We consider the questions of whether or not large language models (LLMs) have beliefs, and, if they do, how we might measure them. First, we consider whether or not we should expect LLMs to have something like beliefs in the first place. We consider some recent arguments aiming to show that LLMs cannot have beliefs. We show that these arguments are misguided. We provide a more productive framing of questions surrounding the status of beliefs in LLMs, and highlight the empirical (...) nature of the problem. With this lesson in hand, we evaluate two existing approaches for measuring the beliefs of LLMs, one due to Azaria and Mitchell (The internal state of an llm knows when its lying, 2023) and the other to Burns et al. (Discovering latent knowledge in language models without supervision, 2022). Moving from the armchair to the desk chair, we provide empirical results that show that these methods fail to generalize in very basic ways. We then argue that, even if LLMs have beliefs, these methods are unlikely to be successful for conceptual reasons. Thus, there is still no lie-detector for LLMs. We conclude by suggesting some concrete paths for future work. (shrink)

Leitgeb and Pettigrew argue that (1) agents should minimize the expected inaccuracy of their beliefs and (2) inaccuracy should be measured via the Brier score. They show that in certain diachronic cases, these claims require an alternative to Jeffrey Conditionalization. I claim that this alternative is an irrational updating procedure and that the Brier score, and quadratic scoring rules generally, should be rejected as legitimate measures of inaccuracy.

Bayesians often confuse insistence that probability judgment ought to be indeterminate (which is incompatible with Bayesian ideals) with recognition of the presence of imprecision in the determination or measurement of personal probabilities (which is compatible with these ideals). The confusion is discussed and illustrated by remarks in a recent essay by R. C. Jeffrey.

The article responds to some of the points raised by B. van Fraassen concerning probability kinematics and direct inference within the framework of the approach to the revision of probability judgment proposed by Levi in The Enterprise of Knowledge. In particular, the critical importance of the question of direct inference is emphasized and explained.

This paper makes explicit the way in which many theorists of the epistemology of uncertainty, or formal epistemologists, are committed to a version of noncognitivism—one about thoughts that something is likely. It does so by drawing an analogy with metaethical noncognitivism. I explore the degree to which the motivations for both views are similar and how both views have to grapple with the Frege‐Geach Problem about complex thoughts. The major upshot of recognizing this noncognitivism is that it presents challenges and (...) opportunities not only in the philosophy of mind and language but also in epistemology itself. I present some examples where attention to the implicit noncognitivism in formal epistemology has affected or should affect epistemological theory. And I suggest that it is likely that further examples of this sort will arise. (shrink)

A new justification of probabilism is developed that pays close attention to the structure of the underlying space of possibilities. Its central assumption is that rational numerical degrees of bel...

Suppose my utilities are representable by a set of utility assignments, each defined for atomic sentences; suppose my beliefs are representable by a set of probability assignments. Then each of my utility assignments together with each of my probability assignments will determine a utility assignment to non-atomic sentences, in a familiar way. This paper is concerned with the question, whether I am committed to all the utility assignments so constructible. Richard Jeffrey (1984) says (in effect) "no", Isaac Levi (1974) says (...) "yes". I argue for "no", and raise in passing a problem for Levi. (shrink)

I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many have rejected this thesis because it seems to entail that defendants can be found liable solely on the basis of statistical evidence. I argue that this inference is invalid. I do so by developing a view, called Legal Causalism, that combines Thomson's (1986) causal analysis of evidence with recent work in formal theories of causal inference. On this view, legal standards of proof can be (...) reduced to probabilities, but deriving these probabilities involves more than just statistics. (shrink)

Consider the following claim: given the choice between saving a life and preventing any number of people from temporarily experiencing a mild headache, you should always save the life. Many moral theorists accept this claim. In doing so, they commit themselves to some form of ‘moral absolutism’: the view that there are some moral considerations that cannot be outweighed by any number of lesser moral considerations. In contexts of certainty, it is clear what moral absolutism requires of you. However, what (...) does it require of you when deciding under risk? What ought you to do when there is a chance that, say, you will not succeed in saving the life? In recent years, various critics have argued that moral absolutism cannot satisfactorily deal with risk and should, therefore, be abandoned. In this paper, we show that moral absolutism can answer its critics by drawing on—of all things—orthodox expected utility theory. (shrink)

