] and, notwithstanding occasional suggestions to the contrary, [3] factual uncertainty interested medieval thinkers as well.^{^[4]} Finally, as is well known, factual uncertainty has been a central problem in epistemology for at least 200 years.^{^[5]} Despite this impressive lineage – despite the longstanding recognition of the phenomenon of uncertainty about facts – U.S. and U.K. legal theorists in the twentieth century devoted very little attention to factual uncertainty. [6] American and British legal theorists and philosophers were and apparently still are far more interested in matters such as the uncertainty of legal norms and the uncertainty or inconclusive nature of argument about legal norms.^{^[7]} I believe that this imbalance of attention is quite unfortunate. Today I will do just a little bit to correct this imbalance. In my time with you today I will focus on factual uncertainty and factual inference. I will talk about the law’s use of one particular method – the process of “proof” in litigation and adjudication – to make judgments and decisions about uncertain factual propositions. [8]

Factual Proof in Law as a Web of Evidence and Inference

A. Legal Rules as Pegs [9] for the Fabrication of Proof in Litigation [10]

Legal Rules as Conditional Imperatives

Although the focus of my discussion today is factual uncertainty in legal settings rather than legal uncertainty, I cannot afford to ignore legal rules altogether and, so, I shall not do so. But to keep my topic within manageable bounds I will make the provisional assumption that the extent of uncertainty about the identity and the meaning of legal rules is very limited. Toward the end of the lectures, I will relax this assumption.

Legal rules influence factual uncertainty and factual inference in legal settings in a variety of distinct ways. For example, legal rules may speak directly to the inferences that can be drawn from various kinds of evidence, they may serve to filter the evidence that a decision maker is allowed to see, they may instruct a decision maker and trier of fact about the burden of proof and persuasion that one party or another must discharge before a particular verdict can be returned, and legal rules typically regulate how evidence is gathered prior to litigation or trial. These are adjectival rules. But substantive legal rules also influence the course of uncertain factual inference and proof in litigation and also factual inference and discovery in the shadow of possible litigation. Substantive legal rules have this sort of influence because exert they specify the conditions under which particular legal actions or effects should ensue.

It is true that legal rules can serve a wide variety of purposes; for example, legal rules can have hortatory, inspirational, educational, symbolic, and even cathartic purposes. But (as I have already suggested) substantive legal rules^{^[11]} also function as conditional imperatives. Legal rules in the U.S. characteristically (or frequently) take the form of “if, then” statements. [12] These legal “if, then” statements provide that if m, n, and, o conditions or circumstances obtain, then legal action x shall, should, or may be taken, or jural state or relation y shall, should, or may ensue. In the U.S. such antecedent conditions – the conditions in the “if” clause in this sort of “if, then” statement -- are often called the “elements” of legal rules.

Such elements of a legal rule establishing a right or a duty are often called the “essential elements” [13] of the right or duty created or established by that legal rule. The law characterizes the ingredients of legal rules in this fashion – it calls them essential elements -- because of the seemingly-tautological premise that the elements of a right- or duty-creating legal rule set forth the necessary ingredients or conditions for the existence of the right or duty created or established by that legal rule.

· If the doctrine of “essential elements is described and explained in the way that just described it, the doctrine is unobjectionable – providing, of course, that one grants that legal rules are the sources of rights and duties. The doctrine or notion of essential conditions, however, has some capacity to mislead people who are not members of the legal profession. A person without legal training might quite reasonably assume that U.S. law takes the view each of the elements in a legal rule that purports to defines a right or a wrong such as murder is essential for the existence or commission of the right or of a wrong such as murder. This seemingly plausible assumption, however, is usually incorrect. The definitions of rights and wrongs that one finds in particular legal rules are ordinarily not exhaustive definitions. It is usually the case that are alternative ways of creating a right such as a copyright and there are ordinarily alternative ways of committing wrongs such as murder or negligence. What this means is that the purported “essential” elements of a rule that purports to define a matter such as “negligence” are therefore often not “necessary” at all! It is frequently more accurate to say that there are usually alternative paths to the creation of legal rights and legal wrongs and that each of these alternative path has its own set of necessary or essential conditions. For example, the law provides that “murder” can be committed in a number of different ways. In each of these various ways a death is necessary. But “intent to kill” is not a necessary ingredient of all types of murder; it is a necessary ingredient of only a certain kind of murder (“straight murder”). [14] Similarly, for certain types of murder charges – for felony-murder charges – the prosecution must show that any death that resulted due to the defendant’s actions resulted from the commission of a felony by the accused, a felony such as arson or burglary. For this kind of murder charge the commission of a felony other than homicide is an essential element of the crime charged. The commission of a separate felony, however, is not an essential element of different kinds of murder charges, such as depraved-heart or reckless-indifference murder. (The importance of the general point I am making may not be apparent now. But its importance will become more obvious toward the end of my lecture(s), when I have done some talking about the dynamics of proof in litigation and about the wrinkles and surprises that time routinely injects into the process of proof in litigation.

