Although convinced by Frankfurt-style cases that moral responsibility does not require the ability to do otherwise, semicompatibilists have not wanted to accept a parallel claim about moral responsibility for omissions, and so they have accepted asymmetrical requirements on moral responsibility for actions and omissions. In previous work, I have presented a challenge to various attempts at defending this asymmetry. My view is that semicompatibilists should give up these defenses and instead adopt symmetrical requirements on moral responsibility for actions and omissions, (...) and in this paper I highlight three advantages of doing so: first, it avoids a strange implication of the truth of determinism; second, it allows for a principled reply to Philip Swenson’s recent ‘No Principled Difference Argument’; third, it provides a reason to reject a crucial inference rule invoked by Peter van Inwagen’s ‘Direct Argument’ for the incompatibility of moral responsibility and determinism. (shrink)

It is widely thought that Atemporalism—the view that, because God is “outside” of time, he does not foreknow anything —constitutes a unique solution to the problem of freedom and foreknowledge. However, as I argue here, in order for Atemporalism to escape certain worries, the view must appeal to the dependence of God’s timeless knowledge on our actions. I then argue that, because it must appeal to such dependence, Atemporalism is crucially similar to the recent sempiternalist accounts proposed by Trenton Merricks, (...) Philip Swenson, and Jonathan Westphal, and I conclude by briefly sketching some implications of this result. (shrink)

Death can be bad for an individual who has died, according to the “deprivation approach,” by depriving that individual of goods. One worry for this account of death’s badness is the Lucretian symmetry argument: since we do not regret having been born later than we could have been born, and since posthumous nonexistence is the mirror image of prenatal nonexistence, we should not regret dying earlier than we could have died. Anthony Brueckner and John Martin Fischer have developed a response (...) to the Lucretian challenge by arguing that it is rational to have asymmetric attitudes toward posthumous and prenatal nonexistence. Recently, Jens Johansson has criticized the Brueckner/Fischer position, claiming that it is irrelevant whether it is actually rational to care about future pleasures but not past pleasures. What matters, according to Johansson, is whether it would be rational for us to care about past pleasures had we come into existence earlier. In this paper, I add to the conversation between Johansson and Brueckner/Fischer by suggesting a way to defend the latter side’s position in a way that has not yet been suggested. I do this by considering a suggestion of Johansson’s for interpreting the Brueckner/Fischer position and by arguing that Johansson’s worry for the position I consider is actually incoherent. (shrink)

I argue that considerations pertaining to constitutive luck undermine historicism—the view that an agent’s history can determine whether or not she is morally responsible. The main way that historicists have motivated their view is by appealing to certain cases of manipulation. I argue, however, that since agents can be morally responsible for performing some actions from characters with respect to which they are entirely constitutively lucky, and since there is no relevant difference between these agents and agents who have been (...) manipulated into acting from a character bestowed upon them by their manipulators, we should give up historicism. After presenting this argument and defending it against some potential objections, I briefly criticize the standard structuralist alternative and propose a new structuralist position that is shaped by reflection on constitutive luck. (shrink)

This book is a collection of edited interviews from The Free Will Show-a podcast that provides a beginner-friendly introduction to free will while also highlighting recent developments on the topic. The book includes original material as well, including an introduction to the interviews and an afterward with reflections on the podcast by the authors (who are cohosts of The Free Will Show). The book also includes a bibliography and suggestions for further reading after each interview and a glossary of terms (...) at the end of the book. The book will serve well either as a textbook or as an accessible entry-point to the free will debate, whether for an interested non-specialist or a philosopher who works in another area. The first half of this book introduces the main issues and arguments in philosophical debates about free will, including various apparent threats to free will (fatalism, foreknowledge, and determinism), the Consequence Argument, and the problem of luck, among others. The second half of this book introduces the main positions in the debate about free will and determinism, including several varieties of libertarianism and compatibilism, a version of free will skepticism, and some other positions that do not fit neatly into these categories. (shrink)