Epistemic and deontic comparatives differ in how they interact with disjunction. I argue that this difference provides a compelling empirical argument against the semantics of Kratzer, which predicts that all modal comparatives should interact with disjunction in the same way. Interestingly, an identical distinction is found in the semantics of non-modal adjectives: additive adjectives like ‘heavy’ behave logically like epistemic comparatives, and intermediate adjectives like ‘hot’ behave like deontic comparatives. I characterize this distinction formally and argue that the divergence between (...) epistemic and deontic modals explained if we structure their semantics around scalar concepts: epistemic modals should be analyzed using probability , and deontic modals using expected value. (shrink)

This model explores consensus among agents in a population in terms of two properties. The first is a probability of belief change. This value indicates how likely agents are to change their mind in interactions. The other is the size of the agents audience: the proportion of the population the agent has access to at any given time. In all instances, the agents converge on a single belief, although the agents are arational. I argue that this generates a skeptical hypothesis: (...) any instance of purportedly rational consensus might just as well be a case of arational belief convergence. I also consider what the model tells us about increasing the likelihood that one agent’s belief is adopted by the rest. Agents are most likely to have their beliefs adopted by the entire population when their value for PBC is low relative to the rest of the population and their audience sizes are roughly three-quarters of the largest possible audience. I further explore the consequences of dogmatists to the population; individuals who refuse to change their mind end up polarizing the population. I conclude with reflections on the supposedly special character of rationality in belief-spread. (shrink)

We argue that a Bayesian explanation of strategic choices in games requires introducing a psychological theory of belief formation. We highlight that beliefs in epistemic game theory are derived from the actual choice of the players, and cannot therefore explain why Bayesian rational players should play the strategy they actually chose. We introduce the players’ capacity of mindreading in a game theoretical framework with the simulation theory, and characterise the beliefs that Bayes rational players could endogenously form in games. We (...) show in particular that those beliefs need not be ratifiable, and therefore that rational players can form action-dependent beliefs. (shrink)

Roche and Sober (2013; 2014; 2017; 2019) have offered an important new argument that explanatoriness lacks confirmatory significance. My aim in this paper is not only to contend that their argument fails to show that in confirmation ‘there is nothing special about explanatoriness’ (Roche & Sober, 2017: 589), but also to reveal what is special confirmationwise about explanatoriness. I will argue that much of the heavy work in Roche and Sober's argument is done by the dichotomy into which they carve (...) up the philosophical options: either explanatory considerations per se are confirmatorily relevant or they acquire whatever confirmatory significance they may possess only by way of background beliefs and so no differently from non‐explanatory considerations. I will argue that this is a false dichotomy: Explanatoriness per se can have confirmatory relevance even while explanatory considerations acquire their confirmatory relevance only through background opinions. Furthermore, there is ‘something special’ about the background opinions concerning explanations that allow explanatoriness in itself to have confirmatory impact. Unlike other sorts of background, having some background opinions expressly about explanations is indispensable to being an observer at all. (shrink)

Decision theorists tend to treat indicative conditionals with reservation, because they can easily lead a deliberating agent astray. However, many indicatives can be very helpful in contexts of deliberation, so denying them all a role in such contexts seems to be overkill. We show that a recently revived inferential view on conditionals provides a straightforward explanation of why some indicatives are unassertable in contexts of deliberation and hints at a way of telling "deliberationally useless" and "deliberationally useful" conditionals apart.

