The principle of indifference is supposed to suffice for the rational assignation of probabilities to possibilities. Bertrand advances a probability problem, now known as his paradox, to which the principle is supposed to apply; yet, just because the problem is ill‐posed in a technical sense, applying it leads to a contradiction. Examining an ambiguity in the notion of an ill‐posed problem shows that there are precisely two strategies for resolving the paradox: the distinction strategy and the well‐posing strategy. The main (...) contenders for resolving the paradox, Marinoff and Jaynes, offer solutions which exemplify these two strategies. I show that Marinoff’s attempt at the distinction strategy fails, and I offer a general refutation of this strategy. The situation for the well‐posing strategy is more complex. Careful formulation of the paradox within measure theory shows that one of Bertrand’s original three options can be ruled out but also shows that piecemeal attempts at the well‐posing strategy will not succeed. What is required is an appeal to general principle. I show that Jaynes’s use of such a principle, the symmetry requirement, fails to resolve the paradox; that a notion of metaindifference also fails; and that, while the well‐posing strategy may not be conclusively refutable, there is no reason to think that it can succeed. So the current situation is this. The failure of Marinoff’s and Jaynes’s solutions means that the paradox remains unresolved, and of the only two strategies for resolution, one is refuted and we have no reason to think the other will succeed. Consequently, Bertrand’s paradox continues to stand in refutation of the principle of indifference. (shrink)

The evidence of your own eyes has often been regarded as unproblematic. But we know that people make mistaken observations. This can be looked on as unimportant if there issome class of statements that can serve as evidence for others, or if every statement in our corpus of knowledge is allowed to be no more than probable. Neither of these alternatives is plausible when it comes to machine or robotic observation. Then we must take the possibility of error seriously, and (...) we must be prepared to deal with error quantitatively. The problem of using internal evidence to arrive at error distributions is the main focus of the paper. (shrink)

This paper argues that Ramsey's view of the calculus of subjective probabilities as, in effect, logical axioms is the correct view, with powerful heuristic value. This heuristic value is seen particularly in the analysis of the role of conditionalization in the Bayesian theory, where a semantic criterion of synchronic coherence is employed as the test of soundness, which the traditional formulation of conditionalization fails. On the other hand, there is a generally sound rule which supports conditionalization in appropriate contexts, though (...) these contexts are not universal. This sound Bayesian rule is seen to be analogous in certain respects to the deductive rule of modus ponens. (shrink)

Rational analysis (Anderson 1990, 1991a) is an empiricalprogram of attempting to explain why the cognitive system isadaptive, with respect to its goals and the structure of itsenvironment. We argue that rational analysis has two importantimplications for philosophical debate concerning rationality. First,rational analysis provides a model for the relationship betweenformal principles of rationality (such as probability or decisiontheory) and everyday rationality, in the sense of successfulthought and action in daily life. Second, applying the program ofrational analysis to research on human reasoning (...) leads to a radicalreinterpretation of empirical results which are typically viewed asdemonstrating human irrationality. (shrink)

In his review essay on World Statehood, Morgan poses three questions, namely: does my conceptualization imply conflation of agency and structure; is the realist processual account of time contradictory; and have we humans already reached the limit of the possible? I address each question briefly one at a time, arguing that the concept of self-transformative capacity of contexts does not imply conflation; that various processes with different durations can exhibit patterns that can be reasonably discussed and assessed and, with caution, (...) also used in anticipations; and that there is no cosmic law or limit that inevitably hinders humanity's further progress. (shrink)

This book takes purism about knowledge as the default position and defends it from the challenges of pragmatic encroachment. The book is divided into two parts, a negative and a positive one. The negative part critically examines existing purist strategies in response to pragmatic encroachment. The positive part provides a new theory of how practical factors can systematically influence our confidence and explores some implications of such influence.

