INFERENCE PATH

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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