Intuitive Introduction to Fuzzy Logic, with Examples

See Bart Kosko & Satoru Isaka, Fuzzy Logic

Titillating extracts:

Specimen 1: "When mathematicians lack specific algorithms that dictate how a system should respond to inputs, fuzzy logic can control or describe the system by using "commonsense" rules that refer to indefinite quantities. No known mathematical model can back up a truck-and-trailer rig from a parking lot to a loading dock when the vehicle starts from a random spot. Both humans and fuzzy systems can perform this nonlinear guidance task by using practical but imprecise rules such as 'If the trailer turns a little to the left, then turn it a little to the right.'"

Specimen 2: "Applications for fuzzy logic extend beyond control systems. Recent theorems show that in principle fuzzy logic can be used to model any continuous system, be it based in engineering or physics or biology or economics."

Specimen 3: "At the heart of the difference between classical and fuzzy logic is something Aristotle called the law of the excluded middle. In standard set theory, an object either does or does not belong to a set. There is no middle ground : the number five belongs fully to the set of odd numbers and not at all to the set of even numbers. In such bivalent sets, an object cannot belong to both a set and its complement set or to neither of the sets. This principle preserves the structure of logic and avoids the contradiction of an object that both is and is not a thing at the same time.
Sets that are fuzzy, or multivalent, break the law of the excluded middle- to some degree. Items belong only partially to a fuzzy set. They may also belong to more than one set."

Specimen 4: "A few fuzzy systems manage information rather than devices. With fuzzy logic rules, the Japanese conglomerate Omron oversees five medical data bases in a health management system for large firms. The fuzzy systems use 500 rules to diagnose the health of some 10,000 patients and to draw up personalized plans to help them prevent disease, stay fit and reduce stress."

Zadeh, Fuzzy Sets, Soft Computing, Precisiation, and the Law

Law teachers have not yet come to terms with the conceptual revolution that Professor Lotfi Zadeh launched in 1965 with the publication of his truly seminal and pathbreaking paper, Fuzzy Sets, 8 Information Control pp. 338-353.

I was told by a reputable source that this paper is the most-cited scholarly paper of all time.

Although it is understandable that law teachers (at least in the occidental world) have yet to wrestle seriously with Zadeh's revolutionary approach -- indeed, it is arguable that even most reputable logicians, mathematicians, and probability theorists have not yet done so in an adequate way --, the time for excuses is running out. It is now time that law teachers grapple with Zadeh's approach to uncertainty; failing that, it is time that they inform themselves of some of the essentials of Zadeh's approach to uncertainty; and, failing even that, it is, at least, high time that U.S. law teachers support a serious effort by the US legal academy to explore the uses of Zadeh's family of theories for law and in the study of law.

Alas, being at best an amateurish autodidact in mathematics, logic, probability, and related fields, I am ill-equipped to suggest an appropriate starting point for people who wish to learn about soft computing (this is a convenient general label for the family of theories that interest Zadeh) but have no knowledge of set theory or probability theory. However, I suspect that one good starting point for law teachers who do have some familiarity with logic, set theory, and probability might be the latest iteration of Zadeh's recent paper, Toward a Generalized Theory of Uncertainty(GTU) - An Outline (January 20, 2005). If you approach this (detailed outline of a) paper with an open mind -- perhaps with an Eastern or Japanese mind --, you may find many important concepts in this paper, concepts that, in any event, should have particular resonance for law teachers who regularly wrestle with certain forms of uncertainty in law, forms of uncertainty that are often not appreciated by non-lawyers.

If you already have a good feel for Zadeh's general approach and if you would like a less lengthy introduction to his general theory of uncertainty, you might find it profitable to skim a recent exchange of views on the UAI list about "cointensive precisiation." Two of the posts are by Professor Zadeh; one post is by Tod Levitt (a co-founder of the Association for Uncertainty in Artificial Intelligence); and I contributed a post about some forms of uncertainty that (I think) regularly recur in law. The thread starts here.