Relationship between Conditional Legal Imperatives and “Proof of Facts” in Litigation

As I have already noted (and as you already surely knew), the reasons for the existence of legal rules and systems of legal rules are various. But one of the impulses supporting legal systems is the idea or ideal of the “rule of law,” the notion of a Rechtsstaat. Another factor supporting the existence of legal regimes is the common desire for efficient collective regulation of social activity. Because of these two factors and possibly for other reasons as well, [15] there is a widespread and deep-seated belief that it is very important that systems of law authorize and allow the production of serious consequences such as criminal sanctions, the imposition of taxes, property transfers, the transformation of a not-for-profit entity into a for-profit entity only when -- only if -- those conditions are present that the law itself (via legal rules) proclaims to be necessary if certain serious legal actions or consequences are to ensue.

The semi-paradoxical but deeply-felt principle that the administration of legal rules should be bound by legal rules – including the rules and the principles in the rules to be administered – this belief that the law must respect the conditions that the law places on its own application is one reason why the topic of factual uncertainty in law is very important. It is widely assumed that most “elements” of legal rules refer to possible spatio-temporal events. [16] It is also widely (if tacitly) assumed that the bare fact that a particular element is an element of a particular rule means that the right, duty, claim, or defense created by the rule applies or should apply only if it can be said that an instance of the type of possible spatio-temporal event identified by an element of a legal rule is not merely a possibility, but that it was, is, or will be an actuality. In short, there is a widespread and ingrained belief that the application of legal rules is, by the terms of those very rules, conditioned on the existence or non-existence of particular spatio-temporal events or states of a spatio-temporal framework, on “facts.” Given such assumptions and beliefs about the character of the requirements that legal rules appear to embed in themselves, it seems apparent that the law needs sound methods for resolving disagreements in litigation about factual questions. The ability of the law to reach tolerably satisfactory levels of fact finding accuracy may be essential if a legal regime is to be generally regarded as legitimate and some level of accuracy may even be necessary if a legal regime is to be able to survive over the long haul. A legal system that regularly imposes legal consequences when the conditions said to be essential for those consequences are not present is generally thought to be a lawless or unprincipled system of law – and, in extremis, it may not even be perceived as a system of law. [17] And any system of legal rules regularly permits legal consequences to ensue when the law proclaims that they should not ensue would surely be regarded as inefficient – since, practically by hypothesis, such a legal system is quite incapable of realizing its stated objectives except through dumb luck.

· Proof of facts is not a legal sideshow. The process of factual proof in legal settings is a central feature, not only of adjudication and litigation, but also of legal systems as a whole.

Some Peculiarities of Factual Inference in Legal Contexts

Assume now that substantive legal rules are conditional imperatives. Assume, furthermore, that the object of evidentiary processes in legal proceedings is to ascertain the existence or non-existence of the factual requirements for the application of legal rules. Given these assumptions, what can be said about the structure of inference and proof in legal proceedings? I shall start to explore this question next. It is a question with a great many answers.

Some Sources of the Multiplicity of Factual Issues in Litigation: (i) Multiplicity of the Conditions in Conditional Legal Imperatives: Multiplicity of the Elements, or Ingredients, of Rights, Duties, Claims, Charges, and Defenses.