Sentences with slifting parentheticals The formal analysis of natural language, Mouton, The Hague, 1973) grammaticalize an intriguing interaction between truth-conditional meaning and speech act function. In such sentences, the assertion strength of the slifted clause is modulated by the parenthetical, which provides evidential support :480–496, 1952; Asher in J Semant 17:31–50, 2000; Rooryck in Glot Int 5:125–133, 2001; Jayez and Rossari in: Corblin, de Swart Handbook of French semantics, CSLI, Stanford, 2004; Davis et al. in Proc Semant Linguist Theory 17:71–88, (...) 2007; Simons in Lingua 117:1034–1056, 2007; Murray in Semant Pragmat 7:1–53, 2014; Maier and Bary in: Brochhagen et al. Proceedings of the 20th Amsterdam colloquium, 2015; AnderBois in Semant Pragmat 9:1–55, 2016; Hunter in Dialogue Discourse 7:1–35, 2016). Starting with the idea that assertability comes in degrees, this paper develops a probabilistic updatemodel that captures the role of parentheticality as a language tool for qualifying commitments. A crucial role here is played by the rule of Jeffrey conditionalization, which factors in the uncertainty of the parenthetical information itself. The model also derives certain effects of parenthetical modification not found in regular embedding constructions, including the fact that slifting parentheticals are limited to creating upward-entailing environments. (shrink)

Epistemology orthodoxy is a purist one in the sense that it separates out the epistemic from the practical. What counts as evidence is independent of what we care about. Which beliefs count as justified and which count as knowledge are independent of our practical concerns. In recent years, many epistemologists have abandoned such purist views and embraced varying degrees of pragmatic encroachment on the epistemic. I survey a variety of these views and explore the main arguments that proponents of pragmatic (...) encroachment have offered in addition to the main criticisms of the pragmatic approach. (shrink)

L. A. Paul’s Transformative Experience makes the claim that many important life decisions are epistemically and personally transformative in a way that does not allow us to assign subjective values to their outcomes. As a result, we cannot use normative decision theory to make such decisions rationally, or when we modify it to do so, decision theory leads us to choose in a way that is in tension with our authenticity. This paper examines Paul’s version of decision theory, and whether (...) this version in fact admits of the challenge she wants to raise. I focus on her psychological realist view of utilities and beliefs and her notion of rational, authentic preferences as informed by imaginative acquaintance. I argue that Paul fails to engage critically with traditional accounts of decision theory and, on closer inspection, it is not clear that her version of decision theory entails a tension between rational and authentic choice. More importantly, I argue that if her contribution is instead to bring to light the importance of authenticity alongside rational decision-making, the definition she provides of authenticity in fact undermines her argument. (shrink)

In this age of post-Moorean modesty, many of us are inclined to doubt that philosophy is in possession of arguments that might genuinely serve to undermine what we ordinarily believe. It may perhaps be conceded that the arguments of the skeptic appear to be utterly compelling; but the Mooreans among us will hold that the very plausibility of our ordinary beliefs is reason enough for supposing that there must be something wrong in the skeptic’s arguments, even if we are unable (...) to say what it is. In so far then, as the pretensions of philosophy to provide a world view rest upon its.. (shrink)

Is Bayesian decision theory a panacea for many of the problems in epistemology and the philosophy of science, or is it philosophical snake-oil? For years a debate had been waged amongst specialists regarding the import and legitimacy of this body of theory. Mark Kaplan had written the first accessible and non-technical book to address this controversy. Introducing a new variant on Bayesian decision theory the author offers a compelling case that, while no panacea, decision theory does in fact have the (...) most profound consequences for the way in which philosophers think about inquiry, criticism and rational belief. The new variant on Bayesian theory is presented in such a way that a non-specialist will be able to understand it. The book also offers new solutions to some classic paradoxes. It focuses on the intuitive motivations of the Bayesian approach to epistemology and addresses the philosophical worries to which it has given rise. (shrink)

Crucial to bayesian contributions to the philosophy of science has been a characteristic psychology, according to which investigators harbor degree of confidence assignments that (insofar as the agents are rational) obey the axioms of the probability calculus. The rub is that, if the evidence of introspection is to be trusted, this fruitful psychology is false: actual investigators harbor no such assignments. The orthodox bayesian response has been to argue that the evidence of introspection is not to be trusted here; it (...) is to investigators' dispositions--not to their felt convictions--that the psychology is meant to be (and succeeds in being) faithful. I argue that this response, in both its orthodox and convex-set bayesian forms, should be rejected--as should the regulative ideals that make the response seem so attractive. I offer a different variant of bayesianism, designed to give the evidence of introspection its due and thus realize (as I claim the other forms of bayesianism cannot) the prescriptive mission of the bayesian project. (shrink)

