Abstract Finding the western just war criterion of reasonable chance of success to be a contribution to ethical decision making about armed conflict requires dealing with a number of critiques. Specifying ?probability? rather than the alternatives ?hope? or ?chance?, and raising standards of evidence involved, makes the term less vague. Expanding the concept of ?success? to include morally defensible aims that can be achieved without military victory enriches the understanding of the moral relationship between ends and (...) means in armed conflict. Asking decision makers to accept moral responsibility for the costs of possible failure is a unique contribution to the just war criteria. The enriched concept of reasonable probability of success thus offers morally significant insights to prewar jus ad bellum decisions, and can benefit ethical decision-making about whether to continue once fighting has begun. (shrink)

It is a popular view thatpractical deliberation excludes foreknowledge of one's choice. Wolfgang Spohn and Isaac Levi have argued that not even a purely probabilistic self-predictionis available to thedeliberator, if one takes subjective probabilities to be conceptually linked to betting rates. It makes no sense to have a betting rate for an option, for one's willingness to bet on the option depends on the net gain from the bet, in combination with the option's antecedent utility, rather than on the offered (...) odds. And even apart from this consideration, assigning probabilities to the options among which one is choosing is futile since such probabilities could be of no possible use in choice. The paper subjects these arguments to critical examination and suggests that, appearances notwithstanding, practical deliberation need not crowd outself-prediction. (shrink)

In his recent book Warranted Christian Belief (2000), Alvin Plantinga argues that the defender of naturalistic evolution is faced with adefeater for his position: as products of naturalistic evolution, we have no way of knowing if our cognitive faculties are in fact reliably aimed at the truth. This defeater is successfully avoided by the theist in that, given theism, we can be reasonably secure that out cognitive faculties are indeed reliable. I argue that Plantinga’s argument is ultimately based on a (...) faulty comparison, that he is comparing naturalistic evolution generally to one particular model of theism. In light of this analysis, the two models either stand or fall together with respect to the defeater that Plantinga offers. (shrink)

Objective interpretations of probability are usually discussed in two varieties: frequency and propensity accounts. But there is a third, neglected possibility, namely, probabilities as deriving from ranges in suitably structured initial state spaces. Roughly, the probability of an event is the proportion of initial states that lead to this event in the space of all possible initial states, provided that this proportion is approximately the same in any not too small interval of the initial state space. This idea (...) can also be expressed by saying that in the types of situations that give rise to probabilistic phenomena we may expect to find an initial state space such that any "reasonable" density function over this space leads to the same probabilities for the possible outcomes. This "method of arbitrary functions" was introduced by Poincaré, studied and extended by Hopf and more recently by Eduardo Engel, Jan von Plato and Michael Strevens. The natural-range, or method-of-arbitrary-functions approach to probabilities is usually treated as an explanation for the occurrence of probabilistic patterns, whereas I examine its prospects for an objective interpretation of probability, in the sense of providing truth conditions for probability statements that do not depend on our state of mind or information. The main objection to such a proposal is that it is circular, i.e. presupposes the concept of probability, because a measure on the initial state has to be introduced, and density functions over the space are considered. I try to argue that this objection can be successfully met. (shrink)

What are the pillars on which the success of modern science rest? Although philosophers have much discussed what is behind science’s success, this paper argues that much of the discussion is misdirected. The extant literature rightly regards the semantic and inferential tools of formal logic and probability theory as pillars of scientific rationality, in the sense that they reveal the justificatory structure of important aspects of scientific practice. As key elements of our rational reconstruction toolbox, they make (...) a fundamental contribution to our understanding of the success of science.At the same time, any science, however exact, is dominated by approximation, error, and uncertainty, a fact that makes one wonder how science can be so successful. This paper articulates and illustrates general themes—e.g., that truth-preserving arguments often fail to preserve approximate truth—that highlight the need for additional semantic resources. Thus, our proposal is that persistent failures to unravel the reasons behind the success of science in the face of pervasive error and uncertainty should be attributed to an insufficiently rich way of rationally reconstructing scientific and mathematical knowledge. What is missing? This paper claims that there is a third formal method of reasoning that constitutes a distinct pillar on which rests the success of science, namely, perturbation theory. The paper outlines how the representational and inferential tools of perturbation theory differ from those of logic and probability theory, and how they enable us to understand the apparently elusive aspects of the success of science.However, compared to its peers, perturbative reasoning has not received the attention it deserves. As the paper explains, this partly results from the circumstances in which perturbation theory is taught, and partly from the fact that perturbation theory first appears to be a vaguely related collection of methods offering no systematic semantic insight. In an attempt to show that this first impression is wrong, this paper presents its contribution to the semantic dimension of scientific representation and inference in terms of what I call “semantic layering.”. (shrink)

In this paper I will discuss certain aspects of Leibniz's theory and practice of 'soft reasoning' as exemplified by his defence of two central mysteries of the Christian revelation: the Trinity and the Incarnation. By theory and practice of 'soft' or 'broad' reasoning, I mean the development of rational strategies which can successefully be applied to the many areas of human understanding which escape strict demonstration, that is, the 'hard' or 'narrow' reasoning typical of mathematical argumentation. These strategies disclose an (...) 'other' reason, i.e. a complementary set of arguments and methods developed by Leibniz in order to deal with crucial issues such as the 'weighting' of probabilities and truths of fact. I will argue that one of the most compelling examples of the importance and fertility of Leibniz's 'other' reason is provided by his solution to the problems posed by the unique epistemological status of theological mysteries. (shrink)

