What we value, like, endorse, want, and prefer changes over the course of our lives. Richard Pettigrew presents a theory of rational decision making for agents who recognise that their values will change over time and whose decisions will affect those future times.

Accuracy arguments for the core tenets of Bayesian epistemology differ mainly in the conditions they place on the legitimate ways of measuring the inaccuracy of our credences. The best existing arguments rely on three conditions: Continuity, Additivity, and Strict Propriety. In this paper, I show how to strengthen the arguments based on these conditions by showing that the central mathematical theorem on which each depends goes through without assuming Additivity.

I argue that uniquely human forms of ‘Theory of Mind’ are a product of cultural evolution. Specifically, propositional attitude psychology is a linguistically constructed folk model of the human mind, invented by our ancestors for a range of tasks and refined over successive generations of users. The construction of these folk models gave humans new tools for thinking and reasoning about mental states—and so imbued us with abilities not shared by non-linguistic species. I also argue that uniquely human forms of (...) ToM are not required for language development, such that an account of the cultural origins of ToM does not jeopardise the explanation of language development. Finally, I sketch a historical model of the cultural evolution of mental state talk. (shrink)

In a series of papers over the past twenty years, and in a new book, Igor Douven has argued that Bayesians are too quick to reject versions of inference to the best explanation that cannot be accommodated within their framework. In this paper, I survey their worries and attempt to answer them using a series of pragmatic and purely epistemic arguments that I take to show that Bayes’ Rule really is the only rational way to respond to your evidence.

Longtermism is the view that the most urgent global priorities, and those to which we should devote the largest portion of our resources, are those that focus on (i) ensuring a long future for humanity, and perhaps sentient or intelligent life more generally, and (ii) improving the quality of the lives that inhabit that long future. While it is by no means the only one, the argument most commonly given for this conclusion is that these interventions have greater expected goodness (...) per unit of resource devoted to them than each of the other available interventions, including those that focus on the health and well-being of the current population. In this paper, I argue that, even if we grant the consequentialist ethics upon which this argument depends, and even if we grant one of the axiologies that are typically paired with that ethics to give the argument, we are not morally required to choose an option that maximises expected utility; indeed, we might not even be permitted to do so. Instead, I will argue, if the argument's consequentialism is correct, we should choose using a decision theory that is sensitive to risk, and allows us to give greater weight to worse-case outcomes than expected utility theory does. And, I will show, such decision theories do not always recommend longtermist interventions. Indeed, sometimes, they recommend exactly the opposite: sometimes, they recommend hastening human extinction. Many, though not all, will take this as a reductio of the consequentialism or the axiology of the argument. I remain agnostic on the conclusion we should draw. (shrink)

This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...) along with the central challenges these views face. Third, it identifies and critically assesses a series of core philosophical assumptions often adopted by number cognition researchers. Finally, the Element articulates and defends a novel version of pluralism about number concepts. (shrink)

My aim in this paper is to identify the wrong that is done in all cases of testimonial injustice, if there is one. Miranda Fricker (2007) proposes one account of this distinctive wrong, and Gaile Pohlhaus Jr. (2014) offers another. I think neither works. Nor does an account based on giving due respect to the testifier's epistemic competence. Nor does an account based on exposing the testifier to substantial risk of harm. Rachel Fraser (2023) describes a further account, and the (...) proposal I favour is a slight amendment of this. (shrink)

Adaptive preferences give rise to puzzles in ethics, political philosophy, decision theory, and the theory of action. Like our other preferences, adaptive preferences lead us to make choices, take action, and give consent. In 'False Consciousness for Liberals', recently published in The Philosophical Review, David Enoch (2020) proposes a criterion by which to identify when these choices, actions, and acts of consent are less than fully autonomous; that is, when they suffer from what Natalie Stoljar (2014) calls an 'autonomy deficit'. (...) According to Enoch, such actions are not protected in the usual way against interference by others; there is not the same prohibition against trying to prevent someone from acting in a particular way when that action is motivated by such adaptive preferences and is an attempt to satisfy them. In this note, I raise two concerns about Enoch's criterion. (shrink)

