An Essay in Honor of Professor
Lothar Philipps
"Time
is nature's way of preventing people from
thinking of everything at the same time."
Anon.
Picturing Factual Inference in Legal Settings
by Peter Tillers*
© 2004, 2005
in GERECHTIGKEITSWISSENSCHAFT: Kolloquium aus Anlass des 70. Geburtstages von
Lothar Philipps
(B. Schünemann, M.-Th. Tinnefeld, R. Wittmann, eds.;
Berlin, 2005)
1. Pictures versus Words. There is an old saying that a picture is worth 10,000 - or 100,000 - words. But this is not true of every picture. There have been efforts in the past to use pictures to portray factual inference and proof in legal settings. These efforts, however, have met with limited success - and one of them was a spectacular flop. This paper takes another look at the role of visualization of problems of evidence and inference. It proceeds on the assumption that the use of pictures - the use of graphs, diagrams, and charts - to facilitate factual inference and proof in legal settings must be informed by the way the mind organizes its knowledge and acquisition of knowledge of the world. The paper argues that factual inference has four important general properties: the complexity and intricacy of marshaled collections of evidence, the diversity of evidence marshaling methods, the influence of time and change on inference, and the role of imagination and invention in factual inference. The paper argues that these four properties support the conclusion that computer-embedded procedures for the visualization of problems of evidence and inference are most likely to be useful and efficient if they support the capacity of actors in (actual or possible) legal proceedings to shift quickly between global, or synthetic, and granular, or analytic, perspectives on evidence and between different methods of marshaling evidence, and to see in the background, or in faint outline, marshaled collections of evidence that are not the focus of an actor's attention while an actor focuses on some other collections of evidence. There is reason to believe that without such flexible multi-layered techniques for looking at problems of evidence and inference, many proposed ways of picturing collections of evidence and arguments about evidence will be unappealing to prospective users and also inefficient.
Legal Rules, Proof, and Evidence
2. Legal Rules as Conditional Imperatives and Conditional Authorizations, and the Importance of Factual Proof. Many legal rules are conditional imperatives or conditional licenses: many legal rules contain conditional legal mandates or conditional authorizations. The conditions found in such conditional rules frequently refer to possible conditions or states of the world or to possible events in the world; they make the authority for a possible legal result contingent upon the existence or non-existence of instances of specified types of states of the world. The existence of conditional legal imperatives and authorizations is a principal reason for the importance of proof of facts and the submission of evidence in legal proceedings: a primary function - and perhaps the principal function - of the submission of evidence in legal proceedings such as trials is to generate an authoritative determination whether or not instances of the types of events or circumstances that are necessary for a legal result (such as criminal punishment or the incorporation of a business) exist.
3. Relationship between Evidence and Factual Proof. There is a consensus in the legal community in the United States - and probably in most or much of today's world - that in legal proceedings such as adjudicative proceedings disputes about factual questions should be resolved by resort to evidence rather than oracles; i.e., it is generally agreed, negatively stated, that there is no known ontology that designates some particular sliver of the cosmos that provides authoritative answers to questions about states of the cosmos.
Uncertain Inference and Language
4. The Uncertainty of Factual Inference and of Factual Proof. The law
of evidence in the
5. Language and Notation for Talking about Uncertain Factual Inference. There are several formally equivalent ways of talking about uncertain factual inference. One type of discourse makes use of the following notation:
H = factual hypothesis
E = evidence
| = given, on the assumption that
Viewed in this way, the submission of evidence in legal proceedings makes it possible for an assessor of evidence - the "trier of fact" - to make a judgment about
H|E
i.e., factual hypothesis H given evidence E.
6. Nomenclature and Notation for the Link between Evidence and Hypothesis:
Denoting and Picturing Inference. We can and do think of the relationship
between a factual hypothesis H and some evidence E as involving a possible step
from E to H. There are several ways to emphasize the existence of such a
possible step, a step from evidence to some factual hypothesis. One way to do
so is with the sort of graph shown in Figure 1.
The connection between H and E can also be depicted in the manner shown in Expression 1.
In either case - whichever way one may choose to portray the link between E and H - in the English-speaking world the step from E to H is conventionally called "inference."
7. Inference, Uncertainty, and Probability Theory. It is almost impossible to talk about factual inference without taking note of probability theory. If one believes that factual proof involves uncertain rather than conclusive, or indubitable, inference, it is natural to think that probability theory may have important lessons for factual proof and for scholarship about factual proof in legal proceedings. Indeed, the following sort of expression in the standard probability may quite rightly be viewed as a restatement of two of the principal concepts that this paper has discussed to this point:
P(H|E) Expression 2
In this expression (as before):
H = factual hypothesis
E = evidence
| = given
The new symbol here is:
P = probability
Expressions of the form P(H|E) are conditional probabilities. From the standpoint of probability theory a judgment about the relationship between E and H is a judgment about a conditional probability. This means that from the standpoint of probability theory an inference from evidence is a judgment about the probability of a hypothesis such as H given some other proposition, event, or evidence such as E. The probability P of the hypothesis, or proposition, H given E expresses the degree of uncertainty of the proposition H given the proposition, premise, event, or evidence E.
