INFERENCE PATH

8½” x 11″ can make for very tight quarters. Yet, litigators typically must fit their argument maps within this space either for briefs or overheads during testimony/oral argument. And briefs are often restricted to B/W. So space is at a premium.

Here is a one mapping strategy for a Transitive Inference Path.

As I have said on this blog, I struggle with keeping straight the differences between some of the conventional names for objections: a rebutting defeater, a rebuttal, an undercutting defeater, a premise objection, a plain ‘vanilla’ objection, an inference objection, a premise rebuttal, an inference rebuttal, an undercutting exception, an undercutting warrant, a counterargument, etc.

These names are typically reduced to three basic types of objections: 1) the main contention is less acceptable than another contention; 2) an inference is problematic; or, 3) a premise is bad. http://io.uwinnipeg.ca/~walton/papers%20in%20pdf/04%20Godden%20Walton%20Denying%20the%20Antecedent%20ILv24.pdf. Many people struggle with applying these distinctions.

At a finer level of atomicity, using a Transitive Inference Path, there is really only an objection to a predication. And it can be divided into, in my opinion, three more useful distinctions for litigation:

1. The objection is based on an alternate predication.
2. The objection is based on an exception to the predication.
3. The objection is based on the nature of the predication.

The following Transitive Inference Path illustrates these sub-categories. It is drawn from Pollock, How to Reason Defeasibly. http://portal.acm.org/citation.cfm?coll=GUIDE&dl=GUIDE&id=136684

Transitive Inference Path (TIP) argument visualization relies on the “transitivity of predication.” I hesitate expounding on this relation because it leads down a rabbit hole. (Only logicians and philosophers dare tread deeply in that dark place.) But I will share what I have gleaned from standing at the entrance looking in. (The following explanation reflects my understanding largely drawn from the works of Angelelli, such as Predication Theory: Classical vs Modern and the works of Cocchiarella, such as Conceptual Realism and the Nexus of Predication. http://traumstadt.org/angelelli.pdf; http://www.formalontology.it/essays/nexus.pdf

Predication is saying something about its subject. Argument mapping is a visualization of predications designed to reflect paths of inference (e.g. inferential networks). And, in its ontological sense, “predication has been a central, if not the central, issue in philosophy since at least the time of Plato and Aristotle.” (“Philosophical Perspectives on Quantification in Tense and M odal Logic”, in Handbook of Philosophical Logic, vol. 2, eds. D. Gabbay and F. Guenthner, D. Reidel Pub. Co., Dordrecht, 1983, pp. 309-353.) So it must be central to argument mapping as well.

The critical question for a Transitive Inference Path is whether predication is transitive. As an attorney, the standard answer to any question is…it depends. And, in this instance, that is actually a pretty good answer. From a classical (pre-Fregean) perspective, it depends on which type of predication to which you are referring. (Don’t ask me about substitutivity!)

Aristotle states “for all we affirm of the predicate will also be affirmed of the subject.” Categoriae. But, as an attorney, it is always good to also check the fine print. And in this case, Aristotle qualifies his statement. This transitivity relation only applies to predication of a thing “as of a subject.” Categoriae. (According to Angelelli, some literature obscures this fine print or misses it altogether.)

This qualification limits transitivity to essential predication where something is “said of” a subject rather than accidental predication where something is “in” a subject. (I told you this was a rabbit hole.) Paul Crice and Alan Code use the terms IZZing and HAZZing to express these distinctions. http://faculty.washington.edu/smcohen/433/GriceCode.pdf.

Consider the following example:

The apple is red. Red is a color. So an apple is a color.

In this instance, the predication is accidental with the apple HAZZes the color red. So this type of predication is not transitive.

But, in the following example, the predication is essential so that it is transitive.

The apple is red. Something that has the quality is red is the color of a fire truck. So an apple is the color of a fire truck.

A helpful perspective in ensuring that a Transitive Inference Path is correctly structured is seeing that “even accidental predication [HAZZing], implicitly involves some kind of essential predication [IZZing] (i.e., classification).” http://faculty.washington.edu/smcohen/433/GriceCode.pdf.

For example, an apple HAZZes something that IZZes red.

