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Exploring the proof paradoxes

Legal Theory 14 (4):281-309 (2008)

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  1. A unified theory of risk.Jaakko Hirvelä & Niall J. Paterson - forthcoming - Philosophical Quarterly.
    A novel theory of comparative risk is developed and defended. Extant theories are criticized for failing the tests of extensional and formal adequacy. A unified diagnosis is proposed: extant theories consider risk to be a univariable function, but risk is a multivariate function. According to the theory proposed, which we call the unified theory of risk, the riskiness of a proposition is a function of both the proportion and the modal closeness of the possible worlds at which the proposition holds. (...)
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  • The Philosophy of Legal Proof.Lewis Ross - 2024 - Cambridge University Press.
    Criminal courts make decisions that can remove the liberty and even life of those accused. Civil trials can cause the bankruptcy of companies employing thousands of people, asylum seekers being deported, or children being placed into state care. Selecting the right standards when deciding legal cases is of utmost importance in giving those affected a fair deal. This Element is an introduction to the philosophy of legal proof. It is organised around five questions. First, it introduces the standards of proof (...)
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  • The ranges of reasons and creasons.Clayton Littlejohn - 2023 - Asian Journal of Philosophy 2 (2):1-10.
    In this discussion, we look at three potential problems that arise for Whiting’s account of normative reasons. The first has to do with the idea that objective reasons might have a modal dimension. The second and third concern the idea that there is some sort of direct connection between sets of reasons and the deliberative ought or the ought of rationality. We can see that we might be better served using credences about reasons (i.e., creasons) to characterise any ought that (...)
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  • Just probabilities.Chad Lee-Stronach - 2024 - Noûs 58 (4):948-972.
    I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many reject this thesis because it appears to permit finding defendants liable solely on the basis of statistical evidence. To the contrary, I argue – by combining Thomson's (1986) causal analysis of legal evidence with formal methods of causal inference – that legal standards of proof can be reduced to probabilities, but that deriving these probabilities involves more than just statistics.
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  • Algorithmic Decision-making, Statistical Evidence and the Rule of Law.Vincent Chiao - forthcoming - Episteme.
    The rapidly increasing role of automation throughout the economy, culture and our personal lives has generated a large literature on the risks of algorithmic decision-making, particularly in high-stakes legal settings. Algorithmic tools are charged with bias, shrouded in secrecy, and frequently difficult to interpret. However, these criticisms have tended to focus on particular implementations, specific predictive techniques, and the idiosyncrasies of the American legal-regulatory regime. They do not address the more fundamental unease about the prospect that we might one day (...)
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  • The safe, the sensitive, and the severely tested: a unified account.Georgi Gardiner & Brian Zaharatos - 2022 - Synthese 200 (5):1-33.
    This essay presents a unified account of safety, sensitivity, and severe testing. S’s belief is safe iff, roughly, S could not easily have falsely believed p, and S’s belief is sensitive iff were p false S would not believe p. These two conditions are typically viewed as rivals but, we argue, they instead play symbiotic roles. Safety and sensitivity are both valuable epistemic conditions, and the relevant alternatives framework provides the scaffolding for their mutually supportive roles. The relevant alternatives condition (...)
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  • The Foundations of Criminal Law Epistemology.Lewis Ross - 2022 - Ergo: An Open Access Journal of Philosophy 9.
    Legal epistemology has been an area of great philosophical growth since the turn of the century. But recently, a number of philosophers have argued the entire project is misguided, claiming that it relies on an illicit transposition of the norms of individual epistemology to the legal arena. This paper uses these objections as a foil to consider the foundations of legal epistemology, particularly as it applies to the criminal law. The aim is to clarify the fundamental commitments of legal epistemology (...)
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  • Probability of Guilt.Mario Günther - manuscript
    In legal proceedings, a fact-finder needs to decide whether a defendant is guilty or not based on probabilistic evidence. We defend the thesis that the defendant should be found guilty just in case it is rational for the fact-finder to believe that the defendant is guilty. We draw on Leitgeb’s stability theory for an appropriate notion of rational belief and show how our thesis solves the problem of statistical evidence. Finally, we defend our account of legal proof against challenges from (...)