When reading about Zadeh's theories or his papers, it is wise to abandon intellectual and cultural chauvinism. Zadeh's theories generally seem strange to occidental theorists when such theorists first encounter them. But Zadeh's general approach ought not to seem so terribly alien (even initially) to legal theorists, who ought to have, by virtue of their familiarity with certain forms of normative reasoning, an intuitive feel for (i) the notion that some events do not fall clearly either within one category or within one or more another alternative categories but fall instead to some degree both within one category and also, to some degree, within one or more other separate categories or classifications, (ii) the notion that categories (classifications, or sets) themselves have uncertain, or rough, perimeters or boundaries, and (iii) the notion that there are distinct forms of uncertainty, that some of them are semantic, and that not all forms of uncertainty can be pictured, or "captured," adequately by conventional probability theory.

If these intuitions do not move you, you should at least ponder the fact that fuzzy set theory and its affiliates have an enormously wide range of real-world applications. They work! Given this, one should hesitate before calling soft computing nonsense. Soft computing may or may not turn out to be the best way to portray or grapple with uncertainty or with uncertainties of various kinds. But one thing is practically certain:

The "soft" way of thinking about uncertainty that Zadeh initiated in 1965 is not nonsense. It is, instead, a profoundly important new way of thinking about uncertainty. Even if this new way of thinking is not the final answer to the problem or phenomenon of uncertainty, this new way of thinking is an important stepping-stone to a more comprehensive conception of the nature of uncertainty.

.

Brian Leiter and the Reproduction of Willy Lomanhood

While surfing the internet the other day I encountered web pages about a person I knew many years ago, while I was still in college. This person went on to a renowned doctoral program at an illustrious university. Very shortly thereafter she published a book that made a big splash in her field and sold very well to the general public. Her book was favorably noted by the New York Times. Passages from it are now found among collections of famous quotations. And then, to all intents and purposes, this person disappeared. As far as I can determine, she has published nary another word.

This morning (during my spring break) I was listening to WNYC, the local public radio station. I heard a snippet of an interview with Scott A. Sandage. He was discussing his new book Born Losers: A History of Failure in America (Harvard University Press 2005). See the informative review in the Washington Post. Talk in the interview briefly (and inevitably, I suppose) led to mention of Willy Loman. A few moments later Sandage said that he had not tried to study attitudes toward success and failure elsewhere in the world but that anecdotal evidence suggested to him that in at least some parts of the world attitudes toward success and failure differ markedly from those in the United States. He said that when he was still working on his book and mentioned the topic of his book -- failure -- to Americans, the response would usually be an embarrassed silence, but that when he mentioned the topic of his book -- failure -- to Europeans and other non-Americans, his partners in conversation would immediately start grilling him about why Americans are so obsessed with success.

Thoughts about my vanished friend and about the book Born Losers put me in mind of Brian Leiter.

Brian Leiter of the University of Texas maintains a ranking system of American law schools. He also ranks philosophy departments now and then. He also ranks various programs in law schools. He also uses alternative metrics to produce a variety of alternative rankings of American law schools.

Now this business -- the business of ranking law schools, law school programs, and philosophy departments -- is, I suppose, not an unnatural avocation. But Leiter does more than rank various educational institutions and programs. He also reports, in detail, the movement of faculty members -- and rumors of faculty moves -- among American law schools. He has been at it for years now.

Leiter is preoccupied with hierarchy -- but not in the way that Duncan Kennedy once was. Leiter's reports on lateral faculty moves are generally limited to law schools (and, for all I know, philosophy departments) that he apparently considers either elite or above average. The reports often have a breathless quality. For example:

Report 1: "A number of top schools, including Texas, were in the 'hunt' for this scholarly couple this past year!" (Leiter Reports, April 14, 2005)

Report 2: "This marks the first time since roughly the late 1980s that there has been any lateral movement between the two New York schools, and the first time (ever, to my knowledge) that NYU has dislodged a senior faculty member from Columbia. That's a big coup for NYU, ..." (Leiter Reports, April 5, 2005)

I suspect that many of my fellow law teachers share my reaction to Leiter's reports about faculty moves (often to-and-fro) in the American law school world. Leiter's reports about such matters strike me as mildly repellent; they strike me as the equivalent of a gossip column; they seem to amount to chit chat about the doings of the law school world's equivalent of the rich and famous. But, despite my better judgment and instincts, I find that, exactly like a moth to fire, I am occasionally drawn to Leiter's chatter.

I teach at a reasonably-good law school. I also fancy that my standing in my field is reasonably good. Yet I find that I am invariably depressed after I look at the most recent edition of Leiter's reports of law school rankings and faculty movement among law schools; indeed, I invariably feel that I am Willy Loman redux.