It is widely thought that, to be morally responsible for some action or omission, an agent must have had, at the very least, the general ability to do otherwise. As we argue, however, there are counterexamples to the claim that moral responsibility requires the general ability to do otherwise. We present several cases in which agents lack the general ability to do otherwise and yet are intuitively morally responsible for what they do, and we argue that such cases raise problems (...) for various kinds of accounts of moral responsibility. We suggest two alternative approaches to thinking about the connection between moral responsibility and abilities to do otherwise, one of which denies that there is any ability-to-do-otherwise requirement on moral responsibility and the other of which requires only an opportunity to do otherwise. We also argue that a general-ability-to-do-otherwise requirement not only faces counterexamples but also lacks positive motivation. (shrink)

Recently, several authors have utilized the notion of dependence to respond to the traditional argument for the incompatibility of freedom and divine foreknowledge. However, proponents of this response have not always been so clear in specifying where the incompatibility argument goes wrong, which has led to some unfounded objections to the response. We remedy this dialectical confusion by clarifying both the dependence response itself and its interaction with the standard incompatibility argument. Once these clarifications are made, it becomes clear both (...) (1.) that the dependence response does not beg the question against the proponent of the incompatibility argument and (2.) that the dependence response advances the dialectic whether it is developed as a version of Ockhamism or as a version of multiple-pasts compatibilism. (shrink)

An increasingly popular approach to reconciling divine foreknowledge with human freedom is to say that, because God’s beliefs depend on what we do, we are free to do otherwise than what we actually do despite God’s infallible foreknowledge. This paper develops a new challenge for this dependence response. The challenge stems from a case of backward time travel in which an agent intuitively lacks the freedom to do otherwise because of the time-traveler’s knowledge of what the agent will do, and (...) this is so despite the fact that the time-traveler’s knowledge depends on what the agent will do. (shrink)

In this paper, I defend a version of compatibilism against luck-related objections. After introducing the types of luck that some take to be problematic for moral responsibility, I consider and respond to two recent attempts to show that compatibilism faces the same problem of luck that libertarianism faces—present luck. I then consider a different type of luck—constitutive luck—and provide a new solution to this problem. One upshot of the present discussion is a reason to prefer a history-sensitive compatibilist account over (...) a purely nonhistorical structuralist account. (shrink)

Some compatibilists are internalists. On their view, whether an agent is morally responsible for an action depends only on her psychological structure at that time. Other compatibilists are externalists. On their view, an agent’s history can make a difference as to whether or not she is morally responsible. In response to worries about manipulation, some internalists have claimed that compatibilism requires internalism. Recently, Alfred Mele has argued that this internalist response is untenable. The aim of this paper is to vindicate (...) the claim that compatibilism requires internalism, showing where Mele’s argument goes wrong along the way. (shrink)

I argue that any account attempting to do away with resultant or circumstantial moral luck is inconsistent with a natural response to the problem of constitutive moral luck. It is plausible to think that we sometimes contribute to the formation of our characters in such a way as to mitigate our constitutive moral luck at later times. But, as I argue here, whether or not we succeed in bringing about changes to our characters is itself a matter of resultant and (...) circumstantial moral luck. I conclude with a dilemma, both horns of which require accepting some form of moral luck. (shrink)

In Section 1, we begin by asking what, exactly, it might mean for God to “elect” people and how this relates to their agency and freedom. After getting clearer on what God is supposed to elect people to or for, we argue against the view that a person’s will is not involved in the process by which God elects her, which we identify in part as the person’s coming to have faith. But, in Section 2, we consider several reasons for (...) thinking that a person’s free will is not involved in her coming to have faith, as well as a potential problem facing this view. Then, in the next three sections (3, 4, and 5) we examine three views on which one’s free will is involved in one’s coming to faith, corresponding roughly to three systematic views of divine providence. We discuss certain objections to each of these “models of election,” as well as how each speaks to the possibility of the non-elect. In the sixth and final section, we conclude by addressing the concern that any such philosophizing about God is too anthropomorphic. (shrink)

In response to the increasingly popular manipulation argument against compatibilism, some have argued that libertarian accounts of free will are vulnerable to parallel manipulation arguments, and thus manipulation is not uniquely problematic for compatibilists. The main aim of this article is to give this point a more detailed development than it has previously received. Prior attempts to make this point have targeted particular libertarian accounts but cannot be generalized. By contrast, I provide an appropriately modified manipulation that targets all libertarian (...) accounts of freedom and responsibility—an especially tricky task given that libertarian accounts are a motley set. I conclude that if manipulation arguments reveal any theoretical cost then it is one borne by all accounts according to which we are free and responsible, not by compatibilism in particular. (shrink)

