INFERENCE PATH

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.

An inference form of logical necessity works well in litigation. It is enough for the judge or jury to think about the acceptability of your premises. Asking them to also work to make sense of your reasoning can actually be too much of a cognitive load. And adding on the challenge of an unfamiliar visual language can make them down right rebellious.

This is one reason why the transitivity of essential predication (e.g., “is said of”) works so well. While a general form of transitivity (e.g., aRb and bRc, so aRb) can be fallacious, the transitivity of essential predication form is not. And any form of inference, in my experience, can be translated into such a form.

Just be sure you don’t confuse any transitive relation with the transitivity of essential predication. For example, consider the following argument:

It can be risky to rely on this form of inference since it depends on the transitivity of the relationship. Here it works only because “taller than” is transitive.

However, this next form of inference (e.g., transitivity of essential predication} always is valid regardless of the relation. So be sure to keep the distinction clear in your mind.

Dr. Reed, Dr. Walton, and Dr. Macagno wrote a fascinating paper on the origins of argument mapping. Apparently, Richard Whately, in 1836, was the originator of argument mapping. It was an incredible accomplishment.

As depicted below (with Rationale™), his original map used a “mountain (or tree)” design. It is still, with some variations, the conventional visual language used today. This design does, however, have some deficiencies. For example, there is always an unnecessary number of premises to reflect the lines of inference. And there is no defined pattern for reading the map from start to finish. The second map reflects a transitive inference path visual language as an alternative. [I am not addressing the transitivity questions contained within the argument.]

I respectfully disgree with the recent statement from the General Manager of Austhink: “US Government policy also dictates that spending should be directed to assisting the most disadvantaged children. ‘Our product is much more high-end and is aimed at the thinking skills of upper-level students,’ Dr Wraith says“.

Rationale™ is, in my opinion, appropriate for disadvantaged children as well. And the need may even be greater than for advantaged students.

Rationale™ makes reasoning easier for everyone. As Dr. van Gelder points out, it provides a way to “bypass or make up for the deficiencies or limitations of our innate capacities, while on the other, taking advantage of their distinctive strengths.”

One way to make the transition easier to Rationale™ for students is to begin with pencil and paper using worksheet templates. (e.g. DivShare File – transitivity_template.pdf available for download) While the illustration that follows uses a more mature example, the principles remain the same. When using a transitive inference pattern, the reasoning never gets more complex. The path may only get longer. (The template metaphorically represents a path of stepping stones over a stream. And the assumptions are underground supports that hold up the stepping stones.)

The teacher can begin by providing worksheets that are completely filled-out. As the students begin to understand the transitive pattern, the teacher can provide samples with just one stepping stone empty. As understanding increases, more stepping stones can be left empty. (Note that only two stepping stones are required to reach the main contention.)

When leading a judge or juror along your path of reasoning, it is important that they are not required to guess what inferential leaps you want them to make. While it may seem burdensome in preparation, ever stepping stone along the path needs to be depicted.

This is the same requirement whether writing a brief or diagramming an argument. When I taught “Legal Writing” at Willamette Law School, two of the most important words were “So what?” If the attorney or witness cannot answer that implicit question by showing clearly how each statement precisely links to an explicit conclusion, the judge or jury will abandon the path of reasoning.

The argument map drawn from Dr. Tim van Gelder’s recent paper provides an opportunity to illustrate this principle.(http://rtnl.files.wordpress.com/2007/07/rationaleforrationale.pdf) Hopefully, this litigation argument map rigorously and simply provides the answer to the “so what?” question for every premise depicted. Don’t ask the judge or jury to fill in the blanks!

The following is my reply to Dr. Tim van Gelder’s helpful comment (http://inferencepath.edublogs.org/2007/07/29/are-conditionals-really-inferentially-linked-premises/) to the previous post in this blog. Since I have included argument maps in my reply, I could not post my reply in the comments section beneath his post.

Hi Tim,

It is good to hear from you. I am glad to hear that the inference observation of your paper was helpful. The question in your comment points to a larger issue, namely, what visual conventions are most effective for argument mapping.

I think the answer to that question is context dependent. For example, a visual language that may be most effective for developing critical thinking skills or other educational purposes may not be most appropriate for persuading a judge or jury. So, perhaps, the place to begin in designing a visual language is to consider the purpose of the argument mapping.

From my years of experience in designing and presenting argument maps for litigation (and, of course, from your tutoring), I have observed several requirements for a visual language for litigation that may differ from an educational context.