There are many reasons we might want to take the opinions of various individuals and pool them to give the opinions of the group they constitute. If all the individuals in the group have probabilistic opinions about the same propositions, there is a host of pooling functions we might deploy, such as linear or geometric pooling. However, there are also cases where different members of the group assign probabilities to different sets of propositions, which might overlap a lot, a little, (...) or not at all. There are far fewer proposals for how to proceed in these cases, and those there are have undesirable features. I begin by considering four proposals and arguing that they don't work. Then I'll describe my own proposal, which is intended to cover the situation in which we want to pool the individual opinions in order to ascribe an opinion to the group considered as an agent in its own right. (shrink)

The problem of closure for the traditional unstructured possible worlds model of attitudinal content is that it treats belief and other cognitive states as closed under entailment, despite apparent counterexamples showing that this is not a necessary property of such states. One solution to this problem, which has been proposed recently by several authors (Schaffer 2005; Yalcin 2018; Hoek forthcoming), is to restrict closure in an unstructured setting by treating propositional attitudes as question-sensitive. Here I argue that this line of (...) response is unsatisfying as it stands because the problem of closure is more general than is typically discussed. A version of the problem recurs for attitudes like wondering, entertaining, considering, and so on, which are directed at questions rather than propositions. For such questioning attitudes, the appeal to question-sensitivity is much less convincing as a solution to the problem of closure. (shrink)

How much does rationality constrain what we should believe on the basis of our evidence? According to this book, not very much. For most people and most bodies of evidence, there is a wide range of beliefs that rationality permits them to have in response to that evidence. The argument, which takes inspiration from William James' ideas in 'The Will to Believe', proceeds from two premises. The first is a theory about the basis of epistemic rationality. It's called epistemic utility (...) theory, and it says that what it is epistemically rational for you to believe is what it would be rational for you to choose if you were given the chance to pick your beliefs and, when picking them, you were to care only about their epistemic value. So, to say which beliefs are permitted, we must say how to measure epistemic value, and which decision rule to use when picking your beliefs. The second premise is a claim about attitudes to epistemic risk, and it says that rationality permits many different such attitudes. These attitudes can show up in epistemic utility theory in two ways: in the way you measure epistemic value; and in the decision rule you use to pick beliefs. This book explores the latter. The result is permissivism about epistemic rationality: different attitudes to epistemic risk lead to different choices of prior beliefs; given most bodies of evidence, different priors lead to different posteriors; and even once we fix your attitudes to epistemic risk, if they are at all risk-inclined, there is a range of different priors and therefore different posteriors they permit. (shrink)

Frege says, at the end of a discussion of formalism in the Foundations of Arithmetic, that his own foundational program “could be called formal” but is “completely different” from the view he has just criticized. This essay examines Frege’s relationship to Hermann Hankel, his main formalist interlocutor in the Foundations, in order to make sense of these claims. The investigation reveals a surprising result: Frege’s foundational program actually has quite a lot in common with Hankel’s. This undercuts Frege’s claim that (...) his own view is completely different from Hankel’s formalism, and motivates a closer examination of where the differences lie. On the interpretation offered here, Frege shares important parts of the formalist perspective, but differs in recognizing a kind of content for arithmetical terms which can only be made available via proof from prior postulates. (shrink)

Epistemologists who study credences have a well-developed account of how you should change them when you learn new evidence; that is, when your body of evidence grows. What's more, they boast a diverse range of epistemic and pragmatic arguments that support that account. But they do not have a satisfactory account of when and how you should change your credences when you become aware of possibilities and propositions you have not entertained before; that is, when your awareness grows. In this (...) paper, I consider the arguments for the credal epistemologist's account of how to respond to evidence, and I ask whether they can help us generate an account of how to respond to awareness growth. The results are surprising: the arguments that all support the same norms for responding to evidence growth support a number of different norms when they are applied to awareness growth. Some of these norms seem too weak, others too strong. I ask what we should conclude from this, and argue that our credal response to awareness growth is considerably less rigorously constrained than our credal response to new evidence. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