Rational agents seem more confident in any possible event than in an impossible event. But if rational credences are real-valued, then there are some possible events that are assigned 0 credence nonetheless. How do we differentiate these events from impossible events then when we order events? de Finetti (1975), Hájek (2012) and Easwaran (2014) suggest that when ordering events, conditional credences and subset relations are as relevant as unconditional credences. I present a counterexample to all their proposals in this paper. (...) While their proposals order possible and impossible events correctly, they deliver the wrong verdict for disjoint possible events assigned equal positive credence. (shrink)

This thesis is about making decisions when we are uncertain about what will happen, how valuable it will be, and even how to make decisions. Even the most sure-footed amongst us are sometimes uncertain about all three, but surprisingly little attention has been given to the latter two. The three essays that constitute my thesis hope to do a small part in rectifying this problem. The first essay is about the value of finding out how to make decisions. Society spends (...) considerable resources funding people (like me) to research decision-making, so it is natural to wonder whether society is getting a good deal. This question is so shockingly underresearched that bedrock facts are readily discoverable, such as when this kind of information is valuable. My second essay concerns whether we can compare value when we are uncertain about value. Many people are in fact uncertain about value, and how we deal with this uncertainty hinges on these comparisons. I argue that value comparisons are only sometimes possible; I call this weak comparability. This essay is largely a synthesis of the literature, but I also present an argument which begins with a peculiar view of the self: it is as if each of us is a crowd of different people separated by time (but connected by continuity of experience). I’m not the first to endorse this peculiar view of the self, but I am the first to show how it supports the benign view that value is sometimes comparable. We may be uncertain of any decision rules, even those that would tell us how to act when we face uncertainty in decision rules. We may be uncertain of how to decide how to decide how to... And so on. If so, we might have to accept infinitely many decision rules just to make any mundane decision, such as whether to pick up a five-cent piece from the gutter. My third essay addresses this problem of regress. I think all of our decisions are forced: we must decide now or continue to deliberate. Surprisingly, this allows us to avoid the original problem. I call this solution “when forced, do your best”. (shrink)

Historically, hypotheses failed in most cases to correctly forecast the workings of complex biological systems. Francis Crick’s adaptor hypothesis, however, stands out as an exceptional case of a confirmed abstract prediction. This hypothesis presciently anticipated the existence of RNA adaptors that function as bridges between amino acids and the chemically different nucleic acid template for proteins. Crick conjectured that the adaptors are enzymatically charged with cognate amino acids, they bind to complementary protein-coding nucleic acid, and their liberated amino acids are (...) incorporated into growing protein chains. Independently from and concomitantly with Crick’s hypothesis, Mahlon Hoagland and Paul Zamecnik conducted experiments with no guiding theory that culminated in discoveries of the actual adaptors, transfer RNA (tRNA) molecules, and their amino acids charging enzymes. This paper traces the parallel histories of Crick’s adaptor hypothesis and of the experimental discovery of tRNA and compares their relative impacts on the scientific community. Remarkably, despite the brilliance of Crick’s confirmed prognostication, it had marginal impact on practicing scientists. Conversely, Hoagland and Zamecnik’s experimental discoveries and their evidence-based model of protein synthesis had immediate and enduring impact. I discuss possible explanations for the different impacts of the theoretical prediction and experimental identifications of the same entities. (shrink)

Can scientific evidence outstretch what scientists have mentally entertained, or could ever entertain? This article focuses on the plausibility and consequences of an affirmative answer in a special case. Specifically, it discusses how we may treat automated scientific data-gathering systems—especially AI systems used to make predictions or to generate novel theories—from the point of view of confirmation theory. It uses AlphaFold2 as a case study.

Many theories of rational action are predicated on the idea that what it is rational to do in a given situation depends, in part, on what it is rational to believe in that situation. In short: they treat epistemic rationality as explanatorily prior to practical rationality. If they are right in doing so, it follows, on pain of explanatory circularity, that epistemic rationality cannot itself be a form of practical rationality. Yet, many epistemologists have defended just such a view of (...) epistemic rationality. According to them, there is no such thing as a distinctively epistemic form of rationality which could be explanatorily prior to practical rationality. Rather, they maintain, there is just one form of rationality—practical rationality—of which epistemic rationality is a species. What to make of this conflict? The aim of this paper is to motivate a view about the relationship between epistemic and practical rationality which resolves the conflict in a way that should be attractive to both sides. The central idea is to ground both epistemic and practical rationality in an independently motivated notion of evidential probability which is itself to be understood in non-normative terms. Doing so, I argue, allows us to unify epistemic and practical rationality in a way that does justice to the idea that what it is rational to do depends, in part, on what it is rational to believe; and to do so in a way that avoids explanatory circularity. (shrink)

