Abstracts
If the law embodies a culture of implicity, logic’s orientation displays an enthusiasm for the explicit. Logicians put a premium on precision and exactitude, and they reserve a special place for definitions, both biconditional and implicit. It has a considerable bearing on the two-solitudes phenomenon that, for over a century, mainstream logic has been part of mathematics. As the name suggests, mathematical logic serves the interests of mathematics, and its methods are themselves imbued with richly mathematical content. Certainly it would take only the most monomaniacal of mathematical logicians to propose that the logic of legal reasoning is a Boolean lattice or that the secrets of legal relevance are best revealed in a possible worlds semantics for relevant logic. But logic has come a long way in the past 40 years, spurred by developments in computer science, AI, logic programming, dynamic and deontic logics and logics of practical reasoning in which there have been repeated attempts to reconnect with human reasoning in real-life situations. Any number of successes (or partial successes) have already been claimed by theorists working in what collectively has been called the New Logic. It is here that the two-solitudes phenomenon makes least sense, and it is here that prospects of rapprochement are at their best. In companion articles, we have recently explored the logical structure of probability in legal reasoning, as well as the abductive character of the criminal proof standard; In each case, we have attempted to bring to bear upon these legal issues resources from the New Logic. In the present essay we try our hand at relevance.
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(1997), 9 C. R. (5th) 1 (S. C. C.).
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R. v. Starr, [2000] 2 (S. C. C.) 144 at para. 242: “… it will be of great assistance for a jury if the trial judge situates the reasonable doubt standard approximately between [the] two standards.”
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To forestall confusion, what logicians recognize as “implicit” definitions, legal scholars would recognize as explicit definitions. A case in point is the implicit definition of the definite article afforded by Russell’s theory of descriptions ([Russell, 1905]). The theory defines ‘the’ by mapping sentences containing ‘the’ to equivalent sentences not containing ‘the’. Definitions implicit in this sense, Russell also calls “contextual”.
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For example, the use of mathematical induction in the proofs of many of the most important metatheorems.
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On this reading, probabilistic relevance has an unmistakable Wigmorean flavour. According to Wigmore, an “identiary fact” is relevant if it can be used to prove or counter a case’s factum probandum (Wigmore, 1983, 1104–1195).
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See here (James, 1941): “Why exclude any data which if admitted would change the apparent probabilities and hence serve, even to a slight degree, to aid the search for truth? Justice Holmes suggested one answer, it is ‘a concession to the shortness of life’ – and perhaps to the shortness of purse of harassed litigants. If any and all evidence may be admissible which … would operate to any extent to alter the apparent probability of some material proposition, the field of judicial inquiry in most cases would be unlimited. Trials would come to an end only by the exhaustion of lawyers’ ingenuity or client’s money, and the trial judge or jury might be overwhelmed and bewildered by the multiplicity of collaterial issues”.
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See also the Australian Law Reform Commission Report 26, Volume 1, Evidence (1985), section 11, Relevance (ALRC, 1985): “It may be concluded that two people, or groups, may have different, but equally rational, views of the relevance of a piece of evidence, depending on their prior experience and conceptions. In a jury case, the experience of jurors may be quite different from that of the trial judge, and consequently their assessment of ‘relevance’ and probative force may vary from his. Therefore, so long as a juror’s assessment of the probabilities in the case might be rationally affected by the proferred evidence, then it is relevant. The trial judge may be doubtful about the probative force of the evidence and yet should admit it because the jury may rationally assess probative force differently from the way he does. That does not mean the jury is acting irrationally or emotionally, but only that they are utilizing their own experience to supply and evaluate appropriate hypotheses of proof.”
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In the legal literature, the having-a-bearing notion of relevance is developed in, e.g., Wills (1938).
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It is interesting that notwithstanding his earlier work on topical relevance, Walton’s discussion of relevance in the law in Walton, (2002) overlooks the factor of materiality. (It is mentioned in passing on p. 20 as one of Wigmore’s conditions on relevance.)
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The tightness of the tie of relevant to materiality is resisted by some writers. According to (Eggleston, 1970, p. 59), “[t]o attempt to confine the evidence to transactions or facts in issue and the surrounding details of those transactions and facts is to exclude some evidence of strong probative value. Unless the definition of ‘surrounding details’ is widened in such a way as to include any facts having logical probative value, then the expression becomes meaningless.”
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The notorious claim of Sextus Empiricus that all valid arguments are question-begging arises from confusing question-begging with circularity.
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If we tell you that we greatly disagree with him, we are not confronting you, since we are not expressing this agreement with you, and we are not confronting him because we are not even addressing him.
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A recent example of how the excessive dialecticization of concepts can lead us astray is Douglas Walton’s demonstration of the difference between probability and plausibility. It is part of the dialectical character of probability that “if you claim that a proposition is probably true, then there is a burden of proof attached …” (Walton, 2002, p. 110). On the other hand, “if you only [sic] claim that a proposition is plausibly true, there is no burden of proof attached.” (p. 110). Since “the dialectical requirements for the reasonable acceptance of the two kinds of speech acts are quite difference” (110), then the two concepts are not the same. We think that we are not alone in seeing two difficulties with this account. First, whether or not one create a burden of proof for oneself in uttering “P’ depends on whether in so doing one asserts something challengable. (“I feel depressed” and “My name is Johan van den Boten” make assertions, but typically they are not challengeable.) Walton thinks that it is intrinsic to utterances of “Probably P” that a challengeable assertion is made, and that intrinsic to utterances of “Plausibly P” that no such assertion is made. Nowhere in the empirical record of actual speech is any such suggestion upheld. But, secondly, even if Walton were right about this, it would have done nothing to demonstrate that when “possibly” occurs in these contexts, it is, as Walton also avers, statistical probability that is at work. (See below).
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The same is also true of a slender minority of lawyers. Alluding to FRE 401’s characterization of probabilistic relevance, (Dejnoska, 2004) has it that “FRE 401 … leaves probability undefined. And if FRE 401 is uninterpreted, it is useless ... The whole question is what probability is in the first place. The fundamental task of probability is to answer that question. Aristotle, Venn, Keynes, Ramsey, Mises, and Reichenbach all agree that probability is the obscure and basic notion needing explanation. But FRE 401 goes in the opposite direction and defines relevance in terms of probability”.
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Keynes’ approach to probability is discernible in Lempert (1977) discussion of logical relevance.
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By these lights, it is a considerable virtue of (Walton, 2002) to emphasize the dominance of plausibilities over aleatory probabilities in legal proceedings. See Chapters 4 and 6.
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See also Learned Hand: “[Evidence’s] relevancy really did not, and indeed could not, demand that it be conclusive; most convictions result from the accumulation of bits of proof which taken singly would not be enough in the mind of a fair-minded person. All that is necessary, and all that is possible, is that each bit may have enough rational connection with the issue to be considered a factor contributing to an answer.” (US v Pugliese 153 F 2d 497, 500 (1945))
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For helpful advice and information, or other forms of support, we warmly thank Dale Jacquette, Ori Simchen, Andrew Jones, Steven Wexler, Andrew Irvine, S. Bradley Armstrong QC, C.L. Woods and K.A. Woods. Research for this essay was supported by the Engineering and Physical Sciences Research Council of the United Kingdom and the Faculty of Arts in the University of British Columbia. We are most grateful for this assistance.
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Gabbay, D.M., Woods, J. (2010). Relevance in the Law. In: Gabbay, D., Canivez, P., Rahman, S., Thiercelin, A. (eds) Approaches to Legal Rationality. Logic, Epistemology, and the Unity of Science, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9588-6_12
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