In this paper, we seek a reliabilist account of justified credence. Reliabilism about justified beliefs comes in two varieties: process reliabilism (Goldman, 1979, 2008) and indicator reliabilism (Alston, 1988, 2005). Existing accounts of reliabilism about justified credence comes in the same two varieties: Jeff Dunn (2015) proposes a version of process reliabilism, while Weng Hong Tang (2016) offers a version of indicator reliabilism. As we will see, both face the same objection. If they are right about what justification is, it (...) is mysterious why we care about justification, for neither of the accounts explains how justification is connected to anything of epistemic value. We will call this the Connection Problem. I begin by describing Dunn’s process reliabilism and Tang’s indicator reliabilism. I argue that, understood correctly, they are, in fact, extensionally equivalent. That is, Dunn and Tang reach the top of the same mountain, albeit by different routes. However, I argue that both face the Connection Problem. In response, I offer my own version of reliabilism, which is both process and indicator, and I argue that it solves that problem. Furthermore, I show that it is also extensionally equivalent to Dunn’s reliabilism and Tang’s. Thus, I reach the top of the same mountain as well. (shrink)

Rescorla (Erkenntnis, 2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla’s new argument by giving a very general Dutch Book argument that applies to many cases of updating beyond those (...) covered by Conditionalization, and then showing how Rescorla’s version follows as a special case of that. Second, I want to show how to generalise R. A. Briggs and Richard Pettigrew’s Accuracy Dominance argument to avoid the assumption that Rescorla has identified (Briggs and Pettigrew in Noûs, 2018). In both cases, these arguments proceed by first establishing a very general reflection principle. (shrink)

Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...) on it. As I show, whether this is possible depends on the formulation of the norm under consideration. (shrink)

This paper explores the relationship between the questioning attitude of wondering and a class of attitudes I call 'epistemic desires'. Broadly, these are desires to improve one's epistemic position on some question. A common example is the attitude of wanting to know the answer to some question. I argue that one can have any kind of epistemic desire towards any question, Q, without necessarily wondering Q, but not conversely. That is, one cannot wonder Q without having at least some epistemic (...) desire directed towards Q. I defend this latter claim from apparent counterexamples due to Friedman (2013) and Drucker (2022), and finish with a proposal on which epistemic desires, particularly the desire for understanding, play an explanatory role in distinguishing wondering from other forms of question-directed thought. (shrink)

I here investigate the sense in which diagonalization allows one to construct sentences that are self-referential. Truly self-referential sentences cannot be constructed in the standard language of arithmetic: There is a simple theory of truth that is intuitively inconsistent but is consistent with Peano arithmetic, as standardly formulated. True self-reference is possible only if we expand the language to include function-symbols for all primitive recursive functions. This language is therefore the natural setting for investigations of self-reference.

When is it legitimate for a government to ‘nudge’ its citizens, in the sense described by Thaler and Sunstein (2008)? In their original work on the topic, Thaler and Sunstein developed the _‘as judged by themselves’ (or AJBT) test_ to answer this question (Thaler and Sunstein 2008, p. 5). In a recent paper, Paul and Sunstein (2019) raised a concern about this test: it often seems to give the wrong answer in cases in which we are nudged to make a (...) decision that leads to what Paul calls a _personally transformative experience_, that is, one that results in our values changing (Paul 2014). In those cases, the nudgee will judge the nudge to be legitimate after it has taken place, but only because their values have changed as a result of the nudge. In this paper, I take up the challenge of finding an alternative test. I draw on my _aggregate utility account_ of how to choose in the face of what Ullmann-Margalit (2006) calls _big decisions_, that is, decisions that lead to these personally transformative experiences (Pettigrew 2019, Chapters 6 and 7). (shrink)

