In discussions of standards of proof, a familiar perspective often emerges. According to what we call specificationism, standards of proof are legal rules that specify the quantum of evidence required to determine that a litigant’s claim has been proven. In so doing, they allocate the risk of error among litigants (and potential litigants), minimizing the risk of certain types of error. Specificationism is meant as a description of the way the rules actually function. We argue, however, (...) that its claims are either mistaken or at a minimum deeply misleading, especially when it comes to standard of proof rules (SPRs) that contain indeterminate formulas, as is typical. As against specificationism, we argue that SPRs are best understood as rules that confer competence to decide whether a given standard has been met—according to whatever vague or inchoate interpretation (if any) of the rule in question triers of fact implicitly or explicitly employ. We call this the competence-norm approach. (shrink)

Could it be right to convict and punish defendants using only statistical evidence? In this paper, I argue that it is not and explain why it would be wrong. This is difficult to do because there is a powerful argument for thinking that we should convict and punish defendants using statistical evidence. It looks as if the relevant cases are cases of decision under risk and it seems we know what we should do in such cases (i.e., maximize expected value). (...) Given some standard assumptions about the values at stake, the case for convicting and punishing using statistical evidence seems solid. In trying to show where this argument goes wrong, I shall argue (against Lockeans, reliabilists, and others) that beliefs supported only by statistical evidence are epistemically defective and (against Enoch, Fisher, and Spectre) that these epistemic considerations should matter to the law. To solve the puzzle about the role of statistical evidence in the law, we need to revise some commonly held assumptions about epistemic value and defend the relevance of epistemology to this practical question. (shrink)

According to Iris Murdoch, the chief experience in morality is the recognition of others, and this is the experience of loving attention. Love is an independent source of moral authority, distinct from the authority of reason. It is independent because it can be attained through moral experiences that are not certified by reason and cannot be achieved by rational deliberation. This view of love calls into question a cluster of concepts, such as rational agency and principled action, which figure prominently (...) in the Kantian characterization of the moral experience and resound through Kant’s account of virtue as an endured but never-ending struggle. But it would be a mistake to conclude that Murdoch’s philosophical project opposes Kant’s without further qualifications. In this chapter, I illustrate some convergence between Kant and Murdoch at the methodological level, in their polemic against reductivism. They both oppose reductivist empiricism on epistemological and moral grounds, because they define the standard of proof in relation to the experience of morality. In Murdoch’s words, the philosophical proof, if there is one, is the same as the moral proof (Murdoch 1997: 361). This is where Kant and Murdoch part ways. While Kant argues that the moral experience is the experience of the impact of reason, which provides self-discipline by constraint, Murdoch holds that the moral standard of proof is love. The transformative power of love allows us to engage with reality and recognize others for what they are, that in which consists the primal moral experience. Murdoch’s argument against Kant’s appeal to principles brings to the fore a crucial issue, which concerns the source of moral authority and the possibility of practical reason. Some of her most popular arguments against Kant are based on an oversimplified view of the impact of reason in moral life, and perhaps they owe part of their fortune to this oversimplification. I shall argue that such arguments miss their intended target, but I also hope to show that Murdoch sketches a distinctive model of the moral proof, which establishes a genuine alternative both to theories of practical reason and to reductivist accounts of the mind and its activities. (shrink)

According to a common conception of legal proof, satisfying a legal burden requires establishing a claim to a numerical threshold. Beyond reasonable doubt, for example, is often glossed as 90% or 95% likelihood given the evidence. Preponderance of evidence is interpreted as meaning at least 50% likelihood given the evidence. In light of problems with the common conception, I propose a new ‘relevant alternatives’ framework for legal standards of proof. Relevant alternative accounts of knowledge state that a (...) person knows a proposition when their evidence rules out all relevant error possibilities. I adapt this framework to model three legal standards of proof—the preponderance of evidence, clear and convincing evidence, and beyond reasonable doubt standards. I describe virtues of this framework. I argue that, by eschewing numerical thresholds, the relevant alternatives framework avoids problems inherent to rival models. I conclude by articulating aspects of legal normativity and practice illuminated by the relevant alternatives framework. (shrink)