In The Logic of Decision Richard Jeffrey defends a version of expected utility theory that advises agents to choose acts with an eye to securing evidence for thinking that desirable results will ensue. Proponents of "causal" decision theory have argued that Jeffrey's account is inadequate because it fails to properly discriminate the causal features of acts from their merely evidential properties. Jeffrey's approach has also been criticized on the grounds that it makes it impossible to extract a unique probability/utility representation (...) from a sufficiently rich system of preferences (given a zero and unit for measuring utility). The existence of these problems should not blind us to the fact that Jeffrey's system has advantages that no other decision theory can match: it can be underwritten by a particularly compelling representation theorem proved by Ethan Bolker; and it has a property called partition invariance that every reasonable theory of rational choice must possess. I shall argue that the non-uniqueness problem can be finessed, and that it is impossible to adequately formulate causal decision theory, or any other, without using Jeffrey's theory as one's basic analysis of rational desire. (shrink)

Given the success of the formal approach, within contemporary epistemology, to understanding degreed belief, some philosophers have recently considered its extension to the challenge of understanding intention. According to them, (1) intentions can also admit of degrees, as beliefs do, and (2) these degreed states are all governed by the norms of the probability calculus, such that the rational norms for belief and for intention exhibit certain structural similarity. This paper, however, raises some worries about (2). It considers two schemes (...) for representing degreed intention, and casts some doubt on applying probabilistic norms to degreed intention on each scheme. And it argues that the norms of Intention–Belief Consistency and Enkrasia cannot plausibly be turned into norms prescribing a simple correspondence relation between one’s degrees of belief and intention. The results suggest a potential structural discrepancy between the norms of theoretical and practical rationality—at least for degreed belief and intention. This potential discrepancy not only raises interesting questions about the intention–belief relation and rational norms for degreed intention. It also poses a new challenge for intention-based expressivism about normative judgment and cognitivism about practical rationality. (shrink)

Isaac Levi and I have different views of probability and decision making. Here, without addressing the merits, I will try to answer some questions recently asked by Levi (1985) about what my view is, and how it relates to his.

There has been a persistent tendency to identify what is called “the freerider problem” in the production of collective goods with the prisoner's dilemma. However, in this article I want to challenge that identification by presenting an analysis of what are in fact a variety of collective action problems in the production of collective goods. My strategy is not to consult any intuitions about what the free-rider problem is; rather I will be looking at the problematic game-theoretic structures of various (...) situations associated with the production of different types of collective goods, thereby showing what sorts of difficulties a community concerned with their voluntary production would face. I call all of these dilemmas free-rider problems because in all of them certain individuals find it rational to take advantage of others' willingness to contribute to the good in a way that threatens its production. Some readers may feel that the term ‘free-rider problem’ is so identified with the prisoner's dilemma that my extension of the term in this way “jars”; if so, I invite them to coin another word for the larger phenomenon. My aim is not to engage in linguistic analysis but to attempt at least a partial analysis of the complicated structure of collective good production. (shrink)

Sometimes epistemologists theorize about belief, a tripartite attitude on which one can believe, withhold belief, or disbelieve a proposition. In other cases, epistemologists theorize about credence, a fine-grained attitude that represents one’s subjective probability or confidence level toward a proposition. How do these two attitudes relate to each other? This article explores the relationship between belief and credence in two categories: descriptive and normative. It then explains the broader significance of the belief-credence connection and concludes with general lessons from the (...) debate thus far. (shrink)

This guide accompanies the following article(s): Jackson, E., Philosophy Compass 15/6 (2020) pp. 1-13 10.1111/phc3.12668.x.

Although much has been written about divine knowledge, and some on divine beliefs, virtually nothing has been written about divine credences. In this essay we comparatively assess four views on divine credences: (1) God has only beliefs, not credences; (2) God has both beliefs and credences; (3) God has only credences, not beliefs; and (4) God has neither credences nor beliefs, only knowledge. We weigh the costs and benefits of these four views and draw connections to current discussions in philosophical (...) theology. (shrink)

