Bill D'Alessandro talks to Kenny Easwaran about fractal music, Zoom conferences, being a good referee, teaching in math and philosophy, the rationalist community and its relationship to academia, decision-theoretic pluralism, and the city of Manhattan, Kansas.

We introduce a family of rules for adjusting one's credences in response to learning the credences of others. These rules have a number of desirable features. 1. They yield the posterior credences that would result from updating by standard Bayesian conditionalization on one's peers' reported credences if one's likelihood function takes a particular simple form. 2. In the simplest form, they are symmetric among the agents in the group. 3. They map neatly onto the familiar Condorcet voting results. 4. They (...) preserve shared agreement about independence in a wide range of cases. 5. They commute with conditionalization and with multiple peer updates. Importantly, these rules have a surprising property that we call synergy - peer testimony of credences can provide mutually supporting evidence raising an individual's credence higher than any peer's initial prior report. At first, this may seem to be a strike against them. We argue, however, that synergy is actually a desirable feature and the failure of other updating rules to yield synergy is a strike against them. (shrink)

Many philosophers have argued that "degree of belief" or "credence" is a more fundamental state grounding belief. Many other philosophers have been skeptical about the notion of "degree of belief", and take belief to be the only meaningful notion in the vicinity. This paper shows that one can take belief to be fundamental, and ground a notion of "degree of belief" in the patterns of belief, assuming that an agent has a collection of beliefs that isn't dominated by some other (...) collection in terms of the overall balance of truth and falsity that it could contain. (shrink)

Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperreals.” This essay argues that this popular (...) view is the result of two mistakes. The first mistake, which this essay calls the “numerical fallacy,” is to assume that a distinction that isn't represented by different numbers isn't represented at all in a mathematical representation. In this case, the essay claims that although the real numbers do not make all relevant distinctions, the full mathematical structure of a probability function does. The second mistake is that the hyperreals make too many distinctions. They have a much more complex structure than credences in ordinary propositions can have, so they make distinctions that don't exist among credences. While they might be useful for generating certain mathematical models, they will not appear in a faithful mathematical representation of credences of ordinary propositions. (shrink)

Expected accuracy arguments have been used by several authors (Leitgeb and Pettigrew, and Greaves and Wallace) to support the diachronic principle of conditionalization, in updates where there are only finitely many possible propositions to learn. I show that these arguments can be extended to infinite cases, giving an argument not just for conditionalization but also for principles known as ‘conglomerability’ and ‘reflection’. This shows that the expected accuracy approach is stronger than has been realized. I also argue that we should (...) be careful to distinguish diachronic update principles from related synchronic principles for conditional probability. (shrink)

Bayesianism is a collection of positions in several related fields, centered on the interpretation of probability as something like degree of belief, as contrasted with relative frequency, or objective chance. However, Bayesianism is far from a unified movement. Bayesians are divided about the nature of the probability functions they discuss; about the normative force of this probability function for ordinary and scientific reasoning and decision making; and about what relation (if any) holds between Bayesian and non-Bayesian concepts.

To the extent that we have reasons to avoid these “bad B -properties”, these arguments provide reasons not to have an incoherent credence function b — and perhaps even reasons to have a coherent one. But, note that these two traditional arguments for probabilism involve what might be called “pragmatic” reasons (not) to be (in)coherent. In the case of the Dutch Book argument, the “bad” property is pragmatically bad (to the extent that one values money). But, it is not clear (...) whether the DBA pinpoints any epistemic defect of incoherent agents. The same can be said for Representation Theorem arguments, since they involve the structure of an agent’s preferences. (shrink)

Taking Joyce’s (1998; 2009) recent argument(s) for probabilism as our point of departure, we propose a new way of grounding formal, synchronic, epistemic coherence requirements for (opinionated) full belief. Our approach yields principled alternatives to deductive consistency, sheds new light on the preface and lottery paradoxes, and reveals novel conceptual connections between alethic and evidential epistemic norms.

