Baker claims to provide an example of mathematical explanation of an empirical phenomenon which leads to ontological commitment to mathematical objects. This is meant to show that the positing of mathematical entities is necessary for satisfactory scientific explanations and thus that the application of mathematics to science can be used, at least in some cases, to support mathematical realism. In this paper I show that the example of explanation Baker considers can actually be given without postulating mathematical objects and thus (...) cannot be used by the mathematical realist. I also show that, despite this, mathematics keeps playing an important methodological role in the explanation and does not reduce to a merely computational or descriptive framework. (shrink)

In this article, I argue that mapping-based accounts of applications cannot be comprehensive and must be supplemented by analyses of other, qualitatively different, forms of application. I support these claims by providing a detailed discussion of the application of mathematics to a problem of election design that is prominent in social choice theory.

In a recent paper (Okasha, Mind 120:83–115, 2011), Samir Okasha uses Arrow’s theorem to raise a challenge for the rationality of theory choice. He argues that, as soon as one accepts the plausibility of the assumptions leading to Arrow’s theorem, one is compelled to conclude that there are no adequate theory choice algorithms. Okasha offers a partial way out of this predicament by diagnosing the source of Arrow’s theorem and using his diagnosis to deploy an approach that circumvents it. In (...) this paper I explain why, although Okasha is right to emphasise that Arrow’s result is the effect of an informational problem, he is not right to locate this problem at the level of the informational input of a theory choice rule. Once the informational problem is correctly located, Arrow’s theorem may be dismissed as a problem. (shrink)

Certain mathematical problems prove very hard to solve because some of their intuitive features have not been assimilated or cannot be assimilated by the available mathematical resources. This state of affairs triggers an interesting dynamic whereby the introduction of novel conceptual resources converts the intuitive features into further mathematical determinations in light of which a solution to the original problem is made accessible. I illustrate this phenomenon through a study of Bertrand’s paradox.

In this paper I introduce a novel strategy to deal with the indiscernibility problem for ante rem structuralism. The ante rem structuralist takes the ontology of mathematics to consist of abstract systems of pure relata. Many of such systems are totally symmetrical, in the sense that all of their elements are relationally indiscernible, so the ante rem structuralist seems committed to positing indiscernible yet distinct relata. If she decides to identify them, she falls into mathematical inconsistency while, accepting their distinctness, (...) she finds herself unable to account for it. I show that the ante rem structuralist has in fact the resources to account for the distinctness of indiscernibles and that these resources come from the very symmetry properties of the mathematical objects that seem to pose problems for her. (shrink)

Peano's axiomatizations of geometry are abstract and non-intuitive in character, whereas Peano stresses his appeal to concrete spatial intuition in the choice of the axioms. This poses the problem of understanding the interrelationship between abstraction and intuition in his geometrical works. In this article I argue that axiomatization is, for Peano, a methodology to restructure geometry and isolate its organizing principles. The restructuring produces a more abstract presentation of geometry, which does not contradict its intuitive content but only puts it (...) into a particular form. (shrink)

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection (...) of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper. (shrink)

Throughout his work, John Dewey seeks to emancipate philosophical reflection from the influence of the classical tradition he traces back to Plato and Aristotle. For Dewey, this tradition rests upon a conception of knowledge based on the separation between theory and practice, which is incompatible with the structure of scientific inquiry. Philosophical work can make progress only if it is freed from its traditional heritage, i.e. only if it undergoes reconstruction. In this study I show that implicit appeals to the (...) classical tradition shape prominent debates in philosophy of mathematics, and I initiate a project of reconstruction within this field. (shrink)

When a law court makes a decision based on the individual deliberation of each judge, a case of judgment aggregation occurs. The possibility that the aggregation's outcome be logically inconsistent, even though it is based on consistent individual judgments, arises relatively easily and has been the subject of several investigations. In this paper I show that this paradoxical behaviour is the effect of decision procedures that are unable to discriminate between logically consistent and logically inconsistent individual judgments. The paradoxes can (...) be resolved by selecting procedures that are not affected by this limitation. (shrink)

The Königsberg bridge problem has played a central role in recent philosophical discussions of mathematical explanation. In this paper I look at it from a novel perspective, which is independent of explanatory concerns. Instead of restricting attention to the solved Königsberg bridge problem, I consider Euler’s construction of a solution method for the problem and discuss two later integrations of Euler’s approach into a more structured methodology, arisen in operations research and genetics respectively. By examining Euler’s work and its later (...) developments, I achieve two main goals. First, I offer an analysis of the role played by mathematics as a problem-solving instrument within scientific enquiry. Second, I shed light on the broader significance of well known contributions to the debate on mathematical explanation. I suggest that these contributions, which are tied to a localised explanatory context, achieve a greater relevance and attain a sharper formulation when they are referred to scientific enquiry at large, as opposed to its possible explanatory outcomes alone. (shrink)

