The orthodox view in statistics has it that frequentism and Bayesianism are diametrically opposed—two totally incompatible takes on the problem of statistical inference. This paper argues to the contrary that the two approaches are complementary and need to mesh if probabilistic reasoning is to be carried out correctly.

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)

Expert probability forecasts can be useful for decision making . But levels of uncertainty escalate: however the forecaster expresses the uncertainty that attaches to a forecast, there are good reasons for her to express a further level of uncertainty, in the shape of either imprecision or higher order uncertainty . Bayesian epistemology provides the means to halt this escalator, by tying expressions of uncertainty to the propositions expressible in an agent’s language . But Bayesian epistemology comes in three main varieties. (...) Strictly subjective Bayesianism and empirically-based subjective Bayesianism have difficulty in justifying the use of a forecaster’s probabilities for decision making . On the other hand, objective Bayesianism can justify the use of these probabilities, at least when the probabilities are consistent with the agent’s evidence . Hence objective Bayesianism offers the most promise overall for explaining how testimony of uncertainty can be useful for decision making. Interestingly, the objective Bayesian analysis provided in Sect. 5 can also be used to justify a version of the Principle of Reflection. (shrink)

Bayesian probability is normally defined over a fixed language or eventspace. But in practice language is susceptible to change, and thequestion naturally arises as to how Bayesian degrees of belief shouldchange as language changes. I argue here that this question poses aserious challenge to Bayesianism. The Bayesian may be able to meet thischallenge however, and I outline a practical method for changing degreesof belief over changes in finite propositional languages.

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)

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 article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

Some arguments are good; others are not. How can we tell the difference? This article advances three proposals as a partial answer to this question. The proposals are keyed to arguments conditioned by different degrees of uncertainty: mild, where the argument’s premises are hedged with point-valued probabilities; moderate, where the premises are hedged with interval probabilities; and severe, where the premises are hedged with non-numeric plausibilities such as ‘very likely’ or ‘unconfirmed’. For mild uncertainty, the article proposes to apply a (...) principle referred to as ‘Jeffrey’s rule’, for the principle is a generalization of Jeffrey conditionalization. For moderate uncertainty, the proposal is to extend Jeffrey’s rule for use with probability intervals. For severe uncertainty, the article proposes that even when lack of probabilistic information prevents the application of Jeffrey’s rule, the rule can be adapted to these conditions with the aid of a suitable plausibility measure. Together, the three proposals introduce an approach to argument evaluation that complements established frameworks for evaluating arguments: deductive soundness, informal logic, argumentation schemes, pragma-dialectics, and Bayesian inference. Nevertheless, this approach can be looked at as a generalization of the truth and validity conditions of the classical criterion for sound argumentation. (shrink)

Comparisons between utilities pose a pressing problem if, while incapable of being grounded, they are required in ethical deliberation. My aim is to consider whether there are epistemological impediments to implementing such ethical choices. Can we find ourselves being persuaded of the ethical need to compare utilities of different individuals, yet unable to do so because the comparisons cannot be warranted? I argue that the problem cannot arise; no plausible moral principle will invoke magnitudes which are inscrutable.

In a recent article, Adam Elga outlines a strategy for “Defeating Dr Evil with Self-Locating Belief”. The strategy relies on an indifference principle that is not up to the task. In general, there are two things to dislike about indifference principles: adopting one normally means confusing risk for uncertainty, and they tend to lead to incoherent views in some ‘paradoxical’ situations. I argue that both kinds of objection can be levelled against Elga’s indifference principle. There are also some difficulties with (...) the concept of evidence that Elga uses, and these create further difficulties for the principle. (shrink)

In previous work I’ve defended an interest-relative theory of belief. This paper continues the defence. It has four aims. -/- 1. To offer a new kind of reason for being unsatis ed with the simple Lockean reduction of belief to credence. 2. To defend the legitimacy of appealing to credences in a theory of belief. 3. To illustrate the importance of theoretical, as well as practical, interests in an interest-relative account of belief. 4. To revise my account to cover propositions (...) that are practically and theoretically irrelevant to the agent. (shrink)

I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but the proof is simpler and proceeds from weaker decision-theoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible.