Naive versions of decision theory take probabilities and utilities as primitive and use expected value to give norms on rational decision. However, standard decision theory takes rational preference as primitive and uses it to construct probability and utility. This paper shows how to justify a version of the naive theory, by taking dominance as the most basic normatively required preference relation, and then extending it by various conditions under which agents should be indifferent between acts. The resulting theory can make (...) all the decisions of classical expected utility theory, plus more in cases where expected utilities are infinite or undefined. Although the theory requires similarly strong assumptions to classical expected utility theory, versions of the theory can be developed with slightly weaker assumptions, without having to prove a new representation theorem for the weaker theory. This alternate foundation is particularly useful if probability is prior to preference, as suggested by the recent program to base probabilism on accuracy and alethic considerations rather than pragmatic ones. (shrink)

In the first paper, I discussed the basic claims of Bayesianism (that degrees of belief are important, that they obey the axioms of probability theory, and that they are rationally updated by either standard or Jeffrey conditionalization) and the arguments that are often used to support them. In this paper, I will discuss some applications these ideas have had in confirmation theory, epistemol- ogy, and statistics, and criticisms of these applications.

In a series of papers, Don Fallis points out that although mathematicians are generally unwilling to accept merely probabilistic proofs, they do accept proofs that are incomplete, long and complicated, or partly carried out by computers. He argues that there are no epistemic grounds on which probabilistic proofs can be rejected while these other proofs are accepted. I defend the practice by presenting a property I call ‘transferability’, which probabilistic proofs lack and acceptable proofs have. I also consider what this (...) says about the similarities between mathematics and, on the one hand natural sciences, and on the other hand philosophy. (shrink)

It is sometimes alleged that arguments that probability functions should be countably additive show too much, and that they motivate uncountable additivity as well. I show this is false by giving two naturally motivated arguments for countable additivity that do not motivate uncountable additivity.

Fine has shown that assigning any value to the Pasadena game is consistent with a certain standard set of axioms for decision theory. However, I suggest that it might be reasonable to believe that the value of an individual game is constrained by the long-run payout of repeated plays of the game. Although there is no value that repeated plays of the Pasadena game converges to in the standard strong sense, I show that there is a weaker sort of convergence (...) it exhibits, and use this to define a notion of ‘weak expectation’ that can give values to the Pasadena game and many others, though not to all games that fail to have a strong expectation in the standard sense. CiteULike Connotea Del.icio.us What's this? (shrink)

I defend a causal reductionist account of the nature of rates of change like velocity and acceleration. This account identifies velocity with the past derivative of position and acceleration with the future derivative of velocity. Unlike most reductionist accounts, it can preserve the role of velocity as a cause of future positions and acceleration as the effect of current forces. I show that this is possible only if all the fundamental laws are expressed by differential equations of the same order. (...) Consideration of the continuity of time explains why the differential equations are all second order. This explanation is not available on non-causal or non-reductionist accounts of rates of change. Finally, I argue that alleged counterexamples to the reductionist account involving physically impossible worlds are irrelevant to an analysis of the properties that play a causal role in the actual world. 1 Background2 Grounding3 Causation4 The Proposal5 Why No Third Derivatives?6 Why Any Derivatives?7 Counterexamples? (shrink)

To answer the question of whether mathematics needs new axioms, it seems necessary to say what role axioms actually play in mathematics. A first guess is that they are inherently obvious statements that are used to guarantee the truth of theorems proved from them. However, this may neither be possible nor necessary, and it doesn’t seem to fit the historical facts. Instead, I argue that the role of axioms is to systematize uncontroversial facts that mathematicians can accept from a wide (...) variety of philosophical positions. Once the axioms are generally accepted, mathematicians can expend their energies on proving theorems instead of arguing philosophy. Given this account of the role of axioms, I give four criteria that axioms must meet in order to be accepted. Penelope Maddy has proposed a similar view in Naturalism in Mathematics, but she suggests that the philosophical questions bracketed by adopting the axioms can in fact be ignored forever. I contend that these philosophical arguments are in fact important, and should ideally be resolved at some point, but I concede that their resolution is unlikely to affect the ordinary practice of mathematics. However, they may have effects in the margins of mathematics, including with regards to the controversial “large cardinal axioms” Maddy would like to support. (shrink)

Bayesians standardly claim that there is rational pressure for agents’ credences to cohere across time because they face bad (epistemic or practical) consequences if they fail to diachronically cohere. But as David Christensen has pointed out, groups of individual agents also face bad consequences if they fail to interpersonally cohere, and there is no general rational pressure for one agent's credences to cohere with another’s. So it seems that standard Bayesian arguments may prove too much. Here, we agree with Christensen (...) that there is no general rational pressure to diachronically cohere, but we argue that there are particular cases in which there is rational pressure to diachronically cohere, as well as particular cases in which interpersonal probabilistic coherence is rationally required. More generally, we suggest that Bayesian arguments for coherence apply whenever a collection (of agents or time slices) has a shared dimension of value and an ability to coordinate their actions in a range of cases relevant to that value. Typically, this shared value and ability to coordinate is very strong across the time slices of one human being, and very weak across different human beings, but there are special cases where these can switch—i.e., some groups of humans will have as much reason for their beliefs to cohere across a particular range of cases as the time slices of one human usually do, but some time slices of a human will have as much freedom to differ in their beliefs from the others as the members of a group usually do. (shrink)