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  • Proof Paradoxes, Agency, and Stereotyping.Aness Kim Webster - 2021 - Philosophical Issues 31 (1):355-373.
    Philosophical Issues, Volume 31, Issue 1, Page 355-373, October 2021.
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  • Knowledge and Legal Proof.Sarah Moss - forthcoming - Oxford Studies in Epistemology.
    Existing discussions of legal proof address a host of apparently disparate questions: What does it take to prove a fact beyond a reasonable doubt? Why is the reasonable doubt standard notoriously elusive, sometimes considered by courts to be impossible to define? Can the standard of proof by a preponderance of the evidence be defined in terms of probability thresholds? Why is statistical evidence often insufficient to meet the burden of proof? -/- This paper defends an account of proof that addresses (...)
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  • Evidence, Risk, and Proof Paradoxes: Pessimism about the Epistemic Project.Giada Fratantonio - 2021 - International Journal of Evidence and Proof:online first.
    Why can testimony alone be enough for findings of liability? Why statistical evidence alone can’t? These questions underpin the “Proof Paradox” (Redmayne 2008, Enoch et al. 2012). Many epistemologists have attempted to explain this paradox from a purely epistemic perspective. I call it the “Epistemic Project”. In this paper, I take a step back from this recent trend. Stemming from considerations about the nature and role of standards of proof, I define three requirements that any successful account in line with (...)
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  • An Epistemic Objection to Racial Profiling.Alexandra Lloyd - forthcoming - Tandf: Social Epistemology:1-9.
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  • Justice in epistemic gaps: The ‘proof paradox’ revisited.Lewis Ross - 2021 - Philosophical Issues 31 (1):315-333.
    This paper defends the heretical view that, at least in some cases, we ought to assign legal liability based on purely statistical evidence. The argument draws on prominent civil law litigation concerning pharmaceutical negligence and asbestos-poisoning. The overall aim is to illustrate moral pitfalls that result from supposing that it is never appropriate to rely on bare statistics when settling a legal dispute.
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  • Profiling, Neutrality, and Social Equality.Lewis Ross - 2022 - Australasian Journal of Philosophy 100 (4):808-824.
    I argue that traditional views on which beliefs are subject only to purely epistemic assessment can reject demographic profiling, even when based on seemingly robust evidence. This is because the moral failures involved in demographic profiling can be located in the decision not to suspend judgment, rather than supposing that beliefs themselves are a locus of moral evaluation. A key moral reason to suspend judgment when faced with adverse demographic evidence is to promote social equality—this explains why positive profiling is (...)
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  • Civil liability and the 50%+ standard of proof.Martin Smith - 2021 - International Journal of Evidence and Proof 25 (3):183-199.
    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, (...)
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  • Legal proof and statistical conjunctions.Lewis D. Ross - 2020 - Philosophical Studies 178 (6):2021-2041.
    A question, long discussed by legal scholars, has recently provoked a considerable amount of philosophical attention: ‘Is it ever appropriate to base a legal verdict on statistical evidence alone?’ Many philosophers who have considered this question reject legal reliance on bare statistics, even when the odds of error are extremely low. This paper develops a puzzle for the dominant theories concerning why we should eschew bare statistics. Namely, there seem to be compelling scenarios in which there are multiple sources of (...)
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  • The “She Said, He Said” Paradox and the Proof Paradox.Georgi Gardiner - 2021 - In Jon Robson & Zachary Hoskins (eds.), The Social Epistemology of Legal Trials. Routledge.
    This essay introduces the ‘she said, he said’ paradox for Title IX investigations. ‘She said, he said’ cases are accusations of rape, followed by denials, with no further significant case-specific evidence available to the evaluator. In such cases, usually the accusation is true. Title IX investigations adjudicate sexual misconduct accusations in US educational institutions; I address whether they should be governed by the ‘preponderance of the evidence’ standard of proof or the higher ‘clear and convincing evidence’ standard. -/- Orthodoxy holds (...)