You can expect that my brief examination here today will show that inconclusive argument or inference about factual questions is quite intricate, quite complex. But we should not rush into that thicket without first considering another source of both the complexity and the instability of inconclusive inferential argument about factual issues in litigation Long before decision makers or actors in litigation engage in intricate (and unstable) reasoning about this or that factual question in litigation -- and, indeed, at the very same time that decision makers engage in such inferential deliberation --, decision makers and participants in litigation may be required – they ordinarily are required – to wend their way through a a different kind of thicket or spider-web, one that that interlocks and interacts with the ins-and-outs of complexes of arguments from and about evidence. This is because in legal settings [18] -- or, to speak more broadly and also more accurately, in settings or situations in which it is expected or thought that legal doctrine may come into play --, decision makers and actors are presented, not with a single inferential task, but with a large array of factual issues and problems. There are at least several distinct reasons for this. One important reason for this is the nature and workings oflawand legal doctrine. In litigation and in adjudication (as well as in many other legal and social contexts) legal rules are frequently a source of the tasks, including the inferential tasks, that decision makers and actors are required, willy-nilly, to perform if they wish to maximize their prospects for favorable outcomes (whether in litigation and adjudication or in other contexts).

But why does the influence of legal rules on outcomes tend to multiply factual issues? Consider my (tentative and possibly controversial) account of the structure and function of legal rules. In my Kelsenesque account of the nature and workings of legal rules, legal rules contain antecedent conditions. These antecedent conditions play a part in determining the factual issues that arise in litigation. My Kelsenesque reading of legal rules implies that evidence must be introduced to establish the existence of an instance of each type of spatio-temporal event that the legal rule upon which one wishes to rely provides is necessary for the application of that legal rule.

So be it.

But if we think about legal rules in this way -- if we think this is the nature of legal rules and that this kind of proof is what the existence of legal rules entails or implies --, we are faced with a mystery, possibly a small mystery, but a mystery nonetheless. This minor mystery is pertinent to the present inquiry: how and why do law and legal doctrine tend to multiply factual issues -- and thereby render inferential argument more intricate and make it less stable?

Most scholars who venture to discuss the structure of factual inference in litigation invariably assume that there is but a single issue in litigation. For example, the issue before the trier of fact, they suppose, might be, “Did Johnny Jones stab Valiant Victim or not?”

The typical picture that such scholars have of factual disputes in litigation looks something like this:

X = death E = evidence potentially suggesting or showing death

FIGURE 1

But the assumption that solitary factual issues are the rule rather than the exception in litigation is rather mysterious.

In reality, there is often controversy and disagreement about quite a large number of factual questions.

There are at least several reasons why this is so.

Let me explore just one of those reasons with you now.

Consider the English common law definition of burglary:

Burglary is the breaking and entering into a dwelling at night with the intent to commit a felony therein.

As you can see, this definition of burglary provides that burglary has quite a few essential elements. The crime of burglary is committed (under English common law) if and only:

i. there was a breaking; e.g., a door latch or a window was broken

ii. there was entry; e.g., if the malefactor’s foot crossed the threshold

iii. the malefactor’s trespass was against a dwelling, a home, and not, for example, an outhouse or a barn

iv. the breaking and entering occurred at night; i.e., after sunset

v. the malefactor had the intent to commit a crime (in addition to the trespass)

vi. the accused had a criminal intent at the time of the breaking and entering; a criminal intent that formed later would not suffice for a conviction of burglary

vii. the miscreant intended to commit a felony (such as rape), and not, for example, merely a misdemeanor

viii. the miscreant intended to commit that felony “therein,” in the dwelling

My list of the elements of the common law crime of burglary suggests that a more descriptive picture of the problems of inference typically faced in litigation would look something like this (Figure 2):

FIGURE 2 [PT1]

Well, as you can see, the inferential task facing the trier of fact faces has become more complex. And, as you know, in the case of a burglary charge, a diagram having the sort of structure shown in Figure 2, would have to have at least eight boxes, or nodes, at the very top.

But such a picture does not yet have nearly enough detail to provide us with a passable picture of the structure of the inferential tasks that triers of fact typically confront in litigation.

