INFERENCE PATH

Ask almost any litigator to define an ”enthymeme” and you will get back a blank stare. But while they likely don’t know that term, successful litigators are experts at filling in the blanks of arguments with implicit premises (i.e., enthymemes). One of our fundamental jobs is to x-ray our opposing counsel’s argument to reveal implicit premises in search of the argument’s weaknesses.

To be successful at this uncovering process, a theory of enthymemes would be helpful. For example, Dr. Douglas Walton presents an intriguing academic theory on enthymemes. http://io.uwinnipeg.ca/~walton/papers%20in%20pdf/07ThreeBases.pdf. For practical purposes in litigation, however, it is less efficient.

The main cause of this inefficiency in litigation is its lack of a single precise design template for any argument that can act as scaffolding for its complete construction. Dr. Walton’s theory, based on CBVK, depends on the litigator knowing many templates to try to find a fit rather than just one. This burdensome complexity is the “36 tricks of the fox compared to the one trick of the hedgehog” issue. Using (defeasible) essential predication transitivity as the sole argument design avoids this burden. (See this post for the possible defeasible nature of essential predication transitivity.) And in the rapid dialogic context of oral argument in court, the litigator needs the most efficient approach.

Since in litigation the conclusion is typically explicit, the first step using the essential predication transitivity (defeasible) design is to separate the subject and predicate of the conclusion into two premises such that the subject of the conclusion is the subject of one premise and the predicate of the conclusion is the predicate of another premise. This step binds the argument at both ends which is not possible using a tree-like approach. Once the ends of the argument are defined, the intervening linking inferential premises are found relying upon the explicit premises and the transitivity pattern. If any inferential leap is found too big, the granularity can be increased. Finally, any necessary underlying assumption premises are determined by simply asking what premises must be acceptable to support a specific inferential premise.

The following argument maps illustrate this essential predication transitivity (defeasible) approach (along with Dr. Walton’s maps) using the arguments drawn from his excellent paper.

There are many ways to describe the single concept of probative weight, probative force, or probative strength. This concept is typically described with these types of physical metaphors. But which metaphor is the most isomorphic? This is an important question since it should determine which one we use in court.

Dr. Douglas Walton provides one perspective:

This analysis depends on what is meant by the expression ‘proving something’, in a sense that requires something more than just a valid (or structurally correct) argument. Such a notion of proving can be expressed in more precise terms by introducing the notion of probative weight. Probative weight is a concept of argument evaluation. The basic idea is that if premises have probative weight, and the argument from these premises to a conclusion is structurally correct, then the premises can throw probative weight onto the conclusion. An argument can be structurally correct if it is deductively valid, inductively strong, or if it fits the structure of a presumptive argumentation scheme. In such a case, the probative weight of the conclusion is increased as a function of two factors of the argument: (1) the probative weight of the premises, and (2) the probative weight (structural strength) of the argument from the premises to the conclusion. This type of case represents an increase in probative weight of a conclusion due to an argument supporting that conclusion…A probatively relevant argument can increase or decrease the probative weight of its conclusion…In a convergent argument, the conclusion needs to be revised upward to the value of the most plausible premise. In a linked argument, the probative weight of the conclusion needs to be revised upward to that of the least plausible premise. http://io.uwinnipeg.ca/~walton/papers%20in%20pdf/04fall_rel.pdf.

I have found this basic idea of an argument that has structural strength which goes from the premises to the conclusion effective in litigation. I respectfully suggest, however, that Dr. Walton’s use  of the term “probative weight” lacks sufficient precision as it is applied to the weight (i.e., heaviness) of the premises, to the structural strength of the argument, and to the substance that is transfered to the conclusion. I propose an alternative metaphoric concept that has more rigor and, I have found, is more effective in litigation to describe the nature of probative weight.

The probative “strength” of an inference bridge (optimally formed by essential predication transitivity) determines the amount (e.g., load) of certainty or acceptability, subjectively assessed by each juror, that each juror believes can reach the conclusion. The probative strength of an inference bridge is determined from the probative strength of each of the individual premises (both inference premises and the supporting assumption premises) which are part of a bridge. A structurally “correct” design of the inference bridge does not add to the strength of the premises. But a poor design can negate their strength. 

As is evident from the metaphor, the strength of any single inference bridge is only as strong as its weakest link (i.e., inference or assumption premise). Further, it becomes clear that multiple bridges that converge on the same conclusion can increase the amount of certainty that can reach it. And depending on their nature (e.g., undercutters, rebuttals) objections can be viewed as stresses that weaken an individual premise or as intervening or alternative bridges with their own strength that lead to different conclusions.

