INFERENCE PATH

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.

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.