The Indifference Principle, its Paradoxes and Kolmogorov's Probability Space.

The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single (...) formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. (shrink)

The distinction between the a priori and the a posteriori is an old and influential one. But both the distinction itself and the crucial notion of a priori knowledge face powerful philosophical challenges. Many philosophers worry that accepting the a priori is tantamount to accepting epistemic magic. In contrast, this Element argues that the a priori can be formulated clearly, made respectable, and used to do important epistemological work. The author's conception of the a priori and its role falls short (...) of what some historical proponents of the notion may have hoped for, but it allows us to accept and use the notion without abandoning either naturalism or empiricism, broadly understood. This Element argues that we can accept and use the a priori without magic. (shrink)

Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails (...) because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief . One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective Bayesian norms are tied up in the very notion of degrees of belief. (shrink)

Schurz (2019, ch. 4) argues that probabilistic accounts of induction fail. In particular, he criticises probabilistic accounts of induction that appeal to direct inference principles, including subjective Bayesian approaches (e.g., Howson 2000) and objective Bayesian approaches (see, e.g., Williamson 2017). In this paper, I argue that Schurz’ preferred direct inference principle, namely Reichenbach’s Principle of the Narrowest Reference Class, faces formidable problems in a standard probabilistic setting. Furthermore, the main alternative direct inference principle, Lewis’ Principal Principle, is also hard to (...) reconcile with standard probabilism. So, I argue, standard probabilistic approaches cannot appeal to direct inference to explicate the logic of induction. However, I go on to defend a non-standard objective Bayesian account of induction: I argue that this approach can both accommodate direct inference and provide a viable account of the logic of induction. I then defend this account against Schurz’ criticisms. (shrink)

Setting out to understand Frege, the scholar confronts a roadblock at the outset: We just have little to go on. Much of the unpublished work and correspondence is lost, probably forever. Even the most basic task of imagining Frege's intellectual life is a challenge. The people he studied with and those he spent daily time with are little known to historians of philosophy and logic. To be sure, this makes it hard to answer broad questions like: 'Who influenced Frege?' But (...) the information vacuum also creates local problems of textual interpretation. Say we encounter a sentence that may be read as alluding to a scientific dispute. Should it be read that way? To answer, we'd need to address prior questions. Is it .. (shrink)

I present three critical points against G.E.R. Lloyd's ‘The Fortunes of Analogy’. First, I argue that Lloyd unduly criticises Aristotle's view of analogies. Second, I argue that Lloyd needs to discuss the means of limiting the semantic stretch of terms, for instance through the distinction between fiat and bona fide boundaries. Third, I point out some terminological issues in Lloyd's account, especially concerning the applicability of validity, soundness, and fallaciousness to analogies.

Many policy decisions take input from collections of scientific models. Such decisions face significant and often poorly understood uncertainty. We rework the so-called confidence approach to tackle decision-making under severe uncertainty with multiple models, and we illustrate the approach with a case study: insurance pricing using hurricane models. The confidence approach has important consequences for this case and offers a powerful framework for a wide class of problems. We end by discussing different ways in which model ensembles can feed information (...) into the approach, appropriate to different collections of models. (shrink)

The financial crisis that began in the US real-estate market in 2007 and culminated in a global economic slump showed bluntly how wrong financial risk models can be. This state of affairs has triggered a number of reactions and observations at the level of the specification and use of models and at a more conceptual/fundamental level. This article focuses on the epistemic features of such models – namely the nature, source, conditions of validity, structure and limits of the knowledge that (...) ‘well-specified’ models generate – so as to assess models in a balanced way, giving due weight to the fundamental determinants of their output and warning against overestimation of their possibilities; clarify the conditions under which models can be validly applied to economic and social relationships; render intelligible why the degree of accuracy that successful models would require is intrinsically unattainable; better understand models’ failure as evidenced by the crisis; and comment on the policy steps being undertaken to prevent similar financial crisis in the future. The analysis applies the principal tenets of critical realism to the daily preoccupations of risk management professionals and financial regulators alike. It is not intended as an intervention into critical realism. It draws on the works of Tony Lawson and Roy Bhaskar, and revisits relevant aspects of John Maynard Keynes’s work, connecting dots amongst them and marrying economic and philosophical analysis with day-to-day financial risk management and regulatory issues. Content Type Journal Article Category Article Pages 462-486 DOI 10.1558/jcr.v11i4.462 Authors Mattia L. Rattaggi, UBS/Cambridge Social Ontology Group Journal Journal of Critical Realism Online ISSN 1572-5138 Print ISSN 1476-7430 Journal Volume Volume 11 Journal Issue Volume 11, Number 4 / 2012. (shrink)

