A true Turing machine requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime, but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar to our world. But curiously enough-and this is (...) the main point of this paper-some of these close worlds have a special spacetime structure that allows TMs to perform certain Turing unsolvable tasks. For example, in one kind of spacetime a TM can be used to solve first-order predicate logic and the halting problem. And in a more complicated spacetime, TMs can be used to decide arithmetic. These new computers serve to show that Church's thesis is a thoroughly contingent claim. Moreover, since these new computers share the fundamental properties of a TM in ordinary operation, a computability theory based on these non-Turing computers is no less worthy of investigation than orthodox computability theory. Some ideas about this new mathematical theory are given. (shrink)

A true Turing machine (TM) requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime (the spacetime of common sense), but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar ("close") to (...) our world. But curiously enough-and this is the main point of this paper-some of these close worlds have a special spacetime structure that allows TMs to perform certain Turing unsolvable tasks. For example, in one kind of spacetime a TM can be used to solve first-order predicate logic and the halting problem. And in a more complicated spacetime, TMs can be used to decide arithmetic. These new computers serve to show that Church's thesis is a thoroughly contingent claim. Moreover, since these new computers share the fundamental properties of a TM in ordinary operation (e.g. intuitive, finitely programmed, limited in computational capability), a computability theory based on these non-Turing computers is no less worthy of investigation than orthodox computability theory. Some ideas about this new mathematical theory are given. (shrink)

Presented here is a new result concerning the computational power of so-called SADn computers, a class of Turing-machine-based computers that can perform some non-Turing computable feats by utilising the geometry of a particular kind of general relativistic spacetime. It is shown that SADn can decide n-quantifier arithmetic but not (n+1)-quantifier arithmetic, a result that reveals how neatly the SADn family maps into the Kleene arithmetical hierarchy. Introduction Axiomatising computers The power of SAD computers Remarks regarding the concept of computability.

In his recent article On Relativity Theory and Openness of the Future (1991), Howard Stein proves not only that one can define an objective becoming relation in Minkowski spacetime, but that there is only one possible definition available if one accepts certain natural assumptions about what it is for becoming to occur and for it to be objective. Stein uses the definition supplied by his proof to refute an argument due to Rietdijk (1966, 1976), Putnam (1967) and Maxwell (1985, 1988) (...) that Minkowski spacetime leaves no room for objective becoming whatsoever. However, Stein's proof does not seem to go far enough. By considering only what events have become from the standpoint of any given event, Stein's uniqueness proof fails from the outset to allow for a more general kind of becoming whereby it is understood to occur from the standpoint of events on the particular worldlines followed by observers. This suggests that there may, after all, be more than one way to define objective becoming in Minkowski spacetime once each observer's worldline is allowed to figure in the definition. This suspicion is further aroused by two recent proposals for objective, worldline-dependent becoming due to Peacock (1992) and Muller (1992) who advocate ways of defining becoming that are not equivalent to the definition Stein's uniqueness proof delivers. Nevertheless, we show that Stein's uniqueness proofcan be extended in a natural way to cover this more general kind of becoming, provided one does not enrich standard Minkowski spacetime by privileging certain sets of worldlines over others in an unwarranted manner. Thus we aim to reinforce Stein's point that standard Minkowski spacetime does make room for objective becoming, but in essentially only one way, despite arguments and proposals to the contrary. (shrink)

This collection of articles on the theme of space and time covers such broad topics as the philosophy of spacetime, spacetime structure, spacetime ontology, the epistemology of geometry, and general relativity.