Frankfurt gave an account of “bullshit” as a statement made without regard to truth or falsity. Austin argued that a large amount of language consists of speech acts aimed at goals other than truth or falsity. We don't want our account of bullshit to include all performatives. I develop a modification of Frankfurt's account that makes interesting and useful categorizations of various speech acts as bullshit or not and show that this account generalizes to many other kinds of act as (...) well. I show that this illuminates some of Graeber's classification of “bullshit jobs,” though it doesn't fully agree with it. (shrink)

In my () I argued that a central component of mathematical practice is that published proofs must be “transferable” — that is, they must be such that the author's reasons for believing the conclusion are shared directly with the reader, rather than requiring the reader to essentially rely on testimony. The goal of this paper is to explain this requirement of transferability in terms of a more general norm on defeat in mathematical reasoning that I will call “convertibility”. I begin (...) by discussing two types of epistemic defeat: “rebutting” and “undercutting”. I give examples of both of these kinds of defeat from the history of mathematics. I then argue that an important requirement in mathematics is that published proofs be detailed enough to allow the conversion of rebutting defeat into undercutting defeat. Finally, I show how this sort of convertibility explains the requirement of transferability, and contributes to the way mathematics develops by the pattern referred to by Lakatos () as “lemma incorporation”. (shrink)

Doxastic TheoriesThe application of formal tools to questions related to epistemology is of course not at all new. However, there has been a surge of interest in the field now known as “formal epistemology” over the past decade, with two annual conference series and an annual summer school at Carnegie Mellon University, in addition to many one-off events devoted to the field. A glance at the programs of these series illustrates the wide-ranging set of topics that have been grouped under (...) this name, ranging from rational choice theory and the foundations of statistics, to logics of knowledge and formal measures of coherence, with much more besides.In this paper I will ignore most of these topics, and just trace some parts of the history of two ideas about belief whose current interaction may lead to future progress. One idea is the idea of belief, disbelief, and suspension of judgment as a meaningful tripartite dis .. (shrink)

Newcomb-like problems are classified by the payoff table of their act-state pairs, and the causal structure that gives rise to the act-state correlation. Decision theories are classified by the one or more points of intervention whose causal role is taken to be relevant to rationality in various problems. Some decision theories suggest an inherent conflict between different notions of rationality that are all relevant. Some issues with causal modeling raise problems for decision theories in the contexts where Newcomb problems arise.

The central aim of this paper is to argue that there is a meaningful sense in which a concept of rationality can apply to a city. The idea will be that a city is rational to the extent that the collective practices of its people enable diverse inhabitants to simultaneously live the kinds of life they are each trying to live. This has significant implications for the varieties of social practices that constitute being more or less rational. Some of these (...) implications may be welcome to a theorist that wants to identify collective rationality with a notion of justice, while others are unwelcome. There are some significant challenges to this use of the concept of rationality, but I claim that these challenges at the city level have parallels at the individual level, and may thus help deepen our understanding of rationality at all levels. (shrink)

I consider the notions of logical probability, degree of belief, and objective chance, and argue that a different formalism for conditional probability is appropriate for each.

Pascal’s Wager holds that one has pragmatic reason to believe in God, since that course of action has infinite expected utility. The mixed strategy objection holds that one could just as well follow a course of action that has infinite expected utility but is unlikely to end with one believing in God. Monton (2011. Mixed strategies can’t evade Pascal’s Wager. Analysis 71: 642–45.) has argued that mixed strategies can’t evade Pascal’s Wager, while Robertson (2012. Some mixed strategies can evade Pascal’s (...) Wager: a reply to Monton. Analysis 72: 295–98.) has argued that Monton is mistaken. We show that Monton is correct, highlight the crucial assumptions that he relies on, and shed some light on the role of mixed strategies in decision theory. (shrink)