I explore how rational belief and rational credence relate to evidence. I begin by looking at three cases where rational belief and credence seem to respond differently to evidence: cases of naked statistical evidence, lotteries, and hedged assertions. I consider an explanation for these cases, namely, that one ought not form beliefs on the basis of statistical evidence alone, and raise worries for this view. Then, I suggest another view that explains how belief and credence relate to evidence. My view (...) focuses on the possibilities that the evidence makes salient. I argue that this makes better sense of the difference between rational credence and rational belief than other accounts. (shrink)

While pragmatic arguments for numerical probability axioms have received much attention, justifications for axioms of qualitative probability have been less discussed. We offer an argument for the requirement that an agent’s qualitative judgments be probabilistically representable, inspired by, but importantly different from, the Money Pump argument for transitivity of preference and Dutch book arguments for quantitative coherence. The argument is supported by a theorem, to the effect that a subject is systematically susceptible to dominance given her preferred acts, if and (...) only if the subject’s comparative judgments preclude representation by a standard probability measure. (shrink)

In this paper I study dynamical models of rational deliberation within the context of Newcomb's problem. Such models have been used to argue against the soundness of the "tickle'" defense of evidential decision theory, which is based on the idea that sophisticated decision makers can break correlations between states and acts by introspecting their own beliefs and desires. If correct, this would show that evidential decision theory agrees with the recommendations of causal decision theory. I argue that an adequate understanding (...) of rational deliberation leads to deliberative processes for which this idea works. My proposal is modest, though. Evidential decision theory cannot always be reconciled with causal decision theory along the lines suggested here, but the agreement between the two theories is broader than previously thought. (shrink)

Reflection and martingale principles are central to models of rational learning. They can be justified in a variety of ways. In what follows we study martingale and reflection principles in the con...

The strategy of updating credences by minimizing the relative entropy has been questioned by many authors, most strongly by means of the Judy Benjamin puzzle. I present a new analysis of Judy Benjamin–like forms of new information and defend the thesis that in general the rational posterior is indeterminate, meaning that a family of posterior credence functions rather than a single one is the rational response when that type of information becomes available. The proposed thesis extends naturally to all cases (...) in which new information is traditionally handled by minimizing the relative entropy. (shrink)

The justificatory force of empirical reasoning always depends upon the existence of some synthetic, a priori justification. The reasoner must begin with justified, substantive constraints on both the prior probability of the conclusion and certain conditional probabilities; otherwise, all possible degrees of belief in the conclusion are left open given the premises. Such constraints cannot in general be empirically justified, on pain of infinite regress. Nor does subjective Bayesianism offer a way out for the empiricist. Despite often-cited convergence theorems, subjective (...) Bayesians cannot hold that any empirical hypothesis is ever objectively justified in the relevant sense. Rationalism is thus the only alternative to an implausible skepticism. (shrink)

In an important 2006 paper, Nishi Shah defends ‘evidentialism’, the position that only evidence for a proposition’s truth constitutes a reason to believe this proposition. In opposition to Shah, Anthony Robert Booth, Andrew Reisner and Asbjørn Steglich-Petersen argue that things other than evidence of truth, so-called non-evidential or ‘pragmatic’ reasons, constitute reasons to believe a proposition. I argue that we can effectively respond to Shah’s pragmatist critics if, following Shah, we are careful to distinguish the evaluation of the reasons for (...) a belief from the process of actually forming a belief and allowing it to influence action. Drawing this distinction is assisted if we utilize Rudolf Carnap’s probabilistic interpretation of what it means to be disposed to believe a claim. (shrink)

My title is intended to recall Terence Fine's excellent survey, Theories of Probability [1973]. I shall consider some developments that have occurred in the intervening years, and try to place some of the theories he discussed in what is now a slightly longer perspective. Completeness is not something one can reasonably hope to achieve in a journal article, and any selection is bound to reflect a view of what is salient. In a subject as prone to dispute as this, there (...) will inevitably be many who will disagree with any author's views, and I take the opportunity to apologize in advance to all such people for what they will see as the narrowness and distortion of mine. (shrink)

This paper discusses the Bayesian updating rules of ordinary and Jeffrey conditionalisation. Their justification has been a topic of interest for the last quarter century, and several strategies proposed. None has been accepted as conclusive, and it is argued here that this is for a good reason; for by extending the domain of the probability function to include propositions describing the agent's present and future degrees of belief one can systematically generate a class of counterexamples to the rules. Dynamic Dutch (...) Book and other arguments for them are examined critically. A concluding discussion attempts to put these results in perspective within the Bayesian approach. (shrink)

In this paper, I present a simple and straightforward logic of induction: a consequence relation characterized by a proof theory and a semantics. This system will be called LI. The premises will be restricted to, on the one hand, a set of empirical data and, on the other hand, a set of background generalizations. Among the consequences will be generalizations as well as singular statements, some of which may serve as predictions and explanations.