Bell’s theorem is often said to imply that quantum mechanics violates local causality, and that local causality cannot be restored with a hidden-variables theory. This however is only correct if the hidden-variables theory fulfils an assumption called Statistical Independence. Violations of Statistical Independence are commonly interpreted as correlations between the measurement settings and the hidden variables. Such correlations have been discarded as “fine-tuning” or a “conspiracy”. We here point out that the common interpretation is at best physically ambiguous and at (...) worst incorrect. The problem with the common interpretation is that Statistical Independence might be violated because of a non-trivial measure in state space, a possibility we propose to call “supermeasured”. We use Invariant Set Theory as an example of a supermeasured theory that violates the Statistical Independence assumption in Bell’s theorem without requiring correlations between hidden variables and measurement settings. (shrink)

Janina Hosiasson-Lindenbaum is a known figure in philosophy of probability of the 1930s. A previously unpublished manuscript fills in the blanks in the full picture of her work on inductive reasoning by analogy, until now only accessible through a single publication. In this paper, I present Hosiasson’s work on analogical reasoning, bringing together her early publications that were never translated from Polish, and the recently discovered unpublished work. I then show how her late work relates to Rudolf Carnap’s approach to (...) “analogy by similarity” developed in the 1960s. Hosiasson turns out to be a predecessor of the line of research that models analogical influence as inductive relevance. A translation of Hosiasson’s manuscript concludes the paper. (shrink)

This paper offers an articulation and defence of the modal account of legal risk in light of a range of objections that have been proposed against this view in the recent literature. It is argued that these objections all trade on a failure to distinguish between the modal nature of risk more generally, and the application of this modal account to particular decision-making contexts, such as legal contexts, where one must rely on a restricted body of information. It is argued (...) that once the modal account of legal risk is properly understood as involving information-relative judgements about the modal closeness of the target risk event, the objections to the view are neutralized. (shrink)

Merging beliefs depends on the relative reliability of their sources. When this is information is absent, assuming equal reliability is unwarranted. The solution proposed in this article is that every reliability profile is possible, and only what holds according to all of them is accepted. Alternatively, one source is completely reliable, but which one is not specified. These two cases motivate two existing forms of merging: maxcons-based merging and disjunctive merging.

At the centenary of Frank H. Knight’s Risk, Uncertainty, and Profit, we explore the continuing relevance of Knightian uncertainty to the theory and practice of entrepreneurship. There are three challenges facing such assessment. First, RUP is complex and difficult to interpret. The key but neglected element of RUP is that Knight’s account is not solely about risk and uncertainty as states of nature, but about how an agent’s beliefs about uncertain outcomes and confidence in those beliefs guide their choices. Second, (...) RUP is Knight’s only effort in this area. His subsequent career led elsewhere, so he did not engage with subsequent interpretations of this work. Third, much of the current literature emphasizes that decisions must be different under the two states of nature with a consequent misunderstanding of entrepreneurial agency. This paper addresses each challenge in sequence. First, we explicate Knight’s approach and explain why that approach is murky. Second, as a complement to Knight’s interpretation, we examine Frank P. Ramsey’s approach to subjective probabilities to help clarify Knight’s murky approach. What links Knight and Ramsey is a shared pragmatism about entrepreneurial agency under uncertainty that depends upon the beliefs about, and confidence in, their judgments of possible outcomes. This Knight-Ramsey approach does not require actor’s behaviors to be determined by the class of uncertain environment they face. We focus on the response by the entrepreneur to the existence of uncertainty in all its forms. We argue that this reductive account provides a foundation to examine common problems in management, including managerial hubris, the interaction between entrepreneurs and venture capitalists, and the need for experimentation in advance of new product and venture launches. Third, we critique current literature that favors epistemic purism about the ontology of risk and uncertainty and ignores Knight-Ramsey pragmatism in meeting uncertainty, such as using formal and informal institutions for uncertainty mitigation. Our account locates Frank Knight’s subtleties in entrepreneurial behavior firmly in the literature on entrepreneurial agency a century later. (shrink)