According to Iris Murdoch, the chief experience in morality is loving attention. Her view calls into question the Kantian account of the standard of moral authority, and ultimately denies that reason might provide moral discernment, validate moral experience or drive us toward moral progress. Like Kant, Murdoch defines the moral experience as the subjective experience of freedom, which resists any reductivist approach. Unlike Kant, she thinks that this free agency is unprincipled. Some of her arguments are based on an oversimplified (...) account of Kant’s theory of reflective agency and discount the discipline of reason, thereby nullifying its practical import. However, Murdoch’s work offers a distinctive view of the standard of proof as a ‘moral proof’, which rehabilitates the transformative power of love and represents a genuine alternative to theories of practical reason as well as to reductivist empiricist views of the mind. (shrink)

The “beyond a reasonable doubt” standard of proof, currently used in criminal trials, is notoriously vague and undermotivated. This paper discusses two popular strategies for justifying our choice of a particular precise interpretation of the standard: the “ratio-to-standard strategy” identifies a desired ratio of trial outcomes and then argues that a certain standard is the one that we can expect to produce our desired ratio, while the “utilities-to-standard strategy” identifies utilities for trial outcomes and then argues that a certain (...) standard maximizes expected utility. I argue that both strategies fail on their own terms, by requiring us to perform calculations that we simply cannot perform. No version of either strategy can be performed by jurors or legislators in our actual epistemic position, in which, since we do not know which of the defendants in our trial system are genuinely innocent and which are genuinely guilty, we cannot determine the extent to which our trial system tends to produce evidence that misleadingly incriminates the innocent or misleadingly exonerates the guilty. But we would need to determine this in order to perform the calculations required by any possible version of the ratio-to-standard or utilities-to-standard strategies. I then suggest some empirical reasons to be pessimistic about the evidence produced by our actual trial system. The upshot is that the “beyond a reasonable doubt” standard lacks a clear interpretation and rationale, nor do we have a promising way to identify an alternative. This is the trouble with standards of proof. (shrink)

Legal reasoning on the requirements and application of law has been studied for centuries, but in this subject area the legal profession maintains predominantly the same stance it did in the time of the Ancient Greeks. There is a gap between the standards of proof, one which has been always demonstrated by percentages and in terms of the evaluation of these standards by percentages by mathematical or statistical methods. One method to fill the gap is Bayes theorem (...) that describes an event’s probability based on conditions that might be related to an event. Bayes theorem can help to establish or confirm a relation between facts and rules if there is sufficient other evidence that connect a party in a procedure with a considered legal action. (shrink)

The Article addresses three main questions. First: Why do some scholars and decision-makers take evidence assessment criteria as standards of proof and vice versa? The answer comes from the fact that some legal systems are more concerned with assessment criteria and others with standards; therefore jurists educated in different contexts tend to emphasize what they are more familiar with, and to assimilate to it what they are less familiar with. Second: Why do systems differ in those respects? (...) Here the answer stems from the historical, institutional and procedural differences that explain why some systems are more concerned with assessment criteria and others with standards of proof. And third, assuming that both criteria and standards are necessary to legal decision-making about facts: How can a system work if it neglects one of these things? Here the Article argues that there is a functional connection between criteria and standards. The functional connection account is distinguished from a functional equivalence account, and some systems and jurisdictions are referred to in greater detail to support the functional connection claim. (shrink)

For more than a half-century, evidence scholars have been exploring whether the criminal standard of proof can be grounded in decision theory. Such grounding would require the emergence of a social consensus about the utilities to be assigned to the four outcomes at trial. Significant disagreement remains, even among legal scholars, about the relative desirability of those outcomes and even about the formalisms for manipulating their respective utilities. We attempt to diagnose the principal reasons for this dissensus and to (...) suggest ways in which a broadly shared evaluation might be forged, both with respect to the appropriate equations for defining the standard of proof and with respect to the appropriate utilities to associate with the various trial outcomes. Where consensus cannot be forged, we hold that remaining differences can probably be finessed. We also suggest ways to elicit the utilities of individuals on these matters so as to avoid the usual flaws of such surveys. Along the way, we note a). the disproportionate role that the Blackstone ratio of errors continues to play in appraisals of the utilities of trial outcomes (despite its unintelligibility in the context of utilities) and b). the persisting belief -for which there is no theoretical basis-that every plausible assignment of utilities will inevitably result in a very high standard of proof. Finally, we examine some of the technical features associated with a proposed rank ordering of the utilities of trial outcomes. (shrink)