At the risk of personal embarrassment, the scorn of my colleagues, and impairment of my standing (if any) in the legal profession at large, I wish to say this: Brian Leiter's reports are not good for the soul. And perhaps they are not good for legal education. Oh, well, shucks: I retract the last suggestion. I can't really say that his reports positively harm American legal education; I haven't done a rigorous economic analysis of the costs and benefits of his "reports" (and I never will). But of this much I am reasonably sure: Brian Leiter's law school faculty gossip column is an example an unhealthy obsession with "success" (in this case, of the academic variety).

Work in your own gardens, folks (law teachers, I mean, and the rest of you too!). Think less about what your neighbors do and think. Yes, you are entitled to seek just compensation for your labors; and, yes, you must eat and some of you have families to feed. But keep in mind that there is a large grain of truth in the notion that good work is its own reward. So, while it's tough medicine and probably hard to swallow, here is my prescription: Try to keep Brian Leiter -- or, in any event, his reports of law faculty moves -- out of your minds. I will try to do likewise. If we succeed, perhaps we will -- as a group, on the whole -- live better and enjoy our wonderful work more. Let's try to keep the number of Willy Lomans on law school faculties to a minimum.

There! I have that off my chest. Now I can get back to Evidence.

N.B. Honestly! I don't know why that Leiter guy never mentions my name!

New Tool for the Investigation of Forensic Fact Investigation and Other Dynamic Legal Processes

If you are interested in multi-entity Bayesian networks [MEBNs] and multi-entity decision graphs [MEDGs] but would prefer to do without quantum theory and the possibility of intelligent & conscious natural processes, you should revisit Kathryn Blackmond Laskey's web page for papers and publications that deal only with applications of MEBNs and MEDGs. See Kathryn Laskey's Papers and Publications The paper titles are self-explanatory. Look close to the top of the web page. Laskey's papers seem to deal with military applications of MEBNs, but I have reason to think that MEDGs in particular would be a powerful tool for the study of forensic fact investigation, which is a dynamic process that involves probabilities, weighting of preferences, interactions among multiple agents, and all that. (But someone with better math skills than I have must undertake this research project. Is there a doctoral candidate or a post-doc out there in cyberspace who wants to try his or her hand at a very difficult but important problem?)

Streaming Audio of E-Symposium Presentations To Be Available April 15

Streaming audio of the oral presentations at the e-symposium on human identification will be available within ca. 24 hours.

I caught fragments of earlier discussions; they struck me as very worthwhile. I plan to listen to them at my leisure this weekend. Topics included fingerprint evidence (five presentations or sessions), DNA evidence (multiple presentations), and other matters such as identification with teeth, bones, etc.

The link to the (free) symposium is in my prior post.

The speakers are well-credentialed and well-spoken.

Ah, here is the link to the symposium on human identification: e-symposium

Human Identification eSymposium

This excellent and free e-symposium is now in progress; it began at 5:30 a.m. Eastern Daylight Savings Time (U.S.).

If you are not able to participate viva voce (as I, alas, cannot), you can apparently access archives of the presentations.

But after a presentation is finished, one can only access the powerpoint file associated with the presentation, it seems, and not video or audio files; and you will not be able to pose questions or take part in chat room discussions.

Is Quantum Computing on the Horizon? Discussion of a Macroscopic Effect of Quantum Processes

YESHIVA UNIVERSITY

PHYSICS DEPARTMENT
2004-2005

PHYSICS COLLOQUIUM

Quantum tunneling of the magnetization in molecular nanomagnets

A lecture by Myriam Sarachik

C.C.N.Y. – C.U.N.Y

Molecular nanomagnets, sometimes referred to as single molecule magnets, have attracted a great deal of recent attention for interesting behavior that is borderline between the classical and quantum mechanical regimes, and because of their potential usefulness for high-density data storage and quantum computation. Quantum mechanical processes are observed in these materials on a macroscopic scale in the form of steps in the magnetization curves. Typical behavior of the class will be examined by considering Mn12-acetate, a particularly simple prototype.

Wednesday, April 13

12:15 PM - Furst 201

More about the Coming Mixed-Court (Mixed-Jury) System in Japan

See Robert Bloom, Jury Trials in Japan (March 16, 2005).