This paper is about a tension between two theses. The first is Value of Evidence: roughly, the thesis that it is always rational for an agent to gather and use cost‐free evidence for making decisions. The second is Rationality of Imprecision: the thesis that an agent can be rationally required to adopt doxastic states that are imprecise, i.e., not representable by a single credence function. While others have noticed this tension, I offer a new diagnosis of it. I show that (...) it arises when an agent with an imprecise doxastic state engages in an unreflective inquiry, an inquiry where they revise their beliefs using an updating rule that doesn't satisfy a weak reflection principle. In such an unreflective inquiry, certain synchronic norms of instrumental rationality can make it instrumentally irrational for an agent to gather and use cost‐free evidence. I then go on to propose a diachronic norm of instrumental rationality that preserves Value of Evidence in unreflective inquiries. This, I suggest, may help us reconcile this thesis with Rationality of Imprecision. (shrink)

An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree in the (...) context of probabilistic epistemology, however, _does_ challenge prominent subjectivist responses to the problem of the priors. (shrink)

A frequentist confidence interval can be constructed by inverting a hypothesis test, such that the interval contains only parameter values that would not have been rejected by the test. We show how a similar definition can be employed to construct a Bayesian support interval. Consistent with Carnap’s theory of corroboration, the support interval contains only parameter values that receive at least some minimum amount of support from the data. The support interval is not subject to Lindley’s paradox and provides an (...) evidence-based perspective on inference that differs from the belief-based perspective that forms the basis of the standard Bayesian credible interval. (shrink)

We are concerned here with how structural properties of language may come to reflect features of the world in which it evolves. As a concrete example, we will consider how a simple term language might evolve to support the principle of indifference over state descriptions in that language. The point is not that one is justified in applying the principle of indifference to state descriptions in natural language. Instead, it is that one should expect a language that has evolved in (...) the context of facilitating successful action to reflect probabilistic features of the world in which it evolved. (shrink)

At the centenary of Frank H. Knight’s Risk, Uncertainty, and Profit (1921), we explore the continuing relevance of Knightian uncertainty to the theory and practice of entrepreneurship. There are three challenges facing such assessment. First, RUP is complex and difficult to interpret. The key but neglected element of RUP is that Knight’s account is not solely about risk and uncertainty as states of nature, but about how an agent’s beliefs about uncertain outcomes and confidence in those beliefs guide their choices. (...) Second, RUP is Knight’s only effort in this area. His subsequent career led elsewhere, so he did not engage with subsequent interpretations of this work. Third, much of the current literature emphasizes that decisions must be different under the two states of nature with a consequent misunderstanding of entrepreneurial agency. This paper addresses each challenge in sequence. First, we explicate Knight’s (1921) approach and explain why that approach is murky. Second, as a complement to Knight’s interpretation, we examine Frank P. Ramsey’s approach to subjective probabilities to help clarify Knight’s murky approach. What links Knight and Ramsey is a shared pragmatism about entrepreneurial agency under uncertainty that depends upon the beliefs about, and confidence in, their judgments of possible outcomes. This Knight-Ramsey approach does not require actor’s behaviors to be determined by the class of uncertain environment (whether risk, uncertainty, or ambiguity) they face. We focus on the response by the entrepreneur to the existence of uncertainty in all its forms. We argue that this reductive account provides a foundation to examine common problems in management, including managerial hubris, the interaction between entrepreneurs and venture capitalists, and the need for experimentation (such as prototyping and market research) in advance of new product and venture launches. Third, we critique current literature that favors epistemic purism about the ontology of risk and uncertainty and ignores Knight-Ramsey pragmatism in meeting uncertainty, such as using formal and informal institutions for uncertainty mitigation. Our account locates Frank Knight’s subtleties in entrepreneurial behavior firmly in the literature on entrepreneurial agency a century later. (shrink)