Randomized controlled clinical trials play an important role in the development of new medical therapies. There is, however, an ethical issue surrounding the use of randomized treatment allocation when the patient is suffering from a life threatening condition and requires immediate treatment. Such patients can only benefit from the treatment they actually receive and not from the alternative therapy, even if it ultimately proves to be superior. We discuss a novel new way to analyse data from such clinical trials based (...) on the use of the recently developed theory of imprecise probabilities. This work draws an explicit distinction between the related but nevertheless distinct questions of inference and decision in clinical trials. The traditional question of scientific interest asks 'Which treatment offers the greater chance of success?' and is the primary reason for conducting the clinical trial. The question of decision concerns the welfare of the patients in the clinical trial, asking whether the accumulated evidence favours one treatment over the other to such an extent that the next patient should decline randomization and instead express a preference for one treatment. Consideration of the decision question within the framework of imprecise probabilities leads to a mathematical definition of equipoise and a method for governing the randomization protocol of a clinical trial. This paper describes in detail the protocol for the conduct of clinical trials based on this new method of analysis, which is illustrated in a retrospective analysis of data from a clinical trial comparing the anti-emetic drugs ondansetron and droperidol in the treatment of postoperative nausea and vomiting. The proposed methodology is compared quantitatively using computer simulation studies with conventional clinical trial designs and is shown to maintain high statistical power with reduced sample sizes, at the expense of a high type I error rate that we argue is irrelevant in some specific circumstances. Particular emphasis is placed on describing the type of medical conditions and treatment comparisons where the new methodology is expected to provide the greatest benefit. (shrink)

ABSTRACTThe jus ad bellum criterion of right intention is a central guiding principle of just war theory. It asserts that a country’s resort to war is just only if that country resorts to war for the right reasons. However, there is significant confusion, and little consensus, about how to specify the CRI. We seek to clear up this confusion by evaluating several distinct ways of understanding the criterion. On one understanding, a state’s resort to war is just only if it (...) plans to adhere to the principles of just war while achieving its just cause. We argue that the first understanding makes the CRI superfluous, because it can be subsumed under the probability of success criterion. On a second understanding, a resort to war is just only if a state’s motives, which explain its resort to war, are of the right kind. We argue that this second understanding of the CRI makes it a significant further obstacle to justifying war. However, this second understanding faces a possible infinite regress problem, wh... (shrink)

The Just War principle of jus ad bellum explicitly requires a reasonable prospect of success; the prevailing view about personal self-defence is that it can be justified even if the prospect of success is low. This chapter defends the existence of this distinction and goes on to explore the normative basis of this difference between defensive war and self-defence and its implications. In particular, the chapter highlights the rationale of the ‘success condition’ within Just War thinking (...) and argues that this condition is grounded in assumptions about the nature of political authority and responsibility that do not apply to personal self-defence. This important difference is commonly ignored or side-lined by contemporary theorists who regard the principles of these two types of conflict as very closely aligned and the moral differences between them as matters of degree only. (shrink)

In this paper, I will attempt to develop and defend a common form of intuitive resistance to the companions in guilt argument. I will argue that one can reasonably believe there are promising solutions to the access problem for mathematical realism that don’t translate to moral realism. In particular, I will suggest that the structuralist project of accounting for mathematical knowledge in terms of some form of logical knowledge offers significant hope of success while no analogous approach offers such (...) hope for moral realism. (shrink)

There is a growing trend in Australia to require lawyers to certify reasonable prospects of success for the cases they bring and defend. New South Wales has led the way with the Legal Profession Act 2004 (NSW) Pt 3.2 Division 10 requiring legal practitioners to certify reasonable prospects of success in all claims for damages. The requirement places a significant onus on lawyers to make a judgment about the merits of a case before it is begun, (...) yet the common law has long provided mechanisms to ensure that cases without prospects of success do not go to trial. This article considers Australian legislative provisions requiring lawyers to certify reasonable prospects of success of cases. It examines the application of the NSW legislation by the courts highlighting the difficulties of interpretation of what constitute 'reasonable prospects of success' and the application of the legislation in the context of the dynamic litigation process. It is argued that these legislated obligations on lawyers will have a detrimental effect on access to justice by denying parties, in particular plaintiffs, the opportunity to have their cases properly and fully determined in the courts. This article examines common law mechanisms for dissuading cases without prospects and argues that the general law is an effective system for ensuring that cases without prospects of success are not maintained. The Australian experience is instructive for consideration of optimal reform packages for the administration of justice and to evaluate the role of any litigation lawyer within the judicial and court process. (shrink)