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  • Belief, Credence and Statistical Evidence.Davide Fassio & Jie Gao - 2020 - Theoria 86 (4):500-527.
    According to the Rational Threshold View, a rational agent believes p if and only if her credence in p is equal to or greater than a certain threshold. One of the most serious challenges for this view is the problem of statistical evidence: statistical evidence is often not sufficient to make an outright belief rational, no matter how probable the target proposition is given such evidence. This indicates that rational belief is not as sensitive to statistical evidence as rational credence. (...)
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  • Explaining the Justificatory Asymmetry between Statistical and Individualized Evidence.Renee Bolinger - 2021 - In Jon Robson & Zachary Hoskins (eds.), The Social Epistemology of Legal Trials. Routledge. pp. 60-76.
    In some cases, there appears to be an asymmetry in the evidential value of statistical and more individualized evidence. For example, while I may accept that Alex is guilty based on eyewitness testimony that is 80% likely to be accurate, it does not seem permissible to do so based on the fact that 80% of a group that Alex is a member of are guilty. In this paper I suggest that rather than reflecting a deep defect in statistical evidence, this (...)
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  • Recent work on the proof paradox.Lewis D. Ross - 2020 - Philosophy Compass 15 (6):e12667.
    Recent years have seen fresh impetus brought to debates about the proper role of statistical evidence in the law. Recent work largely centres on a set of puzzles known as the ‘proof paradox’. While these puzzles may initially seem academic, they have important ramifications for the law: raising key conceptual questions about legal proof, and practical questions about DNA evidence. This article introduces the proof paradox, why we should care about it, and new work attempting to resolve it.
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  • Rehabilitating Statistical Evidence.Lewis Ross - 2019 - Philosophy and Phenomenological Research 102 (1):3-23.
    Recently, the practice of deciding legal cases on purely statistical evidence has been widely criticised. Many feel uncomfortable with finding someone guilty on the basis of bare probabilities, even though the chance of error might be stupendously small. This is an important issue: with the rise of DNA profiling, courts are increasingly faced with purely statistical evidence. A prominent line of argument—endorsed by Blome-Tillmann 2017; Smith 2018; and Littlejohn 2018—rejects the use of such evidence by appealing to epistemic norms that (...)
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  • Proof Paradoxes and Normic Support: Socializing or Relativizing?Marcello Di Bello - 2020 - Mind 129 (516):1269-1285.
    Smith argues that, unlike other forms of evidence, naked statistical evidence fails to satisfy normic support. This is his solution to the puzzles of statistical evidence in legal proof. This paper focuses on Smith’s claim that DNA evidence in cold-hit cases does not satisfy normic support. I argue that if this claim is correct, virtually no other form of evidence used at trial can satisfy normic support. This is troublesome. I discuss a few ways in which Smith can respond.
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  • Justification, knowledge, and normality.Clayton Littlejohn & Julien Dutant - 2020 - Philosophical Studies 177 (6):1593-1609.
    There is much to like about the idea that justification should be understood in terms of normality or normic support (Smith 2016, Goodman and Salow 2018). The view does a nice job explaining why we should think that lottery beliefs differ in justificatory status from mundane perceptual or testimonial beliefs. And it seems to do that in a way that is friendly to a broadly internalist approach to justification. In spite of its attractions, we think that the normic support view (...)
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  • Belief in a Fallen World.Robert Pasnau - 2018 - Res Philosophica 95 (3):531-559.
    In an ideal epistemic world, our beliefs would correspond to our evidence, and our evidence would be bountiful. In the world we live in, however, if we wish to live meaningful lives, other epistemic strategies are necessary. Here I attempt to work out, systematically, the ways in which evidentialism fails us as a guide to belief. This is so preeminently for lives of a religious character, but the point applies more broadly.