The paper provides a conceptual distinction between evidence assessment criteria and standards of proof. Evidence must be assessed in order to check whether it satisfies a relevant standard of proof, and the assessment is operated with some criterion; so both criteria and standards are necessary for fact-finding. In addition to this conceptual point, the article addresses three main questions: Why do some scholars and decision-makers take assessment criteria as standards of proof and vice versa? (...) Why do systems differ as to criteria and standards? How can a system work if it neglects one of these things? The answers to the first and second question come from the historical and procedural differences between the systems. The answer to the third focuses on the functional connection between criteria and standards. (shrink)

According to Iris Murdoch, the chief experience in morality is loving attention. Her view calls into question the Kantian account of the standard of moral authority, and ultimately denies that reason might provide moral discernment, validate moral experience, or drive us toward moral progress. Like Kant, Murdoch defines the moral experience as the subjective experience of freedom, which resists any reductivist approach. Unlike Kant, she thinks that this free agency is unprincipled. Some of her arguments are based on an oversimplified (...) account of Kant’s theory of reflective agency and discount the discipline of reason, thereby nullifying its practical import. However, Murdoch’s work offers a distinctive view of the standard of proof as a “moral proof”, which rehabilitates the transformative power of love and represents a genuine alternative to theories of practical reason as well as to reductivist empiricist views of the mind. (shrink)

In this paper I respond to Marcello Di Bello’s criticisms of the ‘normic account’ of the criminal standard of proof. In so doing, I further elaborate on what the normic account predicts about certain significant legal categories of evidence, including DNA and fingerprint evidence and eyewitness identifications.

The standard of proof applied in civil trials is the preponderance of evidence, often said to be met when a proposition is shown to be more than 50% likely to be true. A number of theorists have argued that this 50%+ standard is too weak – there are circumstances in which a court should find that the defendant is not liable, even though the evidence presented makes it more than 50% likely that the plaintiff’s claim is true. In this (...) paper, I will recapitulate the familiar arguments for this thesis, before defending a more radical one: The 50%+ standard is also too strong – there are circumstances in which a court should find that a defendant is liable, even though the evidence presented makes it less than 50% likely that the plaintiff’s claim is true. I will argue that the latter thesis follows naturally from the former once we accept that the parties in a civil trial are to be treated equally. I will conclude by sketching an alternative interpretation of the civil standard of proof. (shrink)

The evolution of the understanding of evidence-based proof and decision processes in the law, especially criminal law, and standards of proof in this area, has a long-standing and controversial history. Competing accounts cause the legal scholarship to engage in critical and thoughtful exchanges. Some of the divergent views reflect different methodological perspectives similarly recognized in other fields, such as applied psychology and economy, and the broader interdisciplinary research fields of judgment and decision-making, system analysis and decision science. (...) One such methodological perspective asserts that accounts of juridical proof should provide a description and explanation of how the legal system actually works as a whole. Other—more mathematical and analytical accounts—concentrate on how, ideally, legal decision-making under uncertainty ought to be made in order be considered sensible. This paper focuses on the relative plausibility account advocated by Professors Allen and Pardo as an example of the former perspective. Its logical structure and argumentative implications are analysed using elements of decision theory, which is the prime representative of the latter, more mathematical approach to legal proof. Using formal diagrammatic schemes to depict the structural relationships between the core elements of the two accounts, it is demonstrated in what sense they can be considered logically related and congruent. The demonstration shows that the principal disagreements among the proponents of the two examined theories derive from differences in the criteria used to judge the adequacy of competing accounts of legal decision-making, and the level of formalization of the bases of decisions in each candidate account. This structural analysis supports the view that adherence to one or the other of the examined perspectives does not imply a contradiction, but reflects the coverage of different aspects of the same overall decision architecture. Using decision-theoretic notions, our analyses also provide a way to explain RP decisions through an explicit criterion, thus providing a reply to the recurrent critique that RP theory lacks specific means to justify its decisional framework. (shrink)