Matt King has recently argued that the manipulation argument against compatibilism does not succeed by employing a dilemma: either the argument infelicitously relies on incompatibilist sourcehood conditions, or the proponent of the argument leaves a premise of the argument undefended. This article develops a reply to King’s dilemma by showing that incompatibilists can accept its second horn. Key to King’s argument for the second horn’s being problematic is “the parallel manipulation argument.” I argue that King’s use of this argument is (...) problematic, but I suggest that a (modified) parallel manipulation argument is effective for a different, though more restricted, purpose. (shrink)

In this paper, I argue that it is open to semicompatibilists to maintain that no ability to do otherwise is required for moral responsibility. This is significant for two reasons. First, it undermines Christopher Evan Franklin’s recent claim that everyone thinks that an ability to do otherwise is necessary for free will and moral responsibility. Second, it reveals an important difference between John Martin Fischer’s semicompatibilism and Kadri Vihvelin’s version of classical compatibilism, which shows that the dispute between them is (...) not merely a verbal dispute. Along the way, I give special attention to the notion of general abilities, and, though I defend the distinctiveness of Fischer’s semicompatibilism against the verbal dispute charge, I also use the discussion of the nature of general abilities to argue for the falsity of a certain claim that Fischer and coauthor Mark Ravizza have made about their account. (shrink)

This paper presents a new challenge to the thesis that moral responsibility for an omission requires the ability to do the omitted action, whereas moral responsibility for an action does not require the ability to do otherwise than that action. Call this the asymmetry thesis. The challenge arises from the possibility of cases in which an omission is identical to an action. In certain of such cases, the asymmetry thesis leads to a contradiction. The challenge is then extended to recent (...) variations of the asymmetry thesis defended by John Martin Fischer and Carolina Sartorio. Finally, a possible objection to the challenge is addressed. (shrink)

The most popular philosophical account of how death can harm (or be bad for) the deceased is the deprivation account, according to which death is bad insofar as it deprives the deceased of goods that would have been enjoyed by that person had the person not died. In this paper, the author surveys four main challenges to the deprivation account: the No-Harm-Done Argument, the No-Subject Argument, the Timing Argument, and the Symmetry Argument. These challenges are often raised by Epicureans, who (...) (following Epicurus) claim that death cannot harm the deceased, and each challenge is addressed in Thomas Nagel’s classic essay, “Death,” which has been very influential on recent developments in the literature on the philosophy of death. The author of this paper summarizes some of these recent developments as the challenges are considered. (shrink)

Critics of synergism often complain that the view entails Pelagianism, and so, critics think, monergism looks like the only live option. Critics of monergism often claim that the view entails that the blame for human sin ultimately traces to God. Recently, several philosophers have attempted to chart a middle path by offering soteriological accounts which are monergistic but maintain the resistibility of God’s grace. In this paper, we present a challenge to such accounts of the resistibility of grace, namely that (...) they imply that human beings are praiseworthy for omitting to resist God’s grace. Even if such views escape Pelagianism as it is typically defined, they fail to avoid the worry at the heart of prominent criticisms of Pelagianism concerning the praise for a human being’s salvation. At the end of the paper, we suggest three possible solutions to this problem. (shrink)

Is moral responsibility essentially historical, or does an agent's moral responsibility for an action depend only on their psychological structure at that time? In previous work, I have argued that the two main (non‐skeptical) views on moral responsibility and agents’ histories—historicism and standard structuralism—are vulnerable to objections that are avoided by a third option, namely history‐sensitive structuralism. In this paper, I develop this view in greater detail and evaluate the view by comparing it with its three dialectical rivals: skepticism about (...) moral responsibility, historicism, and standard structuralism. Each comparison includes discussion of new work on moral responsibility and agents’ histories, and along the way I offer new arguments for preferring history‐sensitive structuralism, paying special attention to the view's explanatory power. (shrink)