Probability theory - particularly its Bayesian offshoot - is a powerful lens for studying uncertain factual inference and factual proof in legal settings and proceedings. This paper, however, does not deal (at least not directly) with the relationship between probability theory and uncertain factual inference and inconclusive factual proof in legal settings; the enterprise in this paper is orthogonal to probability theory.
Picturing Simple and Complex Inference
8. Picturing Simple Inference. In this paper I want to suggest that there are reasons to suspect or believe that graphic and visual representations of factual proof in legal proceedings can be useful to at least some of the participants in that process. But the account of inference presented in this paper to this point perhaps does not demonstrate pressing need for visual or graphic representations of factual inference. Expressions such as Expression 3
seem perfectly intelligible. Indeed, with inference this simple - this primitive - perhaps we can even dispense with symbolic notation. Suppose E represents "accused's escape from prison" and G, "the criminal guilt of the accused." Do we gain anything by saying or writing E --> G ? It seems we can perfectly understand propositions of the following sort even though they are expressed in ordinary language such as the following:
(i) Given the evidence of the accused's escape from
prison, the accused's criminal guilt is possible.
(ii) Given the evidence of the accused's escape from prison, I infer that the
accused is guilty.
Indeed, there is often a risk that the use of symbolic notation will mask ambiguities and uncertainties that readily appear when ordinary language (such as that immediately above) is used.
But it is premature to conclude that visual and graphic representations of problems of factual inference are bound to be useless. One must consider, for example, that inference is often complex rather than simple.
9. Complex Inference. "Simple" inference involves a single (factual) hypothesis such as H and a single (evidential) premise such as E. "Complex" inference, by contrast, involves more than one inference.
A standard legal example of complex inference involves the question of the probability of the criminal guilt G of a defendant given evidence E of the defendant's escape from prison. Are expressions like Expression 3 sufficient to describe the matter or matters that are in issue when evidence such as E is considered? Many legal observers think not. Many observers think Expression 3 must be expanded to display at least the two inferences in Expression 4.
E = escape
B = defendant's belief in his or her
guilt
G = guilt
10. More Complex Inference: Branching Inference. The existence of complex inference - inference containing more than a single inferential step - creates the possibility of branching inference. Nothing in logic dictates that inferences in a network of inferences always have to take the form of a simple chain. Nothing in logic dictates that an evidential premise can support only one possible inference. Branching inferences are possible.
And sometimes branching links (or branching series of inferences) seem necessary. For example, the problem involving an escape E began as a simple chain. See Expression 1. Simple inference always takes the form of a simple chain. But the problem remained in the form of a simple chain when the problem became complex. See Expression 4. But now suppose that (i) the accused, the escapee, is on trial for robbery and it is possible that at the time of his escape (ii) the accused believed he was guilty of robbery and (ii) the accused believed that he was guilty of murder. In this situation it is altogether probable that Expression 4 no longer describes the problem of evidence and inference very well. Furthermore, the graph in Figure 2 is a better representation of the problem - because the graph in Figure 2 has two chains rooted to the single evidential premise E: unlike Expression 4, the graph in Figure 2 makes it clear that the escape E of the accused supports two alternative series of inferences, one leading to an inference of robbery, the other, to an inference of murder.
Br = accused's belief in his guilt of
robbery
Gr = accused's
guilt of robbery
Bm = accused's
belief in his guilt of murder
Gm = accused's
guilt of murder
11. Another Cause of Complexity in Inference: Source Uncertainty. As
well as having the capacity to sprout branches, chains of inferences can grow
longer. And sometimes they must grow longer if they are to represent problems
of evidence and inference accurately. For example, the forked chain of
inferences in Figure 2 must grow longer if the evidential premise of the chain
- the proposition represent by the first symbol E - is uncertain. The expansion shown in Figure 3 is necessary if
the evidential premise E is
uncertain and rests on an inconclusive testimonial report and everything else
in the complex of inferences remains the same.
E* = a testimonial
report of event E
E = event E
Br = accused's
belief in his guilt of robbery
Gr = accused's
guilt of robbery
Bm = accused's
belief in his guilt of murder
Gm = accused's
guilt of murder
12. Another Source of Complexity in Inference: Expansion of Chains of Inference by Decomposition. By the measure I am now using, the complexity of inference is entirely a function of the number of inferences in a network of inferences. But the number of inferences in a problem depends in part on the eye of the beholder. As the eye of the beholder becomes more refined - as the beholder of a problem dissects the problem of evidence more discretely - the number of possible inferences in a complex of inferences can multiply. For example, the beholder may conclude that one of the links in a chain or network of inferences actually contains several links rather than just one.
Consider the chain of inferences that has evolved into the network found in Figure 3. This network can be granularized and thereby be expanded. Suppose the beholder of the report E* believes (as the American law of evidence supposes) that judgments about the credibility of a witness are not primitive, or irreducible, judgments, but are a composite judgment based on more discrete judgments about various attributes of human sources who appear to make reports such as E*. Suppose, in particular, that the beholder of the problem believes that a composite judgment about believability, or credibility, of such a report depends on judgments about the following attributes of the source of such a report:
N, the ability of the witness to
communicate;
V, the willingness of a person to
assert that which he believes to be true;
O, the extent of the objectivity of
a witness and, thus, the person's ability to interpret the sensory signals that
his sense organs convey to him;
M, the ability of a person to
preserve in memory (in mind) his original interpretation of the sensory signals
conveyed by his sense organs; and, finally,
S, the ability of the witness' sense
organs to correctly record the signals that the environment sends to the
witness' sense organs.