Probabilistic theories of rationality claim that degrees of belief have to satisfy the probability axioms in order to be rational. A standard argument to support this claim is the Dutch Book argument. This paper tries to show that, in spite of its popularity, the Dutch Book argument does not provide a foundation for normative theories of rationality. After a presentation of the argument and some of its criticisms a problem is pointed out: the Dutch Book argument applies only to situations (...) with a specific formal structure. Several attempts to justify the argument for more general situations are considered and rejected. The only way to remedy the shortcoming, it is argued, seems to be the acceptance of a far-reaching and highly implausible empirical hypothesis. (shrink)

Margaret MacDonald (1907–56) was a central figure in the history of early analytic philosophy in Britain due to both her editorial work as well as her own writings. While her later work on aesthetics and political philosophy has recently received attention, her early writings in the 1930s present a coherent and, for its time, strikingly original blend of common-sense and scientific philosophy. In these papers, MacDonald tackles the central problems of philosophy of her day: verification, the problem of induction, and (...) the relationship between philosophical and scientific method. MacDonald’s philosophy of science starts from the principle that we should carefully analyse the elements of scientific practice (particularly its temporal features) and the ways that scientists describe that practice. That is, she applies the techniques of ordinary language philosophy to actual scientific language. MacDonald shows how ‘scientific common-sense’ is inconsistent with both of the dominant schools of philosophy of her day. Bringing MacDonald back into the story of analytic philosophy corrects the impression that in early analytic philosophy, there are fundamental dichotomies between the style of Moore and Wittgenstein, on the one hand, and the Vienna Circle on the other. (shrink)

This commentary focuses on the parts of psychological game theory dealing with preference, as illustrated by team reasoning, and supports the conclusion that these theoretical notions do not contribute above and beyond existing theory in understanding social interaction. In particular, psychology and games are already bridged by a comprehensive, formal, and inherently psychological theory, interdependence theory (Kelley & Thibaut 1978; Kelley et al. 2003), which has been demonstrated to account for a wide variety of social interaction phenomena.

Legal probabilism is the view that juridical fact-finding should be modeled using Bayesian methods. One of the alternatives to it is the narration view, according to which instead we should conceptualize the process in terms of competing narrations of what happened. The goal of this paper is to develop a reconciliatory account, on which the narration view is construed from the Bayesian perspective within the framework of formal Bayesian epistemology.

This paper responds to the generous comments by Alexander Klein and Cheryl Misak on my “American Pragmatism and the Vienna Circle: The Early Years”. First, besides offering some clarification of my original thesis, I argue that Jerusalem was not liable to the anti-Spencerian criticisms by James that Klein adduces in the course of defending James against the charge of psychologism. Then I investigate the impact of Wittgenstein’s Ramsey-derived pragmatism, importantly foregrounded by Misak, on the Vienna Circle and argue that it (...) was mainly limited to Schlick but not recognized as pragmatist, also leaving unaffected the impact of James’s pragmatism on Frank, Hahn and Neurath specified in my original paper. That said, Klein’s and Misak’s comments add significantly to our understanding of long-neglected transatlantic philosophical connections in the early twentieth century. (shrink)

When acting in social contexts, we are often able to voluntarily coordinate our choices with one another. It has been suggested that this ability relies on the adoption of preferences that transcend those of the individuals involved in the social interaction. Conditional game theory provides a formal framework that facilitates the study of coordinated rational choice in a way that disentangles the concepts of individual preference and group agency. We argue that these concepts are complementary: individual preferences are formed in (...) a social context and groups coordinate as socially influenced preferences interact. In particular, we show that if agents can engage in conditional reasoning and can define their preferences in the form of hypothetical propositions, group-level coordination can be grounded only on the preference of individuals. (shrink)

The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from common objections: that it is solipsist; that it is too instrumentalist; that it cannot deal with Wigner's friend scenarios. Three more substantive problems are raised: Can a reasonable ontology be found for the approach? Can it account for explanation in quantum theory? Are subjective (...) probabilities on their own adequate in the quantum domain? The first question is answered in the affirmative, drawing on elements from Nancy Cartwright's philosophy of science. The second two are not: it is argued that these present outstanding difficulties for the project. A quantum Bayesian version of Moore's paradox is developed to illustrate difficulties with the subjectivist account of pure state assignments. (shrink)

The aim of this paper is to present and analyze arguments provided for the Psychological Principle of Non-Contradiction which states that one cannot have, or cannot be described as having, contradictory beliefs. By differentiating two possible interpretations of PNC, descriptive and normative, and examining arguments provided for each of them separately I point out the flaws in reasoning in these arguments and difficulties with aligning PNC with the empirical data provided by research done in cognitive and clinical psychology. I claim (...) that PNC cannot be derived from any metaphysical stance regarding the mental phenomena and that having contradictory beliefs should be regarded as possible. Furthermore, I argue that interpreting a subject as having contradictory beliefs, and therefore abandoning PNC, can be more effective in explaining the phenomena of contradictory beliefs and irrational behaviour than solutions consistent with the PNC. (shrink)