This paper proposes a framework for representing in Bayesian terms the idea that analogical arguments of various degrees of strength may provide inductive support to yet untested scientific hypotheses. On this account, contextual information plays a crucial role in determining whether, and to what extent, a given similarity or dissimilarity between source and target may confirm an empirical hypothesis over a rival one. In addition to showing confirmation by analogy compatible with the adoption of a Bayesian standpoint, the proposal outlined (...) in this paper reveals a close agreement between the fulfillment of Hesse’s (Models and analogies in science, University of Notre Dame Press, 1963) criteria for analogical arguments capable of inductive support and the attribution of confirmatory power by the lights of Bayesian confirmation theory. In this sense, the Bayesian representation not only enriches a framework, Hesse’s, of enduring relevance for understanding scientific activity, but may offer something akin to a proof of concept of it. (shrink)

Tenenbaum and Griffiths (2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (1987) and Tversky’s (1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that generalisation as a Bayesian inference should be seen as a complement to, (...) instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (shrink)

It is usually accepted that deductions are non-informative and monotonic, inductions are informative and nonmonotonic, abductions create hypotheses but are epistemically irrelevant, and both deductions and inductions can’t provide new insights. In this article, I attempt to provide a more cohesive view of the subject with the following hypotheses: (1) the paradigmatic examples of deductions, such as modus ponens and hypothetical syllogism, are not inferential forms, but coherence requirements for inferences; (2) since any reasoner aims to be coherent, any inference (...) must be deductive; (3) a coherent inference is an intuitive process where the premises should be taken as sufficient evidence for the conclusion, which on its turn should be viewed as necessary evidence for the premises in some modal range; (4) inductions, properly understood, are abductions, but there are no abductions beyond the fact that in any inference the conclusion should be regarded as necessary evidence for the premises; (5) monotonicity is not only compatible with the retraction of past inferences given new information, but it is a requirement for it; (6) this explanation of inferences holds true for discovery processes, predictions and trivial inferences. (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)

In this paper, I critically evaluate several related, provocative claims made by proponents of data-intensive science and “Big Data” which bear on scientific methodology, especially the claim that scientists will soon no longer have any use for familiar concepts like causation and explanation. After introducing the issue, in Section 2, I elaborate on the alleged changes to scientific method that feature prominently in discussions of Big Data. In Section 3, I argue that these methodological claims are in tension with a (...) prominent account of scientific method, often called “Inference to the Best Explanation”. Later on, in Section 3, I consider an argument against IBE that will be congenial to proponents of Big Data, namely, the argument due to Roche and Sober Analysis, 73:659–668, that “explanatoriness is evidentially irrelevant.” This argument is based on Bayesianism, one of the most prominent general accounts of theory-confirmation. In Section 4, I consider some extant responses to this argument, especially that of Climenhaga Philosophy of Science, 84:359–368,. In Section 5, I argue that Roche and Sober’s argument does not show that explanatory reasoning is dispensable. In Section 6, I argue that there is good reason to think explanatory reasoning will continue to prove indispensable in scientific practice. Drawing on Cicero’s oft-neglected De Divinatione, I formulate what I call the “Ciceronian Causal-nomological Requirement”, which states, roughly, that causal-nomological knowledge is essential for relying on correlations in predictive inference. I defend a version of the CCR by appealing to the challenge of “spurious correlations,” chance correlations which we should not rely upon for predictive inference. In Section 7, I offer some concluding remarks. (shrink)

This volume is a collection of some of the most important philosophical papers by Peter Gärdenfors. Spanning a period of more than 20 years of his research, they cover a wide ground of topics, from early works on decision theory, belief revision and nonmonotonic logic to more recent work on conceptual spaces, inductive reasoning, semantics and the evolutions of thinking. Many of the papers have only been published in places that are difficult to access. The common theme of all the (...) papers is the dynamics of thought. Several of the papers have become minor classics and the volume bears witness of the wide scope of Gärdenfors’ research and of his crisp and often witty style of writing. The volume will be of interest to researchers in philosophy and other cognitive sciences. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