If the beholder, or assessor, believes that inferences and judgments about each
one of these personal attributes - "testimonial qualities" - are
necessary to assess the credibility of a testimonial report, this assessor must
- if it wants to use representations of the sort under discussion here and if
it wants such representations to be accurate representations of the problem
that it thinks it has before it - this beholder of the escape evidence problem
must expand the graph in Figure 3 so that the graph has the additional links,
or inferences, found in the network shown in Figure 4.
Ec = whether source
of E* states that
which he means to say
Ev = whether source
asserts that which he believes to be true
Em = whether source
now thinks that which he originally thought about sensory data
Eo = whether
source's interpretation of sensory signals is unbiased
Es = whether
source's sensory organs accurately record sensory inputs
13. Another Form of Complexity in Inference: Ancillary Propositions and
Ancillary Evidence. A collection of inferences of the sort found in Figure
4 becomes yet more complex - and acquires a more complex structure - if
ancillary propositions are added. An ancillary proposition is a proposition
that may support a possible inference in a primary series, chain, web, or network
of inferences. If a series of possible inferences forms a ladder and if each
possible inference is a rung, ancillary propositions are handles adjacent to
each rung, that provide support for a climber's ascent from one rung to the
next.
Ancillary propositions can be associated with any step in an inferential chain. They can also be associated with the particular judgments about the testimonial attributes - such as veracity, sensory sensitivity, etc. - that are pertinent to an overall judgment, or inference, about a witness' credibility. Consider once again the hypothetical problem involving the report E* of escape E. In that situation one might well wish to consider a proposition such as D, "A person with severe macular degeneration usually cannot receive or process sensory visual stimuli that are indicative of the characteristics of a person's face at a distance of 30 meters." If this ancillary proposition is added to our existing picture of possible inferences, the argument based on evidence E* might now look like the diagram in Figure 5.
The complex of inferences shown in Figure 5 becomes more intricate if evidence about possible ancillary propositions such as D is taken into account. For example, the person making a judgment about the witness ability to perceive with eyes might be relying on a textbook about diseases and on his possibly faint recollections of newspaper articles about macular degeneration or on conversations with elderly people who purported to recount their conversations with their eye doctors. An example of a diagram that takes such ancillary evidence into account appears in Figure 6.
It would be tedious - and it is unnecessary - to demonstrate by specific examples that elaboration of ancillary inference networks can generate substantial additional complexity and intricacy in complexes of related inferences. Suffice it to say that ancillary inference networks can increase the complexity of complexes of inference in one or more of the following ways:
(i) each link in a primary chain of inferences can be associated with multiple
ancillary propositions rather than with just one,
(ii) any ancillary proposition can be linked to multiple items of evidence - or
to a large mass of ancillary evidence - rather than to just a single piece of
evidence, and
(iii) links between ancillary propositions and the evidence bearing on those
propositions can be indirect rather than direct: the path between ancillary
evidence and propositions can (and frequently do) have the same sort of
ladder-like and web-like structure that primary inference networks frequently
have.
14. Weighing the Costs and Benefits of Visualizing Complex Inference. Some of the particular inference networks and inference diagrams I have discussed may seem complex - and, of course, there is a genuine sense in which the sorts of inference networks and diagrams that I have been discussing are in fact complex: the kinds of inference networks and diagrams that have been considered here can contain numerous nodes and, hence, numerous propositions. But in another sense the types of complex networks and complex diagrams that have been discussed to this point are relatively simple.
The complexity of the networks and diagrams that have been discussed thus far is attributable almost entirely to the number of nodes - and, hence, of propositions - in those networks and diagrams. An inference network or diagram that is complex for this reason can, of course, consume a great deal of the time and resources of a user or fabricator of such a network or diagram. But complexity attributable primarily to the number of propositions in a complex of inferences is arguably not difficult. This is because where complexity exists solely because of the number of possible inferences in a series of inferences there is a relatively simple and effective strategy for attacking problems having this sort of complexity. The obvious strategy for attacking simple chains of inference with numerous nodes is divide-and-conquer: start at the beginning; consider each possible inference in sequence; make a judgment about each such possible inference; and then move on to the next possible inference in a series of inferences and repeat the procedure. Stated differently, the appropriate strategy consists of this: (i) work up a ladder of inference a rung at a time; and (ii) when you have a new foothold on the ladder, leave behind the part of the ladder you stood on before.