“the difficulties in determining questions of fact are greater and more common than those that occur in determining questions of law”

Reading the above sentence one might think it was written in the 1970’s or later when the New Evidence Scholarship started emerging. Actually, the quotation (referring to a statement by Justice Miller) is from A Treatise on Facts or the Weight and Value of Evidence by Charles C. Moore published in 1908! This textbook (described by William L. Twining in Rethinking Evidence: Exploratory Essays (1994)) is an incredible compilation of courts’ generalizations of facts and discussions on inference. (Its use was promoted in Handbook for Naval Officers: An Aid for Examinations for Promotion by Frederick Vallette McNair (1920).)

To illustrate the nature of the treatise, using an example from the “Improbable Testimony Contradicted by Circumstances” section, the following argument map depicts the court’s objection to the defendant’s  reasoning. Com v. Van Horn, 188 Pa. St. 143, 41 Atl. Rep. 469.

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As a part-time adjunct professor, I am fascinated by argument schemes. Ever since I was introduced to them by the incredible work of Professor Douglas Walton, I have sought to better understand them. To me that understanding is an essential path to more fully appreciating practical reasoning from a pedagogical perspective.

But as a full-time litigator and appellate attorney, I searched for a way to make them more relevant in my practice. (My livelihood depends on whether I can actually persuade the judge using argument patterns.) Of course, the application to litigation of “critical questions” is obvious. An explicit list of the assumptions that accompany certain patterns of reasoning is very useful. For example, knowing the inherent assumptions that accompany testimony (e.g., lack of bias, observational ability) makes the targets of cross-examination readily apparent. But the direct application of the patterns themselves had been less obvious to me.

My concern had been that typically argument schemes are presented in their enthymematic (i.e. missing premise) structure. Asking judges to fill in the blanks is a risky business (e.g., judges or juries have never learned the abstract patterns to begin with and inferential leaps by their very nature are risky.)

For example, consider the following argument scheme “Appeal to Expert Opinion”  (Walton, p. 3):

• E is an expert in domain S.
• E asserts that C is known to be true.
• C is within S.
• Therefore, C may be plausibly taken to be true.

There are two difficulties with this enthymematic form of an argument scheme for use in an argument map for a judge or juror. First, there is an obvious missing premise. The inference bridge cannot, no matter how the pieces are linked, reach the conclusion. The judge or juror must make a leap. The second difficulty is that the linkages of the premises are not (except for a student of logic) obvious.

One option, suggested by Walton and Reed, is to use an apparent modus ponens form that reflects “a more  explicit account of the structure of the inference that makes the warrant that the argument is based on more visible.”

• E is an expert in domain S.
• E asserts that C is known to be true.
• C is within S.
• If E is an expert in subject domain S and asserts that C is known to be true, then C may plausibly be taken to be true.
• Therefore, C may be plausibly taken to be true.

The use of this more explicit form solves the first obstacle since the missing premise is made apparent. As Walton and Reed point out, however, Version 2 leads to a controversy: How can a defeasible argument structure use a deductively valid argument form (e.g., modus ponens)? They provide an elegant solution. They suggest that there is a strict modus ponens and a defeasible modus ponens. The distinction depends on whether the conditional is strict or defeasible.

But the second obstacle (i.e., abstract linkage) still exists. While a modus ponens form is obvious to the readers of this blog, it is not obvious to judges and typical jurors who do not read it. Research has shown, however, that transitivity is easily perceived. So a more complete solution might be to use essential Predication TRANSITIVITY to structure any argument scheme.

And the possible controvery of using an argument form of logical necesssity for a defeasible argument can be avoided as suggested for modus ponens by Walton and Reed. Generalizations used in the essential Predication TRANSITIVITY path can be either strict or defeasible. The use of qualifiers can make this apparent.  So the result is, I suggest, that there are two kinds of inference paths of essential Predication TRANSITIVITY, namely, strict and defeasible. (This form may also be helpful in developing justifications of argument schemes.)

For purposes of litigation, the argument map also needs to make a visual distinction between inferentially linked premises and assumptions while still maintaining both of them within the inferential network of the argument scheme. The practice of adding assumptions as attached notes of “critical questions” or intermingled with linked premises just creates, in my experience, confusion and obscures the details of the interconnecting web of the argument. see http://wiki.austhink.com/Brief+explanation+of+Argumentation+Schemes.

