INFERENCE PATH

A previous post in this blog discusses the risk in leaving some premises implicit in an argument map. This post uses another example drawn from Austhink Consulting’s recent report to help illustrate this risk. (I use this report because it is one of the finest examples of the power of argument mapping.)

The argument maps in the report were created with Rationale™ software using the typical argument mapping visual language (i.e., pyramid). The graphical conventions of pyramid permit implicit inferential premises. This lack of strict scaffolding permits an argument pyramid to be inadvertently designed with a faulty structure.

In contrast, an argument map created with Rationale™ using path does not permit an argument with a faulty structure. The reason is that path relies upon an interlocking premise structure that cannot be built with implicit inferential premises. This structure uses an inference method called “argument essential predication transitivity” ( ADEPT™ ). In litigation using a reasoning process that reduces risk of error is a sound decision.

A portion of Austhink Consulting’s argument mapping is shown below.  p. 45.                                    
                                         

An application of the no danglers rule indicates that the terms “combat weight” and “sound decision” are danglers. This is a clue that there might be a problem. Trying to fit the premises into a path structure illuminates the problem.

The first step is to shift to a left-to-right orientation and place first in order the premise whose subject is the same as the subject of the main conclusion.

The next step is to insert the predicate of the main conclusion as the predicate of the second inferential premise and to make space for the interlocking subject of that second inferential premise.

The next step is to insert the subject of the second inferential premise as an appropriate transitive match for the predicate of the first inferential premise.

This process reveals that, as structured in the Austhink Consulting report, premise 1A-a, as shown in the first map above, does not link or connect the other premise to the main conclusion. The two premises do not work together. This is a flaw in the reasoning structure as depicted in the argument map in the report.

This flaw in visual representation comes at a critical point in the argument. The reason is that the “pivotal claim” intended to be represented is “that maintaining the tank capability was necessary if our Army was to have the ‘combat weight’ to achieve its mission without undue risk.” p. 44. The following path map illustrates one possible correct version of the inferential relationships as indicated by the narrative. The path map below could be translated back into a pyramid map by adding redundant premises.

As this layer of the pyramid map is corrected, every layer beneath it will also need adjustment so that each premise acting as support is properly worded and placed correctly in the inferential network.

The above process was performed to illustrate the nature of using argument maps in litigation. Litigation is about two adversaries engaged in conflict with the goal of each of the parties to persuade the judge or jury. This context necessitates that in preparing a trial exhibit every single element be tested for an anticipated attack intended to reduce its credibility. Of course, in litigation, the opposing party then has an opportunity to show how that effort was itself flawed. Unlike in litigation, I always welcome such replies in this collegial atmosphere since understanding, not winning, is the goal. This process of ongoing critical examination will, hopefully, advance the art of argument mapping to everyone’s benefit.

In litigation, presenting argument maps with implicit premises (i.e., enthymemes) is often appropriate. But it can be risky. Without the scaffolding that comes from depiciting all the premises, arguments may appear to the judge to lack sufficient rigor and precision. Or they may just appear to be confusing with the nature of the inference unclear.

A portion of an argument map from an Austhink Consulting report titled “Why Tanks? Why Abrams?” helps illustrate this risk. (I highly recommend reading this report. It is the most effective, dynamic, and innovative use of argument mapping for a large scale project that I have ever seen. I will enjoy and benefit from studying it for years to come. It is one of the best “arguments” for the power of argument mapping.)

The following map is the top tier of a large comprehensive map from the report which presents its final conclusion and most general reason. Based on the explanation of the visual grammar of this map, claims 1A-a and 1A-b are intended to represent two co-premises that comprise a single reason. But a quick examination of them reveals, in my opinion, that this is not so. The two co-premises are actually portions of two separate reasons. This is obvious because the Rabbit and Holding Hands rules are not followed. There are missing premises.

Based on claim 1A-a, the other co-premise need only state that “buying the Abrams tanks was buying new tanks” to complete a single reason. In fact, buying any of the competing tanks (i.e., Leopard 2 and Challenger 2) could also be valid co-premises resulting in their purchases as “sound decisions” as shown below.