So when creating a Transitive Inference Path, be careful that the linkage between the co-premises is phrased to represent an essential predication to maintain the transitivity as shown below.

Generally, just cut the sentence in half starting with the verb, add “something” or “someone”, and make the result the subject of the next sentence.

Whether a premise is linked or convergent in relation to other premises is an essential question when argument mapping. The answer determines whether the premise is correctly placed on the map. But, surprisingly for such an important question, leading scholars cannot agree on the test to determine the answer. http://homepage.mac.com/ryanal/Philosophy/linked%20convergent%20again.pdf.

Scholars have generally agreed, however, that even when using agreed upon definitions, the determination can be difficult for students. According to Professor Tim van Gelder “this is one of the most difficult of all the concepts we will deal with.  Getting it right is one of the biggest challenges in argument mapping!” http://www.austhink.com/reason/tutorials/Tutorial_2/print.htm. Similarly, Professor Twardy observes that “[e]ven very bright students get it wrong surprisingly often.” http://www.csse.monash.edu.au/~ctwardy/Papers/reasonpaper.pdf

I have suggested that there is actually a better solution than the customary ones to this challenge. When a Transitive Inference Path argument schema is used, there is a bright-line test that suffers none of the problems of abstraction (e.g. do the premises help each other; connect in some manner; work together; synergistically enhance probative force?) of other tests.

Bright-line test: Premises are linked when they both fit within the same transitive inference path that connects the subject of the contention (aka conclusion) with its predicate. And a premise can only fit within this path if its phrasing can be adjusted such that its subject and predicate can be matched with identical terms from the adjoining premises on either side within the interlocking string of transitive premises.

With this test, the following type of simple linked/convergent problem illustrated by Professor Twardy cannot occur. http://www.csse.monash.edu.au/~ctwardy/Papers/reasonpaper.pdf

Of course, even with a transitive test, the solution is not always so obvious. What this test reveals is that the linked/convergent determination can depend on uncovering more necessary hidden premises that begin to hint at the interlocking connection. For example, in the following Rationale Transitive Inference Path (TIP) maps, the determination and resulting placement of the premise in question might not be at first apparent, as shown in the first map, until  another premise in the path is uncovered, as shown in the second map.

Peter Tillers makes the excellent observation that “[f]undamental theoretical considerations and differences lead to different mapping strategies.” http://groups.google.com/group/rationale/browse_thread/thread/2baf32ff6d3c417e. This is certainly true. When attempting to persuade a judge or jury, however, a mapping strategy and underlying argument schema that is intuitively obvious to non-scholars at first impression is indispensable.

For years, I have used argument maps in briefs and as trial exhibits. A mapping strategy that requires explanation or demands a significant cognitive load of the judge or jury can actually do harm to the case. This is because generating confusion in the adjudicator due to the complexity or lack of rigor of the mapping strategy reduces credibility of the advocate. And the advocate, and ultimately their client, is blamed for the discomfort of the confusion.

This is why modeling all inference (e.g. deductive, inductive, and abductive) as a function of transitivity, as in Inference Path mapping, has been, in my litigation experience, so successful. Adults’ ability to chain together long strings of transitive inferences is so “unbounded” that it has been named “inferential promiscuity.” http://www.ling.ed.ac.uk/~jim/litloe.pdf. Evidence suggests that people can even make these transitive inferential connections without conscious cognitive processes or explicit logical reasoning. http://faculty.virginia.edu/levylab/Publications/script/Hippocampal/Hippo%20TI/Greene_et_al2001.pdf; http://psych.colorado.edu/~oreilly/papers/FrankRudyLevyOReilly05.pdf. Transitive inference has even been displayed in a variety of animal species. http://www.cs.helsinki.fi/group/cosco/Teaching/CoscoSeminar/spring2007/articles/watanabe-2006.pdf. (So, perhaps, you can test out your Inference Path maps with your pets.)

The previous post illustrated that, for the same argument, Inference Path mapping  produces a smaller proposition and argument density than Hierarchical Pyramid mapping. This condensing increases readability. http://jac.gsu.edu/jac/6/Articles/4.htm. Readability is also increased, in my opinion, through consistently structuring premises in a transitive manner even without multiple reason layers.

