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)

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)

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)

An introduction to philosophical research on the standards of legal proof.

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 debate on the ethical permissibility of autonomous weapon systems (AWS) is deadlocked. It could therefore benefit from a differentiated assignment of the burden of proof. This is because the discussion is not purely philosophical in nature, but has a legal and security policy component and aims to avoid the most harmful outcomes of an otherwise unchecked development. Opponents of a universal AWS ban must clearly demonstrate that AWS comply with the Law of Armed Conflict (LOAC). This requires extensive (...) testing of specific models to verify compliance in realistic combat situations; working on appropriate testing regimes is also one of the most important future tasks for AWS ethics. In this context, however, it is easy to refute the claim put forward by prohibitionists that AWS violate LOAC a priori. A state’ s right to ensure security and the protection of human rights through military capacity has a high ethical value. Other arguments against the use of AWS that are not based on LOAC conformity must therefore meet a substantial burden of proof, as they call on governments to abandon a military technology which is at least potentially transformative. None of those objections meet this standard. They include not only culturally or even individually divergent norms and ideas regarding the use of weapons, but also consequentialist (security policy) concerns on the one hand and so-called deontological arguments on the other. While the former at least point to the need for essential regulation, the latter are based on rather dubious premises. For the purposes of solutions beneficial to humanity, prohibitionist should formulate narrower and more specific points of criticism. (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)

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)

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)

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 and considers what justifies them. Second, it discusses whether we should use different standards in different cases. Third, it asks whether trials should end only in binary outcomes (e.g. guilty or not guilty) or rather use more fine-grained or precise verdicts. Fourth, it considers whether proof is simply about probability, concentrating on the famous 'Proof Paradox'. Finally, it examines who should be trusted with deciding trials, focusing on the jury system. (shrink)

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)

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 that the ‘preponderance’ standard is satisfied if the evidence adduced renders the litigated claim more likely than not. On this view, I argue, ‘she said, he said’ cases satisfy the ‘preponderance’ standard. But this consequence conflicts with plausible liberal and feminist claims. In this essay I contrast the ‘she said, he said’ paradox with legal epistemology’s proof paradox. I explain how both paradoxes arise from the distinction between individualised and non-individualised evidence, and I critically evaluate responses to the ‘she said, he said’ paradox. (shrink)

Abstract: When do we meet the standard of proof in a criminal trial? Some have argued that it is when the guilt of the defendant is sufficiently probable on the evidence. Some have argued that it is a matter of normic support. While the first view provides us with a nice account of how we ought to manage risk, the second explains why we shouldn’t convict on the basis of naked statistical evidence alone. Unfortunately, this second view doesn’t (...) help us understand how we should manage risk (e.g., the risk of violating rights against wrongful conviction) and faces counterexamples of its own. I shall defend an alternative approach that builds on the strengths of these two accounts. On the approach defending here, it is objectively suitable to punish iff we know a defendant to be guilty. To determine what is consistent with procedural justice and to determine what we prospectively ought to do, we need to think about the risks we face of deviating from this objective ideal. (shrink)

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.

Sentencing outcomes turn on moral and evaluative determinations. For example, a finding of “irreparable corruption” is generally a precondition for juvenile life without parole. A finding that the “aggravating factors outweigh the mitigating factors” determines whether a defendant receives the death penalty. Should such moral determinations that expose defendants to extraordinary penalties be subject to a standard of proof? A broad range of federal and state courts have purported to decide this issue “in the abstract and without reference (...) to our sentencing case law,” as the Supreme Court recently put it. Kansas v. Carr, 577 U.S. 108, 119 (2016). According to these courts, “it would mean nothing” to ask whether the defendant “deserves mercy beyond a reasonable doubt” or “more-likely-than-not deserves it” because moral questions are not “factual.” Instead, moral determinations are highly subjective “value calls” to which concepts of doubt and certainty do not intelligibly apply. -/- Implicit in these rulings is a controversial view of the nature of moral judgment. This Article traces the contours of the view and argues that it is out of step with the way the broader public thinks about morality and fails to address the issues defendants have raised. Courts should avoid wading into such controversial waters for two reasons. First, the judiciary has historically maintained neutrality on issues of significant public concern. Second, even if moral determinations are not factual, applying a standard of proof to at least some moral decisions at sentencing would change the outcome of the sentencer’s deliberations, and improve the legitimacy of the legal system. For the reasonableness of doubt depends on context; and moral questions—"are you certain the defendant deserves death?”—make salient the stakes relative to which a person should decide what to believe about ordinary empirical matters. On the resulting view, reasonable doubt in the final moral analysis is not just intelligible, but essential for correcting a bias in the structure of the bifurcated criminal trial that systematically disadvantages defendants: the tendency for de-contextualized "factual findings” in the guilt phase to control outcomes at sentencing. (shrink)