ONE OF THE MOST INTRIGUING EPISODES in Schelling’s philosophical development is the transition from the System des transzendentalen Idealismus to the Darstellung meines Systems der Philosophie, the starting point of the identity system. Looking back on that latter text, Schelling in 1805 declares that “then to me the light went on in philosophy.” This sounds as if the preceding years of philosophical investigation, including the System des transzendentalen Idealismus that was written one year earlier, had to be considered merely propaedeutic (...) and that the Darstellung was his real entry into philosophy. Schelling maintained this view of his philosophical development and in the contemporary Schelling-Forschung scholars widely agree that the Darstellung, being the outset of the identity system, marks the birthplace of so-called absolute idealism—to which Hegel’s system of philosophy probably still is the most spectacular and successful heir. But if this common interpretation is true—and I would not deny it in the generality in which it is stated—then the question inevitably arises: what happened in the transition from the System des transzendentalen Idealismus to the Darstellung, and above all, what made this transition possible? What, in other words, caused the constitution of absolute idealism? (shrink)

Research into the cognition of conditionals has predominantly focused on conditional reasoning, producing a range of theories which explain associated phenomena with considerable success. However, such theories have been less successful in accommodating experimental data concerning how agents assess the probability of indicative conditionals. Since an acceptable account of conditional reasoning should be compatible with evidence regarding how we evaluate conditionals’ likelihoods, this constitutes a failing of such theories. Section 1 introduces the most dominant established approach to conditional (...) reasoning: mental models theory. Surveying a range of experimental results, I show that mental models theory (along with competing theories) is incapable of fully accounting for findings regarding judgements about conditionals’ probabilities. Section 2 introduces an alternative account of deductive reasoning, the erotetic theory, recently proposed by Koralus and Mascarenhas (2013). Section 3 argues that, given a natural extension, this theory is able to explain the otherwise unaccounted for data. (shrink)

Fifty years of effort in artificial intelligence (AI) and the formalization of legal reasoning have produced both successes and failures. Considerable success in organizing and displaying evidence and its interrelationships has been accompanied by failure to achieve the original ambition of AI as applied to law: fully automated legal decision-making. The obstacles to formalizing legal reasoning have proved to be the same ones that make the formalization of commonsense reasoning so difficult, and are most evident where legal reasoning has (...) to meld with the vast web of ordinary human knowledge of the world. Underlying many of the problems is the mismatch between the discreteness of symbol manipulation and the continuous nature of imprecise natural language, of degrees of similarity and analogy, and of probabilities. (shrink)

This paper addresses and rejects claims that one can demonstrate experimentally that most untutored subjects are systematically and incurably irrational in their probability judgements and in some deductive reasoning tasks. From within a strongly subjectivist theory of probability, it develops the notions of resiliency —a measure of stability of judgements—and robustness —a measure of expected stability. It then becomes possible to understand subjects' behaviour in the Wason selection task, in examples which have been claimed to involve a 'base-rate (...) fallacy', in appearing to ignore laws of large numbers and to overestimate their own success rate as entirely rational: a matter of combining first-order probability assignments with judgements about the robustness of those assignments. (shrink)

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology. -/- The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., the (...) cosmological constant on the number of observers it allows for. However, uniform probability distributions usually appealed to in such arguments are an inadequate representation of indifference, and lead to unfounded predictions. It has been argued that this inability to represent ignorance is a fundamental flaw of any inductive framework using additive measures. In the first paper, I examine how imprecise probabilities fare as an inductive framework and avoid such unwarranted inferences. In the second paper, I detail how this framework allows us to successfully avoid the conclusions of Doomsday arguments in a way no Bayesian approach that represents credal states by single credence functions could. -/- There are in the cosmology literature several kinds of arguments referring to self- locating uncertainty. In the multiverse framework, different "pocket-universes" may have different fundamental physical parameters. We don’t know if we are typical observers and if we can safely assume that the physical laws we draw from our observations hold elsewhere. The third paper examines the validity of the appeal to the "Sleeping Beauty problem" and assesses the nature and role of typicality assumptions often endorsed to handle such questions. -/- A more general issue for the use of probabilities in cosmology concerns the inadequacy of Bayesian and statistical model selection criteria in the absence of well-motivated measures for different cosmological models. The criteria for model selection commonly used tend to focus on optimizing the number of free parameters, but they can select physically implausible models. The fourth paper examines the possibility for Bayesian model selection to circumvent the lack of well-motivated priors. (shrink)

Kearns and Star have previously recommended that we measure the degree to which a reason supports a conclusion, either about how to act or what to believe, as the conditional probability of the conclusion given the reason. I show how to properly formulate this recommendation to allow for dependencies and conditional dependencies among the considerations being aggregated. This formulation allows us to account for how considerations, which do not themselves favour a specific conclusion, can modify the strength of a (...) reason for that conclusion, and thus to explain the intensifiers and attenuators described by Dancy. The formulation also accounts for the workings of partial undercutters in epistemology. I then show how my account avoids the counterexamples that Brunero levied against probability-based theories of the strengths of reasons. My account supports the theory, suggested by Kearns and Star, that the strengths of reasons are measured by conditional probabilities. If my account is successful, then it will count in favour of the idea that the strengths of reasons are measured on the same scale as are conditional probabilities. (shrink)