Celem tego tekstu jest rekonstrukcja i analiza argumentów przedstawianych za Psychologiczną Zasadą Niesprzeczności, stwierdzającą, że żaden podmiot nie może mieć sprzecznych przekonań lub być opisany jako posiadający sprzeczne przekonania. Poprzez rozróżnienie dwóch możliwych interpretacji PZN, deskryptywnej i normatywnej, oraz dokładne zbadanie argumentacji przedstawionej dla każdej z nich z osobna, wskazuję zawarte w nich błędy oraz problemy związane z uzgodnieniem ich z wynikami badań prowadzonych w psychologii poznawczej i klinicznej. Uzasadniam, dlaczego PZN nie może być wyprowadzona z żadnego ze stanowisk metafizycznych (...) dotyczących nastawień sądzeniowych i że posiadanie sprzecznych przekonań powinno być uznane za możliwe. Następnie piszę, dlaczego zinterpretowanie niektórych podmiotów jako posiadających sprzeczne przekonania może być bardziej efektywne w wyjaśnianiu przypadków nieracjonalnego zachowania niż rozwiązania zgodne z PZN. (shrink)

According to success semantics, a belief’s content is that which guarantees the success of the actions that the belief, in combination with the relevant desires, would cause. One worry with the view is that it seems to apply only to full beliefs and fares poorly in dealing with partial beliefs. For example, if Ida’s partial belief that p is of strength 0.5, she may act in a way that would fulfill her desires if p were in fact false—assuming that she (...) desires money, she may well accept a bet that pays her $500 if not-p and costs her nothing otherwise. In response to the worry, defenders of success semantics hold that the content of a partial belief is simply that which guarantees the success of the actions it would cause were it a full belief. But, as I’ll argue in this paper, such a response is unsatisfactory. (shrink)

Suppose we wish to provide a naturalistic account of intentionality. Like several other philosophers, we focus on the intentionality of belief, hoping that we may later supplement our account to accommodate other intentional states like desires and fears. Now suppose that we also take partial beliefs or credences seriously. In cashing out our favoured theory of intentionality, we may for the sake of simplicity talk as if belief is merely binary or all-or-nothing. But we should be able to supplement or (...) modify our account to accommodate credences. I shall argue, however, that it is difficult to do so with respect to certain causal or teleological theories of intentionality-in particular, those advanced by the likes of Stalnaker (Inquiry, 1984) and Millikan (J Philos 86:281–297, 1989). I shall first show that such theories are tailor-made to account for the intentionality of binary beliefs. Then I shall argue that it is hard to extend or supplement such theories to accommodate credences. Finally, I shall offer some natural ways of modifying the theories that involve an appeal to objective probabilities. But unfortunately, such modifications face problems. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Bayesian prior probabilities have an important place in probabilistic and statistical methods. In spite of this fact, the analysis of where these priors come from and how they are formed has received little attention. It is reasonable to excuse the lack, in the foundational literature, of detailed psychological theory of what are the mechanisms by which prior probabilities are formed. But it is less excusable that there is an almost total absence of a detailed discussion of the highly differentiating nature (...) of past experience in forming a prior. The focus here is on what kind of account, even if necessarily schematic, can be given about the psychological mechanisms back of the formation of Bayesian priors. The last section examines a detailed experiment relevant to how priors are learned. (shrink)

Theoria, Volume 87, Issue 1, Page 247-251, February 2021.

Satisficing is a central concept in both individual and social multiagent decision making. In this paper we first extend the notion of satisficing by formally modeling the tradeoff between costs and decision failure. Second, we extend this notion of “neo”-satisficing into the context of social or multiagent decision making and interaction, and model the social conditioning of preferences in a satisficing framework.

This paper defends two related claims about belief. First, the claim that unlike numerical degrees of belief, comparative beliefs are primitive and psychologically real. Second, the claim that the fundamental norm of Probabilism is not that numerical degrees of belief should satisfy the probability axioms, but rather that comparative beliefs should satisfy certain constraints.

The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...) Winkler Risk Analysis, 19, 187–203, [7]; Dietrich and List [14]; Herzberg Theory and Decision, 1–19, [28]). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi, 3–11, [39]), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus. (shrink)

This paper discusses a challenge for Comparativists about belief, who hold that numerical degree of belief (in particular, subjective probability) is a useful fiction, unlike comparative belief, which they regard as real. The challenge is to make sense of claims like ‘I am twice as confident in A as in B’ in terms of comparative belief only. After showing that at least some Comparativists can meet this challenge, I discuss implications for Zynda’s [2000] and Stefánsson’s [2017] defences of Comparativism.

We explore which types of probabilistic updating commute with convex IP pooling. Positive results are stated for Bayesian conditionalization, imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of externally Bayesian pooling operators due to Wagner :336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.