The divide-and-conquer strategy - the one-step-at-time strategy - is relatively straightforward and it is relatively easy to keep the requirements of that procedure in mind. The divide-and-conquer strategy for tackling a series of inferences has the additional advantage of allowing completed steps to be put out of mind; once an inference has been considered and assessed, only the "bottom line" of a completed series of assessments of a series of possible inferences needs to be kept in mind: once some possible inference in a series of possible inferences has been assessed, only the last assessment (of some possible inference in a series of possible inferences) needs to be kept in mind. These features of the divide-and-conquer strategy - the strategy of climbing an inference ladder one rung at a time and leaving already-climbed rungs behind and out of mind - suggest that the advantages of visualizing problems of complex inference may not be as great as might be imagined. Perhaps human beings can wend their way - step by step - through "complex" problems of evidence and inference without the support of crutches such as graphs, charts, and diagrams. And if crutches are needed to work through a long series of inference, perhaps a handwritten list of the series of inferences to be considered is quite enough.
A friendly observer might rush to the defense of proponents of visualization and say:
This is ridiculous. Visual representations of problems of evidence and inference are not a magic bullet: they will not solve all problems, and perhaps we can get along without them. But charts, diagrams, and graphs are bound to be helpful to some degree. There is really nothing to debate. Visualize!
As much as I would like to embrace the advice of such a sympathetic observer, I cannot. My hypothetical observer's defense of visualization assumes that visualization is costless. This assumption is unfounded.
The use of picture-thinking to portray factual inference conducted in the shadow of the law does exact a price - and the price exacted by some techniques of visualizing problems of evidence might be heavy. For example, some proposed methods of visualizing inferential problems make use of an "unnatural" grammar, one that is not already familiar to potential users, and a considerable investment of time would be required to master the grammar of some types of visual representations. Furthermore, it is possible and probable that deployment of some techniques for developing pictures of problems of evidence and inference would demand substantial investments of time and resources even after mastery of the grammar of a particular method of visual representation has been achieved.
Historical experience suggests it is prudent to be wary of claims about the
benefits of visualizing problems of evidence and inference. One effort at
picture-thinking by
Source: John H. Wigmore, PRINCIPLES OF JUDICIAL PROOF (1ST ED., 1917). See also John H. Wigmore, THE SCIENCE OF JUDICIAL PROOF AS GIVEN BY LOGIC, PSYCHOLOGY, AND GENERAL EXPERIENCE AND ILLUSTRATED IN JUDICIAL TRIALS (3d ed. 1937) .
Wigmore forced his students to chart problems of evidence. Wigmore also tried to get lawyers to use his charting methods. But he had no success in that quarter. And after Wigmore's death, no students bothered to use Wigmore's charting method. In short, Wigmore's method of charting evidence and inference sank like a lead balloon.
It is possible that the project of charting evidence and argument about evidence is doomed to failure. It is also possible there is a different explanation for Wigmore's flop: it is possible that his charts were a flop because they were cluttered and badly-designed; it is possible that Wigmore's efforts foundered because his diagrams were poor pictures. Perhaps, then, the real question is not whether pictures, charts, graphs, and diagrams can be useful, but what kinds of pictures or diagrams are likely to be useful.
But if we accept this hypothesis, we face the really hard question: What particular kinds of pictures, diagrams, charts, and graphs are likely to prove useful to participants who are involved in inferential activity conducted in the shadow of possible or actual legal proceedings?
To begin to answer this question, it is necessary to look deeper into the manner in which human beings organize their knowledge of their world.
Picturing "Hard" Complex
Inference
15. Non-Markov Patterns of Inference. Earlier in this paper I largely dismissed the thesis that the existence of complex inference alone warrants the use of visual crutches in forensic factual investigation and proof. But my dismissal of that thesis was inordinately cavalier. cavalier. I dismissed the argument from complexity on the ground that some forms of complex inference are "simple." But even if there is a simple procedure for attacking long chains of possible inference, it is almost surely useful to use some sort of a chart or tabular checklist to keep track of progress in addressing a long series of inferences. But it is unnecessary to revisit the question of the importance of visualization in such "simple complex" contexts. The reason is that in the real world the inferences to be assessed almost never take the form of a linear series. Consider the diagram found in Figure 8.
The diagram in Figure 8 illustrates the simple fact that a link in a lower part of an inferential ladder can have a tendril - that a rung, or node, in linked series of inferences can be attached to an arc that extends, not only to the next rung in a ladder of inferences, but to some rung further up. Figure 8 depicts a situation in which if the person assessing the evidence believes that the inclination of a witness to try to tell the truth may be influenced by - may be affected by - some proposition further up the chain of inferences. For example, Walter is asked whether or not his son Albert escaped from prison. Walter may be less inclined to make a truthful report E* of Albert's escape E than of another person's escape if Walter believes that a finding of Albert's escape E would perceptibly increase the chance that his son Albert would be convicted of murder. The lateral generation-skipping arc expresses the proposition that the veracity of Walter may be affected by the ultimate factual issue in the case.
In the type of situation pictured in Figure 8 - a situation in which there is a possibility that direct links may exist between lower and upper parts of inference chains or ladders - a person assessing the escape evidence E* must not chop off the bottom of an inferential ladders before he or she has assessed possible connections between the lower and the upper parts of the ladders of inference that he is trying to construct and climb. In this situation the sort of divide-and-conquer strategy that I described is not available; the appropriate procedure here is not tackle each inference in a series of inferences in the order in which inferences appear in a chain or ladder. The existence of lateral generation-skipping links amounts to an assertion that some rungs in inference ladders must be considered "out of order."