The following is a simple self-test of readability comparing different argument schemas. The Rationale maps on the left-hand side use conventional scaffolding and are examples from Austhink (the leader in argument mapping). The Rationale arguments maps on the right-hand side are the same argument depicted as a precise transitive inference using an Inference Path. To create a precise transitive inference the advocate simply ensures that the subject of the main contention is joined to its predicate by a series of interlocking sentences in a transitive path as illustrated below. (A smaller descriptor than a predicate can also be sequenced in a transitive path as illustrated in the final comparison.)

Following this transitive rule, the advocate is never unsure whether co-premises are linked or whether there are missing co-premises.

Which argument maps below do you think would be more readable to the mapping uninitiated judge or jury? Sometimes the difference may seem slight (particularly if you are already skilled in reading argument maps), yet, in litigation why not maximize the persuasive effort and minimize confusion.

One of the advantages of Inference Path mapping versus Hierarchical Pyramid mapping is a reduced proposition and argument density. This improved efficiency increases readability and comprehension.

The following comparison illustrates how Hierarchical Pyramid mapping adds two premises for every one premise in Inference Path mapping. In litigation, this rapid growth in complexity is a tremendous disadvantage.

Dan Prager presents an interesting variation of Pyramid mapping of a previous Path map I had posted.  http://dailykibitz.blogspot.com/2007/05/suspect-for-murder.html. I very much appreciate the collegial exchange in our mutual attempts to advance argument mapping.

Dan’s variation of typical Pyramid mapping  moves in the direction of the structural rigor demanded by the scaffolding in Inference Path mapping (aka Path mapping). I would suggest that there are benefits in coming the rest of the way over to Inference Path mapping for several reasons:

• One of the strengths of Inference Path mapping is the strict rigor of always chaining co-premises as interlocking sentences with the predicate of one co-premise becoming the subject of the next co-premise. This scaffolding ensures that there can be no hidden premises. (With increased granularity there, of course, can always be more co-premises.) In Dan’s example, there are missing co-premises that are necessary for the inference steps. (I have added them in my example below.) This problem is always avoided with Inference Path mapping.
• By separating the subject and predicate of the main contention in Inference Path mapping, the actual inference steps of the subject of the main contention to join with its matching predicate can be explicitly portrayed in a metaphorical stepping manner. It is, thus, clear to the reader how many actual “leaps” are needed to reach the main contention. This number is important when arguing in litigation about the weakness of the inference path because of the excessive number of “leaps” needed.
• Dan’s example uses the same space in the green box to depict co-premises and “conditionals.” This overlap creates confusion for the reader as to the premise type based on this shared location.
• One advantage of Inference Path mapping is the increased readability that results from designing the most efficient proposition and argument density. This also results in less actual space needed which is critical in presenting exhibits in briefs or in court. Even when adding the missing hidden premises from Dan’s map, the Inference Path example below still has far fewer premises than Dan’s map. This occurs because Inference Path mapping visually indicates the interim subconclusions through the “inference step” dotted arrows. This avoids the necessity of adding actual additional premises as done in Dan’s example.
• For purposes of litigation, a clear visual distinction, as done in Inference Path mapping, between the premises of the plaintiff and defendant is critical. (If Rationale would allow the orange rebuttal boxes to be changed to red, there would be no need to use orange and red as the colors for one of the litigants.) 
• When the co-premises are linked in a horizontal manner, it is easier to check if the sentences are interlocking since the predicate of one co-premise is adjoining the subject of the next co-premise.
• Dan’s observation that “cited law” needs to be reflected is easily done with Inference Path mapping.
• Inference Path mapping maintains a strong metaphorical integrity with argument as walking along a path. And when “conditionals” are depicted beneath a co-premise the concept of support is visual enhanced.
• By maintaining scaffolding of interlocking co-premises in Inference Path mapping, typical structural fallacies in an argument are made readily apparent.

I look forward to continued dialogue.