This thesis has two goals. Firstly, we consider the problem of model selection for the purposes of prediction. In modern science predictive mathematical models are ubiquitous and can be found in such diverse fields as weather forecasting, economics, ecology, mathematical psychology, sociology, etc. It is often the case that for a given domain of inquiry there are several plausible models, and the issue then is how to discriminate between them – this is the problem of model selection. We consider approaches (...) to model selection that are used in classical [also known as frequentist] statistics, and fashionable in recent years methods of Akaike Information Criterion [AIC] and Bayes Information Criterion [BIC], the latter being a part of a broader Bayesian approach. We show the connection between AIC and BIC, and provide comparison of performance of these methods. Secondly, we consider some philosophical arguments that arise within the setting of the model selection approaches investigated in the first part. These arguments aim to provide counterexamples to the epistemic thesis of scientific realism, viz., that predictively successful scientific theories are approximately true, and to the idea that truth and predictive accuracy go together. We argue for the following claims: 1) that none of the criticisms brought forward in the philosophical literature against the AIC methodology are devastating, and AIC remains a viable method of model selection; 2) that the BIC methodology likewise survives the numerous criticisms; 3) that the counterexamples to scientific realism that ostensibly arise within the framework of model selection are flawed; 4) that in general the model selection methods discussed in this thesis are neutral with regards to the issue of scientific realism; 5) that a plurality of methodologies should be applied to the problem of model selection with full awareness of the foundational issues that each of these methodologies has. (shrink)

The debates between Bayesian, frequentist, and other methodologies of statistics have tended to focus on conceptual justifications, sociological arguments, or mathematical proofs of their long run properties. Both Bayesian statistics and frequentist (“classical”) statistics have strong cases on these grounds. In this article, we instead approach the debates in the “Statistics Wars” from a largely unexplored angle: simulations of different methodologies’ performance in the short to medium run. We conducted a large number of simulations using a straightforward decision problem based (...) around tossing a coin with unknown bias and then placing bets. In this simulation, we programmed four players, inspired by Bayesian statistics, frequentist statistics, Jon Williamson’s version of Objective Bayesianism, and a player who simply extrapolates from observed frequencies to general frequencies. The last player functions as a benchmark: a statistical methodology should at least outperform a crude form of induction. We focused on the performance of these methodologies in guiding the players towards good decisions. Unlike an earlier simulation study of this type, we found no systematic difference in performance between the Bayesian and frequentist players, provided the Bayesian used a flat prior and the frequentist used a low confidence level. Unlike that study, we were able to use Big Data methods to mitigate problems of random error in the simulation results. The Williamsonian player, who is a novel element of our study, also had no systematic differences in their performance, provided that they use a low confidence level. These players performed similarly even in the very short run, when players were making different decisions. Our study indicates that all three methodologies should be taken seriously by philosophers and practitioners of statistics. However, the frequentist and Williamsonian performed poorly when their confidence levels were high, and the Bayesian was surprisingly harmed by biased priors, providing some unexpected lessons for these methodologies when facing this type of decision problem. (shrink)

Exposed in 1948, within his masterpiece on the scope and limits of human knowledge, the epistemological tenets that Bertrand Russell regarded as fundamental elements in the construction of scientific knowledge, are still worthy of a detailed discussion today. Given the excellence of the author, it will not be surprising to see that Russell's gnoseologic postulates, even for the present scientific view, address some of the most controversial questions still to be solved in the theory of knowledge.

This paper argues that representationalism of a Fodorian variety can accommodate the fact that beliefs come in degrees. First, it responds to two key arguments to the contrary. Second, it builds upon these responses and outlines a novel representationalist theory of degrees of beliefs. I call this theory dispositional representationalism, as it involves direct appeal to our dispositions to form representations and propositional attitudes concerning them.