In this paper I defend mathematical nominalism by arguing that any reasonable account of scientific theories and scientific practice must make explicit the empirical non-mathematical grounds on which the application of mathematics is based. Once this is done, references to mathematical entities may be eliminated or explained away in terms of underlying empirical conditions. I provide evidence for this conclusion by presenting a detailed study of the applicability of mathematics to measurement. This study shows that mathematical nominalism may be regarded (...) as a methodological approach to applicability, illuminating the use of mathematics in science. (shrink)

In this paper I examine Field’s account of the applicability of mathematics from a measurementtheoretic perspective. Within this context, I object to Field’s instrumentalism, arguing that it depends on an incomplete analysis of applicability. I show in particular that, once the missing piece of analysis is provided, the role played by numerical entities in basic empirical theories must be revised: such revision implies that instrumentalism should be rejected and mathematical entities be regarded not merely as useful tools but also as (...) conceptual schemata by means of which we can articulate our understanding of experience. (shrink)

In this paper I study the activity of mathematical problem-solving in scientific practice, focussing on enquiries in mathematical social science. I identify three salient phases of mathematical problem-solving and adopt them as a reference frame to investigate aspects of applications that have not yet received extensive attention in the philosophical literature.

Using a basic theorem from mathematical logic, I show that there are field-extensions ofRon which a class of orderings that do not admit any real-valued utility functions can be represented by uncountably large families of utility functions. These are the lexicographically decomposable orderings studied in Beardon et al. (2002a). A corollary to this result yields an uncountably large family of very simple utility functions for the lexicographic ordering of the real Cartesian plane. I generalise these results to the lexicographic ordering (...) of \mathbb{R}^n, for every n > 2, and to lexicographic products of lexicographically decomposable chains. I conclude by showing how almost all of these results may be obtained without any appeal to the Axiom of Choice. (shrink)

In this paper I raise some objections to Field’s characterization of applied mathematics, showing, by means of three examples, that it is too restrictive. While doing so, I articulate a different and wider account of applicability. I conclude with an argument supporting its compatibility with an anti-realistic view on the existence of mathematical entities.

Highly idealized models, such as the Hawk-Dove game, are pervasive in biological theorizing. We argue that the process and motivation that leads to the introduction of various idealizations into these models is not adequately captured by Michael Weisberg’s taxonomy of three kinds of idealization. Consequently, a fourth kind of idealization is required, which we call hypothetical pattern idealization. This kind of idealization is used to construct models that aim to be explanatory but do not aim to be explanations.

Postmodern alienation -- Jameson's dialectical levels -- Baudrillard's hostile worlds -- Foucault's system of thought.

What are the philosophical views of professional philosophers, and how do these views change over time? The 2020 PhilPapers Survey surveyed around 2000 philosophers on 100 philosophical questions. The results provide a snapshot of the state of some central debates in philosophy, reveal correlations and demographic effects involving philosophers' views, and reveal some changes in philosophers' views over the last decade.

A leading political theorist’s groundbreaking defense of ideal conceptions of justice in political philosophy Throughout the history of political philosophy and politics, there has been continual debate about the roles of idealism versus realism. For contemporary political philosophy, this debate manifests in notions of ideal theory versus nonideal theory. Nonideal thinkers shift their focus from theorizing about full social justice, asking instead which feasible institutional and political changes would make a society more just. Ideal thinkers, on the other hand, question (...) whether full justice is a standard that any society is likely ever to satisfy. And, if social justice is unrealistic, are attempts to understand it without value or importance, and merely utopian? Utopophobia argues against thinking that justice must be realistic, or that understanding justice is only valuable if it can be realized. David Estlund does not offer a particular theory of justice, nor does he assert that justice is indeed unrealizable—only that it could be, and this possibility upsets common ways of proceeding in political thought. Estlund engages critically with important strands in traditional and contemporary political philosophy that assume a sound theory of justice has the overriding, defining task of contributing practical guidance toward greater social justice. Along the way, he counters several tempting perspectives, including the view that inquiry in political philosophy could have significant value only as a guide to practical political action, and that understanding true justice would necessarily have practical value, at least as an ideal arrangement to be approximated. Demonstrating that unrealistic standards of justice can be both sound and valuable to understand, Utopophobia stands as a trenchant defense of ideal theory in political philosophy. (shrink)

David Hume's Enquiry concerning Human Understanding is the definitive statement of the greatest philosopher in the English language. His arguments in support of reasoning from experience, and against the "sophistry and illusion"of religiously inspired philosophical fantasies, caused controversy in the eighteenth century and are strikingly relevant today, when faith and science continue to clash. The Enquiry considers the origin and processes of human thought, reaching the stark conclusion that we can have no ultimate understanding of the physical world, or indeed (...) our own minds. In either sphere we must depend on instinctive learning from experience, recognizing our animal nature and the limits of reason. Hume's calm and open-minded skepticism thus aims to provide a new basis for science, liberating us from the "superstition" of false metaphysics and religion. His Enquiry remains one of the best introductions to the study of philosophy, and his edition places it in its historical and philosophical context. (shrink)