Mark Jago presents an original philosophical account of meaningful thought: in particular, how it is meaningful to think about things that are impossible. We think about impossible things all the time. We can think about alchemists trying to turn base metal to gold, and about unfortunate mathematicians trying to square the circle. We may ponder whether God exists; and philosophers frequently debate whether properties, numbers, sets, moral and aesthetic qualities, and qualia exist. In many philosophical or mathematical debates, when (...) one side of the argument gets things wrong, it necessarily gets them wrong. As we consider both sides of one of these philosophical arguments, we will at some point think about something that’s impossible. Yet most philosophical accounts of meaning and content hold that we can’t meaningfully think or reason about the impossible. -/- In The Impossible, Jago argues that we often gain new information, new beliefs, and, sometimes, fresh knowledge through logic, mathematics, and philosophy. That is why logic, mathematics, and philosophy are useful. We therefore require accounts of knowledge and belief, of information and content, and of meaning which allow space for the impossible. Jago’s aim in this book is to provide such accounts. He gives a detailed analysis of the concept of hyperintensionality, whereby logically equivalent contents may be distinct, and develops a theory in terms of possible and impossible worlds. Along the way, he provides a theory of what those worlds are and how they feature in our analysis of normative epistemic concepts: knowledge, belief, information, and content. (shrink)

It is time to bring the rich resources of these traditions into the contemporary debate about the nature of self. This volume is the first of its kind.

Nondescriptivist views in many areas of philosophy have long been associated with the commitment that in contrast to other domains of discourse, there are no propositions in their particular domain. For example, the ‘no truth conditions’ theory of conditionals1 is understood as the view that conditionals don’t express propositions, noncognitivist expressivism in metaethics is understood as advocating the view that there are not really moral propositions,2 and expressivism about epistemic modals is thought of as the view that there is no (...) such thing as the proposition that Jack might be at home, over and above the proposition that Jack is at home.3 Of course, it is nearly always acknowledged that advocates of a nondescriptivist theory need not deny that there are conditional, moral, or modal propositions ‘at the end of the day’ – for if they also endorse a deflationary reading of talk about propositions, as famously advocated by Simon Blackburn, then they can employ such deflationary talk just as much as the rest of us. They just don’t appeal to propositions to do any of the work in their theories. Rather, they ‘earn the right’ to talk about propositions.4 It is the aim of this paper to upset this way of thinking about the proper attitude of nondescriptivists toward propositions, and to advocate a more constructive and in some ways more radical alternative on behalf of the nondescriptivist. I will begin by introducing and developing a set of problems that are faced by any nondescriptivist theory which tries to do without propositions. All of these problems are easily solved by any view which postulates propositions across the board, but none of them are solved by merely deflationary talk about propositions – their most promising solutions require propositions to do real theoretical work, and therefore the problems themselves remind us of and illustrate some of the important reasons why it is worth positing propositions in the first place.. (shrink)

In this paper, I describe some of what I take to be the more interesting features of friendship, then explore the extent to which other virtues can be reconstructed as sharing those features. I use trustworthiness as my example throughout, but I think that other virtues such as generosity & gratitude, pride & respect, and the producer’s & consumer’s sense of humor can also be analyzed with this model. The aim of the paper is not to demonstrate that all moral (...) virtues are exactly like friendship in all important respects, but rather to articulate a fruitful model in which to explore the virtues. Section 2 explores the relational nature of friendship, drawing on Aristotle’s discussion of friendship in the Nicomachean Ethics. Section 3 catalogues four motivations for taking seriously the friendship model of virtue. Section 4 applies the friendship model in depth to the virtue of trustworthiness. (shrink)

Gaining information can be modelled as a narrowing of epistemic space . Intuitively, becoming informed that such-and-such is the case rules out certain scenarios or would-be possibilities. Chalmers’s account of epistemic space treats it as a space of a priori possibility and so has trouble in dealing with the information which we intuitively feel can be gained from logical inference. I propose a more inclusive notion of epistemic space, based on Priest’s notion of open worlds yet which contains only those (...) epistemic scenarios which are not obviously impossible. Whether something is obvious is not always a determinate matter and so the resulting picture is of an epistemic space with fuzzy boundaries. (shrink)