The correct solution to complex problems, such as those involved in international relations, can generally be discovered ex post but not predicted ex ante. Economics and game theory attempt to model such complexity, but have difficulty taking into account psychological subtleties, the myriad factors that each agent considers when making a decision, and cultural differences. And understanding that one is dealing with a system—that is, with interacting factors instead of with insulated monads—may not make the questions any more amenable to (...) prediction, particularly because the more unique an event, the less likely it is to be foreseen. Jervis's analysis of complex systems may therefore be more of a contribution to the historical sciences than to predictive social science. (shrink)

Recent claims, mainly from computer scientists, concerning a largely automated and model-free data-intensive science have been countered by critical reactions from a number of philosophers of science. The debate suffers from a lack of detail in two respects, regarding the actual methods used in data-intensive science and the specific ways in which these methods presuppose theoretical assumptions. I examine two widely-used algorithms, classificatory trees and non-parametric regression, and argue that these are theory-laden in an external sense, regarding the framing of (...) research questions, but not in an internal sense concerning the causal structure of the examined phenomenon. With respect to the novelty of data-intensive science, I draw an analogy to exploratory as opposed to theory-directed experimentation. (shrink)

Contrary to formal theories of induction, I argue that there are no universal inductive inference schemas. The inductive inferences of science are grounded in matters of fact that hold only in particular domains, so that all inductive inference is local. Some are so localized as to defy familiar characterization. Since inductive inference schemas are underwritten by facts, we can assess and control the inductive risk taken in an induction by investigating the warrant for its underwriting facts. In learning more facts, (...) we extend our inductive reach by supplying more localized inductive inference schemes. Since a material theory no longer separates the factual and schematic parts of an induction, it proves not to be vulnerable to Hume's problem of the justification of induction. (shrink)

A constantly changing social reality means economic theories, even if correct today, need to be constantly revised, updated, or abandoned. To maintain an up-to-date understanding of its subject matter, economists have to continuously assess their theories even those that appear to be empirically corroborated. Economics could gain from a method that describes and is capable of generating novel explanatory hypotheses. A pessimistic view on the existence of such a method was famously articulated by Karl Popper in The Logic of Scientific (...) Discovery. He wrote ‘there is no such a thing as a logical method of having ideas or a logical reconstruction of this process.’ Herbert Simon responded to Popper and argued the opposite, namely, that there is a model of discovery and its name is abduction. Simon acknowledges his debt to Charles Peirce – the first modern logician to explicitly formulate a theory of abduction – and explains that abduction is a model of discovery that works as a problem-solving heuristic encoded.. (shrink)

The purpose of this paper is to discuss the role of financial practice in the development of mathematics as applied in human judgement. The basis of the paper is in historical research from the 1990s that argues that the monetisation of western commerce, which abstracted value into quantified price, was synthesised with scholastic analysis resulting in a “mathematical mechanistic world picture” that led to the widespread use of mathematics in science from the seventeenth century. An aspect of this process was (...) the quantification of chance that led to the development of mathematical probability, the branch of mathematics most relevant to judgement and the focus of this paper. Ideas from this historical research are related to the fundamental theorem of asset pricing, the foundational theory of contemporary financial mathematics. The paper observes that vestiges of medieval scholastic attitudes to financial ethics can be discerned in the FTAP, offering a novel interpretation of the mathematical theorem. The paper then considers the Dutch book argument, the most popular justification for subjective probability. The paper’s main contribution is in describing the significance of financial practice in validating the DBA and the paper explains how the FTAP addresses some criticisms of how the DBA represents beliefs. The conclusions emphasise the distinction between pure and practical reasoning and that this should be mirrored in a distinction between the mathematics of physica and practica. This point is important as mathematics is becoming more widespread in modelling, and directing, social systems. (shrink)

One popular test for distinguishing linked and convergent argument structures is Robert Yanal's Ordinary Summing Test. Douglas Walton, in his comprehensive survey of possible candidates for the linked/convergent distinction, advocates a particular version of Yanal's test. In a recent article, Alexander Tyaglo proposes to generalize and verifY Yanal's algorithm for convergent arguments, the basis for Yanal's Ordinary Summing Test. In this paper I will argue that Yanal's ordinary summing equation does not demarcate convergence and so his Ordinary Summing Test fails. (...) Hence, despite Walton's recommendation or Tyaglo's generalization, the Ordinary Summing Test should not be used for distinguishing linked argument structures from convergent argument structures. (shrink)