Situations of the sort pictured by Figure 8 are common rather than rare. For example, a variety of testimonial attributes - the memory, the veracity, and sensory sensitivity, etc., of witnesses - may be affected by the kind of event or state whose existence or non-existence is reported; people are better able to perceive, remember, etc., certain types of events than other kinds of events.
Graph theory teaches that the complexity of a network and the difficulty of performing the tasks depicted by a network are not solely a function of the number of nodes in a network. The complexity of an inference network and the difficulty of the task it describes are also a function of the pattern of links between the nodes in a network. The existence of the sort of "lateral" links of the sort found in Figure 8 greatly increases the complexity of inference networks.
Graphs like those in Figure 8 are non-Markov networks. Markov networks limit the types of dependencies that can occur between conditional probabilities in inference networks and thus limit the computational demands that probabilistic inference networks can create. The concern of this paper is not with the computational demands that are generated by non-Markov patterns in inference networks; my concern now is not to try to devise procedures that minimize the difficulty of computing dependent conditional probabilities. But the fact that non-Markov networks greatly increase the difficulty of computing conditional probabilities in inference networks is suggestive: it supports the suspicion that the sort of pattern of possible inferences found in Figure 8 greatly increases both the complexity and magnitude of the task of assessing possible inferences and that, therefore, visualizations of at least some kinds of problems of evidence and inference may substantially help people who must tackle such complex and difficult inferential work.
But while the complexity and the difficulty of patterns of inference such as those depicted in Figure 8 may alone justify the suspicion that some methods of visualizing problems of evidence and inference in legal settings are likely to be useful, I prefer not to make the argument for the benefits of visualization depend entirely on the indubitable existence of the sort "complex complex inference" found in Figure 8. There are more powerful arguments for the proposition that visual representations of problems of evidence and inference are likely to be beneficial. Furthermore, those additional considerations suggest how problems such as those in Figure 8 can be usefully visualized.
Picturing
Diverse Dynamic Cyclical Inferential Activity
16. General Principles. For present purposes three properties of the process of human assessment are particularly important:
(i) Human inferential activity is dynamic; it occurs in and over time.
(ii) Human inferential activity is cyclical; time's wiles and human imagination
frequently require that previously-traversed inferential terrain be revisited.
(iii) Human inference involves diverse evidence marshaling strategies, and no
known algorithm or rule specifies how such distinct evidence marshaling
strategies interact.
These properties of human inference suggest that the benefits of visual representations are substantial and, perhaps more important, they suggest that certain specific types of visualization are likely to be particularly beneficial.
17. Multiplicity of Methods of Marshaling Evidence: "MarshalPlan." Effective investigation - and, also, I believe, effective assessment of factual hypotheses in general - involves an ensemble of methods of organizing or marshaling evidence. Figure 9 is a representation of some important marshaling methods. (This ensemble of evidence marshaling strategies has acquired the moniker MarshalPlan.)
18. Illustration of the Interactions between Distinct Evidence Marshaling Strategies: Time Lines and Scenarios. Space does not allow discussion of the details of all of the various methods of organizing and storing evidence represented by the icons in Figure 9. I will discuss just a few of those evidence marshaling methods and I will begin with a brief discussion of time lines and scenarios and the relationships between them. Later I will talk about the marshaling method that I call "case theory."
19. Definitions of Time Lines and Scenarios. A time line is a
possible chronological order of a series of possible events. Possible events
are those suggested by evidence. A scenario, by contrast, is a hypothesis about
the possible connections or influences between possible events over time; a
scenario is a hypothesis about the influence of prior events on subsequent
events. Furthermore, while a scenario may include events that have some
evidential support, scenarios can also contain possible events for which there
is no support except human imagination and the other events in the scenario: in
scenarios purely conjectural events are permitted.
20. Relationship between the Number of Evidentiary Details and the Number of Time Lines. Small quantities of evidence can generate a large quantity of distinct possible chronological sequences of possible events. Take a simple example. Suppose that there are reports of just the following four events:
XX states, "There was never a man as detestable as YY."
XX strikes YY's head.
YY strikes XX's head.
YY's skull cracks.
How many factual hypotheses or possibilities might the reports of these four
events suggest or support?
Assume that the reports of these four events are perfectly credible and
believable. Thus, our reflections about these four reported events concern only
their chronological order.
Even if we make this simplifying assumption, it is fairly obvious that the reports
of the four events can support or suggest a variety of factual hypotheses or
possibilities.
For example, the reports of the four events suggest following the possible sequence of possible events (Sequence #1):
YY strikes XX in the head.
XX strikes YY's head.
YY's skull cracks.
XX states, "There was never a man as detestable as YY."
The following possible sequence of possible events - Sequence #2 - is also
supported by the reports of four events described above:
XX states, "There was never a man as detestable as YY."
XX strikes YY's head.
YY strikes XX's head.
YY's skull cracks.
Sequence #3 is also supported or suggested by the previously-described reports
of four events:
YY strikes XX in the head.
YY's skull cracks.
XX strikes YY's head.