I discuss three ways of responding to the logical omniscience problems faced by traditional ‘possible worlds’ epistemic logics. Two of these responses were put forward by Hintikka and the third by Cresswell; all three have been influential in the literature on epistemic logic. I show that both of Hintikka's responses fail and present some problems for Cresswell’s. Although Cresswell's approach can be amended to avoid certain unpalatable consequences, the resulting formal framework collapses to a sentential model of knowledge, which defenders (...) of the ‘possible worlds’ approach are frequently critical of. (shrink)

We argue that the interaction of biased media coverage and widespread employment of the recognition heuristic can produce epistemic injustices. First, we explain the recognition heuristic as studied by Gerd Gigerenzer and colleagues, highlighting how some of its components are largely external to, and outside the control of, the cognitive agent. We then connect the recognition heuristic with recent work on the hypotheses of embedded, extended, and scaffolded cognition, arguing that the recognition heuristic is best understood as an instance of (...) scaffolded cognition. In section three, we consider the double-edged sword of cognitive scaffolding. On the one hand, scaffolds can reduce the internal processing demands on cognitive agents while increasing their access to information. On the other hand, the use of scaffolding leaves cognitive agents increasingly vulnerable to forming false beliefs or failing to form beliefs at all about particular topics. With respect to the recognition heuristic, agents rely on third parties (such as the media) to report not just what’s true but also what’s important or valuable. This makes cognitive agents relying on these third parties vulnerable to two erroneous influences: 1) because they don’t recognize something, it isn’t important or valuable, and 2) because they do recognize something, it is important or valuable. Call the latter the Kardashian Inference and the former the Darfur Inference. In section four, we use Fricker’s (2007) concept of epistemic injustice to characterize the nature and harm of these false inferences, with special emphasis on the Darfur Inference. In section five, we use data-mining and an empirical study to show how Gigerenzer’s population estimation task is liable to produce Darfur Inferences. We conclude with some speculative remarks on more important Darfur Inferences, and how to avoid them by scaffolding better. One primary way to accomplish this it to shift the burden of embodying the virtue of epistemic justice from the hearer or consumer of media to the media themselves. (shrink)

This book offers a systematic framework for thinking about the relationship between language and technology and an argument for interweaving thinking about technology with thinking about language. The main claim of philosophy of technology—that technologies are not mere tools and artefacts not mere things, but crucially and significantly shape what we perceive, do, and are—is re-thought in a way that accounts for the role of language in human technological experiences and practices. Engaging with work by Wittgenstein, Heidegger, McLuhan, Searle, Ihde, (...) Latour, Ricoeur, and many others, the author critically responds to, and constructs a synthesis of, three "extreme", idealtype, untenable positions: only humans speak and neither language nor technologies speak, only language speaks and neither humans nor technologies speak, and only technology speaks and neither humans nor language speak. The construction of this synthesis goes hand in hand with a narrative about subjects and objects that become entangled and constitute one another. Using Words and Things thus draws in central discussions from other subdisciplines in philosophy, such as philosophy of language, epistemology, and metaphysics, to offer an original theory of the relationship between language and technology centered on use, performance, and narrative, and taking a transcendental turn. (shrink)

This study examines the role of corporate philanthropy in the management of reputation risk and shareholder value of the top 100 ASX listed Australian firms for the 3 years 2011–2013. The results of this study demonstrate the business case for corporate philanthropy and hence encourage corporate philanthropy by showing increasing firms’ investment in corporate giving as a percentage of profit before tax, increases the likelihood of an increase in shareholder value. However, the proviso is that firms must also manage their (...) reputation risk at the same time. There is a negative association between corporate giving and shareholder value which is mitigated by firms’ management of reputation. The economic significance of this result is that for every cent in the dollar the firm spends on corporate giving, Tobin’s Q will decrease by 0.413 %. In contrast, if the firm increase their reputation by 1 point then Tobin’s Q will increase by 0.267 %. Consequently, the interaction of corporate giving and reputation risk management is positively associated with shareholder value. These results are robust while controlling for potential endogeneity and reverse causality. This paper assists both academics and practitioners by demonstrating that the benefits of corporate philanthropy extend beyond a gesture to improve reputation or an attempt to increase financial performance, to a direct collaboration between all the factors where the benefits far outweigh the costs. (shrink)