Before I go on to develop a more nuanced picture of the structure of problems of inference and proof in litigation, let me pause to make one important general observation:

One object of litigation and of proof in litigation is to generate answers to questions. But litigation is not an attempt to answer any questions that may happen to interest the parties or the trial judge. Law is an authoritative system. This authoritative system, as we have seen, specifies – authoritatively – the conditions under which specified legal consequences are to ensue or are allowed to ensue. What you must note here is that the law constrains ordinary human inclinations and curiosity by providing that litigation must resolve certain questions that the law regards as important. (Those questions are framed by the elements of the rights, and rules etc. that are in play in the lawsuit in question.) So the bottom line is that legal rules pose some of the questions that must be addressed by evidence in litigation. Furthermore, the authoritative character of the law and legal rules mean that some questions that the parties or the trial judge might think should be addressed and answered in the dispute for the court cannot be addressed or resolved – because the law authoritatively views some factual propositions as immaterial to the resolution of the controversy before the court. So authoritative law both raises and forecloses some factual questions. [19]

Sources of the Multiplicity of Factual Issues in Litigation: (ii) The Generic or “Abstract” Character of the Elements of Legal Rules

Although the diagram in Figure 2 is useful – Figure 2 does capture an important feature of factual proof (and persuasion) in litigation and adjudication –, the diagram in Figure 2 misrepresents – by omission – a very important feature of the relationship between the elements of a legal rule – i.e., the law’s definition of a legal rule -- and the factual issues in a legal proceeding such as a lawsuit. The diagram in Figure 2 suggests that the elements of a legal rule are themselves possible facts in issue and that the evidence in a lawsuit goes to the question of the truth or falsity of those elements. But there is something very wrong with this picture; there is a fundamental error, the nature of which becomes apparent if we bring to mind that the elements of a legal rule are part of the definition of a legal rule or a legal right. Evidence of the sort that I have mentioned in my discussion thus far cannot show that the elements of a legal rule, the ingredients of a legally-prescribed definition of a rule, are true or false. There is, to be sure, a link between evidence and the elements of legal rules but the nature of that link does not resemble the sort of direct link that Figure 2 seems to suggest.

The matters represented by letters such as X in Figure 2 are the ingredients or elements of legal rules – e.g., “intent to kill”, “death” of a “person.” “Elements” or ingredients such as these are not themselves particular spatio-temporal events; they are not particular states of a spatio-temporal framework (except, of course, to the extent that any principle or rule – such as F = MA – is itself a spatio-temporal event). Elements of legal rules – the conditions found in conditional legal imperatives – are, instead, “abstract” or generic; i.e., a statement or legal principle or proposition such as the statement that a person commits murder if and only if he or she has an “intent to kill” does not amount to the proposition or hypothesis that a particular person in a particular place and time has, had, or will have an intent to kill. The factual matters at issue in litigation, however, are typically about such specific spatio-temporal events or states; the factual matters in dispute in a lawsuit are usually not about the (possibly factual!) question whether it is true or false to say that the law calls killing murder only if a killer intended to kill. [20] There is, therefore, a distinction between the elements of a legal rule and the factual hypotheses that are ultimately in issue in a legal proceeding such as a trial.

The distinction I am making between disputes about the elements or ingredients of a legal rule and disputes about factual matters is not merely of scholastic significance. The distinction is important because observers who wish to understand uncertainty in law need to understand that the “essential elements” of legal rules – the generic ingredients of legal rules -- do not, by themselves, establish which of a vast number – an uncountably large and possibly an infinite number – of possible “ultimate” [21] factual propositions are in issue in a legal proceeding such as a trial. [22]

Since the conditions in conditional legal imperatives are usually generic, such generic conditions can be satisfied by – or “instantiated” in – any one of a very large number of spatio-temporal events. For example, an “intent to kill” is a requirement for the commission of a certain kind of murder (“straight murder,” or, “intent-to-kill murder”). An example of a typical factual issue (in litigation) is whether or not Sammy Smith had the intent to kill at 5:30 p.m. on June 1, 2003. An affirmative answer to this question about Sammy Smith is not the only way that the generic intent requirement for murder can be satisfied in a legal proceeding. It is not even the only way that an intent requirement can be satisfied in a trial of a murder charge against Sammy Smith. For example, the intent requirement in a trial involving Sammy Smith can also be satisfied by evidence showing that Sammy Smith had an intent to kill on July 15, 2003.