XX states, "There was never a man as detestable as YY."
It is unnecessary to catalogue every possible sequence of the four reported
events. It is enough to observe that Sequence #1, Sequence #2, and Sequence #3
are not identical factual hypotheses; they are different.
The point made here can be generalized: where n = the number of events, the number of possible temporal sequences of those events is n! This means that if there are just five (5) reported events, the number of possible event sequences is 120. If there are just ten (10) reported events, the number of possible event chronologies is 3,628,800.
§
The number of possible time lines increases dramatically if events have
duration and can overlap. The number of possible time lines again increases
dramatically if differences in the amount of time between events are thought to
produce distinct time lines.
21. Interactions between Scenarios and Times Lines. Although scenarios and time lines differ (in the ways mentioned), time lines nevertheless are related to scenarios. For example, while time lines are not themselves scenarios, they have the ability to suggest scenarios: events in time lines are the rungs on which scenarios - causal hypotheses that include purely conjectural events - are often hung.
The following symbols can be used to construct event chronologies, or time lines:
This notation can be used to construct time lines such as the one shown in Figure 10.
The notation shown below can be used to construct scenarios:
The time line in Figure 10 can provoke or suggest the formation of the scenario in Figure 11.
Causal hypotheses can be draped over events in time lines because even though events in time lines are only "possible" events, in time lines possible events have some evidential support. This is important for scenario analysis in legal settings because when actors have the possibility of legal proceedings in mind, actors want to construct scenarios that have a palpable, or perceptible, chance of being true. Evidential support provides some reason to think that more than wholly-unanchored imagination suggests that some particular scenario may be true.
21. Contraction and Expansion of Factual Possibilities by Scenarios. Scenarios can reduce the number of possible event sequences in play. There are at least two ways in which this can happen. First, some sequences of possible events do not occur in scenarios because although a prior event in one temporal sequence may be reasonably believed to influence some subsequent event, a causal nexus between two such events does not necessarily exist if the temporal order of the two events is reversed. For example, it is reasonable to think that the falling of a rock from the sky helps to create a hole in the ground but it may be implausible to think that the emergence of a hole in the ground causes a rock to fall from the sky. Second, some possible events in time lines become uninteresting possibilities in scenarios because some events in time lines lack significant evidential support and are also not strongly suggested by events in a plausible scenario.
But scenarios also have a feature that allows expansion of factual possibilities, a type of expansion that cannot occur with time lines. In scenarios, purely conjectural events - events without direct evidential support - are permissible. If imagination is allowed free reign, a vast number of scenarios and conjectured events can be built around benchmark events, around the black circles denoting events that have evidential support. For example, Figure 12 shows a second scenario draped over the time line scaffold in Figure 10.
Many other scenarios are possible.
22. General Lessons of the Examples of the Interaction between Time Lines and Scenarios. The sort of interaction I have illustrated between scenarios and time lines occurs, in a general way, among other forms of evidence marshaling. These interactions have three important features.
First, each of the evidence marshaling methods involved in such interactions has the ability to generate - and with just a little effort and detail, each strategy ordinarily does generate - structures of great density and intricacy.
Second, the interactions among the structures generated by the various evidence marshaling strategies are not regulated by any discernible rule or algorithm.
Third, the interactions among the various evidence marshaling methods are cyclical rather than acyclical.
§ For example, a time line may suggest a scenario, which may suggest the possibility of some new evidence, which is then acquired, which results a new set of time lines, which may in turn suggest new scenarios … and round and round we go.
23. Obstacles to Explicit Visualization of Problems of Evidence and Inference. The complex of features enumerated in ¶ 22 generates a variety of obstacles to any attempt to make the process of fact investigation and assessment explicit, to make the process of factual inference one that is discernible by conscious thought. One obstacle is the problem of the coordination or harmonization of the multiple evidence marshaling strategies that human beings either do use or should use to make well-supported guesses about factual questions in legal proceedings. Although no rule that I have been able to discern describes the manner in which the various marshaling strategies are related, these evidence marshaling strategies nevertheless influence each other. For example, perceived inconsistencies among the various structures or complexes generated by the multiple evidence marshaling methods shown in Figure 9 can bring the whole house tumbling down: they can lead us to the conclusion either that the available evidence and information does not offer substantial support for some factual hypothesis or that a person armed with the conclusions and judgments generated by the various marshaling strategies is not yet in a position to make a sound judgment about some problem of evidence and inference.
24. A General Picture of Harmonization of the Results of Diverse Evidence Marshaling Strategies. The diagram in Figure 13 illustrates the kind of coordination or harmonization that an investigator, trial lawyer, or trier of fact would want to achieve - and perhaps must achieve? - to satisfactorily resolve a problem of evidence and inference in a legal setting.
Figure 13 represents the sort of position that actors such as trial lawyers might aspire to reach when they participate in the process of factual proof in legal settings.
Note that Figure 13 is a picture.
Is such a picture - or any similar picture or diagram - of any use in guiding actors such as lawyers to their objective? This is the central question addressed by this paper.
24. The Potential Benefits of General Pictures of Problems of Evidence and Inference. There are several reasons to think that these sorts of general pictures could be helpful to participants in forensic investigation and proof.