During multiple testing, researchers often adjust their alpha level to control the familywise error rate for a statistical inference about a joint union alternative hypothesis (e.g., “H1,1 or H1,2”). However, in some cases, they do not make this inference. Instead, they make separate inferences about each of the individual hypotheses that comprise the joint hypothesis (e.g., H1,1 and H1,2). For example, a researcher might use a Bonferroni correction to adjust their alpha level from the conventional level of 0.050 to 0.025 (...) when testing H1,1 and H1,2, find a significant result for H1,1 (p < 0.025) and not for H1,2 (p > .0.025), and so claim support for H1,1 and not for H1,2. However, these separate individual inferences do not require an alpha adjustment. Only a statistical inference about the union alternative hypothesis “H1,1 or H1,2” requires an alpha adjustment because it is based on “at least one” significant result among the two tests, and so it refers to the familywise error rate. Hence, an inconsistent correction occurs when a researcher corrects their alpha level during multiple testing but does not make an inference about a union alternative hypothesis. In the present article, I discuss this inconsistent correction problem, including its reduction in statistical power for tests of individual hypotheses and its potential causes vis-à-vis error rate confusions and the alpha adjustment ritual. I also provide three illustrations of inconsistent corrections from recent psychology studies. I conclude that inconsistent corrections represent a symptom of statisticism, and I call for a more nuanced inference-based approach to multiple testing corrections. (shrink)

Animal rights and moral theories -- Arguing for one's species -- Utilitarianism and animals : Peter Singer's case for animal liberation -- Tom Regan : animal rights as natural rights -- Virtue ethics and animals -- Contractarianism and animal rights -- Animal minds.

Bringing together the latest scientific advances and some of the most enduring subtle philosophical puzzles and problems, this book collects original historical and contemporary sources to explore the wide range of issues surrounding the nature of life. Selections ranging from Aristotle and Descartes to Sagan and Dawkins are organised around four broad themes covering classical discussions of life, the origins and extent of natural life, contemporary artificial life creations and the definition and meaning of 'life' in its most general form. (...) Each section is preceded by an extensive introduction connecting the various ideas discussed in individual chapters and providing helpful background material for understanding them. With its interdisciplinary perspective, this fascinating collection is essential reading for scientists and philosophers interested in astrobiology, synthetic biology and the philosophy of life. (shrink)

Epistemology -- Power I -- Power II -- Subjectivity -- Resistance -- Critique -- Ethics.

The effectiveness of decision rules depends on characteristics of both rules and environments. A theoretical analysis of environments specifies the relative predictive accuracies of the “take-the-best” heuristic (TTB) and other simple strategies for choices between two outcomes based on binary cues. We identify three factors: how cues are weighted; characteristics of choice sets; and error. In the absence of error and for cases involving from three to five binary cues, TTB is effective across many environments. However, hybrids of equal weights (...) (EW) and TTB models are more effective as environments become more compensatory. As error in the environment increases, the predictive ability of all models is systematically degraded. Indeed, using the datasets of Gigerenzer et al. (1999, Simple Heuristics That Make Us Smart, New York: Oxford University Press), TTB and similar models do not predict much better than a naïve model that exploits dominance. Finally, we emphasize that the results reported here are conditional on binary cues. (shrink)

From his earliest work on personal identity to his last on the value of truthfulness, the ideas and arguments of Bernard Williams - in the metaphysics of personhood, in the history of philosophy, but especially in ethics and moral psychology - have proved sometimes controversial, often influential, and always worth studying. This book provides a comprehensive account of Williams's many significant contributions to contemporary philosophy. Topics include personal identity, various critiques of moral theory, practical reasoning and moral motivation, truth and (...) objectivity, and the relevance of ancient Greece to modern life. It not only positions Williams among these important philosophical topics, but also with regard to the views of other philosophers, including prominent forerunners such as Hume and Nietzsche and contemporary thinkers such as, Nagel, McDowell, MacIntyre and Taylor. The fragmentary nature of Williams's work is addressed and recurring themes and connections within his work are brought to light. (shrink)