This example illustrates the confusion that can result from not making explicit all the co-premises. The narrative in the report confirms that there are two separate reasons. It concluded that “[t]he decision to buy new Abrams A1M1 AIM tanks…was sound. p. 5. It was sound because buying new tanks was a sound decision (to maintain tank capability.) And “in maintaining that capability,” buying the Abrams tanks was sound because they were a better buy for the Army than any other available tank would have been. p. 5.

So one approach would be to consider these two claims as part of two separate reasons as shown below. (An essential predication transitivity map is also depicted.)

But an examination of the narrative suggests a different argument map. The first claim (i.e., A1-a) provides no diagnosticity to distinguish between the three available tanks. Buying any of them would have been a “sound decision. So either there are two final conclusion: “Buying Abrams was a sound decision. And buying Abrams was the soundest decision.” Or more likely, there is just one final conclusion: ”Buying Abrams was the soundest decision.” And a supporting (non-inferential) assumption is that “the purchase of new tanks (in general) was a sound decision.” This argument structure is shown below.

These examples illustrate why using essential predication transitivity always avoids this potential lack of clarity that can result from using other argument structures. There are never implicit inferential premises with an essential predication transitivity approach. (There may be differing degrees of granularity.) And the linkage between the co-premises is always obvious. In litigation, such precision and clarity is essential.

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.

sdfs

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.

http://creativecommons.org/licenses/sa/1.0/

What is the glue that links premises to their conclusion? I have been suggesting in this blog that the transitivity of predication (essential) is one glue that can bind any argument…at least for practical purposes in litigation. I didn’t know until I read an article this week that, therefore, I am a hedgehog.

Leo Groarke wrote an intriguing article on logic using the Greek parable of the Fox and the Hedgehog. In a review of the article, Preyer and Mans state that “[t]he fox uses 36 tricks to escape his enemies, the hedgehog has only one, but this one and only trick works perfectly. The fox symbolizes of course the type of argumentation theory, which uses many type of glues while the hedgehog has only logic to tie premises and conclusion together.”

Dr. Leo Groarke states that deduction is a glue that can bind any argument. My sole bottle of reasoning glue is, instead, filled with the transitivity of predication. And, further, I suggest that it is the optimum glue for litigation.

Dr. John Woods is, apparently, a fox who disagrees. After just posting a discussion on the importance of using a reasoning mode of “logical necessity” in litigation, I ironically read a wonderful article by Dr. John Woods, “Eight Theses Reflecting on Stephen Toulmin.” Dr Woods’ Thesis One is that “[t]he validity standard is nearly always the wrong standard for real-life reasoning.” In the domain of litigation, I respectfully disagree. (Admittedly, I did not fully comprehend all of his reasoning in the article. This fact is not a reflection of its coherence, but rather my own limitations. Even so, the article was enlightening for me.)

Consider the following argument map.

In civil litigation, the goal is to design a bridge of stepping stones that is perceived as more “sound” (e.g., less uncertain, less risky, safer to traverse, or more stable) than one’s opponent’s, that infallibly leads to one’s main contention on the other side of the bridge. In criminal litigation, the goal for the prosecution is to design such a bridge that the jury believes that they can cross beyond a reasonable doubt.

In my opinion, building a bridge in which the stepping stones may be 100% stable and certain but which may not lead to the main contention (e.g., questions raised on validity or logical necessity) is much less useful in litigation. Validity is, admittedly, not the goal, but it is one of the standards, in my opinion, of a compelling bridge design in litigation.

Dr. Woods argues that proof based on validity is a “brittle” accomplishment since “a single disruption of the reasoner’s knowledge-set” can render the argument “impotent.” He states that “[v]alidity is wholely indifferent to new information.” But the attorney is not indifferent.