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  • Legal Burdens of Proof and Statistical Evidence.Georgi Gardiner - 2018 - In David Coady & James Chase (eds.), Routledge Handbook of Applied Epistemology. New York: Routledge, Taylor & Francis Group.
    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 (...)
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  • La Verdad en el Gnosticismo.Clayton Littlejohn - 2016 - Análisis. Revista de Investigación Filosófica 3:217-241.
    Hay dos supuestos sobre el valor epistémico que guían las discusiones más recientes sobre éste. El primero es que hay algo bueno con respecto a la creencia verdadera. El segundo supuesto es que es posible que dos creencias difieran en su valor incluso si ambas creencias son igualmente correctas. El veritista tiene fácil explicar el primer supuesto, pero tiene más difícil explicar el segundo. Para explicarlo, el veritista tiene que mostrar que las creencias verdaderas pueden diferir en su valor porque (...)
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  • Truth, knowledge, and the standard of proof in criminal law.Clayton Littlejohn - 2020 - Synthese 197 (12):5253-5286.
    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). (...)
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  • The Truth in Gnosticism.Clayton Littlejohn - forthcoming - Análisis. Revista de Investigación Filosófica.
    The paper discusses some challenges to veritism, the view that the fundamental epistemic good is knowledge. It looks like the best way to meet these challenges might be to appeal to some of Sosa's ideas about the value of achievements, but I argue that the performance normativity framework only gives us part of what we want. What we need is a more radical break with the veritist approach. We need to embrace gnosticism, the view that knowledge is the fundamental epistemic (...)
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  • Between Probability and Certainty: What Justifies Belief.Martin Smith - 2016 - Oxford, GB: Oxford University Press UK.
    This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...)
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  • Belief, credence, and norms.Lara Buchak - 2014 - Philosophical Studies 169 (2):1-27.
    There are currently two robust traditions in philosophy dealing with doxastic attitudes: the tradition that is concerned primarily with all-or-nothing belief, and the tradition that is concerned primarily with degree of belief or credence. This paper concerns the relationship between belief and credence for a rational agent, and is directed at those who may have hoped that the notion of belief can either be reduced to credence or eliminated altogether when characterizing the norms governing ideally rational agents. It presents a (...)
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  • Statistical Evidence, Sensitivity, and the Legal Value of Knowledge.David Enoch, Levi Spectre & Talia Fisher - 2012 - Philosophy and Public Affairs 40 (3):197-224.
    The law views with suspicion statistical evidence, even evidence that is probabilistically on a par with direct, individual evidence that the law is in no way suspicious of. But it has proved remarkably hard to either justify this suspicion, or to debunk it. In this paper, we connect the discussion of statistical evidence to broader epistemological discussions of similar phenomena. We highlight Sensitivity – the requirement that a belief be counterfactually sensitive to the truth in a specific way – as (...)
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  • Statistical evidence and algorithmic decision-making.Sune Holm - 2023 - Synthese 202 (1):1-16.
    The use of algorithms to support prediction-based decision-making is becoming commonplace in a range of domains including health, criminal justice, education, social services, lending, and hiring. An assumption governing such decisions is that there is a property Y such that individual a should be allocated resource R by decision-maker D if a is Y. When there is uncertainty about whether a is Y, algorithms may provide valuable decision support by accurately predicting whether a is Y on the basis of known (...)
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  • Corroboration.Georgi Gardiner - 2023 - American Philosophical Quarterly 60 (2):131-148.
    Corroborating evidence supports a proposition that is already supported by other initial evidence. It bolsters or confirms the original body of evidence. Corroboration has striking psychological and epistemic force: It potently affects how people do and should assess the target proposition. This essay investigates the distinctive powers of corroborating evidence. Corroboration does not simply increase the quantifiable probability of the adjudicated claim. Drawing on the relevant alternatives framework, I argue that corroboration winnows remaining uneliminated error possibilities. This illuminates the independence, (...)
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  • (1 other version)Criminal Proof: Fixed or Flexible?Lewis Ross - 2023 - Philosophical Quarterly (4):1-23.