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 the Epistemic Project should meet. I then consider three recent epistemic accounts on which the standard is met when the evidence rules out modal risk (Pritchard 2018), normic risk (Ebert et al. 2020), or relevant alternatives (Gardiner 2019 2020). I argue that none of these accounts meets all the requirements. Finally, I offer reasons to be pessimistic about the prospects of having a successful epistemic explanation of the paradox. I suggest the discussion on the proof paradox would benefit from undergoing a ‘value-turn’. (shrink)

Is it right to convict a person of a crime on the basis of purely statistical evidence? Many who have considered this question agree that it is not, posing a direct challenge to legal probabilism – the claim that the criminal standard of proof should be understood in terms of a high probability threshold. Some defenders of legal probabilism have, however, held their ground: Schoeman (1987) argues that there are no clear epistemic or moral problems with convictions based (...) on purely statistical evidence, and speculates that our aversion to such convictions may be nothing more than an irrational bias. More recently, Hedden and Colyvan (2019, section VI) describe our reluctance to convict on the basis of purely statistical evidence as an ‘intuition’, but suggest that there may be no ‘in principle’ problem with such convictions (see also Papineau, forthcoming, section 6). In this paper, I argue that there is, in some cases, an in principle problem with a conviction based upon statistical evidence alone – namely, it commits us to a precedent which, if consistently followed through, could lead to the deliberate conviction of an innocent person. I conclude with some reflections on the idea that the criminal justice system should strive to maximise the accuracy of its verdicts – and the related idea that we should each strive to maximise the accuracy of our beliefs. (shrink)

The current industrial revolution is said to be driven by the digitization that exploits connected information across all aspects of manufacturing. Standards have been recognized as an important enabler. Ontology-based information standard may provide benefits not offered by current information standards. Although there have been ontologies developed in the industrial manufacturing domain, they have been fragmented and inconsistent, and little has received a standard status. With successes in developing coherent ontologies in the biological, biomedical, and financial domains, an (...) effort called Industrial Ontologies Foundry (IOF) has been formed to pursue the same goal for the industrial manufacturing domain. However, developing a coherent ontology covering the entire industrial manufacturing domain has been known to be a mountainous challenge because of the multidisciplinary nature of manufacturing. To manage the scope and expectations, the IOF community kicked-off its effort with a proof-of-concept (POC) project. This paper describes the developments within the project. It also provides a brief update on the IOF organizational set up. (shrink)

I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many have rejected this thesis because it seems to entail that defendants can be found liable solely on the basis of statistical evidence. I argue that this inference is invalid. I do so by developing a view, called Legal Causalism, that combines Thomson's (1986) causal analysis of evidence with recent work in formal theories of causal inference. On this view, legal standards of proof (...) can be reduced to probabilities, but deriving these probabilities involves more than just statistics. (shrink)

Recent attempts to resolve the Paradox of the Gatecrasher rest on a now familiar distinction between individual and bare statistical evidence. This paper investigates two such approaches, the causal approach to individual evidence and a recently influential (and award-winning) modal account that explicates individual evidence in terms of Nozick's notion of sensitivity. This paper offers counterexamples to both approaches, explicates a problem concerning necessary truths for the sensitivity account, and argues that either view is implausibly committed to the impossibility of (...) no-fault wrongful convictions. The paper finally concludes that the distinction between individual and bare statistical evidence cannot be maintained in terms of causation or sensitivity. We have to look elsewhere for a solution of the Paradox of the Gatecrasher. (shrink)

This note discusses three issues that Allen and Pardo believe to be especially problematic for a probabilistic interpretation of standards of proof: (1) the subjectivity of probability assignments; (2) the conjunction paradox; and (3) the non-comparative nature of probabilistic standards. I offer a reading of probabilistic standards that avoids these criticisms.