One of the most fascinating and continually debated arguments in the philosophical literature on the badness of death comes from the work of Lucretius (Titus Lucretius Carus, circa 99-55 BCE). This chapter will focus on Lucretius’s famous Symmetry Argument. I will begin by saying more about what exactly Epicureanism teaches about death — and why Epicureans thought it could not be bad. After that, I will provide the passage from Lucretius’s epic poem that includes his reasons for thinking that death (...) cannot be bad and will show how Lucretius’s passage has been regimented into the Symmetry Argument against the badness of death. Next, I will discuss the lasting influence of Lucretius’s argument, summarizing some common ways of responding. Finally, I will turn to two other passages from Lucretius’s poem, both of which suggest that it is actually good (both for us and for the world) that our lives come to an end, and I will conclude by considering the implications of Lucretius’s thought for political policy. (shrink)

Natural compatibilists say that moral responsibility is compatible with natural (or causal) determinism, where natural events and laws of nature determine everything that happens. Theological compatibilists say that moral responsibility is compatible with theological determinism, where God (rather than natural events/laws) determines everything that happens. Some philosophers accept natural compatibilism but reject theological compatibilism, and, in this chapter, I argue that this combination of views is untenable I start with a discussion of why someone might be attracted to this combination (...) of views in the first place, which includes a discussion of the manipulation argument against compatibilism. Some natural compatibilists endorse “soft-line” responses to this argument—responses which imply theological incompatibilism. I argue that such “soft-line” approaches cannot succeed, and along the way I argue that their failure undermines Jason Turner’s recent compatibilist free will defense (in response to the problem of evil). I wrap up by considering some implications of my conclusion that natural compatibilists should be theological compatibilists, including whether my conclusion highlights the “cost” of compatibilism, as proponents of manipulation arguments sometimes allege, and also whether anything follows with regard to God’s standing to blame determined human agents. (shrink)

According to John Martin Fischer and Anthony Brueckner’s unique version of the deprivation approach to accounting for death’s badness, it is rational for us to have asymmetric attitudes toward prenatal and posthumous nonexistence. In previous work, I have defended this approach against a criticism raised by Jens Johansson by attempting to show that Johansson’s criticism relies on an example that is incoherent. Recently, Duncan Purves has argued that my defense reveals an incoherence not only in Johansson’s example but also in (...) Fischer and Brueckner’s approach itself. Here I argue that by paying special attention to a certain feature of Fischer and Brueckner’s approach, we can dispense of not only Johansson’s criticism but also of Purves’s objection to Fischer and Brueckner’s approach. (shrink)

Many find it intuitive that having been manipulated undermines a person's free will. Some have objected to accounts of free will like Harry Frankfurt's (according to which free will depends only on an agent's psychological structure at the time of action) by arguing that it is possible for manipulated agents, who are intuitively unfree, to satisfy Frankfurt's allegedly sufficient conditions for freedom. Drawing resources from Greg Egan's "Reasons to Be Cheerful" as well as from stories of psychologically sophisticated artificial intelligence (...) (such as Isaac Asimov's "The Bicentennial Man"), I rebut this objection to "structuralist" accounts of free will, arguing that the very possibility of free will for persons like us requires that we admit that a person can be free even when lacking control over the character from which she acts. I conclude with some implications for the freedom and personhood of artificial intelligences. (shrink)

Like most episodes of Black Mirror, “Hang the DJ” raises a host of philosophical questions. While there is much from this episode to explore, this chapter will explore something that has not yet been addressed in other work, namely the connection between “Hang the DJ” and questions about free will and determinism (or indeterminism, as the case may be). This chapter will proceed as follows: first, I will sketch some reasons for thinking that, if determinism is true, then no one (...) has or exercises free will. One type of response to determinism’s threat to free will is to accept the incompatibility of free will and determinism and to maintain that we nevertheless have free will. Theorists who endorse indeterministic accounts of free will are called libertarians in the free will debate (but please do not confuse them with political libertarians). Second, I will explain a bit more of the mechanics of libertarianism. Third, I will discuss an influential challenge to libertarianism that has come to be known as the “rollback argument.” The mechanics of this challenge will resemble the plot twist of “Hang the DJ.” Fourth, and finally, I will explore the episode’s portrayal of the value of undetermined choice. (shrink)