You can see where I am going: the number of possible spatio-temporal events or states that could “instantiate” or “exemplify” or “satisfy” a generic legal requirement such as the generic requirement of an “intent to kill” is very large. Although I do not mean or want to suggest that generic legal requirements such as “intent to kill” place no constraints on the factual hypotheses that can come to be in dispute in a legal proceeding – there are, after all, a very large number of possible spatio-temporal events or states that could not “instantiate” or “exemplify” or “satisfy” a generic legal requirement such as the generic requirement of an “intent to kill” –, I do want to reiterate that the number of possible particular spatio-temporal events that, were they to occur, would instantiate, exemplify, or satisfy a generic requirement such as the generic condition “intent to kill”, – the number of such possible spatio-temporal states having the capacity to serve as instances of a general class of events – is plainly very large, and it may well be infinite. (Even if the number of such possible events or states is not infinite, the number of such possible spatio-temporal events is very large, and probably uncountably large, I would think.)

So what?

The “so what” is in part revealed by the kind of diagram that we must construct if we are to capture the difference between, on the one hand, a generic legal requirement, and, on the other hand, a particular historical event that seems to constitute an example or an instance of a generic legal requirement. The picture in Figure 3 seems to do the trick. (Please note that this picture rests on the simplifying but potentially misleading assumption that the satisfaction of only a single generic legal requirement is ordinarily in question in a lawsuit or proceeding.)

FIGURE 3

By now you may be asking yourselves – by now you should be asking yourselves – what sort of a thing you are looking at when you look at the diagram in Figure 3. The diagram seems to have some of the characteristics of graphs. For example, the diagram seems to have nodes and arcs. But the nodes are peculiar, aren’t they?

The first oddity is that the diagram in Figure 3 seems to have two or perhaps even three kinds of nodes. The diagram has a rectangular node as well as two circular ones. The two circular nodes are in different colors. Is this kosher? Are the rectangular nodes meant to be qualitatively different from the circular nodes? And are the two different colors meant to express a fundamental difference between green circular nodes and yellow circular nodes. Does the use of such distinctive shapes and colors amount to an attempt to make qualitative distinctions among different kinds of nodes? If so, is this permissible within the framework of graph theory? (Isn’t a node just a node?)

The second feature of the diagram that may strike some of you as odd is that the directed arcs – they all appear to be directed arcs (but are they really?) – the directed arcs (if that is what they are) run upwards rather than downwards in the diagram in Figure 3. This feature alone may not lead you to say that the thing in Figure 3 is not a graph. But you might well wonder why the diagram does not follow the convention employed in many Bayes nets, which is to make directed arcs run downwards, from a hypothesis such as X – or should we say X₁? – to matters E that serve as evidence of X or (alternatively) X₁?

Let me grant that the graph in Figure 3 is a strange-looking graph and let me also stipulate that it may not be a graph at all, not a single or pure one, in any event. Let me also stipulate that the questions I myself have asked about Figure 3 are both interesting and important. But for the moment, let’s put aside the question of whether the picture or diagram in Figure 3 is a true graph and let’s just assume I have the right to draw my picture the way I have in fact drawn it. Is anything gained thereby?

The answer is, “Yes.”

We gain at least two things from the sort of diagram or picture found in Figure 3. First, the fact that an arc passes from X₁ to X (or the reverse) suggests that the connection between X and X₁ can be insecure. Stated differently, the presence of that arc suggests that the step from X₁ to X, or vice-versa, involves some kind of inference, the drawing of some kind of a conclusion. If that is what this kind of arc suggests or implies, it performs a valuable service. That’s because some sort of an inferential process, some sort of the drawing of conclusions, is in fact at play in the relationship between generic legal principles and specific events or states of the world: as all of you almost certainly know, there can be argument and there often is argument – vigorous and extensive argument! – about the strength and the nature of the connection between the two types of propositions. Even the fact that the arc runs upward, from X₁ to X₂, is a fortunate fortuity – because the upward direction of the arc suggests that there can even be debate about the direction in which inference runs and it perhaps suggests that particular spatio-temporal events may sometimes help to constitute or shape generic legal requirements or principles. (In the eyes of a person schooled in the common law, this last possibility does not seem at all strange or bizarre.)