In this paper, I ask three questions of the liberal. In each, I fill in philosophical detail around a certain sort of complaint raised in current public debates about their position. In the first, I probe the limits of the liberal's tolerance for civil disobedience; in the second, I ask how the liberal can adjudicate the most divisive moral disputes of the age; and, in the third, I suggest the liberal faces a problem when there is substantial disagreement about the (...) boundaries of the rational and the reasonable. (shrink)

Development plans at different levels – from local to global – aspire to eliminate poverty, famine, to make health care accessible, to create better access to education, to improve transportation, employment, and the quality of life, all within next decades. Yet, these plans collide with the reality of climate change, more precisely the Anthropocene, which already creates high-dimensional conflicts. These will only intensify within decades because climate change and other consequences of the environment global devastation lead to a real decrease (...) of resources. These resources enable not only development but also an elementary reproduction of the essential preconditions of life. The current model of development has substantially contributed to the intensification of unequal accessibility to resources and existing conflicts have thus heightened and new ones have emerged. Water as an essential resource will cause new conflicts. Growing population, expansion of deserts and a sea level rise then increase conflicts for the land. Heat waves occur more often which strengthens conflicts for land suitable for human life, meaning that inhabitable areas are spreading. Therefore there is a need to re-evaluate the character and hierarchy of resources and their accessibility, and also concepts of development. The existing development of humankind has been done at the expense of others in many cases and mainly at the expense of the environment. The current situation raises a question of climate justice from both historical and systematic viewpoints. It opens a need to reformulate the concept of human rights from the perspective of their essential environmental preconditions and to define the status of environmental migrants. (shrink)

This work is the transcript of a theological dialogue I had with ChatGPT that spanned a couple of days. I began it merely out of curiosity over how ChatGPT might respond to questions and challenges I posed. As it progressed, I became increasingly impressed with the nuance, depth, and relevance of its responses. The dialogue became, for me, something of a contemplative exercise. I still don’t know quite how to understand the ability of generative A.I. to respond with such (apparent) (...) understanding and even insight. -/- I’ve decided to post this dialogue, not only because of the puzzle it poses concerning A.I, but even more, because I believe that the theological conclusions ‘we’ arrived at have real merit. -/- In the end, the theological views expressed here echo those that I’ve expressed in other works of mine, but the expression of these views are enhanced by the way ChatGPT picks up on them, rephrases them, elaborates upon them, and often places them in the context of the classical theological tradition. -/- I might add that I have been an A.I. skeptic for some time now, concerned over the potential dangers of A.I. in general. But this dialogue, anyway, reveals its potential use as a vehicle for reflection, even profound reflection. -/- . (shrink)

The more the number of people who live on Earth grows, the more significant are the cuts individuals must accept in realization of their own freedom, so as not to limit the freedom of others. With the growing population on the finite planet the real space for freedom of each individual decreases. Moreover, the growth of complexity of the global industrial civilization increases the degree of interdependence on one hand, on the other the degree of mutual trust decreases as a (...) result of the imperative of growth and profit, and without it no human society can function in the long term. Access to sources necessary for the realization of fundamental freedoms is unequal, and, in fact, it thus limits its accessibility for the majority of human population. Philosophical reflection then should cope with question, whether the range of guaranteed freedoms can be broadened or at least sustained when the space for its realization with the growing human population struggling for increasingly limited resources narrows. (shrink)