Hobart’s classic 1934 paper “Free Will as Involving Determination and Inconceivable Without It” has been widely cited as an example of an argument for the view that free will requires the truth of determinism. In this paper, I argue that this reading of Hobart’s paper is mistaken and that we should instead read Hobart as arguing that an agent exercises their free will only if the proximate causes of the agent’s action deterministically cause their action. After arguing that Hobart’s view, (...) rightly understood, escapes the problems typically raised for Hobart’s compatibilism, I also argue that Hobart’s view is problematic for different reasons. Nevertheless, I argue that there is a crucial insight to be gleaned from Hobart’s paper—one that provides compatibilists with a new recipe for challenging libertarian accounts of free will. (shrink)

One way that philosophers have attempted to defend free will against the threat of fatalism and against the threat from divine beliefs has been to endorse timelessness views. In this paper, I argue that, in order to respond to general worries about fatalism and divine beliefs, timelessness views must appeal to the notion of dependence. Once they do this, however, their distinctive position as timelessness views becomes otiose, for the appeal to dependence, if it helps at all, would itself be (...) sufficient to block worries about fatalism and divine beliefs. I conclude by discussing some implications for dialectical progress. (shrink)

One way that philosophers have attempted to defend free will against the threat of fatalism and against the threat from divine beliefs has been to endorse timelessness views (about propositions and God’s beliefs, respectively). In this paper, I argue that, in order to respond to general worries about fatalism and divine beliefs, timelessness views must appeal to the notion of dependence. Once they do this, however, their distinctive position as timelessness views becomes otiose, for the appeal to dependence, if it (...) helps at all, would itself be sufficient to block worries about fatalism and divine beliefs. I conclude by discussing some implications for dialectical progress. (shrink)

This paper explores what the metaphysics of time travel might teach us about moral responsibility. We take our cue from a recent paper by Yishai Cohen, who argues that if time travel is metaphysically possible, then one of the most influential theories of moral responsibility (i.e., Fischer and Ravizza’s) is false. We argue that Cohen’s argument is unsound but that Cohen’s argument can serve as a lens to bring reasons-responsive theories of moral responsibility into sharper focus, helping us to better (...) understand actual-sequence theories of moral responsibility more generally and showing how actual-sequence theorists should respond to a recent criticism. (shrink)

This volume celebrates the career of John Martin Fischer, whose work on a wide range of topics over the past forty years has been transformative and inspirational. Fischer's semicompatibilist view of free will and moral responsibility is perhaps the most widely discussed view of its kind, and his emphasis on the significance of reasons-responsiveness as the capacity that underlies moral accountability has been widely influential. Aside from free will and moral responsibility, Fischer is also well-known for his work on freedom (...) and foreknowledge, the problem of evil, the badness of death, the meaning of life, and the allure of immortality. This volume gathers new essays by leading scholars on some of the major themes of Fischer's work, and it also includes a new piece by Fischer in which he offers a systematic reflection on and defense of the motivations that have shaped his theorizing about moral responsibility. Freedom, Responsibility, and Value will be of interest to scholars and students working on a variety of issues in metaphysics, ethics, and philosophy of religion. (shrink)

Since at least the time of Epicurus, philosophers have debated whether death could be bad for the one who has died, since death is a permanent experiential blank. But a different puzzle about death’s badness arises when we consider the death of a person who is paradise-bound. The first purpose of this paper is to develop this puzzle. The second purpose of this paper is to suggest and evaluate several potential attempts to solve the puzzle. After rejecting two seemingly attractive (...) suggestions, I argue that there are two types of solution to the puzzle that can succeed. The first type of solution simply denies that death can be bad for the paradise-bound. I argue that the main worry for this type of solution, namely that it gives up the common-sense view about death’s badness, is only a prima facie worry. The second type of solution maintains that death can be bad for the paradise-bound because it can deprive her of certain goods, which allows those who are attracted to this type of solution to adopt the deprivation account of death’s badness. I consider three views of the relation between the paradise-bound and paradise that are consistent with the deprivation account, connecting my discussion of paradise with the extant literature on death’s badness. (shrink)