I defend a weak version of the Pigou-Dalton principle for chances. The principle says that it is better to increase the survival chance of a person who is more likely to die rather than a person who is less likely to die, assuming that the two people do not differ in any other morally relevant respect. The principle justifies plausible moral judgements that standard ex post views, such as prioritarianism and rank-dependent egalitarianism, cannot accommodate. However, the principle can be justified (...) by the same reasoning that has recently been used to defend the core axiom of ex post prioritarianism and egalitarianism, namely, Pigou-Dalton for well-being. The arguably biggest challenge for proponents of Pigou-Dalton for chances is that it violates State Dominance for social prospects. However, I argue that we have independent reason for rejecting State Dominance for social prospects, since it prevents a social planner from properly respecting people's preferences. (shrink)

Should we act only for the sake of what we might bring about (causal decision theory); or is it enough for a decent motive that our action is highly correlated with something desirable (evidential decision theory)? The conflict between these points of view is embodied in Newcomb's problem. It is argued here that intuitive evidence from familiar decision contexts does not enable us to settle the issue, since the two theories dictate the same results in normal circumstances. Nevertheless, there are (...) several reasons to reject the causal approach: (1) its relative complexity; (2) its commitment to the existence of situations in which every possible act would be irrational; (3) its incorporation of an arbitrary time bias; and (4) its implicit distinction between what ought to be done and what ought to be hoped for. (shrink)

The Two Envelopes Problem is a beautiful and quite confusing problem in decision theory which is ca. 35 years old and has provoked at least 150 papers directly addressing the problem and displaying a surprising variety of different responses. This paper finds decisive progress in an approach of Priest and Restall in 2003, contends that the recent papers having appeared since did not really go beyond that paper, argues further that Priest’s and Restall’s solution is still not complete, and proposes (...) a completion of their solution. If the analysis is correct, this work has the potential of laying the Two Envelopes Problem at rest. (shrink)

Pascal’s Wager is simply too good to be true—or better, too good to be sound. There must be something wrong with Pascal’s argument that decision-theoretic reasoning shows that one must (resolve to) believe in God, if one is rational. No surprise, then, that critics of the argument are easily found, or that they have attacked it on many fronts. For Pascal has given them no dearth of targets.

Pascal’s Wager is simply too good to be true—or better, too good to be sound. There must be something wrong with Pascal’s argument that decision-theoretic reasoning shows that one must believe in God, if one is rational. No surprise, then, that critics of the argument are easily found, or that they have attacked it on many fronts. For Pascal has given them no dearth of targets.

Philosophical Perspectives, Volume 35, Issue 1, Page 189-205, December 2021.

RÉSUMÉ : Depuis l’ouvrage classique de Goodman, on sait que toute théorie de l’induction doit comporter une composante non formelle. Or, la liberté théorique offerte par le recours à un tel élément implique des responsabilités. Cet article propose comme desideratum d’une théorie de l’induction qu’elle rende compte de la dynamique de sa composante non formelle. Ce desideratum, qui est nouveau, n’est pas satisfait par les principales théories existantes de l’induction. L’identification de l’importance de la dynamique a pourtant l’avantage de suggérer (...) une voie vers une théorie plus acceptable et plus compléte de l’induction. ABSTRACT: Since Goodman’s classic monograph, it has been known that any reasonable theory of induction must involve non formal elements. However, the right to make theoretical use of such an element comes with responsibilities. This article argues for an apparently new desideratum for a theory of induction: namely, that it accounts for the dynamics of the non formal element used. None of the main existing theories of induction satisfies this desideratum. The recognition of the importance of dynamics does however have the advantage of suggesting where to look for a more acceptable and complete theory of induction. (shrink)