First, it useful to have a map that amounts to a reasonable conjecture about the path that one should or might take in the attempt to investigate or to prove a case in some legal forum. One needs some plan of attack - if one is not to engage in proof-related activity aimlessly. The mere fact that one may have to modify or even abandon a tentative plan of attack does not demonstrate otherwise. It is necessary to make some bets about which possible proof-related activities are likely to pan out.
Second, the sort of picture found in Figure 13 is useful because it provides a coherent and meaningful way of putting parts of a case or problem together. Studies by psychologists and others show or strongly suggest that people's ability to remember and retrieve information is generally greatly enhanced if they organize information in a way that is meaningful to them, according to some pattern that they can discern and keep in mind.
Third, the diagram in Figure 13 is useful even though it leaves out an enormous amount of detail. The diagram is useful precisely because it leaves out an enormous amount of detail.
The ability of human beings to make sense of things depends on simplification. Detail, when excessive, is clutter. Clutter impedes thought. The excision of unnecessary detail facilitates a global perspective, a synthetic perspective, the ability to see the relationships between major parts of a large problem. This sort of synthetic, or global, perspective is essential for the effective functioning of any complex activity that involves the simultaneous operation of multiple processes. Trying to resolve a complex problem of evidence and inference is a bit like pulling a cart with a donkey and a horse; you have to know how a donkey works and you have to know how a horse works but you also have to know how a donkey and a horse work together. And woe be to you if you try to use a hyena and a leopard together!
25. A Key Requirement for the Use of General Maps and Pictures in Inference: Pictures Must Allow Users to See the General Picture while Keeping Important Details in Mind. Synthetic thinking is essential but it is not the only important form of thinking for assessment of evidence. Fine-grained inspection of evidence, problems of evidence, and argument about evidence is equally important; it is essential. The unquestioned importance of detail presents a couple of puzzles. First, human beings are incapable of keeping everything they know or believe fully in mind at the same time. How do they manage to manage inference? Second, if both global and granular perspectives are important but if human beings lack the capacity to keep everything in mind at the same time, is it possible to construct pictures that enable human beings to see the general picture and itty-bitty parts simultaneously?
This paper does not address the first puzzle. The discussion in this paper instead proceeds on the premise that human beings do somehow manage to make use of massive amounts of detail that they cannot possibly keep fully in mind at any given time. The insight that human beings manage to do this is important - because this insight amounts to the important plausible hypothesis that the brains of human beings are able to draw on thoughts and beliefs that the minds of human beings do not have fully in mind. So, for example, perhaps one of the reasons why human beings can have a sense or feel for the relationships between wholes and parts is that human brains have a capacity to draw on thoughts that once were explicit - that once were close to the center of the mind's eye - but that are now tacit, that now lie at the periphery of the mind's eye and explicit thought.
The argument of this paper proceeds on the (substantiated!) premise that the brain or mind makes use of thoughts, judgments, beliefs, memories, inferences, suppositions, etc., without having all such matters fully in mind. Despite the difficulty of doing so, human beings somehow manage to manage large and small parts of problems simultaneously. It is a fair guess that the ability of human beings to perform this difficult task is partly attributable to the ability of human beings to think about things even when they do not explicitly or directly attend to some of the thoughts that they think about such things.
This premise - the italicized hypothesis immediately above - is the basic foundation for my theses about the likely benefits of certain sorts of visual representations of problems of evidence and inference. My argument in general is that there is a need for visual crutches that improve the ability of human beings to make use of the pertinent thoughts that human beings have in the backs of their heads.
26. Two Different Kinds of "Tacit" Cognitive Processes. There are some mental process that (now) cannot be controlled (except at the fringes) by conscious attention. Visual perception is an example. Although we can generally control where we move our eyes, we cannot direct the brain to change the way it processes visual sensory stimuli. But some tacit mental processes are not so deeply submerged.
Some mental processes are "tacit" only in the sense that human beings are not attending to them, are not devoting primary attention to them. Some of the examples of marshaling operations that have been discussed in this paper are examples of thinking that is only comparatively tacit, thinking and thoughts that are not wholly below, or inaccessible to, explicit thought. For example, some of the things that human beings keep in the backs of their heads are thoughts that once were explicit, that once commanded comparatively direct attention became relatively tacit only because the primary attention of the actor shifted to other matters.
Human beings cannot devote direct, or intense, attention to everything at the same time; when human beings direct attention to certain matters, they reduce the attention they devote to other matters. But when attention is focused on some matters, many thoughts about other matters to which the mind is relatively inattentive remain important and many such thoughts continue to work and churn - in the back of the mind. A key thesis of this paper is that people have thoughts that are half-in-mind; and such half-in-mind thoughts, such thoughts in the back of the head, are important in human reasoning about factual hypotheses.