In a series of recent papers, Justin Capes and Philip Swenson and Michael Robinson have proposed new versions of the flickers of freedom reply to Frankfurt-style cases. Both proposals claim, first, that what agents in FSCs are morally responsible for is performing a certain action on their own, and, second, that agents in FSCs retain robust alternative possibilities—alternatives in which the agent freely omits to perform the pertinent action on their own. In this paper, I argue that, by attending to (...) the details of the omissions in question, it becomes clear that agents in FSCs lack robust alternatives of this sort, for in the alternative sequences such agents do not freely omit. Since the problem for these recent proposals arises from their attempt to show that agents in FSCs retain robust alternatives, I go on to consider whether the flicker theorist might be better off either revising or rejecting the robustness requirement on alternative possibilities. I argue that neither alternative is available to the flicker theorist, and yet I also point out that the reasons why these alternatives are unavailable serve to highlight what exactly is at issue in the debate between leeway and sourcehood theorists, namely the grounds of our freedom. (shrink)

Recently, John Maier has developed a unified account of various agentive modalities. According to him, however, adopting the account provides an alternative framework for thinking about free will and moral responsibility, one that reveals an unacceptable instability in semicompatibilism. In this paper, I argue that Maier is mistaken about the implications of his account and sketch a semicompatibilist proposal that can, without countenancing any instability, accept Maier’s unified account of the agentive modalities.

Manipulated Agents: A Window to Moral Responsibility. By Mele Alfred R..).

John Martin Fischer and Anthony L. Brueckner have argued that a person’s death is, in many cases, bad for him, whereas a person’s prenatal non-existence is not bad for him. Their suggestion relies on the idea that death deprives the person of pleasant experiences that it is rational for him to care about, whereas prenatal non-existence only deprives him of pleasant experiences that it is not rational for him to care about. Jens Johansson has objected to this justification of ‘The (...) Asymmetry’ between the badness of death and pre-natal non-existence on the grounds that what it is actually rational for us to care about is irrelevant to the question of whether the event is bad for us. Taylor Cyr has recently argued that Jens Johansson’s objection to Fischer’s and Brueckner’s position relies on an incoherent example, and is thus unsuccessful. I argue that Cyr’s attempt to defend Fischer and Brueckner in fact illustrates that their position is incoherent, and that Johansson’s objection therefore succeeds. (shrink)

In defense of the Deprivation Approach to the badness of death against the Lucretian objection that death is relevantly similar to prenatal nonexistence, John Martin Fischer and Anthony L. Brueckner have suggested that whereas death deprives us of things that it is rational for us to care about, prenatal nonexistence does not. I have argued that this suggestion, even if correct, does not make for a successful defense of the Deprivation Approach against the Lucretian objection. My criticism involved a thought (...) experiment in which a person avoids being tortured. Recently, Taylor Cyr has defended Fischer and Brueckner’s approach, arguing that my thought experiment is incoherent. In this response, I question both the truth and relevance of Cyr’s incoherence claim. (shrink)

The discussion of good and evil must not be confined to the sterile lecture halls of academics but related instead to ordinary human feelings, needs, and desires, says noted philosopher Richard Taylor. Efforts to understand morality by exploring human reason will always fail because we are creatures of desire as well. All morality arises from our intense and inescapable longing. The distinction between good and evil is always clouded by rationalists who convert the real problems of ethics into complex (...) philosophical puzzles. In the first part of Good and Evil, Taylor looks for a more meaningful conception by reexamining and rejecting the whole rationalistic tradition that dominates philosophical ethics. The second part provides an empirical explanation of good and evil, noting that one does not have to look too far to find prime examples of the failure of fixed moral rules. Including important commentary on Joseph Fletcher's groundbreaking situation ethics, and Aristotle's virtues (e.g., magnanimity and pride), Taylor rounds out the book by developing a philosophy of aspiration--personal worth as an ethical ideal--to replace the morality of duty. He offers a modified form of situation ethics to fit the contemporary problems we face. (shrink)

Discusses contemporary notions of the self, and examines their origins, development, and effects.

The place of religion in society has changed profoundly in the last few centuries, particularly in the West. In what will be a defining book for our time, Taylor takes up the question of what these changes mean, and what, precisely, happens when a society becomes one in which faith is only one human possibility among others.