Many welfarists wish to assign to each possible state of the world a numerical value that measures something like its moral goodness. How are we to determine this quantity? This paper proposes a contractualist approach: a legitimate measure of moral goodness is one that could be justified to each member of the population in question. How do we justify a measure of moral goodness to each individual? Each individual recognises the measure of moral goodness must be a compromise between the (...) different levels of well-being within the population. Some compromises are more reasonable than others; and some are better justifiable to a given member of the population than others. Each member recognises that the social chooser's measure of moral goodness is going to have to deviate from the well-being function of at least some of the members of the population. But we can nonetheless justify it to each of them if it doesn't deviate more than is necessary, and if the deviations from each member are given equal weighting in whatever process we use to determine it. This paper proposes that we begin with a measure of the distance from a proposed compromise to an individual's level of well-being, and then say that the moral goodness is the candidate compromise that minimizes the sum of distances from it to the individuals' levels of well-being. I describe a range of such measures of distance and show that some give utilitarianism, others different versions of prioritarianism. (shrink)

Veritism says that the fundamental source of epistemic value for a doxastic state is the extent to which it represents the world correctly: that is, its fundamental epistemic value is deter...

We often learn the opinions of others without hearing the evidence on which they're based. The orthodox Bayesian response is to treat the reported opinion as evidence itself and update on it by conditionalizing. But sometimes this isn't feasible. In these situations, a simpler way of combining one's existing opinion with opinions reported by others would be useful, especially if it yields the same results as conditionalization. We will show that one method---upco, also known as multiplicative pooling---is specially suited to (...) this role when the opinions you wish to pool concern hypotheses about chances. The result has interesting consequences: it addresses the problem of disagreement between experts; and it sheds light on the social argument for the uniqueness thesis. (shrink)

This paper clarifies the usage of Albert Hirschman’s categories of market behaviour as of exit and voice in debates about workplace democracy by taking seriously his critique of the neoclassical analysis of competition. Pro-market liberals are generally hostile to the idea of workplace democracy and tend to favour top-down hierarchies as a way of organising labour. This hostility is generally inspired by the neoclassical analysis of exploitation and efficiency, which leads them to defend distributions achieved through exit-based competitive equilibria. Following (...) Hirschman, I propose to consider a hypothetical alternative: a democratic equilibrium, reached through the use of voice. I show that it would present the same appealing characteristics than its competitive counterpart while also accounting for the non-ideal conditions in which markets operate. Support for free markets should entail support for workplace democracy minimally understood as a strengthening of voice. (shrink)

Die eudaimonistische Tugendethik sieht sich, was ihre innere Struktur anbelangt, standardmäßig mit den Vorwürfen des Egoismus und Anthropozentrismus konfrontiert, was auch das Projekt einer ökologischen Tugendethik zu gefährden scheint. Der vorliegende Artikel versucht, ausgehend von der Tugendethik Erich Fromms, eine neue Perspektive auf diese Standardvorwürfe zu entwickeln, indem er den theoretischen Implikationen nachgeht, die die Anerkennung der Biophilie – der Liebe zum Leben – als eine der Tugenden des Menschen für den Frommschen Ansatz hat. Die zunächst noch exegetisch ausgerichtete Diskussion (...) der werkinternen Relation von humanistischer und biophiler Ethik bei Erich Fromm leitet schließlich zu einer stärker systematisch ausgerichteten Diskussion der inneren Dynamik von selbst- und umweltbezogenen Tugenden im tugendhaften Akteur über. In diesem Zuge wird deutlich gemacht, dass das selbstbezogene Streben nach eigener Eudaimonie und das umweltbezogene Streben nach der Förderung des Objekts der eigenen Liebe zwar durchaus miteinander in einen Konflikt geraten können, dass dieser Konflikt aber nicht zur Selbstauslöschung der Tugendethik führt, sondern stattdessen im tugendhaften Akteur eine produktive Dynamik entfaltet. Die klassische Gegenüberstellung von Anthropozentrismus und Biozentrismus innerhalb der Ethik lässt sich auf diese Weise unterlaufen. (shrink)