I have two concerns about Pugh et al ’s case that vaccine requirements without a natural immunity exception are unjustified.1 First, the scientific question they suggest must be answered to justify the policy is in my view the wrong one, or at least not the only relevant one. Second, the authors set up a standard for public health regulation that will be often unattainable, risking paralysis of public health authorities. Pugh et al suggest two legitimate bases for vaccine mandates: ‘the (...) prevention of severe outcomes from COVID-19 and the reduction of viral transmission.’ Governments and employers have a legitimate interest in protecting the health of their citizens and workers, respectively. To maximally accomplish these goals, the relevant scientific question for whether people with prior infection should be subject to a vaccine mandate is: in persons who have been previously infected, does vaccination enhances protection against severe disease and/or infection and transmission? The relevant comparison, if one is trying to maximise protection in the population, is not vaccination vs prior infection, but vs prior infection alone. I am unaware of a systematic review of this question, but the answer in two recent studies appears to be that the combination is more protective.2,3 The comparison the authors propose, in contrast, seems to be one based on an unstated conception of fairness and adequacy: if vaccination alone provides some level of protection, and prior infection can’t be shown to provide an inferior level, then prior infection should be an acceptable alternative to vaccination to satisfy mandates. No argument is given to support the greater relevance of the comparison the authors emphasise. A second and independent concern is that the authors’ proposal …. (shrink)

Five errors that fit under the category of jumping to a conclusion are identified: (1) arguing from premises that are insufficient as evidence to prove a conclusion (2) fallacious argument from ignorance, (3) arguing to a wrong conclusion, (4) using defeasible reasoning without being open to exceptions, and (5) overlooking/suppressing evidence. It is shown that jumping to a conclusion is best seen not as a fallacy itself, but as a more general category of faulty argumentation pattern underlying these errors and (...) some related fallacies. (shrink)

The present article proceeds from the mainstream view that the conceptual framework underpinning adversarial systems of criminal adjudication, i.e. a mixture of common-sense philosophy and probabilistic analysis, is unsustainable. In order to provide fact-finders with an operable structure of justification, we need to turn to epistemology once again. The article proceeds in three parts. First, I examine the structural features of justification and how various theories have attempted to overcome Agrippa’s trilemma. Second, I put Inferential Contextualism to the test and (...) show that a defeasible structure of justification allocating epistemic rights and duties to all participants of an inquiry manages to dissolve the problem of scepticism. Third, I show that our epistemic practice already embodies a contextualist mechanism. Our problem was not that our Standard of Proof is inoperable but that it was not adequately conceptualized. Contextualism provides the framework to articulate the abovementioned practice and to treat ‘reasonable doubts’ as a mechanism which we can now describe in detail. The seemingly insurmountable problem with our efforts to define the concept “reasonable doubts” was the fact that we have been conflating the surface features of this mechanism and its internal structure, i.e. the rules for its use. (shrink)

The present article proceeds from the mainstream view that the conceptual framework underpinning adversarial systems of criminal adjudication, i.e. a mixture of common-sense philosophy and probabilistic analysis, is unsustainable. In order to provide fact-finders with an operable structure of justification, we need to turn to epistemology once again. The article proceeds in three parts. First, I examine the structural features of justification and how various theories have attempted to overcome Agrippa’s trilemma. Second, I put Inferential Contextualism to the test and (...) show that a defeasible structure of justification allocating epistemic rights and duties to all participants of an inquiry manages to dissolve the problem of scepticism. Third, I show that our epistemic practice already embodies a contextualist mechanism. Our problem was not that our Standard of Proof is inoperable but that it was not adequately conceptualized. Contextualism provides the framework to articulate the abovementioned practice and to treat ‘reasonable doubts’ as a mechanism which we can now describe in detail. The seemingly insurmountable problem with our efforts to define the concept “reasonable doubts” was the fact that we have been conflating the surface features of this mechanism and its internal structure, i.e. the rules for its use. (shrink)