The emphasis on the limitations of objectivity, in specific guises and networks, has been a continuing theme of contemporary analytic philosophy for the past few decades. The popular sport of baiting feminist philosophers — into pointing to what's left out of objective knowledge, or into describing what methods, exactly, they would offer to replace the powerful objective methods grounding scientific knowledge — embodies a blatant double standard which has the effect of constantly putting feminist epistemologists on the defensive, on (...) the fringes, on the run.This strategy can only work if objectivity is transparent, simple, stable, and clear in its meaning. It most certainly is not. In fact, taking objectivity as a sort of beautiful primitive, self-evident in its value, and all-powerful in its revelatory power, requires careless philosophy, and the best workers in metaphysics, epistemology, and philosophy of science have made reworked definitions of objectivity absolutely central to their own projects. In fact, classic feminist concerns with exploring the impact of sex and gender on knowledge, understanding, and other relations between human beings and the rest of the world fall squarely within the sort of human and social settings thatare already considered central in most current analytic metaphysics, epistemology, and philosophy of science. I argue that the burden of proof is clearly on those who wish toreject the centrality and relevance of sex and gender to our most fundamental philosophical work on knowledge and reality. (shrink)

The current standard interpretation of Moore’s proof assumes Moore offers a solution to Kant’s famously posed problem of an external world, which Moore quotes at the start of his 1939 lecture “Proof of an External World.” As a solution to Kant’s problem, Moore’s proof fails utterly. Similarly, a second received interpretation imputes an aim of refuting metaphysical idealism that Moore’s proof does not at all achieve. This study departs from the received interpretations to credit Moore’s (...) stated aim for the proof Moore performed in his 1939 lecture that is to impose a counter-example to an explicitly stated presupposition of Kant’s famously posed problem of an external world. The outcome would therefore subvert Kant’s problem. There is not, however, any rival external world problem that Moore commends in place of Kant’s problem. (shrink)

This paper puts forward three critiques of pardo’s second-order proof rules thesis. The first criticism states that these rules are not suitable to guide the interpretation of standards of proof rules because they confuse matters of legal interpretation with matters of epistemology. The second criticism states that second-order proof rules are affected by the same indeterminacy problems they are designed to resolve, thereby rendering them unsuitable for the task they are purposely designed for. The third criticism renders (...) pardo’s proposal redundant. a reconceptualization of second-order proof rules is offered. (shrink)

Euclid's classic proof about the infinitude of prime numbers has been a standard model of reasoning in student textbooks and books of elementary number theory. It has withstood scrutiny for over 2000 years but we shall prove that despite the deceptive appearance of its analytical reasoning it is tautological in nature. We shall argue that the proof is more of an observation about the general property of a prime numbers than an expository style of natural deduction of (...) the proof of their infinitude. (shrink)

A proof P of a theorem T is transferable when a typical expert can become convinced of T solely on the basis of their prior knowledge and the information contained in P. Easwaran has argued that transferability is a constraint on acceptable proof. Meanwhile, a proof P is fixable when it’s possible for other experts to correct any mistakes P contains without having to develop significant new mathematics. Habgood-Coote and Tanswell have observed that some acceptable proofs are (...) both fixable and in need of fixing, in the sense that they contain nontrivial mistakes. The claim that acceptable proofs must be transferable seems quite plausible. The claim that some acceptable proofs need fixing seems plausible too. Unfortunately, these attractive suggestions stand in tension with one another. I argue that the transferability requirement is the problem. Acceptable proofs need only satisfy a weaker requirement I call “corrigibility”. I explain why, despite appearances, the corrigibility standard is preferable to stricter alternatives. (shrink)