Examining the social and political upheavals that characterized the collapse of public judgment in early modern Europe, Liberating Judgment offers a unique account of the achievement of liberal democracy and self-government. The book argues that the work of John Locke instills a civic judgment that avoids the excesses of corrosive skepticism and dogmatic fanaticism, which lead to either political acquiescence or irresolvable conflict. Locke changes the way political power is assessed by replacing deteriorating vocabularies of legitimacy with a new language (...) of justification informed by a conception of probability. For Locke, the coherence and viability of liberal self-government rests not on unassailable principles or institutions, but on the capacity of citizens to embrace probable judgment. The book explores the breakdown of the medieval understanding of knowledge and opinion, and considers how Montaigne's skepticism and Descartes' rationalism--interconnected responses to the crisis--involved a pragmatic submission to absolute rule. Locke endorses this response early on, but moves away from it when he encounters a notion of reasonableness based on probable judgment. In his mature writings, Locke instructs his readers to govern their faculties and intellectual yearnings in accordance with this new standard as well as a vocabulary of justification that might cultivate a self-government of free and equal individuals. The success of Locke's arguments depends upon citizens' willingness to take up the labor of judgment in situations where absolute certainty cannot be achieved. (shrink)

Introduction: Not many writers have made suggestions about Saul’s mental state as reported in the Judaic-Christian bible. He became king under the tutelage of Samuel, a highly-respected prophet of the Israelite God, Yahweh. At some points during his reign, the biblical narrative depicted him as, at least, mentally unstable, if not decidedly insane. Modern-day writers, in some cases have provided lists of conditions, which purport to represent Saul’s psychological malady. None, however proves adequate or appropriate to encompass the complexity of (...) his behavior. The Safety-Oriented Personality Style (SOPS) or Phobicentric Psychopathology (PCP) appears to offer the best explanation of Saul’s psychological condition. Purpose: The main purpose of this paper is to offer a modern-day analysis/explanation of Saul’s apparently disturbed behavior. Evidence for the facts about Saul’s fascinating presentation is adduced both from the biblical passages and from present-day psychological theory. The previous explanations of the psychological disorder that plagued Saul, the first king of Israel, have focused on depression, post-traumatic stress disorder, hysteria, and bipolar disorder. The associated symptoms, however, have been vague and, in some cases, apparently unrepresentative of psychological nosology or, in general, they fail to conform to the prevailing nomenclature. Method: The present study introduces the Safety-Oriented Personality Style (SOPS) or Phobicentric Psychopathology (PCP), a relatively newly-unveiled chronic, anxiety-based disorder, to provide the “best” explanation of the ancient king’s perplexing conduct. Biblical passages pertaining to the topic provide the historical context of the events, which depict Saul’s provable psychopathology. Result: The evidence seems to clearly indicate that the explanation that Saul’s actions were mainly controlled by SOPS/PCP, a chronic anxiety disorder, is valid, applying most aptly to his reaction to David’s military and religious successes, and even to the recorded circumstances of his death. Conclusion: The historical account of Saul’s life and death, recorded primarily in the Christian bible, has remained intriguing, though somewhat esoteric. Probably as a result, its portrayal in the psychological literature has been scant. While the SOPS/PCP construct has apparently helped to provide grounds for diagnostic consensus that Saul’s problem was chronic anxiety, the newness of SOPS/PCP would tend to limit its purview. On a different but relevant level, the study also demonstrates the feasibility of common endeavors between the scientific and theological communities. (shrink)