I focus my discussion on the well-known Ellsberg paradox. I find good normative reasons for incorporating non-precise belief, as represented by sets of probabilities, in an Ellsberg decision model. This amounts to forgoing the completeness axiom of expected utility theory. Provided that probability sets are interpreted as genuinely indeterminate belief, such a model can moreover make the “Ellsberg choices” rationally permissible. Without some further element to the story, however, the model does not explain how an agent may come to have (...) unique preferences for each of the Ellsberg options. Levi holds that the extra element amounts to innocuous secondary “risk” or security considerations that are used to break ties when more than one option is rationally permissible. While I think a lexical choice rule of this kind is very plausible, I argue that it involves a greater break with xpected utility theory than mere violation of the ordering axiom. (shrink)

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian (...) reasoning with idealized models in science. (shrink)

Consequentialists often assume rational monism: the thesis that options are always made rationally permissible by the maximization of the selfsame quantity. This essay argues that consequentialists should reject rational monism and instead accept rational pluralism: the thesis that, on different occasions, options are made rationally permissible by the maximization of different quantities. The essay then develops a systematic form of rational pluralism which, unlike its rivals, is capable of handling both the Newcomb problems that challenge evidential decision theory and the (...) unstable problems that challenge causal decision theory. (shrink)

If we think, as Ramsey did, that a degree of belief that P is a stronger or weaker tendency to act as if P, then it is clear that not only uncertainty, but also vagueness, gives rise to degrees of belief. If I like hot coffee and do not know whether the coffee is hot or cold, I will have some tendency to reach for a cup; if I like hot coffee and know that the coffee is borderline hot, I (...) will have some tendency to reach for a cup. Suppose that we take degrees of belief arising from uncertainty to obey the laws of probability and that we model vagueness using degrees of truth. We then encounter a problem: it does not look as though degrees of belief arising from vagueness should obey the laws of probability. One response would be to countenance two different sorts of degrees of belief: degrees of belief arising from uncertainty, which obey the laws of probability; and degrees of belief arising from vagueness, which obey a different set of laws. I argue, however, that if a degree of belief that P is a stronger or weaker tendency to act as if P, then this option is not open. Instead, I propose an account of the behaviour of degrees of belief that integrates subjective probabilities and degrees of truth. On this account, degrees of belief are expectations of degrees of truth. The account explains why degrees of belief behave in accordance with the laws of probability in cases involving only uncertainty, while also allowing degrees of belief to behave differently in cases involving only vagueness, and in mixed cases involving both uncertainty and vagueness. Justifications of the account are given both via Dutch books and in terms of epistemic accuracy. (shrink)

This paper is a reply to some of Scott Soames ' comments on my colloquium paper Marcus, Kripke, and the Origin of the New Theory of Reference. Except for the indicated parts added in May, 1995, this paper was written on December 16th–25th, 1994 as my reply to Soames for the APA colloquium in Boston, December 28, 1994. In this paper, I argue that Soames ' contention that Marcus is not one of the primary founders of contemporary nondescriptivist theories of (...) reference is false. Soames presents numerous arguments for his thesis that Marcus did not originate ideas later elaborated upon by Kripke, but his arguments are unsound; they are based in part on a misunderstanding of Marcus' theory and in part on an inadequate grasp of some of the key notions of the New Theory of Reference, such as the notion of a posteriori necessities and the notion of reference-fixing descriptions. (shrink)

This paper presents a new solution to the problems for orthodox decision theory posed by the Pasadena game and its relatives. I argue that a key question raised by consideration of these gambles is whether evaluative compositionality (as I term it) is a requirement of rationality: is the value that an ideally rational agent places on a gamble determined by the values that she places on its possible outcomes, together with their mode of composition into the gamble (i.e. the probabilities (...) assigned to them)? The paper first outlines a certain simple response to the Pasadena game and identifies two problems with this response, the second of which is that it leads to a wholesale violation of evaluative compositionality. I then argue that rationality does not require decision makers to factor in outcomes of arbitrarily low probability. A method for making decisions which flows from this basic idea is then developed, and it is shown that this decision method (Truncation) leads to a limited — as opposed to wholesale — violation of evaluative compositionality. The paper then argues that the truncation method yields solutions to the problems posed by the Pasadena game and its relatives that are both attractive in themselves and superior to those yielded by alternative proposals in the literature. (shrink)

The question of coherence of rules for changing degrees of belief in the light of new evidence is studied, with special attention being given to cases in which evidence is uncertain. Belief change by the rule of conditionalization on an appropriate proposition and belief change by "probability kinematics" on an appropriate partition are shown to have like status.