Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby (...) it provides foundations for accounts of defeasible or nonmonotonic reasoning. It has widespread applications in philosophy, it proves to be most useful in Artificial Intelligence, and it has started to find applications as a model of reasoning in psychology. (shrink)

There are currently two robust traditions in philosophy dealing with doxastic attitudes: the tradition that is concerned primarily with all-or-nothing belief, and the tradition that is concerned primarily with degree of belief or credence. This paper concerns the relationship between belief and credence for a rational agent, and is directed at those who may have hoped that the notion of belief can either be reduced to credence or eliminated altogether when characterizing the norms governing ideally rational agents. It presents a (...) puzzle which lends support to two theses. First, that there is no formal reduction of a rational agent’s beliefs to her credences, because belief and credence are each responsive to different features of a body of evidence. Second, that if our traditional understanding of our practices of holding each other responsible is correct, then belief has a distinctive role to play, even for ideally rational agents, that cannot be played by credence. The question of which avenues remain for the credence-only theorist is considered. (shrink)

We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of belief are those representable (...) by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism—in which the probability functions are taken relative to intuitionistic logic—rather than by adopting a radically non-Kolmogorovian, for example, nonadditive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response among those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability of a Dutch Book argument justifying the selection of intuitionistic probability functions as guides to rational betting behavior when due consideration is paid to the fact that bets are settled only when/if the outcome bet on becomes known. (shrink)

Corroborating Testimony, Probability and Surprise’, Erik J. Olsson ascribes to L. Jonathan Cohen the claims that if two witnesses provide us with the same information, then the less probable the information is, the more confident we may be that the information is true (C), and the stronger the information is corroborated (C*). We question whether Cohen intends anything like claims (C) and (C*). Furthermore, he discusses the concurrence of witness reports within a context of independent witnesses, whereas the witnesses in (...) Olsson's model are not independent in the standard sense. We argue that there is much more than, in Olsson's words, ‘a grain of truth’ to claim (C), both on his own characterization as well as on Cohen's characterization of the witnesses. We present an analysis for independent witnesses in the contexts of decision-making under risk and decision-making under uncertainty and generalize the model for n witnesses. As to claim (C*), Olsson's argument is contingent on the choice of a particular measure of corroboration and is not robust in the face of alternative measures. Finally, we delimit the set of cases to which Olsson's model is applicable. 1 Claim (C) examined for Olsson's characterization of the relationship between the witnesses 2 Claim (C) examined for two or more independent witnesses 3 Robustness and multiple measures of corroboration 4 Discussion. (shrink)

In this paper, we look at reasoning with evidence and facts in criminal cases. We show how this reasoning may be analysed in a dialectical way by means of critical questions that point to typical sources of doubt. We discuss critical questions about the evidential arguments adduced, about the narrative accounts of the facts considered, and about the way in which the arguments and narratives are connected in an analysis. Our treatment shows how two different types of knowledge, represented as (...) schemes, play a role in reasoning with evidence: argumentation schemes and story schemes. (shrink)

The paper takes a closer look at the role of knowledge and evidence in legal theory. In particular, the paper examines a puzzle arising from the evidential standard Preponderance of the Evidence and its application in civil procedure. Legal scholars have argued since at least the 1940s that the rule of the Preponderance of the Evidence gives rise to a puzzle concerning the role of statistical evidence in judicial proceedings, sometimes referred to as the Problem of Bare Statistical Evidence. While (...) this puzzle has led to the development of a multitude of accounts and approaches in the legal literature, I argue here that the problem can be resolved fairly straightforwardly within a knowledge-first framework. (shrink)

This essay presents results about a deviation from independence measure called focused correlation . This measure explicates the formal relationship between probabilistic dependence of an evidence set and the incremental confirmation of a hypothesis, resolves a basic question underlying Peter Klein and Ted Warfield's ‘truth-conduciveness’ problem for Bayesian coherentism, and provides a qualified rebuttal to Erik Olsson's claim that there is no informative link between correlation and confirmation. The generality of the result is compared to recent programs in Bayesian epistemology (...) that attempt to link correlation and confirmation by utilizing a conditional evidential independence condition. Several properties of focused correlation are also highlighted. Introduction Correlation Measures 2.1 Standard covariance and correlation measures 2.2 The Wayne–Shogenji measure 2.3 Interpreting correlation measures 2.4 Correlation and evidential independence Focused Correlation Conclusion Appendix CiteULike Connotea Del.icio.us What's this? (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)