The second valuable contribution made by the visual distinction between nodes of type X and nodes of the type X₁ is that the spatial separation between the two makes it possible to represent the important proposition that multiple historical events or states of the space-time framework have the capacity to instantiate or satisfy a generic legal requirement. Thus, the distinction between generic legal requirements and factual circumstances makes it possible to draw the sort of picture that appears in Figure 4: [PT2]

Here X is, again, a generic requirement and it can, again, have a meaning such as “intent to kill.” As before, X₁ represents a particular historical event. We might use it to refer to a possible event such as “Sammy’s intent, on June 1, 1983, at 3:00 p.m., to kill Valiant.” X₂ is a separate event. X₂ might represent an event such as “Sammy’s intent, on July 15, 1988, at 4:15 p.m., to kill Valiant.”

· In U.S. legal proceedings it is common – particularly but not exclusively in civil cases – for a party to proceed to trial with multiple alternative distinct hypotheses about events or states of the world that allegedly instantiate(d) some generic requirement such as “intent” or “cause-in-fact.”

There are at least two reasons why it is helpful to have a visual representation that maintains and displays a distinction between propositions of the form X₁ and X₂. First, propositions such as these are different propositions because these two propositions are propositions about distinct spatio-temporal events. (Thus, one proposition might be true and the other, false.) Our representations of the process of inference and proof in litigation at a minimum ought to correctly identify the contested propositions or hypotheses that may become the object of evidentiary submissions and evidential argument in legal proceedings.

Second, since separate propositions such as X₁ and X₂ concern distinct events or states of the world, the evidence pertinent to one hypothesis – e.g., X₁ – may not be pertinent (or not pertinent in the same way or to the same degree) to another hypothesis such as X₂. If we wish to use diagrams to display and dissect the force and direction of evidence in litigation, we must, of course, clearly identify the propositions to which evidence is directed. The separation between X₁ and X₂ is useful, in short, because the separation makes it possible to see clearly that evidence that is pertinent to one possible historical instantiation of a generic legal requirement may not be pertinent to a separate possible historical instantiation of the same generic legal condition or requirement. Thus, we are now able to recognize that the situation shown in Figure 5 is entirely possible and, quite probably, very common.

Consider an illustration of the meaning of the diagram in Figure 5. The diagram might be used to represent a situation in a criminal prosecution for a murder that perhaps was committed long ago – or perhaps not. In this hypothetical case Sammy Smith is on trial in the year 2003 for the murder of Valiant Victim. E₁ might represent Sammy’s statement on May 15, 1983, “Gee, I despise Valiant.” E₂ might represent Sammy’s alleged statement on July 2, 1998, “Valiant’s behavior at my birthday party on July 4, 1952, still infuriates me.” [23] X₁ might represent the hypothesis of “the killing of Valiant Victim by Sammy Smith on August 1, 1983.” X₂ might represent the hypothesis or proposition, “Sammy Smith killed Valiant Victim on July 4, 1998.” [PT3]

· Once it is understood that a question about X normally devolves into questions about propositions or hypotheses such as X₁ and X₂ – and that similar things happen ordinarily happen to other (generic) elements of a legal rule (such as the legal rule defining “murder”), we are in a position to see that the ultimate factual question at a trial is very likely not

P([A|E₁] + [B|E₂] + … [Z|E_n])

but instead some variant of a question or proposition of the following sort:

P({[A₁|EA₁] or [A₂|EA₂] or … {[A_n|EA_n]} + {[B₁|EB₁] or [B₂|EB₂] or … [B_n|E|EB_n]} + … {[Z₁|EZ₁] or … [Z_n|EZ_n]})

Inference Networks in a Legal Style

Now let’s remove our gaze from the connection between the legal scaffolding for juridical proof – from the legal pegs on which factual issues and, below them, webs of evidence and inference hang -- and let’s look only at the webs of evidence and inference that hang from, or are attached to, hypotheses about specific spatio-temporal states or events. So, in terms of the notation above, let’s consider the connection between some A_n and some E_n. What is the nature of that connection?

The answer to this question is not straightforward. The thrust of your answer might well depend, for example, (at least) in part on whether you subscribe to some variant of Bayesianism or, instead, to some variant of a so-called Baconian theory of inference or induction. But perhaps we can at least agree on this much (at least provisionally): the question before us is how we should think about a proposition of the form P(A_n | E_n) – or, more broadly, how we should think about the task or problem or phenomenon of inferring the value of hypothesis given some evidence. Let me make several observations about how some scholars, including some influential legal scholars, have conceived of this phenomenon or task.