A Problem in Relevance, Conditional Relevance, and Dependent Conditional Probability

A crime is committed. The perpetrator leaves behind a shirt. The issue at trial is identity: Did the defendant commit the crime or was it someone else? At the trial the prosecutor offers to show that twenty different dogs at twenty different times were allowed to sniff the shirt left at the scene of the crime and that each of those dogs separately led the dog handlers to the defendant.

Evidence is also presented at the trial about the ability or inability of each of the 20 dogs to follow a scent. The jurors consider each dog and the evidence about each dog separately. They conclude, in each instance, that each dog more probably than not cannot follow a scent.

Should the jurors have been told in this case to disregard evidence about the tracking behavior of the dogs (that each of the twenty dogs led dog handlers to the defendant) if the jurors conclude that it is more probable than not that each dog cannot follow a scent? Alternative statement of the problem: Should the trial judge refuse to admit the dog-tracking evidence if the trial judge concludes that there is insufficient evidence to permit a reasonable jury to conclude that it is more probable than not that each dog is capable of tracking a scent -- if, that is, the trial judge concludes that a reasonable jury would have to find that it is more probable than not that each dog cannot follow a scent?

See Federal Rules of Evidence 104(b), 401 & 402.

What Is Nonlinear Reasoning?

Well, now that we've figured out what Justice Souter meant by linear reasoning, let's figure out what he might have thought that nonlinear reasoning is.

Doesn't nonlinear reasoning have something to do with complexity? Chaos?

Here's a possibility:

Nonlinear reasoning = complex reasoning

Mmm, that doesn't sound quite right. Ah, I have it:

Nonlinear reasoning = chaotic reasoning

Mmm, that doesn't sound quite right either. He couldn't have had that in mind, could he?

Oh, I have it now. How silly of me. Here it is:

Nonlinear reasoning = reasoning about chaotic systems

So evidence and inference in litigation are chaotic?

Mmm ... , can that be?

Well, over time -- in time -- ... perhaps. Cf. P Tillers, The Explosive Dynamic Complexity of Evidentiary Processes Associated with Litigation; Spotty Semiotics.

But wait a minute. What does it mean to say a system is chaotic? Does it mean that the brain of (wo)man cannot decipher it (to some degree)? Does it mean that the mind of (wo)man cannot explicitly decipher it (to any degree)?

Is weather a chaotic system? Does it help to talk about it -- even in the absence of (the computational power of) computers? {Red sky in the morning ..., ....} Mmmm, well, if weather is mind-numbingly chaotic, there must degrees of chaos, no? (The chances that it will be sunny in Seattle on July 1, 2004, are excellent. I will wager [offline] $100 that on July 1, 2004, it will be sunny in Seattle. {We will have to define "sunny." (I am not being cute or hypermodern.)}

What Is Linear Reasoning?

Justice Souter thinks (see my previous two posts) that reasoning about the relevance of evidence does not involve linear reasoning.

What is linear reasoning?

Is it Linear Logic? See, e.g., Trobin Brauener, Preface, INTRODUCTION TO LINEAR LOGIC v (1996):

Linear Logic was introduced by J.-Y. Girard in 1987 and it has attracted much attention from computer scientists, as it is a logical way of coping with resources and resource control.

Does linear reasoning amount to reasoning with linear equations? See, e.g., hyperdictionary at http://www.hyperdictionary.com/dictionary/linear+equation:

[n] a polynomial equation of the first degree

Is linear reasoning, reasoning about spaces defined by two or more rectilinear coordinates? Reasoning with linear differential equations? Is nonlinear reasoning, reasoning about spaces defined by curvilinear coordinates? Does nonlinear reasoning involve equations that generate curved lines in rectilinear space? ...

What, precisely, is a "linear scheme of reasoning"? And is all analysis or argument about evidence linear? What makes Souter (or his law clerks) think so?

Does Souter believe that reason cannot portray (i) exponential increases or (ii) the influence of multiple variables?

Does Souter believe that logic cannot "handle" scenarios?

Decision theory deals with alternative scenarios. Judea Pearl's subtle logic certainly deals with causal scenarios. So does Glenn Shafer's. [Souter said that a syllogism is not a story. This is true. {Did anyone ever assert the contrary?} But even if a syllogism is not a story, does it follow that deliberation about alternative scenarios or about alternative stories lies entirely beyond logic? If so, what makes Souter (or you) think so?]

News Flash: Six Judicial Opinions See Some Merit in Souter's Thesis of Non-Linear Reasoning about Evidence!

Six judicial opinions found that the phrase "linear scheme of reasoning" was not so insensible that it should not be quoted. See

United States v. Becht, 267 F.3d 767 (8th Cir. 2001)

United States v. Hill, 249 F.3d 707 (8th Cir, 2001)

United States v. Pabon-Cruz, 255 F. Supp. 2d 200 (S.DN.Y., 2003)

Blue Cross & Blue Shield of N.J., Inc. v. Philip Morris, Inc., 138 F. Supp. 2d 357 (E.D.NY., 2001)

Briggs v. Dalkon Shield Claimants Trust, 1997 U.S. Dist. LEXIS 17335 (D. Md., 1997)

State v. Alexander, 214 Wis. 2d 628, 571 N.W.2d 662 (1997)

Birth and Death of Postmodern Evidence -- the Rise and Sudden Decline of a New Non-Science of Evidence -- in the Halls of the Supreme Court

Seven years ago Justice Souter proclaimed (on behalf of the Supreme Court), "Evidence ... has force beyond any linear scheme of reasoning." This proclamation, made in Old Chief v. United States, 519 U.S. 172 (1997), was issued in support of the contention that reason cannot reveal all the ways in which evidence may be relevant to factual issues at a trial.

Ever since 1997 I have been telling my students that this eruption of postmodern evidence theory in the halls of the Supreme Court would be brief. I have discovered that Souter's irrationalist, intutionist, or holist perspective on evidential argument apparently did not even have a half a half-life: a LEXIS search (conducted on March 7, 2004) shows that not one single opinion by any court in the United States (from the highest to the lowest, state or federal) has used Souter's dismissive phrase "linear scheme of reasoning."

I have not used variants of "linear" in my search -- variants such as "nonlinear." So it is possible that some judge somewhere has seen merit in Justice Souter's theory that the mind of (wo)man cannot divine or articulate the various ways in which evidence may be relevant.

Postscript: I do not belief that all steps in or features of inference can be made explicit. However, Justice Souter's evidential intuitionism cannot easily co-exist with fundamental assumptions of the administration of the rules of evidence in trials -- with, for example, the rule or principle that an offeror of evidence has an obligation to inform the trial court of the purpose and relevance of the evidence it offers. Furthermore, there is a big (and unwarranted) step from the proposition that not everything can be spelled out to the proposition that nothing can be spelled out.

Further postscript: Nonlinear mathemtical reasoning may be hard to follow, but it is -- contrary to some rumor -- explicit reasoning.

Urgent additional postscript: Whoops! Well, perhaps my LEXIS search was misphrased. I have found one opinion that quotes Justice Souter's phrase. See United States v. Becht, 267 F.3d 767 (8th Cir., August 21, 2001). There may be others. I will report back (but I will not perform revisionist surgery on my original message, I will not delete my mistake).