Focused correlation compares the degree of association within an evidence set to the degree of association in that evidence set given that some hypothesis is true. A difference between the confirmation lent to a hypothesis by one evidence set and the confirmation lent to that hypothesis by another evidence set is robustly tracked by a difference in focused correlations of those evidence sets on that hypothesis, provided that all the individual pieces of evidence are equally, positively relevant to that hypothesis. (...) However, that result depends on a very strong equal relevance condition on individual pieces of evidence. In this essay, we prove tracking results for focused correlation analogous to Wheeler and Scheines’s results but for cases involving unequal relevance. Our result is robust as well, and we retain conditions for bidirectional tracking between incremental confirmation measures and focused correlation. (shrink)

Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships (...) among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis. (shrink)

This paper examines Lockie’s theory of libertarian self-determinism in light of the question of prediction: “Can we know (or justifiably believe) how an agent will act, or is likely to act, freely?” I argue that, when Lockie's theory is taken to its full logical extent, free actions cannot be predicted to any degree of accuracy because, even if they have probabilities, these cannot be known. However, I suggest that this implication of his theory is actually advantageous, because it is able (...) to explain and justify an important feature of the practices we use to determine whether someone has acted culpably: our hostility to the use of predictive evidence. (shrink)

Jonathan Cohen has claimed that in cases of witness agreement there is an inverse relationship between the prior probability and the posterior probability of what is being agreed: the posterior rises as the prior falls. As is demonstrated in this paper, this contention is not generally valid. In fact, in the most straightforward case exactly the opposite is true: a lower prior also means a lower posterior. This notwithstanding, there is a grain of truth to what Cohen is saying, as (...) there are special circumstances under which a thesis similar to his holds good. What characterises these circumstances is that they allow for the fact of agreement to be surprising. In making this precise, I draw on Paul Horwich's probabilistic analysis of surprise. I also consider a related claim made by Cohen concerning the effect of lowering the prior on the strength of corroboration. 1 Introduction 2 Cohen's claim 3 A counterexample 4 A weaker claim 5 A counterexample to the weaker claim 6 The grain of truth in Cohen's claim 7 Prior probability and strength of corroboration 8 Conclusion. (shrink)

Do privacy rights restrict what is permissible to infer about others based on statistical evidence? This paper replies affirmatively by defending the following symmetry: there is not necessarily a morally relevant difference between directly appropriating people’s private information—say, by using an X-ray device on their private safes—and using predictive technologies to infer the same content, at least in cases where the evidence has a roughly similar probative value. This conclusion is of theoretical interest because a comprehensive justification of the thought (...) that statistical inferences can violate privacy rights is lacking in the current literature. Secondly, the conclusion is of practical interest due to the need for moral assessment of emerging predictive algorithms. (shrink)

The notion of individualised evidence holds the key to solve the puzzle of statistical evidence, but there’s still no consensus on how exactly to define it. To make progress on the problem, epistemologists have proposed various accounts of individualised evidence in terms of causal or modal anti-luck conditions on knowledge like appropriate causation, sensitivity and safety. In this paper, I show that each of these fails as satisfactory anti-luck condition, and that such failure lends abductive support to the following conclusion: (...) once the familiar anti-luck intuition on knowledge is extended to individualised evidence, no single causal or modal anti-luck condition on knowledge can succeed as the right anti-luck condition on individualised evidence. This conclusion casts serious doubts on the fruitfulness of the move from anti-luck conditions on knowledge to anti-luck conditions on individualised evidence. I expand on these doubts and point out further aspects where epistemology and the law come apart: epistemic anti- luck conditions on knowledge do not adequately characterise the legal notion of individualised evidence. (shrink)

The paper offers a new understanding of induction in the empirical sciences, one which assimilates it to induction in geometry rather than to statistical inference. To make the point a system of notions, essential to logically sound induction, is defined. Notable among them are arbitrary object and particular property. A second aim of the paper is to bring to light a largely neglected set of assumptions shared by both induction and deduction in the empirical sciences. This is made possible by (...) appealing to the logic of common nouns and applying it to the logic of natural-kind terms.This strategy yields a new insight into the concept of natural kinds. While the strategy reveals deep affinity between empirical induction and deduction it also reveals two problems peculiar to induction. This helps to explain the intuition that induction is the more problematic of the two. The paper does not set out ‘to solve the problem of induction’. 1The paper has benefited from the support and critical comments of several friends: Steven Davis, Kevin Dunbar, Anil Gupta, Michael Hallett, Ray Jackendoff and Storrs McCall. Two friends, however, deserve special thanks, Michael Makkai and Gonzalo Reyes. Many of the points made in the paper, otherwise unacknowledged, are due to their generosity and patience. In fact, the paper can be seen as an application of the logic of kinds on which Gonzalo Reyes has been working for several years. (shrink)