This paper describes an attempt to repurpose Kant’s a priori psychology as the architectural blueprint for a machine learning system. First, it describes the conditions that must be satisfied for the agent to achieve unity of experience: the intuitions must be connected, via binary relations, so as to satisfy various unity conditions. Second, it shows how the categories are derived within this model: the categories are pure unary predicates that are derived from the pure binary relations. Third, I describe how (...) Kant’s cognitive architecture has been implemented in a computer system (the Apperception Engine) and show in detail what it is like for the system to construct a unified experience from a sequence of raw sensory input. (shrink)

This article outlines the role of globalized mass media in the perception of environmental and social threats and its reciprocal conditionality in the globalized society. It examines the reasons why the global environmental crisis will not lead to a world-wide environmental movement for change of the basic imperatives of the world economicpolitical system. Coherency between globalized mass media and wide-spreading of consumer lifestyle exists despite the fact that it deepens the devastation of environment and social conflicts. Globalized mass media owned (...) by transnational corporations are not only a part of the current global economic-political system, but also the prerequisite of its creation and existence, as well as social contradictions and conflicts. (shrink)

In a study drawing from both evolutionary biology and the social sciences, evidence and argument is assembled in support of the comprehensive appli- cation of selfish gene theory to the human population. With a focus on genes giving rise to characteristically-human cooperation (“cooperative genes”) in- volving language and theory of mind, one may situate a whole range of pat- terned behaviour—including celibacy and even slavery—otherwise seeming to present insuperable difficulties. Crucially, the behaviour which tends to propa- gate the cooperative genes (...) may be “at cost” to the genes of some who may be party to the cooperation itself. Explanatory insights are provided by Trivers’ parent-offspring conflict theory, Lack’s principle, and Hamilton’s kin selec- tion mechanism. A primary observation is that cooperation using language and theory of mind is itself interdependent with full human conceptualization of a world of objects and of themselves as embodied beings. Human capaci- ties inhering in, or arising out of, the ability to cooperate are also responsible for a vitally important long-term process, the domestication of animals and p- lants. The approach illuminates the difference between animal and human sexual behaviour, and the emergence of kinship systems. Again, recent pat- terns of population growth become much more explicable. It is argued that the gene is the single controlling replicator; the notion of the meme as a sec- ond independent replicator is flawed. (shrink)

Much of our information comes to us indirectly, in the form of conclusions others have drawn from evidence they gathered. When we hear these conclusions, how can we modify our own opinions so as to gain the benefit of their evidence? In this paper we study the method known as geometric pooling. We consider two arguments in its favour, raising several objections to one, and proposing an amendment to the other.

The desirability of what actually occurs is often influenced by what could have been. Preferences based on such value dependencies between actual and counterfactual outcomes generate a class of problems for orthodox decision theory, the best-known perhaps being the so-called Allais Paradox. In this paper we solve these problems by extending Richard Jeffrey's decision theory to counterfactual prospects, using a multidimensional possible-world semantics for conditionals, and showing that preferences that are sensitive to counterfactual considerations can still be desirability maximising. (...) We end the paper by investigating the conditions necessary and sufficient for a desirability function to be an expected utility. It turns out that the additional conditions imply highly implausible epistemic principles. (shrink)

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...) successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s. (shrink)

When is a belief justified? There are three families of arguments we typically use to support different accounts of justification: arguments from our intuitive responses to vignettes that involve the concept; arguments from the theoretical role we would like the concept to play in epistemology; and arguments from the practical, moral, and political uses to which we wish to put the concept. I focus particularly on the third sort, and specifically on arguments of this sort offered by Clayton Littlejohn in (...) Justification and the Truth-Connection and Amia Srinivasan in ‘Radical Externalism’ : 395–431, 2018) in favour of externalism. I counter Srinivasan’s argument in two ways: first, I show that the internalist’s concept of justification might figure just as easily in the sorts of structural explanation Srinivasan thinks our political goals require us to give; and I argue that the internalist’s concept is needed for a particular political task, namely, to help us build more effective defences against what I call epistemic weapons. I conclude that we should adopt an Alstonian pluralism about the concept of justification. (shrink)

On what basis should we embrace a religious belief? In this article I argue that religious faith should be viewed, not as a conclusion we arrive at after reviewing the evidence, but as an existential decision we make through which we define ourselves.