The present article proceeds from the mainstream view that the conceptual framework underpinning adversarial systems of criminal adjudication, i.e. a mixture of common-sense philosophy and probabilistic analysis, is unsustainable. In order to provide fact-finders with an operable structure of justification, we need to turn to epistemology once again. The article proceeds in three parts. First, I examine the structural features of justification and how various theories have attempted to overcome Agrippa’s trilemma. Second, I put Inferential Contextualism to the test and (...) show that a defeasible structure of justification allocating epistemic rights and duties to all participants of an inquiry manages to dissolve the problem of scepticism. Third, I show that our epistemic practice already embodies a contextualist mechanism. Our problem was not that our Standard of Proof is inoperable but that it was not adequately conceptualized. Contextualism provides the framework to articulate the abovementioned practice and to treat ‘reasonable doubts’ as a mechanism which we can now describe in detail. The seemingly insurmountable problem with our efforts to define the concept “reasonable doubts” was the fact that we have been conflating the surface features of this mechanism and its internal structure, i.e. the rules for its use. (shrink)

The present article proceeds from the mainstream view that the conceptual framework underpinning adversarial systems of criminal adjudication, i.e. a mixture of common-sense philosophy and probabilistic analysis, is unsustainable. In order to provide fact-finders with an operable structure of justification, we need to turn to epistemology once again. The article proceeds in three parts. First, I examine the structural features of justification and how various theories have attempted to overcome Agrippa’s trilemma. Second, I put Inferential Contextualism to the test and (...) show that a defeasible structure of justification allocating epistemic rights and duties to all participants of an inquiry manages to dissolve the problem of scepticism. Third, I show that our epistemic practice already embodies a contextualist mechanism. Our problem was not that our Standard of Proof is inoperable but that it was not adequately conceptualized. Contextualism provides the framework to articulate the abovementioned practice and to treat ‘reasonable doubts’ as a mechanism which we can now describe in detail. The seemingly insurmountable problem with our efforts to define the concept “reasonable doubts” was the fact that we have been conflating the surface features of this mechanism and its internal structure, i.e. the rules for its use. (shrink)

In the first of a trilogy of articles published in the New England Journal of Medicine in May 2015, physician–journalist Lisa Rosenbaum observes that the crucial question regarding conflicts of interest between physicians and commercial industry is the extent to which interactions between the two are “beneficial or harmful to patients?”. She goes on to note that the answer to this question “depends on how you define harm,”1 and argues that many of the claims of harm flowing from COI are (...) incomplete, insufficient, or are based on “suggestive extrapolations from data”. If there are benefits to be gained from physician–industry relationships, and if the evidence... (shrink)

A common strategy in bioethics is to posit a prima facie case in favour of one policy, and to then claim that the burden of proof falls on those with opposing views. If the burden of proof is not met, it is claimed, then the policy in question should be accepted. This article illustrates, and critically evaluates, examples of this strategy in debates about the sale of organs by living donors, human enhancement, and the precautionary principle. We highlight (...) general problems with this style of argument, and particular problems with its use in specific cases. We conclude that the burden ultimately falls on decision-makers to choose the policy supported by the best reasons. (shrink)

In order to perform certain actions – such as incarcerating a person or revoking parental rights – the state must establish certain facts to a particular standard of proof. These standards – such as preponderance of evidence and beyond reasonable doubt – are often interpreted as likelihoods or epistemic confidences. Many theorists construe them numerically; beyond reasonable doubt, for example, is often construed as 90 to 95% confidence in the guilt of the defendant. -/- A family of influential (...) cases suggests standards of proof should not be interpreted numerically. These ‘proof paradoxes’ illustrate that purely statistical evidence can warrant high credence in a disputed fact without satisfying the relevant legal standard. In this essay I evaluate three influential attempts to explain why merely statistical evidence cannot satisfy legal standards. (shrink)