Bayesian reasoning, defined here as the updating of a posterior probability following new information, has historically been problematic for humans. Classic psychology experiments have tested human Bayesian reasoning through the use of word problems and have evaluated each participant’s performance against the normatively correct answer provided by Bayes’ theorem. The standard finding is of generally poor performance. Over the past two decades, though, progress has been made on how to improve Bayesian reasoning. Most notably, research has demonstrated that the (...) use of frequencies in a natural sampling framework —as opposed to single-event probabilities—can improve participants’ Bayesian estimates. Furthermore, pictorial aids and certain individual difference factors also can play significant roles in Bayesian reasoning success. The mechanics of how to build tasks which show these improvements is not under much debate. The explanations for why naturally-sampled frequencies and pictures help Bayesian reasoning remain hotly contested, however, with many researchers falling into ingrained “camps” organized around two dominant theoretical perspectives. The present paper evaluates the merits of these theoretical perspectives, including the weight of empirical evidence, theoretical coherence, and predictive power. By these criteria, the ecological rationality approach is clearly better than the heuristics and biases view. Progress in the study of Bayesian reasoning will depend on continued research that honestly, vigorously, and consistently engages across these different theoretical accounts rather than staying “siloed” within one particular perspective. The process of science requires an understanding of competing points of view, with the ultimate goal being integration. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:121. HUME'S Of Scepticism with regard to reason: A STUDY IN CONTRASTING THEMES.* This paper attempts to describe the complex dialectical interplay among the contrasting rational, sceptical and naturalist elements which appear in Section I, Part IV of Book I of Hume's Treatise of Human Nature. At the same time we shall try to show that, contrary to Hume's own evaluation of that section, it is the sceptical element, (...) in which the unreliability of reason is supposedly demonstrated, as opposed to the naturalist element, in which its unreliability is supposed to remain hidden from us, that deserves to triumph. With these two goals in mind and in order to make it easier for the reader to follow the inevitable twists and turns of the dialectic, we have divided the paper into two three-sectioned parts. The first part bears the title "Reason and Scepticism", while the second part bears the title "Naturalism". The first section of Part I is concerned with proving that Hume's attempted reduction of all knowledge to probability is frustrated by his failure to explain how we can make mistakes in simple operations with small numbers. If so, the first phase of his sceptical assault against reason fails to dislodge her from her throne. If the second section is right, the second stage of the sceptical assault fares no better. For Hume's attempted reduction of all probabilities to zero is shown to rely on an unsatisfactory formula for calculating the probabilities in question. In the third section an effort is made to show that the attempted reduction of the second section, i_f it had been a success instead of a failure, would have destroyed reason but left scepticism intact. *I should like to thank Howard Sobel for his penetrating and unsparing criticism of an earlier version of this paper. 122. Hume's conviction, on the other hand, that the flawed reduction in question is unflawed and destroys both leads to a prolonged discussion, initiated in the first section of Part II, of his naturalism. Indeed, this theme dominates the rest of the paper. Thus it deserves a part to itself. If we are correct in the first section of Part II, Hume's naturalism is best interpreted as a doctrine of instincts relying for its doctrinal status upon a failure to accept the conclusion of the sceptical argument directed against reason. But, as we try to bring out in the second section, the specific psychological inability with which Hume could in the final analysis give substance to this failure of acceptance is left without any causal foundation. Finally, in the third section that inability is seen to run afoul of reason as Hume himself understands it. And note is taken of the fact that reason so understood and the sceptical argument directed against reason that Hume adopts for his own both commit him willy-nilly to rejecting for good or ill one standard definition of knowledge. Reason and Scepticism Nowhere are the rational elements in Hume's philosophy more in evidence, ironically enough, than in Section I, Part IV of Book I of the Treatise entitled Of Scepticism with regard to reason. For it is there we are told in the very first paragraph that in all demonstrative sciences the rules are certain and infallible. Our reason, moreover, must be consider ' d as a kind of cause, of which truth is the natural effect. (T180) In other words, reason, left to its own devices, would produce truth and, presumably, only truth. Anyone who steadfastly adheres to such principles will reject out of hand one kind of scepticism with regard 123. to reason. That is the kind which results from the alleged discovery that reason, left to its own devices, compels us to embrace one or more contradictions, an obvious form of 2 falsity. It is a kind of scepticism which Bayle cultivated so assiduously. And yet, despite the influence which Bayle 's writings exerted upon Hume, they never convinced him of the viability of this kind of scepticism. On the contrary, apart from some wavering in the Enquiry, he was as adamant as any Leibnizian rationalist that right reason3 ing leads only... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:121. HUME'S Of Scepticism with regard to reason: A STUDY IN CONTRASTING THEMES.* This paper attempts to describe the complex dialectical interplay among the contrasting rational, sceptical and naturalist elements which appear in Section I, Part IV of Book I of Hume's Treatise of Human Nature. At the same time we shall try to show that, contrary to Hume's own evaluation of that section, it is the sceptical element, (...) in which the unreliability of reason is supposedly demonstrated, as opposed to the naturalist element, in which its unreliability is supposed to remain hidden from us, that deserves to triumph. With these two goals in mind and in order to make it easier for the reader to follow the inevitable twists and turns of the dialectic, we have divided the paper into two three-sectioned parts. The first part bears the title "Reason and Scepticism", while the second part bears the title "Naturalism". The first section of Part I is concerned with proving that Hume's attempted reduction of all knowledge to probability is frustrated by his failure to explain how we can make mistakes in simple operations with small numbers. If so, the first phase of his sceptical assault against reason fails to dislodge her from her throne. If the second section is right, the second stage of the sceptical assault fares no better. For Hume's attempted reduction of all probabilities to zero is shown to rely on an unsatisfactory formula for calculating the probabilities in question. In the third section an effort is made to show that the attempted reduction of the second section, i_f it had been a success instead of a failure, would have destroyed reason but left scepticism intact. *I should like to thank Howard Sobel for his penetrating and unsparing criticism of an earlier version of this paper. 122. Hume's conviction, on the other hand, that the flawed reduction in question is unflawed and destroys both leads to a prolonged discussion, initiated in the first section of Part II, of his naturalism. Indeed, this theme dominates the rest of the paper. Thus it deserves a part to itself. If we are correct in the first section of Part II, Hume's naturalism is best interpreted as a doctrine of instincts relying for its doctrinal status upon a failure to accept the conclusion of the sceptical argument directed against reason. But, as we try to bring out in the second section, the specific psychological inability with which Hume could in the final analysis give substance to this failure of acceptance is left without any causal foundation. Finally, in the third section that inability is seen to run afoul of reason as Hume himself understands it. And note is taken of the fact that reason so understood and the sceptical argument directed against reason that Hume adopts for his own both commit him willy-nilly to rejecting for good or ill one standard definition of knowledge. Reason and Scepticism Nowhere are the rational elements in Hume's philosophy more in evidence, ironically enough, than in Section I, Part IV of Book I of the Treatise entitled Of Scepticism with regard to reason. For it is there we are told in the very first paragraph that in all demonstrative sciences the rules are certain and infallible. Our reason, moreover, must be consider ' d as a kind of cause, of which truth is the natural effect. (T180) In other words, reason, left to its own devices, would produce truth and, presumably, only truth. Anyone who steadfastly adheres to such principles will reject out of hand one kind of scepticism with regard 123. to reason. That is the kind which results from the alleged discovery that reason, left to its own devices, compels us to embrace one or more contradictions, an obvious form of 2 falsity. It is a kind of scepticism which Bayle cultivated so assiduously. And yet, despite the influence which Bayle 's writings exerted upon Hume, they never convinced him of the viability of this kind of scepticism. On the contrary, apart from some wavering in the Enquiry, he was as adamant as any Leibnizian rationalist that right reason3 ing leads only... (shrink)

The problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. -/- Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities (...) of conditionals violate standard probability theory. -/- This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. -/- We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. -/- We address two common objections to Adams' view: that the relevant probabilities are ‘probabilities only in name’, and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. -/- Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. (shrink)

Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through information or experience; induction and belief change are one and same topic, after all. The most basic of these rules is simply to conditionalize with respect to the information received; and there are similar and more general rules. 1 Hence, a fundamental reason for the epistemological (...) class='Hi'>success of probability theory is that there at all exists a well-behaved concept of conditional probability. Still, people have, and have reasons for, various concerns over probability theory. One of these is my starting point: Intuitively, we have the notion of plain belief; we believe propositions2 to be true (or to be false or neither). Probability theory, however, offers no formal counterpart to this notion. Believing A is not the same as having probability 1 for A, because probability 1 is incorrigible3; but plain belief is clearly corrigible. And believing A is not the same as giving A a probability larger than some 1 - c, because believing A and believing B is usually taken to be equivalent to believing A & B.4 Thus, it seems that the formal representation of plain belief has to take a non-probabilistic route. Indeed, representing plain belief seems easy enough: simply represent an epistemic state by the set of all propositions believed true in it or, since I make the common assumption that plain belief is deductively closed, by the conjunction of all propositions believed true in it. But this does not yet provide a theory of induction, i.e. an answer to the question how epistemic states so represented are changed tbrough information or experience. There is a convincing partial answer: if the new information is compatible with the old epistemic state, then the new epistemic state is simply represented by the conjunction of the new information and the old beliefs. This answer is partial because it does not cover the quite common case where the new information is incompatible with the old beliefs. It is, however, important to complete the answer and to cover this case, too; otherwise, we would not represent plain belief as conigible. The crucial problem is that there is no good completion. When epistemic states are represented simply by the conjunction of all propositions believed true in it, the answer cannot be completed; and though there is a lot of fruitful work, no other representation of epistemic states has been proposed, as far as I know, which provides a complete solution to this problem. In this paper, I want to suggest such a solution. In [4], I have more fully argued that this is the only solution, if certain plausible desiderata are to be satisfied. Here, in section 2, I will be content with formally defining and intuitively explaining my proposal. I will compare my proposal with probability theory in section 3. It will turn out that the theory I am proposing is structurally homomorphic to probability theory in important respects and that it is thus equally easily implementable, but moreover computationally simpler. Section 4 contains a very brief comparison with various kinds of logics, in particular conditional logic, with Shackle's functions of potential surprise and related theories, and with the Dempster - Shafer theory of belief functions. (shrink)

Intellectual courage requires acting to promote epistemic goods despite significant risk of harm. Courage is distinguished from recklessness and cowardice because the expected epistemic benefit of a courageous action outweighs (in some sense) the threatened harm. Sometimes, however, inquirers pursue theories that are not best supported by their current evidence. For these inquirers, the expected epistemic benefit of their actions cannot be explained by appeal to their evidence alone. The probability of pursuing the true theory cannot contribute enough to (...) the expected epistemic benefit for the action to count as courageous rather than reckless. Thus, there must be some other epistemic consideration which favors their action, besides evidence for their theory. I argue that the proper account of intellectual courage requires recognition of inquisitive reasons: a distinct category of epistemic reasons which concern successful inquiry. This category includes reasons to think a theory itself is promising, e.g., that the theory suggests potentially fruitful new research. It also includes social epistemic reasons, e.g., that pursuing a theory will improve the distribution of cognitive labor. Inquisitive reasons help explain why researchers who pursue improbable theories count as intellectually courageous, rather than reckless. The expected epistemic benefit of an action is partially determined by the inquisitive reasons in its favor. On my account, intellectually courageous inquiry requires acting in a way that is sensitive to inquisitive reasons. (shrink)