Bayesians standardly identify irrelevance with probabilistic irrelevance. However, there are cases where e is probabilistically irrelevant to h but intuitively e is relevant to h. For instance, ‘Die A came up 1 and die B came up 1, 3, 5 or 6’ is probabilistically irrelevant to ‘Die A came up odd and die B came up even’, yet, intuitively, it is not, irrelevant to that claim, in the sense that ‘Sydney has a harbour Bridge’ is irrelevant to it. In the (...) context of decision making this notion of irrelevance combined with such rules as ‘Do not expend resources on irrelevant evidence’ leads to bad results. A stronger notion of irrelevance fitting our intuitions and the contexts of decision making is proposed: e is irrelevant to h if and only if every part of e is probabilistically irrelevant to every part of h. However, we need to take care in determining what counts as part of a statement. (shrink)

An indifference principle says that your credences should be distributed uniformly over each of the possibilities you recognise. A chance deference principle says that your credences should be aligned with the chances. My thesis is that, if we are anti-Humeans about chance, then these two principles are incompatible. Anti-Humeans think that it is possible for the actual frequencies to depart from the chances. So long as you recognise possibilities like this, you cannot both spread your credences evenly and defer to (...) the chances. I discuss some weaker forms of indifference which will allow anti-Humeans to defer to the chances. (shrink)

Economists tend to view ignorance as ?rational,? neglecting the possibility that ignorance is unintentional. This oversight is reflected in economists? model of ?information search,? which can be fruitfully contrasted with ?information browsing.? Information searches are designed to discover unknown knowns, whose value is calculable ex ante, such that this value justifies the cost of the search. In this model of human information acquisition, there is no primal or ?radical? ignorance that might prevent people from knowing which information to look for, (...) lacking omniscience. Unlike ignorance that is rationally chosen on the basis of an accurate cost/benefit calculation, radical ignorance can explain human error. An account of error as grounded in radical ignorance bypasses the need to appeal to irrationality in order to explain economic (and other) mistakes. (shrink)

Although it may seem from its formalism that game theory must have sprung from the mind of John von Neumann as a corollary of his work on computers or theoretical physics, it should come as no real surprise to philosophers that game theory is the articulation of a historically developing philosophical conception of rationality in thought and action. The history of ideas about rationality is deeply contradictory at many turns. While there are theories of rationality that claim it is fundamentally (...) social and aims at understanding and molding all facets of human psychological life, game theory takes rationality to be essentially located in individuals and to concern only the means to achieve predetermined ends. Thus, there are some thinkers who have made important contributions to this history who do not appear in the story of game theory at all, among them, Plato, Kant, and Hegel. There is, however, a clear trail to follow linking theories of instrumental rationality from Aristotle to the nineteenth-century marginalist economists and ultimately to von Neumann and Morgenstern and contemporary game theorists, that historically grounds game theory as a model of rational interaction. (shrink)

We defend three controversial claims about preference, credence, and choice. First, all agents (not just rational ones) have complete preferences. Second, all agents (again, not just rational ones) have real-valued credences in every proposition in which they are confident to any degree. Third, there is almost always some unique thing we ought to do, want, or believe.

Where E is the proposition that [If H and O were true, H would explain O], William Roche and Elliot Sober have argued that P(H|O&E) = P(H|O). In this paper I argue that not only is this equality not generally true, it is false in the very kinds of cases that Roche and Sober focus on, involving frequency data. In fact, in such cases O raises the probability of H only given that there is an explanatory connection between them.

In 1947 Donald Cary Williams claimed in The Ground of Induction to have solved the Humean problem of induction, by means of an adaptation of reasoning first advanced by Bernoulli in 1713. Later on David Stove defended and improved upon Williams’ argument in The Rational- ity of Induction (1986). We call this proposed solution of induction the ‘Williams-Stove sampling thesis’. There has been no lack of objections raised to the sampling thesis, and it has not been widely accepted. In our (...) opinion, though, none of these objections has the slightest force, and, moreover, the sampling thesis is undoubtedly true. What we will argue in this paper is that one particular objection that has been raised on numerous occasions is misguided. This concerns the randomness of the sample on which the inductive extrapolation is based. (shrink)

The twin goals of this essay are: to investigate a family of cases in which the goal of guaranteed convergence to the truth is beyond our reach; and to argue that each of three strands prominent in contemporary epistemological thought has undesirable consequences when confronted with the existence of such problems. Approaches that follow Reichenbach in taking guaranteed convergence to the truth to be the characteristic virtue of good methods face a vicious closure problem. Approaches on which there is a (...) unique rational doxastic response to any given body of evidence can avoid incoherence only by rendering epistemology a curiously limited enterprise. Bayesian approaches rule out humility about one’s prospects of success in certain situations in which failure is typical. (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)

This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method appropriate for the model considered. A unified treatment of subjective decision (...) weights results for most of the decision models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We generalize Savage’s nonatomiticy condition (“P6”) and his assumption of (sigma) algebras of events, while fully maintaining his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty, such as definitions of ambiguity aversion and pessimism. (shrink)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)

Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief. (shrink)

The aim of this thesis is to improve our understanding of how to assess and communicate uncertainty in areas of research deeply afflicted by it, the assessment and communication of which are made more fraught still by the studies’ immediate policy implications. The IPCC is my case study throughout the thesis, which consists of three parts. In Part 1, I offer a thorough diagnosis of conceptual problems faced by the IPCC uncertainty framework. The main problem I discuss is the persistent (...) ambiguity surrounding the concepts of ‘confidence’ and ‘likelihood’; I argue that the lack of a conceptually valid interpretation of these concepts compatible with the IPCC uncertainty guide’s recommendations has worrying implications for both the IPCC authors’ treatment of uncertainties and the interpretability of the information provided in the AR5. Finally, I show that an understanding of the reasons behind the IPCC’s decision to include two uncertainty scales can offer insights into the nature of this problem. In Part 2, I review what philosophers have said about model-based robustness analysis. I assess several arguments that have been offered for its epistemic import and relate this discussion to the context of climate model ensembles. I also discuss various measures of independence in the climate literature, and assess the extent to which these measures can help evaluate the epistemic import of model robustness. In Part 3, I explore the notion of the ‘weight of evidence’ typically associated with Keynes. I argue that the Bayesian is bound to struggle with this notion, and draw some lessons from this fact. Finally, I critically assess some recent proposals for a new IPCC uncertainty framework that significantly depart from the current one. (shrink)

The thesis consists of an introduction and five papers. The introduction gives a brief historical survey of empirical investigations into the effectiveness of medicinal interventions, as well as surveys of the concept of evidence and of the history and philosophy of experiments. The main ideas of the EBM movement are also presented. Paper I: Concerns have been raised that clinical trials do not offer reliable evidence for some types of treatment, in particular for highly individualised treatments, for example traditional homeopathy. (...) With respect to individualised treatments, it is argued that such concerns are unfounded. There are two minimal conditions related to the nature of the treatments that must be fulfilled for evaluability in a clinical trial, namely the proper distinction of treatment groups and the elimination of confounding variables or variations. These conditions do not preclude the testing of individualised medicine. Paper II: Traditionally, mechanistic reasoning has been assigned a negligible role in the EBM literature. When discussed, mechanistic reasoning has almost exclusively been positive – both in an epistemic sense of claiming that there is a mechanistic chain and in a health-related sense of there being claimed benefits for the patient. Negative mechanistic reasoning has been neglected. I distinguish three main types of negative mechanistic reasoning and subsume them under a new definition. One of the three distinguished types, which is negative only in the health-related sense, has a corresponding positive counterpart, whereas the other two, which are epistemically negative, do not have such counterparts, at least not that are particularly interesting as evidence. Accounting for negative mechanistic reasoning in EBM is therefore partly different from accounting for positive mechanistic reasoning. Paper III: Evidence hierarchies are lists of investigative strategies ordered with regard to the claimed strength of evidence. They have been used for a couple of decades within EBM, particularly for the assessment of evidence for treatment recommendations, but they remain controversial. An under-investigated question is what the order in the hierarchy means. Four interpretations of the order are distinguished and discussed. The two most credible ones are, in rough terms, “typically stronger” and “ideally stronger”. The GRADE framework seems to be based on the “typically stronger” reading. Even if the interpretation of an evidence hierarchy were established, hierarchies appear to be rather unhelpful for the task of evidence aggregation. However, specifying the intended order relation may help sort out disagreements. Paper IV: There are three main arguments for randomisation that connect inseparably to theoretical concepts: Randomisation is useful for performing null hypothesis testing. Randomisation is needed for plausible causal inferences from treatment to effect. Randomisation is acceptable and computationally convenient in a Bayesian setting. A critical scrutiny of these arguments shows that is acceptable in the context of clinical trials. As for, it is argued that randomisation only provides weak reasons for drawing causal inferences in the context of real clinical trials. Argument is weak because it is controversial among Bayesians, and because formally Bayesian analyses of trial results are rarely asked for. Paper V: Practical arguments for randomisation are arguments with no necessary connections to theoretical frameworks like null hypothesis testing or causal inferences. Four common practical arguments in the context of clinical trials are distinguished and assessed: Randomisation contributes to allocation concealment. Randomisation contributes to the baseline balance of treatment groups. Randomisation decreases self-selection bias. Randomisation removes allocation bias. Argument is rejected. Arguments and are approved. Argument is rejected if it is formulated so as to be independent from and, but it is true that randomisation contributes to balance through the mechanisms mentioned in and. It is judged that may be the strongest single argument. (shrink)