This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation, those of an equivalence relation, and other properties appropriate for an equality relation in linear logic. The guiding idea is that equality of proofs is induced by coherence, understood as the existence of a faithful functor from a syntactical category into a category whose arrows (...) correspond to diagrams. Edges in these diagrams join occurrences of variables that must remain the same in every generalization of the proof. It is found that assumptions about equality of proofs for equality are parallel to standard assumptions about equality of arrows in categories. They reproduce standard categorial assumptions on a different level. It is also found that assumptions for a preordering relation involve an adjoint situation. (shrink)

A common description of a mathematical proof is as a logically structured sequence of assertions, beginning from accepted premises and proceeding by standard inference rules to a conclusion. Does this description match the language of proofs as mathematicians write them in their research articles? In this chapter, we use methods from corpus linguistics to look at the prevalence of imperatives and instructions in mathematical preprints from the arXiv repository. We find thirteen verbs that are used most often to form (...) imperatives in proofs, and that these show up significantly more often within proofs than in the surrounding mathematical writing. We also show that there are many more verbs used to form a diverse selection of instructions in proofs. These findings are at odds with the view of proofs as sequences of assertions. Instead, we argue in favour of the recipe model of proofs: that proofs are like recipes, giving instructions for mathematical actions to be carried out. (shrink)

The notion of “the burden of proof” plays an important role in real-world argumentation contexts, in particular in law. It has also been given a central role in normative accounts of argumentation, and has been used to explain a range of classic argumentation fallacies. We argue that in law the goal is to make practical decisions whereas in critical discussion the goal is frequently simply to increase or decrease degree of belief in a proposition. In the latter case, it (...) is not necessarily important whether that degree of belief exceeds a particular threshold (e.g., ‘reasonable doubt’). We explore the consequences of this distinction for the role that the “burden of proof” has played in argumentation and in theories of fallacy. (shrink)

If proofs are nothing more than truth makers, then there is no force in the standard argument against classical logic (there is no guarantee that there is either a proof forA or a proof fornot A). The standard intuitionistic conception of a mathematical proof is stronger: there are epistemic constraints on proofs. But the idea that proofs must be recognizable as such by us, with our actual capacities, is incompatible with the standard intuitionistic explanations of the meanings (...) of the logical constants. Proofs are to be recognizable in principle, not necessarily in practice, as shown in section 1. Section 2 considers unknowable propositions of the kind involved in Fitch''s paradox:p and it will never be known thatp. It is argued that the intuitionist faces a dilemma: give up strongly entrenched common sense intuitions about such unknowable propositions, or give up verificationism. The third section considers one attempt to save intuitionism while partly giving up verificationism: keep the idea that a proposition is true iff there is a proof (verification) of it, and reject the idea that proofs must be recognizable in principle. It is argued that this move will have the effect that some standard reasons against classical semantics will be effective also against intuitionism. This is the case with Dummett''s meaning theoretical argument. At the same time the basic reason for regarding proofs as more than mere truth makers is lost. (shrink)

On the standard view, all presumptions share the same deontic function: they asymmetrically allocate the burden of proof. But what, exactly, does this function amount to? Once presumptions are rejected, do they place the burden of arguing, the burden of explanation, or the most general burden of reasoning on their opponents? In this paper, I take into account the differences between cognitive and practical presumptions and argue that the standard accounts of deontic function are at least ambiguous, and likely (...) implausible. As a result, they require qualifications. (shrink)

I discuss two types of evidential problems with the most widely touted experiments in evolutionary psychology, those performed by Leda Cosmides and interpreted by Cosmides and John Tooby. First, and despite Cosmides and Tooby's claims to the contrary, these experiments don't fulfil the standards of evidence of evolutionary biology. Second Cosmides and Tooby claim to have performed a crucial experiment, and to have eliminated rival approaches. Though they claim that their results are consistent with their theory but contradictory to (...) the leading non-evolutionary alternative, Pragmatic Reasoning Schemas theory, I argue that this claim is unsupported. In addition, some of Cosmides and Tooby's interpretations arise from misguided and simplistic understandings of evolutionary biology. While I endorse the incorporation of evolutionary approaches into psychology, I reject the claims of Cosmides and Tooby that a modular approach is the only one supported by evolutionary biology. Lewontin's critical examinations of the applications of adaptationist thinking provide a background of evidentiary standards against which to view the currently fashionable claims of evolutionary psychology. (shrink)