Debates over health care have focused for so long on economics that the proper goals for medicine seem to be taken for granted; yet problems in health care stem as much from a lack of agreement about the goals and priorities of medicine as from the way systems function. This book asks basic questions about the purposes and ends of medicine and shows that the answers have practical implications for future health care delivery, medical research, and the education of medical (...) students. The Hastings Center coordinated teams of physicians, nurses, public health experts, philosophers, theologians, politicians, health care administrators, social workers, and lawyers in fourteen countries to explore these issues. In this volume, they articulate four basic goals of medicine — prevention of disease, relief of suffering, care of the ill, and avoidance of premature death — and examine them in light of the cultural, political, and economic pressures under which medicine functions. In reporting these findings, the contributors touch on a wide range of diverse issues such as genetic technology, Chinese medicine, care of the elderly, and prevention and public health. The Goals of Medicine clearly demonstrates the importance of clarifying the purposes of medicine before attempting to change the economic and organizational systems. It warns that without such examination, any reform efforts may be fruitless. (shrink)

Particularists in ethics emphasize that the normative is holistic, and invite us to infer with them that it therefore defies generalization. This has been supposed to present an obstacle to traditional moral theorizing, to have striking implications for moral epistemology and moral deliberation, and to rule out reductive theories of the normative, making it a bold and important thesis across the areas of normative theory, moral epistemology, moral psychology, and normative metaphysics. Though particularists emphasize the importance of the holism of (...) the normative, however, it is not something that they have been able to explain. In this paper I’ll show how to use a small number of simple and, I’ll argue, independently compelling assumptions in order to both predict and explain the holistic features of the normative with respect to the non-normative. The basic idea of the paper is simple. It is that normative claims are holistic because they are general, rather than because they defy generalization. (shrink)

The sense of smell occupies a peculiar intermediate position within Aristotle's theory of sense perception: odours, like colours and sounds, are perceived at a distance through an external medium of air or water; yet in their nature they are intimately related to flavours, the proper objects of taste, which for Aristotle is a form of touch. In this paper, I examine Aristotle's claims about odour and smell, especially in De Anima II.9 and De Sensu 5, to see what light they (...) shed on his theory of sense perception more generally. In the first half, I argue that neither of the two most influential recent ways of understanding Aristotle's theory of perception can adequately account for what he says about the sense of smell. In the second half, I offer my own positive account, considering and resolving various puzzles raised by Aristotle's claims about the nature of odour and its relation to flavour. Finally, I conclude that Aristotle's discussions of odour and smell suggest a plausible and interesting way of understanding the relationship, on his view, between ordinary, material changes in the sense organs and the activation of the capacity to perceive, considered merely as such. (shrink)

In this paper, I argue that there is a picture of how law works that most legal theorists are implicitly committed to and take to be common ground. This Standard Picture (SP, for short) is generally unacknowledged and unargued for. SP leads to a characteristic set of concerns and problems and yields a distinctive way of thinking about how law is supposed to operate. I suggest that the issue of whether SP is correct is a fundamental one for the philosophy (...) of law, more basic, for example, than the issue that divides legal positivists and anti-positivists, at least as the latter issue is ordinarily understood. The goals of the paper are fourfold: 1) to identify and articulate in some detail the Standard Picture; 2) to show that SP is widely held and has important consequences for other debates in the philosophy of law; 3) to show that SP leads to a serious theoretical problem; 4) to sketch an alternative picture that promises to avoid this problem. I emphasize the modesty of these goals in one respect. I make no claim to refute SP or to fully develop and defend an alternative picture. (shrink)

This article is a précis of Mark C. Murphy’s _Divine Holiness and Divine Action_ (Oxford University Press, 2021), which offers an account of God’s holiness and of the difference this view of God’s holiness should make to our understanding of divine action.