Professor Bloom worries in part that professional judges in Japan's emerging mixed system (for criminal trials) will dominate the lay judges a/k/a the assessors a/k/a the jurors, and that Japanese attitudes toward hierarchy and status will enhance such domination. Professor Bloom recommends various measures to enhance the prospects for autonomous deliberation by lay members of Japanese mixed-courts.

Some of Professor Bloom's recommendations bring back personal memories. In the early 1990s, when Latvia was gaining its independence, I accompanied ("led" would be the wrong word) a group of law teachers from the U.S. and Europe to Riga to discuss reform of the former Soviet system of civil and criminal justice in Latvia. In one session, a very young member of the Procurator's Office, after hearing a debate between John Langbein and Richard Lempert over trial by jury, proposed some measures to enhance the prospect of independent deliberation and decision by lay members of Latvia's mixed-court system. For example, he proposed that lay judges and professional judges initially deliberate separately and arrive at tentative initial decisions, and only then deliberate together to reach a final verdict or judgment.

I wonder if the tendency of lay judges in Japan to defer to professional judges will really be more pronounced there than elsewhere. The concerns that Professor Bloom voices about lay juror deference to professional judges in Japan are eerily similar to the concerns that I have had and have heard other people express about lay deference to professional judges in both Latvia and Germany. I had this concern about undue lay deference because of my personal experiences as well as from my scattered reading in professional literature. In the early 90s I chatted with some trial judges in Latvia about the role of lay assessors. Furthermore, I am fairly familiar at a personal level with both German and Latvian "culture": I was born in Latvia, and I spent a year at the University of Munich as a university student and another year in Munich as a "guest professor." Based on such sources of information I once had the firm sense that Latvian and German members of mixed courts would be more deferential to professional judges than lay persons in the U.S. would be under similar circumstances. Now I am much less sure about this. (Important disclosure: I have done no systematic study of the question, and I have not recently examined any of the literature that attempts to compare national, social, or ethnic differences in attitudes toward status and hierarchy or such comparative differences in the tendency toward group conformity in such settings.)

One Hundred Years of Uncertainty

For more about quantum theory and uncertainty see Brian Greene (professor of physics & mathematics, Columbia University), One Hundred Years of Uncertainty, NYTimes Online (Op-Ed, April 8, 2005)

Professor Greene gives you quantum theory made simple -- but not inaccurate. (Quantum theory made simple is the only kind I can handle.)

But there's nothing in Greene's Op-Ed about quantum computing. (I wonder: Was Professor Greene consulted on the decision by the NYTimes editor's to classify his paper as opinion?)

Oh yes, about this business of quantum computing: if the human brain does quantum computing, do human beings really need the simplifying heuristics that Kahneman and others said or suggested that human beings need to get along in this world?

The mind is a subtle thing. Well, some minds ... :-)

N.B. Part of the lesson of jury studies such as those done by Reid Hastie et al. in Inside the Jury is that the "ordinary" mind -- i.e., the mind of the ordinary person -- is a very powerful and subtle instrument -- at least with regard to the storing and analysis of ordinary (non-technical) evidence. (And such ordinary minds seem to do better with [ordinary] evidence when they work in groups -- e.g., the ordinary mind seems to function better when it works with eleven other ordinary minds on an ordinary jury to dissect and assess the evidence, at least in a typical case, one that does not involve much technical ledgerdemain. [Granted, such "typical" cases are becoming less common.])

Another thing to keep in mind [so to speak] is that human beings, to make inferences about their environment and the world, do not need to have everything they know consciously in mind at all times. See P. Tillers, Picturing Inference (2005).

Syndrome Evidence in the Michael Jackson Case

I have sworn not to gossip about the Michael Jackson case. But now I must capitulate. Slate has a trenchant critique of syndrome evidence -- child sexual abuse accommodation syndrome [CSAAS] evidence. The writer uses the Jackson case as his foil. See David Feige, Yet more junk science to confound the legal system (April 6, 2005).

The Reunion of Ontology and Epistemology?: Kathryn Raymond Laskey's Proposal

I have speculated here that the emergence of computer science heralds the reunion of ontology and epistemogy (which includes a theory of uncertain inference). I have even speculated that quantum theory and quantum computing may (someday) have help effect this remarriage. Now there is someone who does far more than speculate. See the fascinating paper by Kathryn Blackmond Laskey, Quantum Physical Symbol Systems.