In this paper I criticize the current standards for the acceptability of expert testimony in current US legislation. The standards have been the subject of much academic literature after the Frye and Daubert cases. I expose what I call the Paradox of Proof, and argue that the historical and current standards have sidestepped the problem of determining who is an expert and who is not in a court of law. I then investigate the problem of recognizing (...) expertise from the layperson’s standpoint, and suggest what courses of action the future research ought to take on the problem of identifying expertise. (shrink)

In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not well-defined quantities in the 4D space-time and, contrary to the general belief, the usual Maxwell equations with the 3D E and B are not in agreement with the special relativity. The 4-vectors E a and B a , as well-defined 4D quantities, (...) are introduced instead of ill-defined 3D E and B. The proof is given in the tensor and the Clifford algebra formalisms. (shrink)

We present a formal, mathematical model of argument structure and evaluation, taking seriously the procedural and dialogical aspects of argumentation. The model applies proof standards to determine the acceptability of statements on an issue-by-issue basis. The model uses different types of premises (ordinary premises, assumptions and exceptions) and information about the dialectical status of statements (stated, questioned, accepted or rejected) to allow the burden of proof to be allocated to the proponent or the respondent, as appropriate, for (...) each premise separately. Our approach allows the burden of proof for a premise to be assigned to a different party than the one who has the burden of proving the conclusion of the argument, and also to change the burden of proof or applicable proof standard as the dialogue progresses from stage to stage. Useful for modeling legal dialogues, the burden of production and burden of persuasion can be handled separately, with a different responsible party and applicable proof standard for each. Carneades enables critical questions of argumentation schemes to be modeled as additional premises, using premise types to capture the varying effect on the burden of proof of different kinds of questions. (shrink)

Ferdinand Schoeman (1986) attempts to refute six arguments that I gave in The Probable and the Provable (1977, pp. 49-120) for not analyzing the standards of forensic proof in terms of any concept of probability that conforms to the familiar principles of the mathematical calculus of chance. But he evidently does not appreciate the strength of the case for rejecting the validity of any such analysis. In the course of discussing his criticisms, I shall add a seventh argument (...) to fortify my position, though I concede that the second of my original arguments has to be discarded. (shrink)

The standard of proof in criminal trials in many liberal democracies is proof beyond a reasonable doubt, the BARD standard. It is customary to describe it, when putting a number on it, as requiring that the fact finder be at least 90% certain, after considering the evidence, that the defendant is guilty. Strikingly, no good reason has yet been offered in defense of using that standard. A number of non-consequentialist justifications that aim to support an even higher standard (...) have been offered; all are morally unsound. Meanwhile, consequentialist arguments plausibly support a substantially lower standard — in some cases so low as to undermine the idea that punishment is what is at stake. In this paper, I offer a new retributive justification that supports excluding the instrumental benefits of punishment from the balance that sets the standard. The resulting balance supports a standard arguably in the ballpark of the customary understanding of BARD: a standard requiring that the fact finder have a high, though not maximally high, degree of confidence that the defendant is guilty. (shrink)

In the present paper we show that any at most countable linearly-ordered commutative residuated lattice can be embedded into a commutative residuated lattice on the real unit interval [0, 1]. We use this result to show that Esteva and Godo''s logic MTL is complete with respect to interpretations into commutative residuated lattices on [0, 1]. This solves an open problem raised in.