Judges and jurors must make decisions in an environment of ignoranceand uncertainty for example by hearing statements of possibly unreliable ordishonest witnesses, assessing possibly doubtful or irrelevantevidence, and enduring attempts by the opponents to manipulate thejudge''s and the jurors'' perceptions and feelings. Three importantaspects of decision making in this environment are the quantificationof sufficient proof, the weighing of pieces of evidence, and therelevancy of evidence. This paper proposes a mathematical frameworkfor dealing with the two first aspects, namely the quantification ofproof (...) and weighing of evidence. Our approach is based on subjectivelogic, which is an extension of standard logic and probability theory,in which the notion of probability is extended by including degrees ofuncertainty. Subjective Logic is a framework for modelling humanreasoning and we show how it can be applied to legalreasoning. (shrink)

© The Author 2018. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: [email protected] article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model...Philosophy of law was until recently dominated by abstract investigation into the nature of law, a pursuit known as ‘general jurisprudence’. In this way, it resembled a branch of metaphysics or mid-twentieth century philosophy of mind, seeking to uncover the essential properties (...) of a general and multiply realizable phenomenon. Today, philosophers study law with a sharper focus, and with a more specialized lens – that of ethicists, for example, or epistemologists, or philosophers of action.That is not to say there has been a drop in groundbreaking work in general jurisprudence (see, for... (shrink)

A generation before Beardsley, legal scholar John Henry Wigmore invented a scheme for representing arguments in a tree diagram, aimed to help advocates analyze the proof of facts at trial. In this essay, I describe Wigmore's "Chart Method" and trace its origin and influence. Wigmore, I argue, contributes to contemporary theory in two ways. His rhetorical approach to diagramming provides a novel perspective on problems about the theory of reasoning, premise adequacy, and dialectical obligations. Further, he advances a novel solution (...) to the problem of assessing argument quality by representing the strength of argument in meeting objections. (shrink)

This paper introduces what is called the intersubjective interpretation of the probability calculus. Intersubjective probabilities are related to subjective probabilities, and the paper begins with a particular formulation of the familiar Dutch Book argument. This argument is then extended, in Section 3, to social groups, and this enables the concept of intersubjective probability to be introduced in Section 4. It is then argued that the intersubjective interpretation is the appropriate one for the probabilities which appear in confirmation theory whether of (...) a Bayesian or a Popperian variety. The final section of the paper states and tries to answer an objection due to Putnam. (shrink)

Lilian Bermejo-Luque has posed these questions:1.What is the relationship between presumption and presumptive inference? 2.What are the correctness conditions for presumptions and presumptive inferences? Cohen’s method of relevant variables, Toulmin’s model, and Rescher’s theory of plausibility suggest answers. An inference is presumptive just in case its warrant transfers presumption from its premises to its conclusion. A warrant licencing an inference from the claim that an empirical property φ holds to the claim that some other property ψ holds is backed by (...) observation of a constant conjunction of those properties. The stronger the backing, the stronger the warrant. Warrants may be defeated by instances of φ holding in conjunction with some property χ and ψ not holding. The method of relevant variables directs us to organize such defeating properties into relevant variables. We then test the strength of a warrant by seeing how many variables fail to have a value which defeats the warrant. The more variables with no defeater, the stronger the warrant. We may construct a canonical ordering of the relevant variables by ranking them according to the plausibility of their including defeating values. We may evaluate the strength not only of empirically backed warrants, but warrants backed by institutional rules, such as a branch of law, or by a priori intuited connections between properties. An inference rule will be presumptive just in case the plausibility of its warrant being defeated is below some specified level. (shrink)

We argue that Cohen’s concept of inductive or ampliative probability facilitates proper explication of sufficient strength for non-demonstrative arguments conforming to the Toulmin model. The data and claims of such arguments are singular statements. We may epistemically classify the warrants of such arguments as empirical (either physical or personal), institutional, or evaluative. Backing evidence and rebutting considerations vary with the epistemic type of warrant, but in each case the notion of ampliative probability for arguments with warrants of that type can (...) be characterized. We may then use ampliative probability to define sufficient strength and related notions for Toulmin arguments. (shrink)

Many philosophers have pointed out that statistical evidence, or at least some forms of it, lack desirable epistemic or non-epistemic properties, and that this should make us wary of litigations in which the case against the defendant rests in whole or in part on statistical evidence. Others have responded that such broad reservations about statistical evidence are overly restrictive since appellate courts have expressed nuanced views about statistical evidence. In an effort to clarify and reconcile, I put forward an interpretive (...) analysis of why statistical evidence should raise concerns in some cases but not others. I argue that when there is a mismatch between the specificity of the evidence and the expected specificity of the accusation, statistical evidence—as any other kind of evidence—should be considered insufficient to sustain a conviction. I rely on different stylized court cases to illustrate the explanatory power of this analysis. (shrink)

We critically examine Bermejo-Luque’s account of the logical dimension of argumentation and its logical or semantic evaluation. Our considerations concern her views on inference claims, validity, logical normativity, warrants, necessity, warrants and the justification of inferences, ontological versus epistemic modal qualifiers, ontological versus epistemic probability, and ontological versus conditional probability.