Ontology and Evidence

Evidence and inference in their modern form (in US law, in any event) presuppose the death (or nonexistence) of a grand ontology -- a general theory of (or about being), a theory that sees some sectors of being as the foundation and basis of everything else. Much or most contemporary (US legal) thinking takes the view that anything can in principle be evidence of anything else. But if one has an ontology -- a theory that points to an accessible, or intelligible, foundation of things --, then the best evidence of how things stand in the world is how things stand at the foundation of everything that one sees in the world.

In Western intellectual history ontologies came to an end with the rise of the nominalism that was British empiricism. After Hume, philosophy was possible as epistemology, but not as ontology. Kant rebuffed Hume's skepticism -- or attempted to do so -- by giving causality theoretical validity. Did Kant (perhaps despite himself) thereby rejuvenate ontology? I think not. If Kant vindicated causality, he vindicated the thesis that there are -- or that we can rationally believe that there are -- mechanisms in the world that lead to the phenomena that we see. But Kant's theory of causality did not give primacy to any particular sector of being, to any particular set of mechanisms -- e.g., DNA, quantum processes, or whatnot. Hence, (wo)man cannot (rationally) "privilege" -- give epistemic priority to -- any particular sector of the cosmos when seeking to draw inferences about phenomena in the world.

N.B. But perhaps quantum processes (of some kind) are the foundation of "everything." I gather that some or many physicists and scientists think that this is the case. So do we now have, once again, a universal ontology? I think not. If such physicists and their spiritual allies are correct -- and I am definitely not in a position to challenge them -- their universal ontology is not an accessible ontology; i.e., we (and they) do not yet know how to use this alleged foundation of everything (e.g., quantum mechanics or whatnot) to explain how many or most phenomena in the world happen. (Perhaps in the fullness of time we will know how to do this, but we and the quantum theorists are not there yet.)

Juries in Japan?

An Associated Press report calls them "juries." Jury Duty 101: New courtroom for citizen participation shown, The Japan Times (online) (March 25, 2005).

A law journal article calls them "lay assessors." Kent Anderson & Mark Nolan, Lay Participation in the Japanese Justice System: A Few Preliminary Thoughts Regarding the Lay Assessor System (saiban-in seido) from Domestic Historical and International Psychological Perspectives, 37 Vanderbilt Journal of Transnational Law L. 935 (October, 2004).

Regardless of the label, Japan has resolved to implement a "mixed court" procedure that will have some of the attributes of the sort of trial by jury that is found here in the U.S. -- and, fairly said, relatively more of the attributes of some European systems that require the participation of both legally-trained judges and lay "assessors," or judges.

Anderson & Nolan write (footnotes omitted):

On May 21, 2004, the Japanese Diet passed an act creating a lay assessor system. ...

The key features of the new law include the following. First, in contested cases the panel will be composed of six lay members and three professional judges. For cases in which the defendant has confessed or does not dispute the charges, the panel will be made up of four lay persons and one professional judge. In both events, the panel will determine the verdict and sentence by a simple majority of all members, although at least one layperson and one judge must consent to the majority. The proceeding will apply to defendants accused of crimes where the maximum penalty is death or indefinite imprisonment with hard labor, or where the victim dies because of an intentional criminal act. ... Finally, the law provides that the procedure will come into force "within five years of its publication" - viz., by May 2009.

The AP report quoted (above) in The Japan Times (online) states:

They tried on the black robes, sat in the high-backed chairs, and asked about everything from what to wear to how long they'd be away from work. It was just the basics for Japan's opening day of Jury Duty 101.

Organized by the Justice Ministry, last week's seminar at a Tokyo courthouse offered the public its first chance to find out about jury trials being introduced as part of the country's most drastic judicial reforms since the war.

At present, courts only rely on panels of three judges.

The new system, expected to start by 2009, would let ordinary citizens be jurors, giving them the right to determine guilt or innocence in serious criminal cases.

Can revised rules of evidence (in Japan) be far behind?