Leibniz proposed the ‘Most Determined Path Principle’ in seventeenth century. According to it, ‘ease’ of travel is the end purpose of motion. Using this principle and his calculus method he demonstrated Snell’s Laws of reflection and refraction. This method shows that light follows extremal (local minimum or maximum) time path in going from one point to another, either directly along a straight line path or along a broken line path when it undergoes reflection or refraction at plane or spherical (concave (...) or convex) surfaces. The extremal time path avoided the criticism that Fermat’s least time path was subjected to, by Cartesians who cited examples of reflections at spherical surfaces where light took the path of longest time. Thereby it became the standard method of demonstration of Snell’s Laws. Ptolemy’s theorem is a fundamental theorem in geometry. A special case of it offers a method of finding the minimum sum of the two distances of a point from two given fixed points. We show in this paper that Leibniz’s calculus proof of Snell’s Laws violates Ptolemy’s theorem, whereby Leibniz’s proof becomes invalid. (shrink)

The universality assumption (“U”) that quantum wave states only evolve by linear or unitary dynamics has led to a variety of paradoxes in the foundations of physics. U is not directly supported by empirical evidence but is rather an inference from data obtained from microscopic systems. The inference of U conflicts with empirical observations of macroscopic systems, giving rise to the century-old measurement problem and subjecting the inference of U to a higher standard of proof, the burden of (...) which lies with its proponents. This burden remains unmet because the intentional choice by scientists to perform interference experiments that only probe the microscopic realm disqualifies the resulting data from supporting an inference that wave states always evolve linearly in the macroscopic realm. Further, the nature of the physical world creates an asymptotic size limit above which interference experiments, and verification of U in the realm in which it causes the measurement problem, seem impossible for all practical purposes if nevertheless possible in principle. This apparent natural limit serves as evidence against an inference of U, providing a further hurdle to the proponent’s currently unmet burden of proof. The measurement problem should never have arisen because the inference of U is entirely unfounded, logically and empirically. (shrink)

Over almost a half-century, evidence law scholars and philosophers have contended with what have come to be called the “Proof Paradoxes.” In brief, the following sort of paradox arises: Factfinders in criminal and civil trials are charged with reaching a verdict if the evidence presented meets a particular standard of proof—beyond a reasonable doubt, in criminal cases, and preponderance of the evidence, in civil trials. It seems that purely statistical evidence can suffice for just such a level (...) of certainty in a variety of cases where our intuition is that it would nonetheless be wrong to convict the defendant, or find in favor of the plaintiff, on merely statistical evidence. So, we either have to convict with statistical evidence, in spite of an intuition that this is unsettling, or else explain what (dispositive) deficiency statistical evidence has. -/- Most scholars have tried to justify the resistance to relying on merely statistical evidence: by relying on epistemic deficiencies in this kind of evidence; by relying on court practice; and also by reference to the psychological literature. In fact, I argue, the epistemic deficiencies philosophers and legal scholars allege are suspect. And, I argue, while scholars often discuss unfairness to civil defendants, they ignore a long history of relying on statistical evidence in a variety of civil matters, including employment discrimination, toxic torts, and market share liability cases. Were the dominant arguments in the literature to prevail, it would extremely difficult for plaintiffs to recover in a variety of cases. -/- The various considerations I advance lead to the conclusion that when it comes to naked statistical evidence, philosophers and legal scholars who argue for its insufficiency have been caught with their pants down. (shrink)

It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of these equivalences lies in the set existence principles that are necessary and sufficient to prove those theorems. In this article I analyse the role of set existence principles in reverse mathematics, and argue that they are best understood as closure conditions on the powerset (...) of the natural numbers. (shrink)

Definitions I presented in a previous article as part of a semantic approach in epistemology assumed that the concept of derivability from standard logic held across all mathematical and scientific disciplines. The present article argues that this assumption is not true for quantum mechanics (QM) by showing that concepts of validity applicable to proofs in mathematics and in classical mechanics are inapplicable to proofs in QM. Because semantic epistemology must include this important theory, revision is necessary. The one I (...) propose also extends semantic epistemology beyond the ‘hard’ sciences. The article ends by presenting and then refuting some responses QM theorists might make to my arguments. (shrink)