Belief and credence are often characterized in three different ways—they ought to govern our actions, they ought to be governed by our evidence, and they ought to aim at the truth. If one of these roles is to be central, we need to explain why the others should be features of the same mental state rather than separate ones. If multiple roles are equally central, then this may cause problems for some traditional arguments about what belief and credence must be (...) like. I read the history of formal and traditional epistemology through the lens of these functional roles, and suggest that considerations from one literature might have a role in the other. The similarities and differences between these literatures may suggest some more general ideas about the nature of epistemology in abstraction from the details of credence and belief in particular. (shrink)

There is general agreement in mathematics about what continuity is. In this paper we examine how well the mathematical definition lines up with common sense notions. We use a recent paper by Hud Hudson as a point of departure. Hudson argues that two objects moving continuously can coincide for all but the last moment of their histories and yet be separated in space at the end of this last moment. It turns out that Hudson’s construction does not deliver mathematically continuous (...) motion, but the natural question then is whether there is any merit in the alternative definition of continuity that he implicitly invokes. (shrink)

As is clear from the other articles in this volume, logic has applications in a broad range of areas of philosophy. If logic is taken to include the mathematical disciplines of set theory, model theory, proof theory, and recursion theory (as well as first-order logic, second-order logic, and modal logic), then the only other area of mathematics with such wide-ranging applications in philosophy is probability theory.

_ Infinity, Causation, and Paradox _, by PrussAlexander. Oxford: Oxford University Press, 2018. Pp. xiii + 207.

Probability and logic are two branches of mathematics that have important philosophical applications. This article discusses several areas of intersection between them. Several involve the role for probability in giving semantics for logic or the role of logic in governing assignments of probability. Some involve probability over non-classical logic or self-referential sentences.

Arguments for probabilism aim to undergird/motivate a synchronic probabilistic coherence norm for partial beliefs. Standard arguments for probabilism are all of the form: An agent S has a non-probabilistic partial belief function b iff (⇐⇒) S has some “bad” property B (in virtue of the fact that their p.b.f. b has a certain kind of formal property F). These arguments rest on Theorems (⇒) and Converse Theorems (⇐): b is non-Pr ⇐⇒ b has formal property F.

The historical context of the philosophical work of St. Thomas Aquinas, by D. Knowles.--Form and existence, by P. Geach.--Categories, by H. McCabe.--Analogy as a rule of meaning for religious language, by J. F. Ross.--Nominalism, by P. Geach.--St. Thomas' doctrine of necessary being, by P. Brown.--The proof ex motu for the existence of God; logical analysis of St. Thomas' arguments, by J. Salamucha.--Infinite causal regression, by P. Brown.--St. Thomas Aquinas and the language of total dependence, by J. N. Deck.--Divine foreknowledge and (...) human freedom, by A. Kenny.--Intellect and imagination in Aquinas, by A. Kenny.--The immortality of the soul, by H. McCabe.--Aquinas on intentionality, by P. Sheehan.--The scholastic theory of moral law in the modern world, by A. Donagan.--The first principle of practical reason, by G. G. Grisez. (shrink)

In this companion to his best-selling translation of The Dhammapada, Eknath Easwaran explains how The Dhammapada is a perfect map for the spiritual journey. Said to be the text closest to the Buddha’s actual words, The Dhammapada is a collection of short teachings that his disciples memorized during his lifetime. Easwaran presents The Dhammapada as a guide to spiritual perseverance, progress, and ultimately enlightenment — a heroic confrontation with life as it really is, with straight answers to our (...) deepest questions. We witness the heartbreak of death, for instance — what does that mean for us? What is love? How does karma work? How do we follow the spiritual life in the midst of work and family? Does nirvana really exist, and if so, what is it like to be illumined? In his interpretation of Buddhist themes, illustrated with stories from the Buddha’s life, Easwaran offers a view of the concept of Right Understanding that is both exhilarating and instructive. He shares his experiences on the spiritual path, giving the advice that only an experienced teacher and practitioner can offer, and urges us to answer for ourselves the Buddha’s call to nirvana — that mysterious, enduring state of wisdom, joy, and peace. (shrink)

This book uses literary examples makes the case for understanding law and the legal system through the lens of philosophical pragmatism. For pragmatists, experience is everything; and they argue against understanding the world through any abstraction, maintaining that it is simply too complicated to fit into categories or theories. Legal pragmatism is the application of this philosophy to the making of law, the practice of law, and the practice of judging. This book maintains that the best way to understand legal (...) pragmatism is not through bare theoretical exegesis but through literature; that is, through stories that cast light on various pragmatic aspects of law. Engaging a range of literary sources, including works by Seamus Heaney, Hilary Mantel, Harper Lee and Ian McEwan, the book makes a compelling case for the contemporary relevance of pragmatism. This book will appeal to legal theorists, law and literature/humanities scholars; readers of literary criticism; and those with interests in pragmatist philosophy. (shrink)

