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.

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

In the field of human rights, expressions like justice and legal reform are closely linked to the process of harmonization of domestic and international human rights standards. Harmonization of human rights standards can be described as a process wherein international human rights are incorporated or given full effect to at the domestic level. [i] To harmonize the two set of standards i.e. domestic and international is viewed as both a commitment and obligation of states under international law. [ii] In terms (...) of state practice, the process of harmonization may entail a set of actions including adoption of laws and creation of mechanisms for enforcement and redressal of violations. -/- At the international level, the harmonization agenda is actively promoted at forums including the Universal Periodic Review (UPR) or during consultations between states and human rights treaty bodies, etc. Questions on whether states are in compliance with their international human rights commitments under treaties and other resolutions are to a large extent determined based on the extent of harmonization. Other pertinent questions being whether existing domestic laws are compatible with international human rights standards? What conditions obstruct and facilitate harmonization of human rights standards? Are there any parameters to measure harmonization? -/- While harmonization is widely promoted, its study and assessment is complex. (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 lie detector test has long been treated with suspicion by the law. Recently, several authors have called this suspicion into question. They argue that the lie detector test may have considerable forensic benefits, particularly if we move past the classic, false-positive prone, autonomic nervous system-based (ANS-based) control question test, to the more reliable, brain-based, concealed information test. These authors typically rely on a “comparative advantage” argument to make their case. According to this argument, we should not be so suspicious (...) of lie detection evidence if it has comparative advantages over the epistemic methods currently utilised by the legal system. In this article, I add to this growing support by making a novel comparative advantage argument in favour of brain-based lie detection evidence. The argument focuses on the P300 concealed information test (P300 CIT), which has several unique properties, and on the effect it may have on pre-trial bargaining in criminal cases rather than in-court evidence. The thesis is that P300 CIT could allow for innocent defendants to credibly signal their innocence to investigators and prosecutors during pre-trial bargaining more effectively than current proposed methods for doing the same thing. I defend this argument from a number of objections, and suggest that it opens up an interesting avenue in the ongoing debate about the merits of this technology. Although the argument is presented with the criminal law in mind, it could form part of a more general cumulative case in favour of this technology. (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.

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)

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)

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)

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)

The current standard interpretation of Moore’s proof assumes he 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 would fail utterly. A second received interpretation imputes an aim of refuting metaphysical idealism that Moore’s proof does not at all achieve. This study departs from received interpretations to credit the aim (...) Moore announced for the proof Moore performed in his 1939 lecture. Moore’s aim was to impose a counter-example to a stated presupposition of Kant’s problem of an external world. Moore’s lecture nevertheless neither endorses a replacement for Kant’s problem nor acknowledges that an immediate implication of achieving his announced aim would subvert Kant’s famously posed problem of an external world. (shrink)

In recent years, the concept of “integrity” has been frequently discussed by scholars, and deployed by courts, in the domain of criminal procedure. In this paper, we are particularly concerned with how the concept has been employed in relation to the problem of the admissibility of evidence obtained improperly. In conceptualising and addressing this problem, the advocates of integrity rely on it as a standard of conduct for the criminal justice authorities and as a necessary condition for (...) the state authority to condemn and punish. We raise a series of challenges that need answering before integrity can perform these roles. Our aim is not to show that integrity is useless in normative theorising about the admissibility of evidence, and about the criminal process in general. Rather, it is to give guidance for the elaboration of a theory of integrity that is cogent, coherent, and has useful implications for the process of proof. (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)

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 United Nations Convention on the Rights of Persons with Disabilities (CRPD) is being used to argue for wider recognition of the legal capacity of people with mental disabilities. This raises a question about the implications of the Convention for attributions of criminal responsibility. The present paper works towards an answer by analysing the relationship between legal capacity in relation to personal decisions and criminal acts. Its central argument is that because moral and political considerations play an essential (...) role in setting the relevant standards, legal capacity in the context of personal decisions and criminal acts should not be thought of as two sides of the same coin. The implications of particular moral or political norms are likely to be different in these two legal contexts, and this may justify asymmetries in the relevant standards for legal capacity. However, the analysis highlights a fundamental question about how much weight moral or political considerations should be given in setting these standards, and this is used to frame a challenge to those calling for significantly wider recognition of the legal capacity of people with mental disabilities on the basis of the Convention. (shrink)

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)

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)

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.

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)

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)

The prosecution of international crimes is a challenge both under international and domestic law. Taking the example of international criminal law (ICL) , the fullest realization of its objectives is influenced by many factors including; (a) the adoption of appropriate laws by states, (b) the adequacy of the ICL framework on definitions of crimes and principles of criminal responsibility, (c) the level of political control and involvement in decision making related to investigation, prosecution or extradition, (d) Problems with (...) exclusion including restrictions on the rights of victims with regard to the proceedings and to reparation, and (e) The application of provisions for amnesties and similar measures of impunity. -/- Over the years, the mandate of States under ICL has expanded. Key reforms under ICL and domestic laws have been led by the above mentioned concerns. The scope of state obligations, in particular, has been shaped by the standards adopted under the ICL framework including the "duty to prosecute" international crimes. The article discusses the normative significance of the "duty to prosecute". (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)

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)

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)

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)

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.

