Academic journal article Notre Dame Law Review

# Death of Paradox: The Killer Logic beneath the Standards of Proof

Academic journal article Notre Dame Law Review

# Death of Paradox: The Killer Logic beneath the Standards of Proof

## Article excerpt

The prevailing but contested view of proof standards is that fact-finders should determine facts by probabilistic reasoning. Given imperfect evidence, they first should ask themselves what they think the chances are that the burdened party would be right were the truth to become known, and they then should compare those chances to the applicable standard of proof.

I contend that for understanding the standards of proof the modern versions of logic--in particular, fuzzy logic and belief functions--work better than classical logic and probability theory. This modern logic suggests that fact-finders first assess evidence of an imprecisely perceived and described reality to form a fuzzy degree of belief in a fact's existence, and they then apply the standard of proof by comparing their belief in a fact's existence to their belief in its negation.

This understanding nicely explains how the standard of proof actually works in the law world. While conforming more closely to what we know of people's cognition, the new understanding captures better how the law formulates and manipulates the standards and it also gives a superior mental image of the fact-finders' task. One virtue of this conceptualization is that it is not a radical reconception. Another virtue is that it nevertheless manages to resolve some stubborn problems of proof including the infamous conjunction paradox.

```TABLE OF CONTENTS

INTRODUCTION

I. ASSESSING EVIDENCE
A. Theories
1. Psychology Theories
2. Probablity Theories
3. Zadeh's Fuzzy Logic
B. Legal Application: Oradated Likelihood

II. COJOINING ASSESSMENTS
A. Fuzzy Operators
1. Maximum and Minimum
2. Product Rule Contrasted
3. Negation Operator
B. Legal Application: Conjunction Paradox

III. ANALYZING BELIERS
A. Shafer's Belief Functions
1. Basics of Theory
2. Negation Operator
3. Lack of Proof
B. Legal Application: Burden of Production

IV. APPLYING STANDARDS
A. Comparison of Beliefs
B. Legal Application: Burden of Persuasion
2. Reformulated View
3. Implications of Reformulation

CONCLUSION
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Le seul veritable voyage, le seul bain de Jouvence, ce ne serait pas d'aller vers de nouveaux paysages, mais d'avoir d'autres yeux, de voir l'univers avec les yeux d'un autre, de cent autres **

INTRODUCTION

We have made tremendous strides, albeit only recently, toward understanding the process of proof. The wonderful "new evidence" scholarship has made especial progress by shifting the focus of evidence scholarship from rules of admissibility to the nature of proof, while opening the door to interdisciplinary insights, including those from psychology. (1) Yet the new work has tended to remain either too wedded or overly hostile to subjective probabilities for evaluating evidence (2) and to Bayes' theorem for combining evidence, (3) and so caused the debates to become "unproductive and sterile." (4) In any event, the debates have left unsolved some troubling problems and paradoxes in our law on proof.

The "New Logic"

One specific diagnosis of this shortcoming is that the new evidence tended to neglect the contemporaneous advances in logic. (5) The new, so-called nonclassical logic looks and sounds much like standard logic but refuses to accept some critical assumptions. (6) Most commonly, the assumption rejected is that every proposition must either be true or be false, an assumption called the principle of bivalence. But if propositions are not bivalent, so that both P and not P can be true and false to a degree, then one can show that sometimes P equals not P--which is a rather disquieting contradiction. (7) Fashioning the new logic thus faced some challenges in its development.

The first move in the new logic of special interest to lawyers relates to and builds on the branch of modern philosophy, beginning with Bertrand Russell's work, that struggled with the problem of vagueness. …

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