Montesquieu, Hume, Voltaire, Diderot, Smith, Gibbon, Bentham... These are among the great thinkers who contributed to the dramatic developments in religion, science, and philosophy that we now call the Enlightenment. Written by a world authority, this brief history of the Enlightenment concludes with a perceptive assessment of the cultural, religious, ethical, and political dimensions of its legacy.

Maureen Junker-Kenny offers a systematic overview of the discipline of theological ethics in the variety of its approaches, which draw upon different philosophical traditions and theological visions in treating its sources. Part One examines the four sources of theological ethics: the Bible, tradition, philosophical accounts of the human, and the individual human sciences. Part Two compares five frameworks in English- and German-speaking theological ethics, based on virtue, worship, natural law, autonomy, and feminist analyses. Part Three compares three types of (...) vision - integralist, praxis-oriented, and discourse-focused -, and Junker-Kenny concludes by situating the investigation of the discipline within contemporary philosophical and theological exchanges on religion in the public sphere. The book provides a framework in which students can locate the specific use of core ethical concepts and argumentations, comparing how each approach relates to the Bible, to historical reason, theological thought, practical self-understandings and interdisciplinary perspectives on ethics in a scientific and technological culture. In an age of globalisation where different cultures, religions, lifestyles and values meet in the workplace, in schools, and in public spaces shaped by religious and cultural traditions, it is necessary to foster the ability to create possibilities and venues for dialogue between different self-understandings. Analysing the variety of approaches to theological ethics helps articulate different visions of what constitutes a fulfilled life, of how the moral vocation of each human being can be supported, and of the role of the Christian faith for ethics. (shrink)

In 1998, the first edition of Anthony Kenny's comprehensive history of Western philosophy was published, to be met with immediate praise and critical acclaim. As the first book since Bertrand Russell's 1945 A History of Western Philosophy to offer a concise single-author review of the complete history of philosophy from the pre-Socratics to the modern masters of the 20th century, Kenny's work fills a critical gap in the modern philosophy reading list and offers valuable guidance for the general (...) reader of philosophy—an ideal starting point for anyone with an interest in great thinkers and the family lines of philosophical evolution. Widely considered to be one of the most thorough and accessible historical reviews in philosophy, An Illustrated Brief History of Western Philosophy has earned an estimable and distinctive reputation, both for the compelling writing style of Anthony Kenny, one of the most respected and accomplished living philosophers, and for the rich collection of paintings, illustrations, maps, and photos included with every chapter to complement this review of 2,500 years of philosophical thought. Newly revised and expanded for a special 20th anniversary publication, the latest edition of An Illustrated Brief History of Western Philosophy contains all of Kenny's original writings on the history of Western philosophy from ancient to modern, along with new writings on the philosophy of the mid-20th century, covering important contributions from continental philosophers and philosophers of the post-Wittgenstein anglophone tradition, including the work of many women who have too often been neglected by the historical record. (shrink)

Throughout his long and distinguished career, Sir Anthony Kenny has encountered some of the most notable and influential leaders of the post-war world. In these brilliantly vivid vignettes Kenny offers telling and often unexpected insights into the achievements, flaws and foibles of sixty public figures—past and present—each of whom has contributed in decisive ways to British political, spiritual, and cultural heritage.

According to proper functionalist theories of warrant, a belief is warranted only if it is formed by cognitive faculties that are properly functioning according to a good, truth-aimed design plan, one that is often thought to be specified either by intentional design or by natural selection. A formidable challenge to proper functionalist theories is the Swampman objection, according to which there are scenarios involving creatures who have warranted beliefs but whose cognitive faculties are not properly functioning, or are poorly designed, (...) or are not aimed at truth. In this paper, we draw lessons from cognitive science in order to develop a novel argument for the conclusion that the Swampman objection fails against proper functionalist theories of warrant. Our argument not only shows that the underlying, central intuition motivating Swampman-like scenarios is false but also motivates proper function as a necessary condition for warrant, thereby lending support to the claim that any theory of knowledge that lacks a proper function requirement is false. (shrink)