1. There is no real opportunity to teach the new visual language to the judge or jury at trial or even in a brief. This means that the visual language must be self-explanatory.
2. The exposure to the map maybe only be for a minute or two. This means it must be so intuitive that it can be clearly understood at a glance by the reader.
3. Because it is always used in a context of conflict, the visual language must allow no vaguenss or ambiguity that can be exploited by the opposing party.
4. Since it will typically represent a relatively complex argument, it must require minimal effort to read to avoid resistance or inattention in the judge or juror.
5. Since it it always used in a persuasion context, its use must not engender a risk of feelings of incompetence or frustration in the reader.
6. Since its sole purpose is to persuade, all features should be designed for that purpose alone. Any concerns that might cause compromising detours for ease of production and pedagogical purposes should be bypassed on the path to the goal of persuasion of a novice reader.
7. Since the readers, including the judge, very likely have no training in informal logic, the visual language needs to require no understanding of “linked” premises and other theoretical features. The connections and inference steps must be based on a common sense understanding of reasoning.
8. Since the judge or jury think in terms of parties, rather than arguments from a pedagogical standpoint, the visual language must easily distinguish the reasoning of each party.

To meet these design requirements, I believe that are several relevant principles.

1. The visual design should resemble as closely as possible the visual language with which the reader already has familiarity. The judge and jury are most familiar with the visual convention of sentences strung front to back in a horizontal path that form separate units. The closer the argument mapping can emulate those conventions, while maintaining its unique attributes, the better.
2. From new research in the metaphorical and embodied nature of thought and reasoning (e.g. http://www.edge.org/3rd_culture/lakoff/lakoff_p1.html), the visual language should harness the advantages of an embodied metaphor for an intuitive understanding of inference as the foundation for the visual language.
3. The visual language should provide the necessary fencing (e.g. scaffolding) to keep the reader on the inference path to avoid any slippage of meaning or the reader getting lost and stopping or straying off the path.
4. The visual language should use colors that identify each party.

The following map uses a visual language I developed that I have so far found best meets these requirements and principles for litigation mapping. It is based on the embodied metaphor of the reader walking in the familiar pattern of left to right horizontally along an inference path. Through the use of transitive inference (e.g. the predicate of one premise is the subject of the next), the reader does not need to understand the difficult concept of “linking” premises. As you have pointed out, understanding this concept can be very difficult. “Logicians and argumentation theorists have found this notion hard to pin down.” http://rtnl.files.wordpress.com/2007/07/rationaleforrationale.pdf.

But with interlocking premises using the transitivity of predication, even children understand the connection naturally. And a transitive inference approach always depicts any necessary hidden premises so the reader does not have to guess at the connection. There must be no gaps in the chain of reasoning that the reader must supply. The inference path also has a START (the subject of the main conclusion) and a FINISH (the predicate of the main conclusion) which bound the reasoning path at both ends and avoids the confusion of basis nodes (e.g. grounds). The different supporting nature of conditionals (e.g. elements of a tort) are depicted in a distinctive manner from the inferentially linked premises. They are shown metaphorically as supporting structures for the premise stepping stones along the inference path. If a conditional is destroyed, the stepping stone that relies upon its support is also at risk.

The following maps illustrate the vagueness in linkage that can result for a juror when a transitive inference path is not followed. The connections following the standard visual conventions are sometimes not obvious even to the practiced eye.

I think this inherent problem of vagueness in linkages with the standard visual conventions is well illustrated by the inferential error that existed in the tort argument map in the Rationale for Rationale™ paper. Likely a number of professional eyes read the map at Austhink and at the Law, Probability, & Risk Journal. Yet, the error was not observed. This is obviously not a reflection on the knowledge and skill of the readers. Rather, I believe it is a result of the vagueness that is inherent in “linked” premises which don’t follow the transitive inference template. (Following “rabbit/hands” is not a complete solution.) Once I translated the standard conventional visual language into the transitive inference visual language, (http://inferencepath.edublogs.org/2007/07/29/are-conditionals-really-inferentially-linked-premises/) the linkage problem was obvious.

Even when a transitive inference approach is used within the conventional pyramid visual language, a number of problems, as illustrated below, still exist. The pyramid approach, typically with a main premise and co-premise as building blocks, requires the unnecessary duplication of premises increasing the complexity of the map as shown below. And since there is not clear START and FINISH, the reader does not have a prescribed path to climb the “mountain” of premises. The reader is forced to wander up and down and up and down without a set order of inference steps to follow. And the vertical travel is, for Western readers, unfamiliar. All of this increases the cognitive load on the jurors…not a good idea.

The conventional visual language, as shown below, does not create “a mountain out of a mole hill.” But it does create a mountain out of a simple path. It is much easier to guide the reader along the well-marked inference path than helping the reader climb a conventional visual language mountain up and down and up and down with no clear route to follow.

Fortunately, Rationale™ is easily adaptable to different visual conventions. I use it for my drafts since it is so user-friendly. I make many changes in my drafts for litigation, and Rationale™ makes that simple and fast.

I want to be clear that adjusting the wording of the premises to fit within a transitive inference path is not always easy. But it can always be done for a structurally valid argument. And for litigation, I want to do the hard work so the judge and jury don’t have to. Its been my experience that if that demand is placed on them by using an unfamiliar visual language, they won’t make the effort.

Best regards,

Joseph