In a 2022 paper, Hamami claimed that the orthodox view in mathematics is that a proof is rigorous if it can be translated into a derivation. Hamami then developed a descriptive account that explains how mathematicians check proofs for rigor in this sense and how they develop the capacity to do so. By exploring introductory texts in computability theory, we demonstrate that Hamami’s descriptive account does not accord with actual mathematical practice with respect to computability theory. We argue instead (...) for an alternative account in which imagination, anticipation, and interpretations of natural language play roles in establishing mathematical rigor. (shrink)

The anti-tuberculosis BCG vaccine was conceived and developed between 1905 and 1921 at Pasteur Institutes in France. Between 1921 and A. Calmette’s death in 1933, the vaccine went through a first period of national and international production and distribution for its use in humans. In France these activities were exclusively carried out by Calmette and his collaborators at the Pasteur Institute in Paris. Initially improvised production in a small room in the cellar gave way in 1931 to the construction of (...) the spacious and magnificent ‘New laboratories for research on tuberculosis and the preparation of the BCG’ within the premises of the Pasteur Institute. Presentation and image-building of the vaccine in France insisted on the fact that the BCG was not a commercial specialty but distributed free of charge. The technical monopoly of its production nevertheless lay with the Paris Pasteur Institute and standardization of scientific proof of safety, efficacy and stability was dominated by that Institute in France. In contrast, the international production and distribution of the vaccine was entrusted and transferred, free of charge, to trustworthy laboratories outside France. Multiplication of producers and users led to an increased need for standardization. For this process the analysis distinguishes between the standardization of scientific proof concerning safety, efficacy and stability of the vaccine and standardization of its medical uses. Whereas standardization was rather successful in the inter-war period in France, the international efforts remained rather unsuccessful. Only after world war II under Scandinavian leadership and in the context of mass vaccination programs supported by the WHO and UNICEF was the international standardization effectively implemented and succeeded at least to some extend. (shrink)

Many legal disputes turn on scientific, especially statistical, evidence. Traditionally scientists have accepted only that statistical evidence which satisfies a 95 percent (or 99 percent) rule — that is, only evidence which has less than five percent (or one percent) probability of resulting from chance.The rationale for this rule is the reluctance of scientists to accept anything less than the best-supported new knowledge. The rule reflects the internal needs of scientific practice. However, when uncritically adopted as a rule for admitting (...) legal evidence, the seemingly innocuous 95 percent rule distorts the balance of interests historically protected by the legal system. In particular, plaintiffs in toxic tort and employment discrimination suits are effectively held to a heavier burden of proof in showing that their injuries were more probably than not caused by the defendant's actions. The result is that too many victims of toxic torts or employment discrimination cannot win legal redress for their injuries. (shrink)

Argues for a minimal level of quantification for the "proof beyond reasonable doubt" standard of criminal law: if a jury asks "Is 60% enough?", the answer should be "No.".

Should we use the same standard of proof to adjudicate guilt for murder and petty theft? Why not tailor the standard of proof to the crime? These relatively neglected questions cut to the heart of central issues in the philosophy of law. This paper scrutinises whether we ought to use the same standard for all criminal cases, in contrast with a flexible approach that uses different standards for different crimes. I reject consequentialist arguments for a radically flexible (...) standard of proof, instead defending a modestly flexible approach on non-consequentialist grounds. The system I defend is one on which we should impose a higher standard of proof for crimes that attract more severe punishments. This proposal, although apparently revisionary, accords with a plausible theory concerning the epistemology of legal judgments and the role they play in society. (shrink)

In recent years, new forms of transnational regulation have emerged, filling the void created by the failure of governments and international institutions to effectively regulate transnational corporations. Among the variety of initiatives addressing social and environmental problems, a growing number of certification systems have appeared in various sectors, particularly agrifood. Most initiatives rely on independent third-party certification to verify compliance with a standard, as it is seen as the most credible route for certification. The effects of third-party audits, however, still (...) need to be empirically investigated. This article provides a critical assessment of the notion of ‘evidence’ which is at the heart of auditing practices. It focuses on the case of the Roundtable on Sustainable Palm Oil (RSPO) and fieldwork carried out in Indonesia, the world’s largest producer of palm oil. In this country, some non-governmental organizations decided to participate in the RSPO in order to use this platform to tackle the issue of land conflicts. They managed to include important clauses regarding indigenous and land rights in the RSPO standard. In practice, however, auditors rarely recognize as valid evidence the forms of proof put forward by local communities. As a result, the whole process risks compounding local power imbalances. (shrink)