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 (...) and suggest a way to vindicate it. (shrink)

In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the (...) case for “n = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it. (shrink)

According to a widely held view in the philosophy of mathematics, direct inferential justification for mathematical propositions (that are not axioms) requires proof. I challenge this view while accepting that mathematical justification requires arguments that are put forward as proofs. I argue that certain fallacious putative proofs considered by the relevant subjects to be correct can confer mathematical justification. But mathematical justification doesn’t come for cheap: not just any argument will do. I suggest that to successfully transmit justification an (...) argument must satisfy specific standards, some of which are social. I contrast my view with Huemer’s inferential conservatism, which makes mathematical justification too easy to get. Although in this article I focus on mathematical inferential beliefs, the view on offer generalizes to other inferential beliefs. (shrink)

Martin Smith has recently proposed, in this journal, a novel and intriguing approach to puzzles and paradoxes in evidence law arising from the evidential standard of the Preponderance of the Evidence. According to Smith, the relation of normic support provides us with an elegant solution to those puzzles. In this paper I develop a counterexample to Smith’s approach and argue that normic support can neither account for our reluctance to base affirmative verdicts on bare statistical evidence nor resolve the (...) pertinent paradoxes. Normic support is, as a consequence, not a successful epistemic anti-luck condition. (shrink)

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. The puzzle is not, however, merely a legal one. Our unwillingness to base beliefs on statistical evidence is by no means limited to the courtroom, and is at odds with almost every general principle that epistemologists have proposed as to how we ought to manage our beliefs. (shrink)

The author revisits the Blue Bus Problem, a famous thought-experiment in law involving probabilistic proof, and presents simple Bayesian solutions to different versions of the blue bus problem. In addition, the author expresses his solutions in standard and visual formats, i.e. in terms of probabilities and natural frequencies.

Discusses the idea that legal proof should use variable standards rather than a single fixed threshold.

In this paper a theoretical definition that helps to explain how the logical structure of legal presumptions is constructed by applying the Carneades model of argumentation developed in artificial intelligence. Using this model, it is shown how presumptions work as devices used in evidentiary reasoning in law in the event of a lack of evidence to assist a chain of reasoning to move forward to prove or disprove a claim. It is shown how presumptions work as practical devices that may (...) be useful in cases in which there is insufficient evidence to prove the claim to an appropriate standard of proof. (shrink)

Medicine, like law, is a pragmatic, probabilistic activity. Both require that decisions be made on the basis of available evidence, within a limited time. In contrast to law, medicine, particularly evidence-based medicine as it is currently practiced, aspires to a scientific standard of proof, one that is more certain than the standards of proof courts apply in civil and criminal proceedings. But medicine, as Dr. William Osler put it, is an "art of probabilities," or at best, a (...) "science of uncertainty." One can better practice medicine by using other evidentiary standards in addition to the "scientific." To employ only the scientific standard of proof is inappropriate, if not impossible; furthermore, as this review will show, its application in medicine is fraught with bias. Evidence is information. It supports or undermines a proposition, whether a hypothesis in science, a diagnosis in medicine, or a fact or point in question in a legal investigation. In medicine, physicians marshal evidence to make decisions on how to best prevent, diagnose, and treat disease, and improve health. In law, courts decide the facts and render justice. Judges and juries assess evidence to establish liability, to settle custody and medical issues, and to determine a defendant's guilt or innocence. (shrink)

Retributive theories of punishment argue that punishing a criminal for a crime she committed is sufficient reason for a justified and morally permissible punishment. But what about when the state gets lucky in its decision to punish? I argue that retributive theories of punishment are subject to “Gettier” style cases from epistemology. Such cases demonstrate that the state needs more than to just get lucky, and as these retributive theories of punishment stand, there is no anti-luck condition. I’ll argue that (...) Gettier-style cases demonstrate an impermissible instance of punishment, even though they meet the conditions of retributive theories of punishment. Retributive theories are, therefore, too weak. The safety condition from epistemology provides the anti-luck condition needed for permissible punishment. I argue that two forms of retributivism, rights-forfeiture and what I call standard retributivism, are both subject to Gettier-style cases. Unlike the literature on standards of proof, this paper argues that safety is a condition on punishment itself, i.e., in all nearby possible worlds, the accuser must correctly accuse the convicted for the crime they actually committed. (shrink)