On Quantum Computing

On quantum computing see Jacob West, The Quantum Computer: An Introduction (2000), including the following passage:

Although computers have become more compact and considerably faster in performing their task, the task remains the same: to manipulate and interpret an encoding of binary bits into a useful computational result. A bit is a fundamental unit of information, classically represented as a 0 or 1 in your digital computer. Each classical bit is physically realized through a macroscopic physical system, such as the magnetization on a hard disk or the charge on a capacitor. A document, for example, comprised of n-characters stored on the hard drive of a typical computer is accordingly described by a string of 8n zeros and ones. Herein lies a key difference between your classical computer and a quantum computer. Where a classical computer obeys the well understood laws of classical physics, a quantum computer is a device that harnesses physical phenomenon unique to quantum mechanics (especially quantum interference) to realize a fundamentally new mode of information processing.

In a quantum computer, the fundamental unit of information (called a quantum bit or qubit), is not binary but rather more quaternary in nature. This qubit property arises as a direct consequence of its adherence to the laws of quantum mechanics which differ radically from the laws of classical physics. A qubit can exist not only in a state corresponding to the logical state 0 or 1 as in a classical bit, but also in states corresponding to a blend or superposition of these classical states. In other words, a qubit can exist as a zero, a one, or simultaneously as both 0 and 1, with a numerical coefficient representing the probability for each state.

Megalomania about Evidence and Information

Judging by curricular offerings, law journal publications, endowed chairs, and similar matters, evidence and the law of evidence have relatively low standing in the elite sectors of the legal academic hierarchy in the US.

Evidence workers of the world unite and throw off your chains!

I am definitely not referring to your chains of inference or your inference networks.

Speak evidential (and uncertain) truth to power!

Tell certain academic bosses:

Bit is It!

Alternatively, tell the benighted but lawful powers-that-be:

Here is how [John Archibald Wheeler] explains it in one of his essays: every it [every particle, every field of force, even the space-time continuum itself] derives its function, its meaning, its very existence entirely even if in some contexts indirectly from the apparatus-elicited answers to yes-or-no questions, binary choices, bits. He nicely sums this all up in a colorful little expression: It from bit. (Heather Wax, Information technology raises new questions about everything: Information is everything and it is everywhere, Science & Technology News (archives))

Alternatively, tell those authoritative and authoritarian dummies:

Stapp states: "...I propose to break away from the cautious stance of the founders of quantum theory, and build a theory of reality by taking seriously what the incredible accuracy of the predictions of the formalism seems to proclaim, namely that nature is best understood as being built around knowings that enjoy the mathematical properties ascribed to them by quantum theory." According to Stapp, reality should be "recognized to be knowledge, rather than substantive matter.... (" Ph. Blanchard & A. JadczykA Way Out of the Quantum Trap, Introduction: Is Quantum Theory the Last Word?

If such inflammatory proclamations are too dangerous or too venturesome for your tastes, try saying instead:

The age of uncertainty is upon us -- and information and evidence are crucial players on the new world stage.

Also tell them that in this age of computer science it is increasingly apparent that although intuition is indispensable for dealing with uncertainty, intuition alone cannot unravel the mysteries of inconclusive evidence and uncertain inference and that thinking carefully about evidence and inference sometimes pays big dividends. (If you don't think so, consult the fuzzy logic that runs your camera.)

Speaking of fuzzy logic: Was Wheeler wrong to equate the problem (or process) of knowledge with the problem (or process) of making binary choices? If quantum processes are the paradigm of all uncertain knowledge, should we not think of the problem or process of knowledge as the problem or process of making choices among a continuum of possibilities? Isn't part of the allure of quantum computing the fact that quanta can assume not just two states but a multiplicity -- i.e., more than two (2) -- states? Quantum theorists, speak!

Simple History

See

P. Tillers, Legal History for a Dummy: A Comment on the Role of History in Judicial Interpretation of the Confrontation Clause

Corpus Delicti in Plures Partes Divisa Est in My Home Town

Much of the dismembered body of a murdered Jersey City Heights woman is still missing ...

...

"Apparently [her husband, the suspect] disposed of a portion of her," said Hudson County Prosecutor Edward DeFazio....

Josanna Saviono's ... head was found in a bowling bag and her feet and one arm were found in the home's attic crawl space...

...

The only body part found during [a] search [on Thursday last] was one verterbrae [sic] ...

...

Investigators believe that after Thursday's search, it is very unlikely that additional body parts will be found....