The Clarke/Rowe version of the Cosmological Argument is sound only if the Principle of Sufficient Reason is true, but many philosophers, including Rowe, think that there is not adequate evidence for the principle of sufficient reason. I argue that there may be indirect evidence for PSR on the grounds that if we do not accept it, we lose our best justification for an important principle of metaethics, namely, the Principle of Universalizability. To show this, I argue that all the other (...) justifications of the Principle of Universalizability on offer, including Richard Hare's, are inadequate. (shrink)

Quietist Moral Realists accept that there are moral facts and properties, while aiming to avoid many of the explanatory burdens thought to fall on traditional moral realists. This chapter examines the forms that Quietist Moral Realism has taken and the challenges it has faced, in order to better assess its prospects. The best hope, this chapter argues, lies in a pragmatist approach that distinguishes the different functions of diverse areas of discourse. This paves the way for a form of Quietism (...) that does not simply remain quiet about the explanatory demands of metaethics, but rather is able to diagnose where they go wrong. By combining a neopragmatic analysis of the discourse with an easy approach to ontology, , we can develop a form of Quietist Moral Realism that is far stronger than critics of quietism have appreciated. (shrink)

Moral status arguments are typically formulated as descriptive statements that tell us something about the world. But philosophy of language teaches us that language can also be used performatively: we do things with words and use words to try to get others to do things. Does and should this theory extend to what we say about moral status, and what does it mean? Drawing on Austin, Searle, and Butler and further developing relational views of moral status, this article explores what (...) it means to conceptualize moral status in a performative way and in a way that reaches deep down to its basis, proposes a distinction between strong and weak versions of this view, and discusses the implications for thinking about the moral status of humans and nonhumans. Next to contributing to theory about performativity in the moral domain in general, this effort helps to reveal, understand, and evaluate the performative dimension of utterances made in public discussions about the moral status of animals and artificial agents such as robots and artificial intelligence. (shrink)

The need for ethical naturalism -- Moral problem-solving as an empirical inquiry -- Where are our values bred? : sources of moral norms -- Intuitive processes of moral cognition -- Moral deliberation as cognition, imagination, and feeling -- The nature of "reasonable" moral deliberation -- There is no moral faculty -- Moral fundamentalism is immoral -- The making of a moral self.

For decades, intelligence and achievement tests have registered significant differences between people of different races, ethnicities, classes, and genders. We argue that most of these differences are explained not as reflections of differences in the distribution of intellectual virtues but as evidence for the metacognitive mediation of the intellectual virtues. For example, in the United States, blacks typically score worse than whites on tests of mathematics. This might lead one to think that fewer blacks possess the relevant intellectual virtues, or (...) that they possess them less fully. However, research on stereotype threat shows that when blacks are not reminded of their race, they do much better on these tests than when they are. Simply raising to salience the race of the student triggers the activation of the stereotype, which in turn leads to poorer performance. However, learning about stereotype threat to a large extent immunizes people against it. This suggests that the psycho-social dimension of intelligence that recognizes the possibility of effects like stereotype threat is a crucial mediating variable in the development and expression of the intellectual virtues. The Socratic, “Know thyself” needs to be expanded to, “Know thyself and thy society.” Self-knowledge and knowledge of relevant stereotypes are a necessary condition for optimal development and expression of the other intellectual virtues. (shrink)

Plato's Republic has proven to be of astounding influence and importance. Justly celebrated as Plato's central text, it brings together all of his prior works, unifying them into a comprehensive vision that is at once theological, philosophical, political and moral. The essays in this volume provide a picture of the most interesting aspects of the Republic, and address questions that continue to puzzle and provoke, such as: Does Plato succeed in his argument that the life of justice is the most (...) attractive one? Is his tripartite analysis of the soul coherent and plausible? Why does Plato seem to have to force his philosopher-guardians to rule when they know this is something that they ought to do? What is the point of the strange and complicated closing Myth of Er? This volume will be essential to those looking for thoughtful and detailed excursions into the problems posed by Plato's text and ideas. (shrink)