Defining qualified reasoning as reasoning containing such loose qualifying words as 'probably,' 'usually,' 'probable, 'likely,' 'ceteris paribus,' and 'primafacie, Ennis argues that typical cases of qualified reasoning, though they might be good arguments, are deductively invalid, implying that such arguments fail soundness standards. He considers and rejects several possible alternative ways of viewing such cases, ending with a proposal for applying qualified soundness standards, which requires employment of sufficient background knowledge, sensitivity, experience and understanding of the situation. All of this (...) takes place as part of the process, introduced elsewhere, of successively applying different legitimate sets of standards until one is found that is satisfied, or none is found, the latter calling for rejection of the argument, the former calling for its acceptance. (shrink)

Many proponents of libertarian freedom assume that the free choices we might make have particular objective probabilities of occurring. In this paper, I examine two common motivations for positing such probabilities: first, to account for the phenomenal character of decision-making, in which our reasons seem to have particular strengths to incline us to act, and second, to naturalize the role of reasons in influencing our decisions, such that they have a place in the causal order as we know it. I (...) argue, however, that neither introspective reflection nor the metaphysics of causation gives us reason for thinking there are such particular objective probabilities of our free choices. (shrink)

We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability to be the conditional probability. In our approach, however, we avoid triviality because the import-export principle is invalid. We then analyze an example of reasoning under partial knowledge where, given a conditional if A then Cas information, the probability of A should intuitively (...) increase. We explain this intuition by making some implicit background information explicit. We consider several iterated conditionals, which allow us to formalize different kinds of latent information. We verify that for these iterated conditionals the prevision is greater than or equal to the probability of A. We also investigate the lower and upper bounds of the Affirmation of the Consequent inference. We conclude our study with some remarks on the supposed "independence" of two conditionals, and we interpret this property as uncorrelation between two random quantities. 2020 Elsevier Inc. All rights reserved. (shrink)

Occasionally, people are called upon to estimate probabilities after an event has occurred. In hindsight, was this an outcome we could have expected? Could things easily have turned out differently? One strategy for performing post hoc probability judgements would be to mentally turn the clock back and reconstruct one's expectations before the event. But if asked about the probability of an alternative, counterfactual outcome, a simpler strategy is available, based on this outcome's perceived closeness to what actually happened. (...) The article presents five studies exploring the relationship between counterfactual closeness and counterfactual probability. The first study indicates that post hoc probabilities typically refer to the counterfactual rather than the factual outcome. Studies 2-5 show that physical, temporal, or conceptual proximity play a decisive role for post hoc probability assessments of counterfactual events. When margins are narrow, the probabilities of, for instance, winning a match (when losing), and of losing (when actually winning) may even be rated higher than the corresponding probabilities of what really happened. Closeness is also more often referred to, and rated to be a better reason for believing there is a ''good chance" of the counterfactual rather than of the factual result occurring. Finally, the closeness of the alternative outcome in success and failure stories is shown to be significantly correlated to its rated probability. (shrink)

Subjective Bayesians typically find the following objection difficult to answer: some joint probability measures lead to intuitively irrational inductive behavior, even in the long run. Yet well-motivated ways to restrict the set of reasonable prior joint measures have not been forthcoming. In this paper I propose a way to restrict the set of prior joint probability measures in particular inductive settings. My proposal is the following: where there exists some successful inductive method for getting to the truth (...) in some situation, we ought to employ a (joint) probability measure that is inductively successful in that situation, if such a measure exists. In order to do show that the restriction is possible to meet in a broad class of cases, I prove a Bayesian Completeness Theorem, which says that for any solvable inductive problem of a certain broad type, there exist probability measures that a Bayesian could use to solve the problem. I then briefly compare the merits of my proposal with two other well-known proposals for constraining the class of admissible subjective probability measures, the leave the door ajar condition and the maximize entropy condition. (shrink)

Iterated conditionals of the form If p, then if q, r are an important topic in philosophical logic. In recent years, psychologists have gained much knowledge about how people understand simple conditionals, but there are virtually no published psychological studies of iterated conditionals. This paper presents experimental evidence from a study comparing the iterated form, If p, then if q, r with the “imported,” noniterated form, If p and q, then r, using a probability evaluation task and a truth‐table (...) task, and taking into account qualitative individual differences. This allows us to critically contrast philosophical and psychological approaches that make diverging predictions regarding the interpretation of these forms. The results strongly support the probabilistic Adams conditional and the “new paradigm” that takes this conditional as a starting point. (shrink)

We propose a discrete time branching process to model the appearance of drug resistance under treatment. Under our assumptions at every discrete time a pathogen may die with probability 1−p or divide in two with probability p. Each newborn pathogen is drug resistant with probability μ. We start with N drug sensitive pathogens and with no drug resistant pathogens. We declare the treatment successful if all pathogens are eradicated before drug resistance appears. The model predicts that (...) class='Hi'>success is possible only if p<1/2. Even in this case the probability of success decreases exponentially with the parameter m=μN. In particular, even with a very potent drug (i.e. p very small) drug resistance is likely if m is large. (shrink)

Iterated conditionals of the form If p, then if q, r are an important topic in philosophical logic. In recent years, psychologists have gained much knowledge about how people understand simple conditionals, but there are virtually no published psychological studies of iterated conditionals. This paper presents experimental evidence from a study comparing the iterated form, If p, then if q, r with the “imported,” noniterated form, If p and q, then r, using a probability evaluation task and a truth-table (...) task, and taking into account qualitative individual differences. This allows us to critically contrast philosophical and psychological approaches that make diverging predictions regarding the interpretation of these forms. The results strongly support the probabilistic Adams conditional and the “new paradigm” that takes this conditional as a starting point. (shrink)

Using national opinion survey data, this research addressed claims in political science that the American electorate is either poorly informed or dependent on party label cues. The results suggested that in situations with missing information, American voters can use their knowledge to successfully infer political party membership of candidates and vote their own party interests.