US criminal courts have recently moved toward seeing juveniles as inherently less culpable than their adult counterparts, influenced by a growing mass of neuroscientific and psychological evidence. In support of this trend, this chapter argues that the criminal law’s notion of responsible agency requires both the cognitive capacity to understand one’s actions and the volitional control to conform one’s actions to legal standards. These capacities require, among other things, a minimal working set of executive functions—a suite of mental (...) processes, mainly realized in the prefrontal cortex, such as planning and inhibition—which remain in significant states of immaturity through late adolescence, and in some cases beyond. Drawing on scientific evidence of how these cognitive and volitional capacities develop in the maturing brain, the authors sketch a scalar structure of juvenile responsibility, and suggest some possible directions for reforming the juvenile justice system to reflect this scalar structure. (shrink)

Analysis is given of the Omega Point cosmology, an extensively peer-reviewed proof (i.e., mathematical theorem) published in leading physics journals by professor of physics and mathematics Frank J. Tipler, which demonstrates that in order for the known laws of physics to be mutually consistent, the universe must diverge to infinite computational power as it collapses into a final cosmological singularity, termed the Omega Point. The theorem is an intrinsic component of the Feynman-DeWitt-Weinberg quantum gravity/Standard Model Theory of Everything (...) (TOE) describing and unifying all the forces in physics, of which itself is also required by the known physical laws. With infinite computational resources, the dead can be resurrected--never to die again--via perfect computer emulation of the multiverse from its start at the Big Bang. Miracles are also physically allowed via electroweak quantum tunneling controlled by the Omega Point cosmological singularity. The Omega Point is a different aspect of the Big Bang cosmological singularity--the first cause--and the Omega Point has all the haecceities claimed for God in the traditional religions. -/- From this analysis, conclusions are drawn regarding the social, ethical, economic and political implications of the Omega Point cosmology. (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)

A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the preservation (...) of the standard meanings of the logical terms in all the admissible interpretations of the logical calculus, as it is proof-theoretically defined. Although classical first-order logic is sound and complete, its standard formalizations fall short to be full formalizations since they allow non-intended interpretations. This fact poses a challenge for the logical inferentialism program, whose main tenet is that the meanings of the logical terms are uniquely determined by the formal axioms or rules of inference that govern their use in a logical calculus, i.e., logical inferentialism requires a categorical calculus. This paper is the first part of a more elaborated study which will analyze the categoricity problem from its beginning until the most recent approaches. I will first start by describing the problem of a full formalization in the general framework in which Carnap (1934/1937, 1943) formulated it for classical logic. Then, in sections IV and V, I shall discuss the way in which the mathematicians B.A. Bernstein (1932) and E.V. Huntington (1933) have previously formulated and analyzed it in algebraic terms for propositional logic and, finally, I shall discuss some critical reactions Nagel (1943), Hempel (1943), Fitch (1944), and Church (1944) formulated to these approaches. (shrink)

How is the burden of proof to be distributed among individuals who are involved in resolving a particular issue? Under what conditions should the burden of proof be distributed unevenly? We distinguish attitudinal from dialectical burdens and argue that these questions should be answered differently, depending on which is in play. One has an attitudinal burden with respect to some proposition when one is required to possess sufficient evidence for it. One has a dialectical burden with respect to (...) some proposition when one is required to provide supporting arguments for it as part of a deliberative process. We show that the attitudinal burden with respect to certain propositions is unevenly distributed in some deliberative contexts, but in all of these contexts, establishing the degree of support for the proposition is merely a means to some other deliberative end, such as action guidance, or persuasion. By contrast, uneven distributions of the dialectical burden regularly further the aims of deliberation, even in contexts where the quest for truth is the sole deliberative aim, rather than merely a means to some different deliberative end. We argue that our distinction between these two burdens resolves puzzles about unevenness that have been raised in the literature. (shrink)

In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction (...) system of Wansing's bi-intuitionistic logic 2Int, which I will turn into a term-annotated form. Therefore, we need a type theory that extends to a two-sorted typed lambda-calculus. I will present such a term-annotated proof system for 2Int and prove a Dualization Theorem relating proofs and refutations in this system. On the basis of these formal results I will argue that this gives us interesting insights into questions about sense and denotation as well as synonymy and identity of proofs from a bilateralist point of view. (shrink)

Growing technological advances in intelligent artifacts and bitter experiences of the past have emphasized the need to use and operate ethics in this field. Accordingly, it is vital to discuss the ethical integrity of having intelligent artifacts. Concerning the method of gathering materials, the current study uses library and documentary research followed by attribution style. Moreover, descriptive analysis is employed in order to analyze data. Explaining and criticizing the opposing views in this field and reviewing the related literature, it is (...) concluded that the proof of the ethical integrity of the intelligent artifacts is possible due to the specific features of these artifacts and their own moral system. (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)

The reasonable person standard is key to both Criminal Law and Torts. What does and does not count as reasonable behavior and decision-making is frequently deter- mined by lay jurors. Hence, laypeople’s understanding of the term must be considered, especially whether they use it predominately in an evaluative fashion. In this corpus study based on supervised machine learning models, we investigate whether laypeople use the expression ‘reasonable’ mainly as a descriptive, an evaluative, or merely a value-associated term. We (...) find that ‘reasonable’ is predicted to be an evaluative term in the majority of cases. This supports prescriptive accounts, and challenges descriptive and hybrid accounts of the term—at least given the way we operationalize the latter. Interestingly, other expressions often used interchangeably in jury instructions (e.g. ‘careful,’ ‘ordinary,’ ‘prudent,’ etc), however, are predicted to be descriptive. This indicates a discrepancy between the intended use of the term ‘reasonable’ and the understanding lay jurors might bring into the court room. (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)