Even if two testimonies in a criminal trial are independent, they are not necessarily more trustworthy than one. But if they are independent in the sense that they are screened off from one another by the crime, then two testimonies raise the probability of guilt above the level that one testimony alone could achieve. In fact this screening-off condition can be weakened without changing the conclusion. It is however only a sufficient, not a necessary condition for concluding that two witnesses (...) are better than one. We will discuss two different conditions, each of them necessary as well as sufficient, and we conclude that one of them is slightly better than the other. (shrink)

Moral dissensus may arise first because persons may disagree over the warrants licensing inferring an evaluative conclusion from premises asserting that properties alleged evaluatively relevant hold. This results in seeing different properties as evaluatively relevant. Secondly, such properties will frequently not be descriptive but interpretive, asserting some nomic connection. Persons may disagree over what evaluatively relevant properties hold in a given case. We explore the possibilities for argumentation to resolve these two types of disagreement.

Our typology is based on two ground adequacy factors, one logical and one epistemic. Logically, the step from premises to conclusion may be conclusive or only ceteris paribus. Epistemically, warrants may be backed a priori or a posteriori. Hence there are four types of arguments: conclusive a priori, defeasible a priori, defeasible a posteriori, and prima facie conclusive a posteriori. We shall give an example of each and compare our scheme with other typologies.

L. J. Cohen has presented an understanding of appraising argument strength which applies to a variety of types of defeasible reasoning. This method can be used to explicate how a body of information may back a warrant and to rank different bodies of evidence on strength of backing. We shall argue that this method allows backing warrants objectively, whether they are inductive warrants backed by observation or moral warrants backed in part a priori. The method also suggests where arguments employing (...) these warrants may be vulnerable to bias bias but need not be infected by it. (shrink)

Varios teóricos del derecho han propuesto el uso de umbrales o estándares de prueba más flexibles y más finamente discriminados. En la medicina es común utilizar estándares que poseen estas características en los procedimientos diagnósticos y en los exámenes médicos. Esta ponencia ofrece un marco probabilístico para establecer estándares de prueba múltiples en cualquier disciplina. La tesis principal es que la evidencia es un concepto umbral con respecto a la probabilidad. Múltiples umbrales pueden ser establecidos en un marco de intervalos (...) de probabilidad para la hipótesis que está siendo puesta a prueba, los cuales reflejan los diferentes grados de apoyo que la evidencia le provee a la hipótesis. Examinando los mecanismos utilizados para establecer los umbrales en medicina, sugiero una manera para establecer umbrales múltiples de prueba en derecho de una manera no arbitraria. (shrink)

Belief is a familiar attitude: taking something to be the case or regarding it as true. But we are more confident in some of our beliefs than in others. For this reason, many epistemologists appeal to a second attitude, called credence, similar to a degree of confidence. This raises the question: how do belief and credence relate to each other? On a belief-first view, beliefs are more fundamental and credences are a species of beliefs, e.g. beliefs about probabilities. On a (...) credence-first view, credences are more fundamental and beliefs are a species of credence, e.g. credence above some threshold. In this thesis, I develop and defend a third view that I call belief-credence dualism. On this view, belief and credence are independent, equally fundamental attitudes, and neither reduces to the other. I begin by motivating the project: why should we care about the relationship between belief and credence? I argue it has broad implications for many debates in epistemology and beyond. Then, I defend dualism, arguing that it can explain features of our mental lives that a credence-first view and a belief-first view cannot. I also argue that dualism has attractive, interesting implications when applied to the pragmatic encroachment debate. Finally, I explore implications of dualism, both for the nature of evidence and how faith might go beyond the evidence but nonetheless be epistemically rational. I conclude that the human mind is, in some ways, complex, but we should be happy with this conclusion also long as each mental state we posit has a clear role to play. (shrink)

First, ranking functions are argued to be superior to AGM belief revision theory in two crucial respects. Second, it is shown how ranking functions are uniquely reflected in iterated belief change. More precisely, conditions on threefold contractions are specified which suffice for representing contractions by a ranking function uniquely up to multiplication by a positive integer. Thus, an important advantage AGM theory seemed to have over ranking functions proves to be spurious.