According to the Doomsday Argument the probability of an impending extinction of mankind is much higher than we think. The adduced reason is that in our assignment of probabilities to soon or not so soon doom we have not fully taken into account that we live in the specific year 2001. This is relevant information, because if I consider myself as an arbitrary member of the human race I have a much higher probability of finding myself living in (...) 2001 on the hypothesis of a soon extinction, Doom Soon, than on the hypothesis of Doom Late---according to the latter hypothesis there are so many more years I could have found myself living in. Accordingly, Bayesian reasoning leads to a posterior probability of the Doom Soon hypothesis, after I have taken the evidence of my birth date fully into account, that is much higher than the prior probability. I show that the Argument is nothing but a rather trivial mathematical exercise in the calculation of posterior from prior probabilities; it is only about the relation between these probabilities and is silent about the concrete values these probabilities should have. Nothing in the Argument supports the conclusion its proponents think it supports, namely that Doom Soon is much more probable than we ordinarily think. The Argument is formally valid, but ineffective. (shrink)

The overall aim of this thesis is to understand Hume’s famous argument concerning induction, and to appraise its success in establishing its conclusion. The thesis accordingly falls into two main parts, the first being concerned with analysis and interpretation of the argument itself, and the second with investigation of possible responses to it. Naturally the argument’s interpretation strongly constrains the range of possible replies, and indeed the results of Part I indicate that the only kind of strategy which stands (...) much prospect of defeating Hume’s argument is one based on a priori probabilistic reasoning – hence the overwhelming majority of Part II is devoted to a thorough investigation of this approach. (shrink)

There are various reasons for favouring Ψ-epistemic interpretations of quantum mechanics over Ψ-ontic interpretations. One such reason is the correlation between quantum mechanics and Liouville dynamics. Another reason is the success of a specific epistemic model (Spekkens, 2007), in reproducing a wide range of quantum phenomena. The potential criticism, that Spekkens' restricted knowledge principle is counter-intuitive, is rejected using `everyday life' examples. It is argued that the dimensionality of spin favours Spekkens' model over Ψ-ontic models. van Enk's extension of (...) Spekkens' model (2007) can even reproduce Bell Inequality violations, but requires negative probabilities to do so. An epistemic account of negative probabilities is the missing element for deciding the battle between Ψ-epistemic and Ψ-ontic interpretations in favour of the former. (shrink)

Defining qualified reasoning as reasoning containing such loose qualifying words as 'probably,' 'usually,' 'probable, 'likely,' 'ceteris paribus,' and 'primafacie, Ennis argues that typical cases of qualified reasoning, though they might be good arguments, are deductively invalid, implying that such arguments fail soundness standards. He considers and rejects several possible alternative ways of viewing such cases, ending with a proposal for applying qualified soundness standards, which requires employment of sufficient background knowledge, sensitivity, experience and understanding of the situation. All of this (...) takes place as part of the process, introduced elsewhere, of successively applying different legitimate sets of standards until one is found that is satisfied, or none is found, the latter calling for rejection of the argument, the former calling for its acceptance. (shrink)

This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in (...) which it occurs. The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning. (shrink)

Our aim in this paper is to bring the woefully neglected literature on predictive modeling to bear on some central questions in the philosophy of science. The lesson of this literature is straightforward: For a very wide range of prediction problems, statistical prediction rules (SPRs), often rules that are very easy to implement, make predictions than are as reliable as, and typically more reliable than, human experts. We will argue that the success of SPRs forces us to reconsider our (...) views about what is involved in understanding, explanation, good reasoning, and about how we ought to do philosophy of science. (shrink)

God has major reasons for intervening in human history by becoming incarnate himself—to identify with our suffering, to provide atonement for our sins, and to reveal truths. Given there is at least a significant probability that there is a God, there is at least a modest probability that he would become incarnate and live a life and provide teaching appropriate to one who sought thereby to realize these goals. Jesus lived and taught in the appropriate way. If it (...) was God incarnate who did so live and teach, he would need to show us that it was God who had done so, and so could be expected to put his signature on that life and teaching by a super-miracle, such as the Resurrection. So there is a modest prior probability in advance of considering the direct historical evidence of the Resurrection, to expect that it would happen to someone who lived and taught as Jesus did. Jesus is the only person in human history about whom there is significant evidence both that he led the appropriate kind of life, and that his life was culminated by a super-miracle. So we do not need too many witnesses to the empty tomb or too many witnesses who claimed to have talked to the risen Jesus, to make it probable that Jesus did indeed rise. We do have some such witness evidence, which it is very improbable would occur unless the Resurrection occurred. In consequence it is overall very probable that the Resurrection occurred. (shrink)