This paper applies a virtue epistemology approach to using the Internet, as to improve our information-seeking behaviours. Virtue epistemology focusses on the cognitive character of agents and is less concerned with the nature of truth and epistemic justification as compared to traditional analytic epistemology. Due to this focus on cognitive character and agency, it is a fruitful but underexplored approach to using the Internet in an epistemically desirable way. Thus, the central question in this paper is: How to use the (...) Internet in an epistemically virtuous way? Using the work of Jason Baehr, it starts by outlining nine intellectual or epistemic virtues: curiosity, intellectual autonomy, intellectual humility, attentiveness, intellectual carefulness, intellectual thoroughness, open-mindedness, intellectual courage and intellectual tenacity. It then explores how we should deploy these virtues and avoid the corresponding vices when interacting with the Internet, particularly search engines. Whilst an epistemically virtuous use of the Internet will not guarantee that one will acquire true beliefs, understanding or even knowledge, it will strongly improve one’s information-seeking behaviours. The paper ends with arguing that teaching and assessing online intellectual virtues should be part of school and university curricula, perhaps embedded in critical thinking courses, or even better, as individual units. (shrink)

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...) Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden 2013, Wronski & Godziszewski 2017, Wronski 2018)--I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's Thesis. I (...) suggest two responses to Hedden's objection. First, we might be permissive: agents are permitted to pay any price that is required or permitted by RT, and they are permitted to pay any price that is required or permitted by MSEU. This allows us to give a revised version of the Dutch Book Argument for Probabilism, which I call the Permissive Dutch Book Argument. Second, I suggest that even the proponent of the Expected Utility Objection should admit that RT gives the correct answer in certain very limited cases, and I show that, together with MSEU, this very restricted version of RT gives a new pragmatic argument for Probabilism, which I call the Bookless Pragmatic Argument. (shrink)

We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising has increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And how do they relate to the individual credences assigned by the members of the particular (...) group in question? According to the credal judgement aggregation principle, linear pooling, the credence function of a group should be a weighted average or linear pool of the credence functions of the individuals in the group. In this chapter, I give an argument for linear pooling based on considerations of accuracy. And I respond to two standard objections to the aggregation principle. (shrink)

Critics have often misunderstood the higher-order theory (HOT) of consciousness. Here we clarify its position on several issues, and distinguish it from other views such as the global The higher-order theory (HOT) of consciousness has often been misunderstood by critics. Here we clarify its position on several issues, and distinguish it from other views such as the global workspace theory (GWT) and early sensory models (e.g. first-order local recurrency theories). For example, HOT has been criticized for over-intellectualizing consciousness. We show (...) that while higher-order states are cognitively assembled, the requirements are actually considerably less than often presumed. In this sense HOT may be viewed as an intermediate position between GWT and early sensory views. Also, we clarify that most proponents of HOT do not stipulate consciousness as equivalent to metacognition or confidence. Further, compared to other existing theories, HOT can arguably account better for complex everyday experiences, such as of emotions and episodic memories. This makes HOT particularly useful as a framework for conceptualizing pathological mental states. (shrink)

Mathematical formalism is the the view that numbers are "signs" and that arithmetic is like a game played with such signs. Frege's colleague Thomae defended formalism using an analogy with chess, and Frege's critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue that (...) for Thomae, the formal standpoint is an _algebraic perspective_ on a domain of objects, and a "sign" is not a linguistic expression or mark, but a representation of an object within that perspective. Thomae exploits a shift into this perspective to give a purely algebraic construction of the real numbers from the rational numbers. I suggest that Thomae's chess analogy is intended to provide a model for such shifts in perspective. (shrink)