A Mathematical Review by John Corcoran, SUNY/Buffalo -/- Macbeth, Danielle Diagrammatic reasoning in Frege's Begriffsschrift. Synthese 186 (2012), no. 1, 289–314. ABSTRACT This review begins with two quotations from the paper: its abstract and the first paragraph of the conclusion. The point of the quotations is to make clear by the “give-them-enough-rope” strategy how murky, incompetent, and badly written the paper is. I know I am asking a lot, but I have to ask you to read the quoted passages—aloud if (...) possible. Don’t miss the silly attempt to recycle Kant’s quip “Concepts without intuitions are empty; intuitions without concepts are blind”. What the paper was aiming at includes the absurdity: “Proofs without definitions are empty; definitions without proofs are, if not blind, then dumb.” But the author even bollixed this. The editor didn’t even notice. The copy-editor missed it. And the author’s proof-reading did not catch it. In order not to torment you I will quote the sentence as it appears: “In a slogan: proofs without definitions are empty, merely the aimless manipulation of signs according to rules; and definitions without proofs are, if no blind, then dumb.”[sic] The rest of my review discusses the paper’s astounding misattribution to contemporary logicians of the information-theoretic approach. This approach was cruelly trashed by Quine in his 1970 Philosophy of Logic, and thereafter ignored by every text I know of. The paper under review attributes generally to modern philosophers and logicians views that were never espoused by any of the prominent logicians—such as Hilbert, Gödel, Tarski, Church, and Quine—apparently in an attempt to distance them from Frege: the focus of the article. On page 310 we find the following paragraph. “In our logics it is assumed that inference potential is given by truth-conditions. Hence, we think, deduction can be nothing more than a matter of making explicit information that is already contained in one’s premises. If the deduction is valid then the information contained in the conclusion must be contained already in the premises; if that information is not contained already in the premises […], then the argument cannot be valid.” Although the paper is meticulous in citing supporting literature for less questionable points, no references are given for this. In fact, the view that deduction is the making explicit of information that is only implicit in premises has not been espoused by any standard symbolic logic books. It has only recently been articulated by a small number of philosophical logicians from a younger generation, for example, in the prize-winning essay by J. Sagüillo, Methodological practice and complementary concepts of logical consequence: Tarski’s model-theoretic consequence and Corcoran’s information-theoretic consequence, History and Philosophy of Logic, 30 (2009), pp. 21–48. The paper omits definitions of key terms including ‘ampliative’, ‘explicatory’, ‘inference potential’, ‘truth-condition’, and ‘information’. The definition of prime number on page 292 is as follows: “To say that a number is prime is to say that it is not divisible without remainder by another number”. This would make one be the only prime number. The paper being reviewed had the benefit of two anonymous referees who contributed “very helpful comments on an earlier draft”. Could these anonymous referees have read the paper? -/- J. Corcoran, U of Buffalo, SUNY -/- PS By the way, if anyone has a paper that has been turned down by other journals, any journal that would publish something like this might be worth trying. (shrink)

In his 1827 work Rationale of Judicial Evidence, Jeremy Bentham famously argued against exclusionary rules such as hearsay, preferring a policy of “universal admissibility” unless the declarant is easily available. Bentham’s claim that all relevant evidence should be considered with appropriate instructions to fact finders has been particularly influential among judges, culminating in the “principled approach” to hearsay in Canada articulated in R. v. Khelawon. Furthermore, many scholars attack Bentham’s argument only for ignoring the realities of juror bias, admitting universal (...) admissibility would be the best policy for an ideal jury. This article uses the theory of epistemic contextualism to justify the exclusion of otherwise relevant evidence, and even reliable hearsay, on the basis of preventing shifts in the epistemic context. Epistemic contextualism holds that the justification standards of knowledge attributions change according to the contexts in which the attributions are made. Hearsay and other kinds of information the assessment of which rely upon fact finders’ more common epistemic capabilities push the epistemic context of the trial toward one of more relaxed epistemic standards. The exclusion of hearsay helps to maintain a relatively high standards context hitched to the standard of proof for the case and to prevent shifts that threaten to try defendants with inconsistent standards. (shrink)