27. Implementing and Testing the Hypothesis of the Importance of Thoughts at the Periphery of Human Attention. I hope to test the hypothesis of the importance of half-submerged thought by developing software that will help people to make use of their half-in-mind thoughts, their semi-tacit and semi-explicit thoughts. I hope to create software that will help people keep in mind and call upon and make better use of or improve the operation or workings of the thoughts they have half-in-mind. Specifically, I hope to develop software that will do things such as the following: (i) represent clearly the general outlines of a problem of evidence and inference while representing more faintly and less prominently but still visibly the details of that general structure; (ii) allow users of the software to shift quickly from one way of organizing evidence while portraying more faintly (on the monitor) the method that immediately before that commanded the user's attention; and (iii) allow the user to shift to some part of the some part of one evidence marshaling structure while making the surrounding structure less prominent but still discernible and, perhaps, also the outlines of other evidence marshaling structures. (I will collaborate with a software developer and designer. I expect that we will make use of devices such as contrast and color and representations of multiple dimensions.)
28. The Importance of Subjective Judgment in the Development of Detailed Pictures. The argument presented in this paper suggests that in some or many episodes of human reasoning the strategy of dividing and conquering problems of evidence and inference - the tactic of working up an inferential ladder one rung at a time, for example - is, for a variety of reasons, hard to do to do; it is hard because, e.g., good human thinking about factual issues is cyclical and good human thinking makes use of a multiplicity of evidence marshaling methods whose interactions are not governed by any ascertainable rule or algorithm; that is to say, if the general account presented here of the way that human beings use various marshaling and analytical strategies is correct, it is frequently difficult to break up a large problem into pieces, assess one piece of the problem, leave that analyzed problem or issue behind, move on to the next piece of puzzle, and repeat this procedure until the entire work of assessment is done. (One difficulty with this seemingly sensible strategy is that it is often necessary to loop back and revisit previously-analyzed pieces of a large inferential puzzle - and the complexes whose interactions must be revisited can interact with each other in a huge variety of ways. Another difficulty is the existence of generation-skipping links in inference networks.)
Such discussions of the intricate character of problems of evidence and the intricate character of reasoning and thinking about problems of evidence do not demonstrate - and they are not designed to demonstrate - that human beings are generally incapable of reasoning about factual issues in legal settings. But what has been said here about the complexity and spontaneity of many mental operations does suggest that people who are engaged in such inferential activity can lose track of their own thoughts.
Unfortunately, the same considerations suggest that it would be extraordinarily difficult and time-consuming to develop pictures that capture the full dimensions and all aspects of the tasks that the mind must undertake when it engages in inferential activity. This obvious conclusion suggests one another obvious - but important - conclusion: charts of human thought about evidence can be valuable but it must be kept in mind that such charts are usually crutches and that whether such crutches are used and the manner in which they are used depend on their usefulness in and for the mind of the user of such visual representations and pictures. So any system for supporting the inferential activities and processes of human actors must take into account that detailed pictures of evidence and reasoning about evidence should be constructed only to the extent that the development of detailed pictures is useful in and for the mind of a real-world human beholder of a complex and difficult problem of evidence and inference.
29. Relationship between Subjective Judgment and Scientific Rigor. The software I envision would have Gestalt-like properties and tendencies. But there is nothing anti-scientific about the sort of software I would like to see developed. It is entirely possible and probable that analysis of some sectors of a problem of factual proof can be automated. Furthermore, for example, there is every reason to believe that parts of some problems raise questions that can be attacked with the methods of hard sciences such as genetics, physics, and so on. (My prospective collaborator is developing data mining methods that can perhaps point to likely instances of financial fraud.)
Conclusion
Long before this paper was a gleam my mind's eye, there were ample grounds for believing that some kinds of pictures and visual representations can improve the quality of factual inference in legal settings. In their ordinary lives human beings occasionally resort to charts, diagrams, graphs, ideographs, and other visual representations when they attempt to puzzle out the answers to various kinds of factual problems - for example, when they consider a question such as "What's the quickest way to East Harlem?" or a complex of related questions such as "Should I abandon teaching and develop software? Am I too old? What would my wife say? How would I pay my bills? What if I get sick?" There is no good reason to think that the usefulness of all visual representations vanishes when the possibility or reality of legal proceedings casts a shadow over human judgment and action.
The more interesting and important question is which sorts of maps, charts, pictures, and graphs can be expected to improve the quality of human inference.
This interesting and important question admits of no universal answer. Human inference - whether in legal settings or not - involves an enormous variety of cognitive operations - such as the methods of thinking found in, for example, astrophysics, weather forecasting, psychiatry, and etiquette, and when people draw on different domains of knowledge, they often find it useful, and sometimes practically essential, to use various visual representations that seem peculiarly useful - or perhaps even necessary - for reasoning within certain domains of human knowledge (e.g., spectral analysis) or for reasoning about particular kinds of natural phenomena (e.g., the rotation of Jupiter).
The argument of this paper presupposes that despite the existence and undeniable importance of specialized techniques for addressing and resolving certain kinds of questions, it is useful to talk about the general structure of human thinking about factual questions and problems. The argument in this paper assumes that a cognitive metastructure envelops specialized inferential techniques and that it is both useful and important to try to fine-tune the workings of that metastructure. Only time and experiment will tell whether the hypothesis of such a general metastructure is fact or fiction. It is, after all, possible that human decisions about when and how to use specialized inferential techniques are matters determined only by irreducible and un-analyzable personal judgment and human intuition.