The previous post illustrated a Rationale Path Map using a vertical convention for linking the co-premises. A horizontal transitive inference path is, perhaps, even easier to construct with Rationale. With this visual convention, the linkage of each co-premise along the inference path is obvious as the predicate of one co-premise becomes the subject of the next co-premise. From one perspective, this structure can be considered a strict construction of the rule of “Holding Hands.” And the inference steps through the process of substitution by the subject of the main contention (e.g. “Robinson”) to reach its predicate is easily observed and explained.

Professor Tillers recently posted a very interesting and informative Rationale argument map for an inference problem in United States v. Robinson, 560 F.2d 507 (2d Cir., 1977) (en banc). http://tillerstillers.blogspot.com/2007/05/tillers-tries-to-be-rationale.html. It is a wonderful illustration of the complexity of witness credibility attributes.

In Rationale software, these attributes, as shown by Professor Tillers, fit functionally alongside the inferential premises. As discussed in an earlier post here, some of the attributes (e.g. the witness was in a position to see and hear the perpetrator) are necessary “conditions” for one to draw an inference from the testimony. Other attributes (e.g. the witness was unbiased) are merely “companions” to a witness argument scheme since they only affect the strength of the inference. For example, the testimony of a biased witness could still have some probative force.

While certainly not always necessary, when a further purpose of an argument map is to be sure to reveal any possible hidden premises (other than “conditions” and “companions” for which an infinite are possible) in the inference steps, the complete Path argument schema ensures this goal. The Path schema provides a rigorous, but simple scaffolding for the designer. It consists of simply joining the subject of the ultimate probandum to its predicate through a series of interlocking sentences in which the predicate of one sentence is the subject of the following sentence. This creates a transitive inference path for the subject of the ultimate probandum to reach its predicate through a series of inference steps. Since each sentence consists of interlocked “co-premises” there is no space for a hidden premise to exist. Note, however, that this claim is not the same as saying that further granulation would not be possible. An infinite number of intervening co-premises could always be imagined. Ensuring no hidden premises simply means that there are no missing co-premises that would be needed for the chain of inference since each co-premise is already interlocked with the next.

The following is a Rationale Path map illustrating these interlocking co-premises for the same inference problem in Robinson. (The issue of witness credibility has been simplified for this different purpose.) This Path map reveals the two co-premises hidden in the Tillers map. These two co-premises are the major flaws in the argument made by the prosecution. As shown below, the first weak co-premise is that “actual possession of a .38 caliber revolver on July 25, 1975 indicates that one possessed a .38 caliber revolver on May 16, 1975 (ten weeks earlier).” The other weak co-premise is that “possessing a .38 caliber revolver on May 16, 1975 (the date of the robbery) indicates that one possesses the actual revolver that was used by the perpetrator at the robbery.” With these co-premises revealed in the inference chain, the attorney can more effectively argue why the inference chain should break at these two links. Or in the alternative, the attorney can effectively argue that the small probative force is easily outweighed by the prejudicial effect. 

One procedure of Path mapping with Rationale is to chain the co-premises up a vertical inference path rather than placing them horizontally within the green box background. But Path mapping is more than this visual convention. The Path argument schema is based on a fundamental structure of argument consisting of an inference path of interlocked sentences such that the predicate of one sentence is the subject of the following sentence.

This schema forms a scaffolding template in constructing arguments that ensures structural validity, inference step clarity, and depiction of all necessary premises.

The following example is drawn from the Rationale Help section of the software. The first Pyramid map follows the conventional construction. The second Pyramid hybrid map changes the visual grammar and strings the co-premises vertically. This syntax change does not, however, create a Rationale Path map. This is because the sentences are not interlocked. The third argument map adjusts the premises so that they are interlocking, thus, creating a Rationale Path map.

Notice that the final argument map removes the unnecesary cognitive burden carried by the first two Pyramid argument maps. Without the interlocking of premises, the first and second maps require added cognitive effort, even if slight, by the reader to fill the implicit inference gaps and reorganize the inference steps. While, certainly, the mind can make the necessary inference connections in the first two maps, readability is reduced and potential inference flaws are less obvious.

In legal settings, these differences can be critical. The attorney should do the extra cognitive effort in constructing the argument, not the factfinder. And by using a Path schema to reconstruct the opposing party’s arguments, any structural flaws and hidden premises are readily apparent.

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