Michaelangelo Conte, Husband Got Rid of Remains, Cops Say, The Jersey Journal p. 1 (March 19, 2005).

Substantive Legal Rules and Preparation for Proof in Litigation

Litigators face an enormous array of possibilities when they engage in litigation.

See, e.g., my blog Is Proof in Litigation Predictable?: Some Obstacles to Systematic Assessment of Decisions about Proof in Litigation

They look not only to the immediate steps that might be taken but also to steps that might be taken after possible immediate steps, and these successor steps are also typically numerous.

See id.

Like chess players, litigators frequently must try to envision the possibilities to a depth of two, three, four, and more levels. (This is clearly not easy to do.)

See id.

If tools for the management of this complex activity are to be developed, it is necessary to spell out the ingredients of this complex activity.

The possibilities that litigators (imagine they) face in litigation are the result of a variety of factors. One of these factors is legal rules. This note attempts to spell out the role that certain types of legal rules play in decision making about proof in litigation.

The legal rules that play a role in lawyers' decision making in and about litigation and proof in litigation are of various kinds.

These legal rules that influence such decision making include substantive legal rules ("theories of liability"), affirmative defenses to substantive theories of liability, and procedural rules of various kinds.

Some substantive legal rules are primary substantive rules that either mandate or authorize the imposition of a legal remedy under various specified types of conditions. Legal professionals sometimes refer to these sorts of rules as "legal theories of liability."

There is another species of substantive rules. These rules create affirmative defenses or defenses in the nature of affirmative defenses. This species of substantive legal rules specifies the types of circumstances under which a set of conditions that is normally, or otherwise, sufficient for liability under some legal theory is overcome or defeated.

Procedural rules also figure in lawyers' decision making in and about litigation and proof in litigation. Many procedural rules are "interim" rules in the sense that many procedural rules specify whether and the manner in which further legal proceedings and further steps in litigation and proof may and may not be taken. Like substantive rules, procedural rules have definitions (whether precise or imprecise) that amount to requirements. These definitions, or requirements, or elements, specify the conditions under which some procedural step may (or may not) transpire. As in the case of substantive rules, each of these primary procedural rules is normally supplemented by a rule or rules that specify the kinds of circumstances or conditions -- the special conditions -- under which any authorization that flows from compliance with the requirements of a primary rules is defeated or overcome.

Interim procedural rules sometimes (but not always) include elements of substantive legal rules that may apply if a legal proceeding mutates into a final phase of adjudication such as a trial. Not all interim procedural rules have this forward-looking and substantive thrust, but in this meditation let's focus on procedural rules that govern proceedings prior to the final phase of adjudication on the merits and on interim procedural rules that do incorporate substantive rules that can in principle apply in a final phase of adjudication such as a trial. So here our focus will be on procedural rules such as those governing summary judgment in civil litigation and we will try to spell out how these sorts of procedural rules can affect or channel litigation and proof processes.

On this blog I have previously noted that proof in litigation involves both (i) the cognitive states (beliefs) of fact finders such as judges and jurors and (ii) the decisions, choices, or acts of such fact finders a/k/a decision makers. See Two Lawyers and a Judge Shape a Lawsuit (1:48. p.m., January 28, 2005). I also noted that actors such as trial lawyers present fact finders with evidence such as the testimony of witnesses in an effort to awaken certain cognitive states (beliefs about facts) and elicit certain decisions (e.g., verdicts) by such fact finders a/k/a decision makers. See A Witness, Two Lawyers, and a Trial Judge Form Some Beliefs, Make Some Statements, and Shape a Lawsuit (4:24 p.m., January 28, 2005)

Although it is useful to appreciate that forensic proof aims to influence both the cognitive states and the choices of fact finders such as jurors and judges, any adequate account of forensic proof should also help to explain which issues or questions become the frame of reference for the lawyerly and adversary battles over the fact finders' beliefs and choices. How does the legal process influence judgments about which beliefs and choices matter in processes such as litigation?

At trial -- in the final phase of factual adjudication -- substantive legal rules play a central role in determining which questions the fact finder must form beliefs and make decisions about. Even before trial, however, substantive legal rules can and normally do play an important role in determining the selection of issues for adjudication at trial. One way in which that happens is by the incorporation of substantive rules in interim procedural rules. Such interim procedural rules serve as gates that can open or close to certain kinds of substantive disputes and battles in later phases of legal proceedings such as trials. In the paragraphs that follow I sketch how "interim procedural rules with substantive content" perform this sort of gatekeeping function.