    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, (...)
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  • Profiling and Proof: Are Statistics Safe?Georgi Gardiner - 2020 - Philosophy 95 (2):161-183.
    Many theorists hold that outright verdicts based on bare statistical evidence are unwarranted. Bare statistical evidence may support high credence, on these views, but does not support outright belief or legal verdicts of culpability. The vignettes that constitute the lottery paradox and the proof paradox are marshalled to support this claim. Some theorists argue, furthermore, that examples of profiling also indicate that bare statistical evidence is insufficient for warranting outright verdicts.I examine Pritchard's and Buchak's treatments of these three kinds of (...)
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  • In defence of the modal account of legal risk.Duncan Pritchard - 2022 - Synthese 200 (4):1-16.
    This paper offers an articulation and defence of the modal account of legal risk in light of a range of objections that have been proposed against this view in the recent literature. It is argued that these objections all trade on a failure to distinguish between the modal nature of risk more generally, and the application of this modal account to particular decision-making contexts, such as legal contexts, where one must rely on a restricted body of information. It is argued (...)
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  • When Does Evidence Suffice for Conviction?Martin Smith - 2018 - Mind 127 (508):1193-1218.
    There is something puzzling about statistical evidence. One place this manifests is in the law, where courts are reluctant to base affirmative verdicts on evidence that is purely statistical, in spite of the fact that it is perfectly capable of meeting the standards of proof enshrined in legal doctrine. After surveying some proposed explanations for this, I shall outline a new approach – one that makes use of a notion of normalcy that is distinct from the idea of statistical frequency. (...)
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  • Knowledge, Individualised Evidence and Luck.Dario Mortini - 2022 - Philosophical Studies 179 (12):3791-3815.
    The notion of individualised evidence holds the key to solve the puzzle of statistical evidence, but there’s still no consensus on how exactly to define it. To make progress on the problem, epistemologists have proposed various accounts of individualised evidence in terms of causal or modal anti-luck conditions on knowledge like appropriate causation, sensitivity and safety. In this paper, I show that each of these fails as satisfactory anti-luck condition, and that such failure lends abductive support to the following conclusion: (...)
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  • Decision-theoretic and risk-based approaches to naked statistical evidence: some consequences and challenges.Rafal Urbaniak, Alicja Kowalewska, Pavel Janda & Patryk Dziurosz-Serafinowicz - 2020 - Law, Probability and Risk 19 (1):67-83.
    In the debate about the legal value of naked statistical evidence, Di Bello argues that (1) the likelihood ratio of such evidence is unknown, (2) the decision-theoretic considerations indicate that a conviction based on such evidence is unacceptable when expected utility maximization is combined with fairness constraints, and (3) the risk of mistaken conviction based on such evidence cannot be evaluated and is potentially too high. We argue that Di Bello’s argument for (1) works in a rather narrow context, and (...)
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  • Trial by Statistics: Is a High Probability of Guilt Enough to Convict?Marcello Di Bello - 2019 - Mind 128 (512):1045-1084.
    Suppose one hundred prisoners are in a yard under the supervision of a guard, and at some point, ninety-nine of them collectively kill the guard. If, after the fact, a prisoner is picked at random and tried, the probability of his guilt is 99%. But despite the high probability, the statistical chances, by themselves, seem insufficient to justify a conviction. The question is why. Two arguments are offered. The first, decision-theoretic argument shows that a conviction solely based on the statistics (...)
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  • On the Normativity of Rationality and of Normative Reasons.Clayton Littlejohn & Julien Dutant - manuscript
    This paper is an early draft of something that we've polished up and posted above: n-1 Guilty Men. Check that one out, if interested.
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  • Safety vs. sensitivity: Possible worlds and the law of evidence.Michael S. Pardo - 2018 - Legal Theory 24 (1):50-75.