Much of the literature on the relationship between belief and credence has focused on the reduction question: that is, whether either belief or credence reduces to the other. This debate, while important, only scratches the surface of the belief-credence connection. Even on the anti-reductive dualist view, belief and credence could still be very tightly connected. Here, I explore questions about the belief-credence connection that go beyond reduction. This paper is dedicated to what I call the independence question: just how independent (...) are belief and credence? I look at this question from two angles: a descriptive one (as a psychological matter, how much can belief and credence come apart?) and a normative one (for a rational person, how closely connected are belief and credence?) Ultimately, I suggest that the two attitudes are more independent than one might think. (shrink)

Whilst Bayesian epistemology is widely regarded nowadays as our best theory of knowledge, there are still a relatively large number of incompatible and competing approaches falling under that umbrella. Very recently, Wallmann and Williamson wrote an interesting article that aims at showing that a subjective Bayesian who accepts the principal principle and uses a known physical chance as her degree of belief for an event A could end up having incoherent or very implausible beliefs if she subjectively chooses the probability (...) of an event F for which she has much poorer evidence. They also argued that their own version of objective Bayesianism is completely immune to that challenge. In this article, after having presented the strongest version of Wallmann’s and Williamson’s argument, I will show that if successful, it has far-reaching consequences and would not only invalidate moderate subjective Bayesianism and imprecise probalism but also a form of objective Bayesianism that relies on conditionalisation, the principal principle, reference classes, and the principle of indifference applied to the most basic partitions. I then argue that their argument can be defeated by adding the rule that it is always irrational to choose a probability that can be computed from the known probabilities associated to one’s other beliefs. I finally argue that the authors’ main intuition that probabilities have different degrees of reliability favours imprecise Bayesianism over precise Bayesianism. (shrink)

I examine the foundations of a just society using the lens of decision theory. The conception of just society is from an individual’s viewpoint: where would I rather live if I have an equal chance of being any individual? Three alternative designs for a just society are examined. These are: laissez-faire, maximin and social minimum. Two assumptions about human nature clarify the distinction among three societies. The first assumption is that a representative individual’s utility function is concave. The second assumption (...) recognizes that redistribution to achieve equality reduces total wealth. A rational individual would prefer a society where one is free to maximize one’s expected utility. A social minimum that includes both the provision of essential human needs and equality of opportunity (education, healthcare, access to capital) for a flourishing life emerges as a candidate solution for the basic structure of society. (shrink)

This thesis is a collection of three self-contained papers on related themes in the area of formal and social epistemology. The first paper explores the possibility of measuring the coherence of a set with multiplicative averaging. It has been pointed out that all the existing probabilistic measures of coherence are flawed for taking the relevance between a set of propositions as the primary factor which determines the coherence of the set. What I show in this paper is that a group (...) of measures, namely the confirmation-based ones, can be saved from this problem if we adopt a nonlinear averaging function to measure the coherence of a set. The second paper discusses how people should conciliate in disagreements. Some epistemologists take linear averaging as the only way of conciliating and claim that conciliating leads to fallacious results. In the paper, I show that the problem is not conciliating, but taking linear averaging as the only way to conciliate. Since there is no reason for us to insist on conciliating with linear averaging, we can adopt nonlinear averaging functions for conciliating and thereby avoid the formal deficiencies. The third paper focuses on the pragmatic results of taking conciliating as a general strategy in disagreements. There is a potential dilemma about conciliating: if everyone always conciliates, it is likely for an epistemic bubble to arise. If everyone refuses to conciliate, an epistemic echo chamber may appear. A possible way of solving the dilemma is to develop a diachronic strategy which tells people how to both conciliate and update their estimate of their interlocutors’ reliability. Although the three papers differ in the subject, they jointly offer some unifying reflections on the way we approach philosophical problems with formal tools. From 5 the first two papers, we see that a formal analysis of a philosophical position is incomplete if philosophers fail to consider a sufficiently wide range of formal tools. The third paper, on the contrary, shows that we should change the ordinary way of modelling a notion if required. This thesis concludes by proposing a pluralistic view of formal methods in formal epistemology. (shrink)