In “Spandrels,” Gould and Lewontin criticized what they took to be an all-too-common conviction, namely, that adaptation to current environments determines organic form. They stressed instead the importance of history. In this paper, we elaborate upon their concerns by appealing to other writings in which those issues are treated in greater detail. Gould and Lewontin’s combined emphasis on history was three-fold. First, evolution by natural selection does not start from scratch, but always refashions preexisting forms. Second, preexisting forms are refashioned (...) by the selection of whatever mutational variations happen to arise: the historical order of mutations needs to be taken into account. Third, the order of environments and selection pressures also needs to be taken into account. (shrink)

The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs. Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techniques that mathematicians adopt to prove their results, and offers advice and strategies for constructing proofs. It will improve students’ ability to understand proofs and construct correct proofs of their own. The (...) first chapter of the text introduces the kind of reasoning that mathematicians use when writing their proofs and gives some example proofs to set the scene. The book then describes basic logic to enable an understanding of the structure of both individual mathematical statements and whole mathematical proofs. It also explains the notions of sets and functions and dissects several proofs with a view to exposing some of the underlying features common to most mathematical proofs. The remainder of the book delves further into different types of proof, including direct proof, proof using contrapositive, proof by contradiction, and mathematical induction. The authors also discuss existence and uniqueness proofs and the role of counter examples. (shrink)

Recent develops in AI technology have led to increasingly sophisticated forms of video manipulation. One such form has been the advent of deepfakes. Deepfakes are AI-generated videos that typically depict people doing and saying things they never did. In this paper, I demonstrate that there is a close structural relationship between deepfakes and more traditional fake barn cases in epistemology. Specifically, I argue that deepfakes generate an analogous degree of epistemic risk to that which is found in traditional cases. Given (...) that barn cases have posed a long-standing challenge for virtue-theoretic accounts of knowledge, I consider whether a similar challenge extends to deepfakes. In doing so, I consider how Duncan Pritchard’s recent anti-risk virtue epistemology meets the challenge. While Pritchard’s account avoids problems in traditional barn cases, I claim that it leads to local scepticism about knowledge from online videos in the case of deepfakes. I end by considering how two alternative virtue-theoretic approaches might vindicate our epistemic dependence on videos in an increasingly digital world. (shrink)

When artificial intelligence (AI) is used to make high-stakes decisions, some worry that this will create a morally troubling responsibility gap—that is, a situation in which nobody is morally responsible for the actions and outcomes that result. Since the responsibility gap might be thought to result from individuals lacking knowledge of the future behavior of AI systems, it can be and has been suggested that deploying explainable artificial intelligence (XAI) techniques will help us to avoid it. These techniques provide humans (...) with certain forms of understanding of the systems in question. In this paper, I consider whether existing XAI techniques can indeed close the responsibility gap. I identify a number of significant limits to their ability to do so. Ensuring that responsibility for AI-assisted outcomes is maintained may require using different techniques in different circumstances, and potentially also developing new techniques that can avoid each of the issues identified. (shrink)

Contemporary republicanism is characterized by three main ideas: free persons, who are not subject to the arbitrary power of others; free states, which try to protect their citizens from such power without exercising it themselves; and vigilant citizenship, as a means to limit states to their protective role. This book advances an economic model of such republicanism that is ideologically centre-left. It demands an exit-oriented state interventionism, one that would require an activist government to enhance competition and resource exit from (...) dominating relationships within markets of all types, be they marital, labour, or residential. The substantial intervention and redistribution necessitated by such an approach make it leftist, while its tendency to work with rather than against the grain of markets makes it centrist. It is, in short, a contribution to progressive republican political thought, but one that is less social-democratic than market-democratic in character. (shrink)

Iris Murdoch and moral philosophy -- Understanding the other: a Gadamerian view on conceptual schemes -- Language not mysterious? -- Celan and the recovery of language -- Nationalism and modernity -- Conditions of an unforced consensus on human rights -- Democratic exclusion (and its remedies?) -- Religious mobilizations -- Themes from a secular age -- The immanent counter-enlightenment -- Notes on the sources of violence: perennial and modern -- The future of the religious past -- Disenchantment-re-enchantment -- What does secularism (...) mean? -- Die blosse Vernunft ("reason alone") -- Perils of moralism -- What was the Axial revolution? (shrink)