When new contradictory information to a stepping stone arrives on the scene, the attorney has at least two options. If the new contradictory information is irrefutable, the attorney redesigns the bridge to accommodate the change in factual topography, but the destination, even with some qualification, can still win the case (unless ethically it becomes apparent that the journey should be abandoned) and the bridge should still connect to that destination with logical necessity. This redesign is typically done by adding qualifiers that increase the precision of the bridge to accommodate the new information. And an increase in precision should lead to a reduction in the perception of uncertainty.

Or in the alternative, the attorney may argue that while the new information may increase the uncertainty of reaching the destination, the reduced level of certainty is still sufficient for the attorney’s client to win.

Consider the two argument maps below using an example drawn from Dr. Woods’. The first map metaphorically illustrates induction. In this case, assuming the premise is accepted, the uncertainty of the argument resides with the unknowns attached to the inference leap. Is it too big a leap for the juror to make? Is a leap to another destination more plausible? Even if the premise seems 100% certain, the juror observes the uncertainty in the inference. There is no logical necessity.

This next argument map depicts the same circumstance using the transitivity of predication as the glue. Here the uncertainty, assuming the first premise is accepted, rests on the stability of the second premise. But the stepping from one stepping stone to the next is easy for the juror. The inference has no uncertainty.

Given that the circumstances are the same, the amount of uncertainty, theoretically, should be the same in both maps. In litigation, in my experience, it doesn’t work that way. Here is, in my opinion, why.

Dr. Woods argues that logic must take into account cognitive orientation. In litigation, this includes the “computational capacity” of the juror as “individual agent.” The individual juror, or even the judge, like other typical adults, have a functional understanding of transitivity according to research. The same cannot necessarily be said for a functional understanding of abduction, every type of presumption inference, and other modes of reasoning. Without this same level of functional familiarity, there is an increase in uncertainty that the juror will not reach the main contention destination because there is additional uncertainty that resides in the computational capacity of the individual agent for non-transivity reasoning bridges.

And if reasoning is bounded by the neurology and consciousness of the individual agent, from a kinesthetic neurology sense, my guess is that people in general are more willing to step onto shaky ground than to make a leap into space.

Further, from a practial reasoning perspective, as depicted in the Toulmin derived argument map example of “Harry is a British subject.” above, every stepping stone relies on assumptions (e.g., the answers to “critical questions”) that support them. While every generalization may not have the single counter-example characteristic, (http://io.uwinnipeg.ca/~walton/papers%20in%20pdf/02modus.pdf), every generalization can be defeated, from a practical perspective, by eliminating a single underlying supporting assumption. From a practical litigation perspective, a transitive predication inference path with ubiqutous underlying supporting assumptions is still a reasoning mode of logical necessity.

Unlike educational contexts, in litigation or even real-time business settings, any explanation of how to read an argument map needs to be of the one-footed variety (e.g., in the time a person can stand on one foot). If it takes a one-hour seminar to learn, or even 10 minutes, in my experience, forget it.

The major difficulty with explaining the visual conventions of standard Mountain (tree-like) argument mapping is that knowing how co-premises, etc. are depicted doesn’t answer the more fundamental question of what the heck is a co-premise…let alone the other typical constructs of argumentation. (I’m still not sure how to describe what is a co-premise without delving into vague conceptualizations.)

Using the transitivity of predication principle avoids this problem. Each sentence, linked in a transitive manner, provides a stepping stone that, if accepted, brings the reader closer to the main contention or conclusion. And the stepping stones are supported by assumptions, the removal of anyone of which, will cause the stone to tumble to the ground. By creating a kinesthetic  metaphor and putting the reader in the picture, their comprehension is intuitive.

The following picture is typical of one I use, if necessary, to explain the fundamentals of reading an argument map. I project it on the screen for about 30 seconds while actually walking along imaginary stepping stones on the courtroom floor explaining what each step means. People just seem to get it.

I have often read the definition of critical thinking as “the art of being right.” But in this fuzzy world of perspectives and paradox, I think a classical bivalent approach misses the mark.

I don’t know a really useful definition of critical thinking. But I define it for my students as our internal process that increases our appreciation and awareness of the places of uncertainty.

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