In searching to explain the abstract concept of the uncertainty existing in an inference-upon-inference chained reasoning structure (e.g., multistage or multilevel), metaphors are sometimes used. Perhaps the most famous is the pigeon soup metaphor used by President Lincoln in the political debate with Hon. Stephen A. Douglas in the 1858 Senatorial campaign in Illinois. Lincoln questioned whether Douglas’ Popular Sovereignty concept, “when it is brought down for close reasoning,” had not been made “as thin as the homeopathic soup that had been made by boiling the shadow of a pigeon that had starved to death.” http://quod.lib.umich.edu/cgi/t/text/text-idx?=moa;idno=ABN2972.0001.001. (Page 212).

However, while it has been claimed that Lincoln was referring to the uncertainty that can result from an inference-upon-inference chain of reasoning structure (e.g., Passantino v. Board of Education, 52 A.D. 2d 935, 383 N.Y.S. 2d 639 (1976)), such is not the case. A review of the debate reveals that Lincoln actually was arguing that changing the Popular Sovereignty concept from its original meaning that the people of a territory had the right to choose between a slave state or a free state to the revised version (to accommodate the Dred Scott decision) that the people of a territory could prevent slavery by refusing to enact legislation that allowed slavery (e.g. “do-nothing sovereignty”), so watered down the original concept that it was now ”as thin as the homeopathic soup that had been made by boiling the shadow of a pigeon that had starved to death.” Lincoln went on to argue that the Dred Scott decision so completely covered the ground on the issue of slavery in the territories that there was “no room for the shadow of of a starved pigeon [i.e., the watered-down Popular Sovereignty concept] to occupy the same ground.” Ironically, Lincoln actually uses an inference-upon-inference reasoning structure to arrive at his own conclusion.

So, if pigeon soup is off the menu, what metaphor might be more appropriate? I believe that Professor Tillers points us to a better alternative. “The rule that one inference cannot be based on another inference and that one presumption cannot be based on another presumption is based on a recognition that when human beings are called upon to draw conclusions from proved facts they may err or speculate, or do both. And the chance of error or speculation increases in proportion to the width of the gap between underlying fact and ultimate conclusion where the gap is bridged by a succession of inferences, each based upon the preceding one.” United States v. Shahane, 517 F.2d 1173, 1178 (8th Cir. 1975). Professor John Woods also uses this gap metaphor. “A theory of evidence is meant to close the gap between what the juror knows and what he desires to know.” http://www.johnwoods.ca/The_Criminal_Abduction_Paradox.pdf

The 10th Circuit builds upon this bridging the gap metaphor by placing the jury in the picture. ”Like many courts that have addressed the issue, we do not foreclose the possibility that a reasonable inference built on yet another reasonable inference may in some cases sustain a conviction. However, we believe the “inference upon inference” rule serves as an appropriate signpost, cautioning reviewing courts to measure the “gap” between fact and conclusion before acquiescing in the jury’s leap.”

Interestingly, the jury leap in Shahane can be depicted in a pretty straightforward manner as shown in the following argument map. When depicted in this manner, it is not a leap at all, but rather, a series of steps across the bridge.

 An exploration of this argument map helps confirm Professor Tillers’ position that the 10th Circuit was mistaken in imagining that the “strength of an inference based on a series of inferences” is so dependent on the number of inferences. Rather, as Professsor Tillers argues, the strength must be assessed based on the entire chain.

And, as Professor Walton explains, this strength (or “probative weight of the conclusion”) depends on two factors. “One is how probable the premises are. The other is how strong the link is between the premises and the conclusion.” Legal Argumentation and Evidence, p. 116. 

Using a visual language based on “essential Predication Transitivity” (ePT)  as illustrated, the total uncertainty is gathered into the first factor since the links of ePT have no uncertainty. This makes it easier to examine the nature of the probative weight of inference-upon-inference.

The following argument map helps reveal two important principles. First, that while increased granularity can increase the number of intervening premises (and thus the gap), the total uncertainty does not change since the original fact does not change. Second, it helps illustrate that the number of inferences is in the eye of the individual juror. Different people can cover the distance in a different number of steps.

Finally, while increasing the granularity theoretically does not increase the uncertainty, from a practical persuasive perspective in litigation, the absence of redundant premises as often occurs with a pyramid structure of reasoning will be more effective in increasing the perception of certainty as illustrated in the following post. http://inferencepath.edublogs.org/2007/08/12/richard-whately-1836-constructed-mountain-argument-maps/.

So, rather than pigeon soup, I propose that the uncertainty in crossing the inference stepping stone bridge (consisting of a string of transitively linked premises, each with degrees of instability to reach the conclusion on the other side) more isomorphically represents the uncertainty of an inference-upon-inference reasoning structure.

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