Epistemic states of uncertainty play important roles in ethical and political theorizing. Theories that appeal to a “veil of ignorance,” for example, analyze fairness or impartiality in terms of certain states of ignorance. It is important, then, to scrutinize proposed conceptions of ignorance and explore promising alternatives in such contexts. Here, I study Lerner’s probabilistic egalitarian theorem in the setting of imprecise probabilities. Lerner’s theorem assumes that a social planner tasked with distributing income to individuals in a population is “completely (...) ignorant” about which utility functions belong to which individuals. Lerner models this ignorance with a certain uniform probability distribution, and shows that, under certain further assumptions, income should be equally distributed. Much of the criticism of the relevance of Lerner’s result centers on the representation of ignorance involved. Imprecise probabilities provide a general framework for reasoning about various forms of uncertainty including, in particular, ignorance. To what extent can Lerner’s conclusion be maintained in this setting? (shrink)

In modern science, the theory of probability is one of the basic tools. Scientists using probability often refer to its objective interpretation. They emphasize that their probabilistic hypotheses concern objective facts, not degrees of belief. Accordingly, the following questions arise: What is the meaning of this type of probabilistic hypothesis? Is the assumption of objectivity necessary? The paper addresses these questions by analyzing objective probability in the context of the scientific debate on determinism. Two types of arguments will be presented. (...) On the one hand, there is the assertion that objective probability can exist only in an indeterministic world. Then, on the other hand — I analyze the assertions of those who believe in the co‑existence of objective probability and determinism. As a result I show that the acceptance of deterministic and indeterministic fields as possible areas where objective probability can occur is extremely problematic. Depending on the chosen area we encounter different types of problems. Therefore, I show that a significant number of these problems are associated with the acceptance of incorrect metaphysical assumptions. And finally, I postulate that the objectivity of probability can be reduced to the epistemic variant. (shrink)

The purpose of this paper is to show that if one adopts conditional probabilities as the primitive concept of probability, one must deal with the fact that even in very ordinary circumstances at least some probability values may be imprecise, and that some probability questions may fail to have numerically precise answers.

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)

Theorists from John Stuart Mill to Robert Nozick have argued that citizens can gain insight into the demands of justice by experimenting with diverse forms of political life. I consider the rationa...

The philosophical background important to Mill’s theory of induction has two major components: Richard Whately’s introduction of the uniformity principle into inductive inference and the loss of the idea of formal cause.

The intuitive Variety of Evidence Thesis states that, ceteris paribus, more varied evidence for a hypothesis confirms it more strongly than less varied evidence. Recent Bayesian analyses have raised serious doubts in its validity. Claveau suggests the existence of a novel type of counter-example to this thesis: a gradual increase in source independence can lead to a decrease in hypothesis confirmation. I show that Claveau’s measure of gradual source independence suffers from two unsuspected types of inconsistencies. I hence put forward (...) a more natural measure of gradual source independence which is not plagued by inconsistencies. Claveau’s counter-examples to the variety of evidence thesis disappear with the measure I suggest. I hence argue that my measure is preferable and that this thesis does at least not seem to be troubled by Claveau’s arguments. (shrink)

In this paper I investigate an alternative to imprecise probabilism. Imprecise probabilism is a popular revision of orthodox Bayesianism: while the orthodox Bayesian claims that a rational agent’s belief-state can be represented by a single credence function, the imprecise probabilist claims instead that a rational agent’s belief-state can be represented by a set of such functions. The alternative that I put forward in this paper is to claim that the expression ‘credence’ is vague, and then apply the theory of supervaluationism (...) to sentences containing this expression. This gives us a viable alternative to imprecise probabilism, and I end by comparing the two accounts. I show that supervaluationism has a simpler way of handling sentences relating the belief-states of two different people, or of the same person at two different times; that both accounts may have the resources to develop plausible decision theories; and finally that the supervaluationist can accommodate higher-order vagueness in a way that is not available to the imprecise probabilist. (shrink)