We consider the complex interactions between rape culture and epistemology. A central case study is the consideration of a deferential attitude about the epistemology of sexual assault testimony. According to the deferential attitude, individuals and institutions should decline to act on allegations of sexual assault unless and until they are proven in a formal setting, i.e., a criminal court. We attack this deference from several angles, including the pervasiveness of rape culture in the criminal justice system, the epistemology of testimony (...) and norms connecting knowledge and action, the harms of tacit idealizations away from important contextual factors, and a contextualist semantics for 'knows' ascriptions. (shrink)

The doctrine of the Trinity is central to mainstream Christianity. But insofar as it posits “three persons” (Father, Son and Holy Spirit), who are “one God,” it appears as inconsistent as the claim that 1+1+1=1. -/- Much of the literature on “The Logical Problem of the Trinity,” as this has been called, attacks or defends Trinitarianism with little regard to the fourth century theological controversies and the late Hellenistic and early Medieval philosophical background in which it took shape. I argue (...) that this methodol- ogy, which I call “the Puzzle Approach,” produces obviously invalid arguments, and it is unclear how to repair it without collapsing into my preferred method- ology, “the Historical Approach,” which sees history as essential to the debate. I also discuss “mysterianism,” arguing that, successful or not, it has a different goal from the other approaches. I further argue that any solution from the His- torical Approach satisfies the concerns of the Puzzle Approach and mysterianism anyway. -/- I then examine the solution to the Logical Problem of the Trinity found in St. Gregory of Nyssa’s writings, both due to his place in the history of the doctrine, and his clarity in explicating what I call “the metaphysics of synergy.” I recast his solution in standard predicate logic and provide a formal proof of its consistency. I end by considering the possibilities for attacking the broader philosophical context of his defense and conclude that the prospects for doing so are dim. In any case, if there should turn out to be any problem with the doctrine of the Trinity at all, it will not be one of mere logical inconsistency in saying that “These Three are One.”. (shrink)

This article examines the domestic use of drones by law enforcement to gather information. Although the use of drones for surveillance will undoubtedly provide law enforcement agencies with new means of gathering intelligence, these unmanned aircrafts bring with them a host of legal and epistemic complications. Part I considers the Fourth Amendment and the different legal standards of proof that might apply to law enforcement drone use. Part II explores philosopher Wittgenstein’s notion of actional certainty as a means to (...) interpret citizens' expectations of privacy with regard to their patterns of movement over time. Part III discusses how the theory of actional certainty can apply to the epistemic challenge of determining what is a “reasonable” expectation of privacy under the law. This Part also investigates the Mosaic Theory as a possible reading of the Fourth Amendment. (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...) some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

The paper deals with the "deuteros plous", literally ‘the second voyage’, proverbially ‘the next best way’, discussed in Plato’s "Phaedo", the key passage being Phd. 99e4–100a3. The second voyage refers to what Plato’s Socrates calls his “flight into the logoi”. Elaborating on the subject, the author first (I) provides a non-standard interpretation of the passage in question, and then (II) outlines the philosophical problem that it seems to imply, and, finally, (III) tries to apply this philosophical problem to the (...) "ultimate final proof" of immortality and to draw an analogy with the ontological argument for the existence of God, as proposed by Descartes in his 5th "Meditation". The main points are as follows: (a) the “flight into the logoi” can have two different interpretations, a common one and an astonishing one, and (b) there is a structural analogy between Descartes’s ontological argument for the existence of God in his 5th "Meditation" and the "ultimate final proof" for the immortality of the soul in the "Phaedo". (shrink)

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of (...) growing computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

An annotated bibliography of legal epistemology.