    ABSTRACTThis article defends the importance of epistemic safety for legal evidence. Drawing on discussions of sensitivity and safety in epistemology, the article explores how similar considerations apply to legal proof. In the legal context, sensitivity concerns whether a factual finding would be made if it were false, and safety concerns how easily a factual finding could be false. The article critiques recent claims about the importance of sensitivity for the law of evidence. In particular, this critique argues that sensitivity does (...)
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  • Meta-uncertainty and the proof paradoxes.Katie Steele & Mark Colyvan - 2023 - Philosophical Studies 180 (7):1927-1950.
    Various real and imagined criminal law cases rest on “naked statistical evidence”. That is, they rest more or less entirely on a probability for guilt/liability derived from a single statistical model. The intuition is that there is something missing in these cases, high as the probability for guilt/liability may be, such that the relevant standard for legal proof is not met. Here we contribute to the considerable debate about how this intuition is best explained and what it teaches us about (...)
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  • Norms of criminal conviction.Jennifer Lackey - 2021 - Philosophical Issues 31 (1):188-209.
    Philosophical Issues, Volume 31, Issue 1, Page 188-209, October 2021.
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  • Privacy rights and ‘naked’ statistical evidence.Lauritz Aastrup Munch - 2021 - Philosophical Studies 178 (11):3777-3795.
    Do privacy rights restrict what is permissible to infer about others based on statistical evidence? This paper replies affirmatively by defending the following symmetry: there is not necessarily a morally relevant difference between directly appropriating people’s private information—say, by using an X-ray device on their private safes—and using predictive technologies to infer the same content, at least in cases where the evidence has a roughly similar probative value. This conclusion is of theoretical interest because a comprehensive justification of the thought (...)
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  • Reconsidering the Rule of Consideration: Probabilistic Knowledge and Legal Proof.Tim Smartt - 2022 - Episteme 19 (2):303-318.
    In this paper, I provide an argument for rejecting Sarah Moss's recent account of legal proof. Moss's account is attractive in a number of ways. It provides a new version of a knowledge-based theory of legal proof that elegantly resolves a number of puzzles about mere statistical evidence in the law. Moreover, the account promises to have attractive implications for social and moral philosophy, in particular about the impermissibility of racial profiling and other harmful kinds of statistical generalisation. In this (...)
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  • Legal proof: why knowledge matters and knowing does not.Andy Mueller - 2024 - Asian Journal of Philosophy 3 (1):1-22.
    I discuss the knowledge account of legal proof in Moss (2023) and develop an alternative. The unifying thread throughout this article are reflections on the beyond reasonable doubt (BRD) standard of proof. In Section 1, I will introduce the details of Moss’s account and how she motivates it via the BRD standard. In Section 2, I will argue that there are important disanalogies between BRD and knowledge that undermine Moss’s argument. There is however another motivation for the knowledge account: combined (...)
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  • Standards and values.Matthew Kotzen - 2021 - Philosophical Issues 31 (1):167-187.
    Philosophical Issues, Volume 31, Issue 1, Page 167-187, October 2021.
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  • Bias and interpersonal skepticism.Robert Pasnau - 2022 - Noûs 56 (1):154-175.
    Recent philosophy has paid considerable attention to the way our biases are liable to encroach upon our cognitive lives, diminishing our capacity to know and unjustly denigrating the knowledge of others. The extent of the bias, and the range of domains to which it applies, has struck some as so great as to license talk of a new form of skepticism. I argue that these depressing consequences are real and, in some ways, even more intractable than has previously been recognized. (...)
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  • Can Self-determined Actions be Predictable?Amit Pundik - 2019 - European Journal of Analytic Philosophy 15 (2):121-140.
    This paper examines Lockie’s theory of libertarian self-determinism in light of the question of prediction: “Can we know (or justifiably believe) how an agent will act, or is likely to act, freely?” I argue that, when Lockie's theory is taken to its full logical extent, free actions cannot be predicted to any degree of accuracy because, even if they have probabilities, these cannot be known. However, I suggest that this implication of his theory is actually advantageous, because it is able (...)
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