Consider some definitions and stipulations:

Legal Theory i = Legal Requirements for Liability under (Essential Legal Elements of) Legal Theory i

Affirmative Defense k to Legal Theory i = Legal Requirements (Essential Conditions) for Defeat of (Essential Elements for Overcoming) Liability under Legal Theory i

Proof (Disproof) of Legal Requirement, Condition, or Element = Evidence Showing an Event (Absence of any Event) Instantiating the Legal Requirement, Condition, or Element

Preliminary Proof (Disproof) of Legal Theory i = Provisional (Preliminary) Proof (Disproof) of Events Instantiating Some or All Essential Elements of Legal Theory i (Affirmative Defense k)

Final Proof (Disproof) of Legal Theory i = Final Proof (Disproof) of Events Instantiating Each Essential Element of Legal Theory i (Affirmative Defense k)

Final (Cognitive) Proof (Disproof) of Legal Theory i = Legally-Sufficient Degree of Persuasion (Strength of Belief) in Authorized Decision Maker of Occurrence (Non-Occurrence) of Events Instantiating Each Essential Element of Legal Theory i (Affirmative Defense k)

Final (Legal) Proof (Disproof) of Legal Theory i = Choice of Decision Maker to Declare Occurrence (Non-Occurrence) of Events Instantiating Each Essential Element of Legal Theory i (Affirmative Defense k)

The moral of the preceding definitional and conceptual story is relatively simple: whether a particular path to a possible final forensic battle -- to possible final proof or disproof of one particular set or sets of substantive legal requirements -- is open or closed frequently depends in part on the outcome of a preliminary skirmish or skirmishes about one or more of those substantive legal requirements, on the outcome of adversary attempts at preliminary proof and disproof of substantive legal requirements. But this simple insight is also basic: armed with this simple insight, it is possible for us to begin developing a tool (e.g. a visual tool), or a procedure, to depict how trial lawyers can organize some of their thinking about the relationship certain kinds of legal rules and the choice in and about proof in litigation that are available to trial lawyers who are engaged in litigation or contemplating the possibility of litigation.

Sample Space Ignorance, and the Nature of Investigation

If you find the logic of standard probability calculus compelling -- as I do -- AND if you are always unsure of your ground -- as I am -- AND if you believe -- as I do -- that fact investigation involves uncertainty, THEN you feel compelled to explain over and over -- and I do! -- why standard probability theory does not capture, or portray, the way thought moves when the mind is engaged in investigative discovery, in relatively radical forms of discovery.

Taking my cue from the thinking or suggestions some very enlightened people (e.g., Glenn Shafer, David Schum), in the past I have said (effectively) that standard probability theory cannot get into gear before and until there are defined hypotheses; one cannot speak meaningfully of the probability of a hypothesis {H|not-H} unless and until one has a hypothesis such as H in hand a/k/a in mind.

By surfing on the web I have found another phrase that describes the situation in which the investigator is engaged in hypothesis formation rather than hypothesis assessment:

sample space ignorance

See Michael James Smithson, Human Judgment and Imprecise Probabilities at SIPTA, Documentation on Imprecise Probability

In probability theory parlance, the sample space is the canvas on which are painted the possibilities that are to be assessed.

The point of this canvas metaphor: in some forms of investigation the possibilities that ought to be in play have not yet been drawn on the canvas, on the sample space, and investigators sometimes must busy themselves with activities that may lead to the drawing of lines that form pictures that may be worth both further thought, deliberation, investigation, and assessment.

Piggish Probabilities

Law teachers sometimes complain that probability theory and mathematical probabilities are too precise and objective for the law. Well let them -- such law teachers, that is -- let such legal scholars consider the possibility of throwing roly poly pigs into the forensic stew!:

Pigs Akilter

and (last picture on page):

Another Random Pig!

N.B. If the pig lands on its snout the player gets ten (10) points, but if the pig lands on its back the player gets only five (5) points. So can we conclude that the probability of a pig on its back is exactly twice as great as the probability of a pig on its snout? (Would you bet your life on it?)