The zetetic turn in epistemology raises three questions about epistemic and zetetic norms. First, there is the relationship question: what is the relationship between epistemic and zetetic norms? Are some epistemic norms zetetic norms, or are epistemic and zetetic norms distinct? Second, there is the tension question: are traditional epistemic norms in tension with plausible zetetic norms? Third, there is the reaction question: how should theorists react to a tension between epistemic and zetetic norms? Drawing on an analogy to practical (...) philosophy, I develop a focal point view to resolve these motivating questions. On the focal point view, traditional epistemic norms and zetetic norms answer different types of normative questions. There is nevertheless a familiar type of evaluative tension between traditional epistemic norms and zetetic norms, but this tension is an unavoidable feature of the normative landscape and not a sign that traditional epistemic norms need revision. But if traditional epistemic norms are not zetetic norms, then in what sense is zetetic epistemology a project for epistemologists? I conclude by articulating a sense in which some nontraditional epistemic norms are zetetic norms, and in which zetetic epistemology is an important part of the study of theoretical rationality. (shrink)

By means of an example, shows the possibility of beliefs that are separately rational whilst together inconsistent.

This book is an attempt to get to the bottom of an acute and perennial tension between our best scientific pictures of the fundamental physical structure of the world and our everyday empirical experience of it. The trouble is about the direction of time. The situation (very briefly) is that it is a consequence of almost every one of those fundamental scientific pictures--and that it is at the same time radically at odds with our common sense--that whatever can happen can (...) just as naturally happen backwards. Albert provides an unprecedentedly clear, lively, and systematic new account--in the context of a Newtonian-Mechanical picture of the world--of the ultimate origins of the statistical regularities we see around us, of the temporal irreversibility of the Second Law of Thermodynamics, of the asymmetries in our epistemic access to the past and the future, and of our conviction that by acting now we can affect the future but not the past. Then, in the final section of the book, he generalizes the Newtonian picture to the quantum-mechanical case and (most interestingly) suggests a very deep potential connection between the problem of the direction of time and the quantum-mechanical measurement problem. The book aims to be both an original contribution to the present scientific and philosophical understanding of these matters at the most advanced level, and something in the nature of an elementary textbook on the subject accessible to interested high-school students. Table of Contents: Preface 1. Time-Reversal Invariance 2. Thermodynamics 3. Statistical Mechanics 4. The Reversibility Objections and the Past-Hypothesis 5. The Scope of Thermodynamics 6. The Asymmetries of Knowledge and Intervention 7. Quantum Mechanics Appendix: Gedankenexperiments with Heat Engines Index Reviews of this book: The foundations of statistical mechanisms are often presented in physics textbooks in a rather obscure and confused way. By challenging common ways of thinking about this subject, Time and Chance can do quite a lot to improve this situation. --Jean Bricmont, Science Albert is perfecting a style of foundational analysis that is uniquely his own...It has a surgical precision...and it is ruthless with pretensions. The foundations of thermodynamics is a topic that has accumulated a good deal of dead wood; this is a fire that will burn and burn. --Simon W. Saunders, Oxford University As usual with Albert's work, the exposition is brisk and to the point, and exceptionally clear...The book will be an extremely valuable contribution to the literature on the subject of philosophical issues in thermodynamics and statistical mechanics, a literature which has been thin on the ground but is now growing as it deserves to. --Lawrence Sklar, University of Michigan. (shrink)

One of the enduring concerns of moral philosophy is deciding who or what is deserving of ethical consideration. Much recent attention has been devoted to the "animal question" -- consideration of the moral status of nonhuman animals. In this book, David Gunkel takes up the "machine question": whether and to what extent intelligent and autonomous machines of our own making can be considered to have legitimate moral responsibilities and any legitimate claim to moral consideration. The machine question poses a fundamental (...) challenge to moral thinking, questioning the traditional philosophical conceptualization of technology as a tool or instrument to be used by human agents. Gunkel begins by addressing the question of machine moral agency: whether a machine might be considered a legitimate moral agent that could be held responsible for decisions and actions. He then approaches the machine question from the other side, considering whether a machine might be a moral patient due legitimate moral consideration. Finally, Gunkel considers some recent innovations in moral philosophy and critical theory that complicate the machine question, deconstructing the binary agent--patient opposition itself. Technological advances may prompt us to wonder if the science fiction of computers and robots whose actions affect their human companions could become science fact. Gunkel's argument promises to influence future considerations of ethics, ourselves, and the other entities who inhabit this world. (shrink)

How should one react when one has a belief, but knows that other people—who have roughly the same evidence as one has, and seem roughly as likely to react to it correctly—disagree? This paper argues that the disagreement of other competent inquirers often requires one to be much less confident in one’s opinions than one would otherwise be.

A new theory of moral and aesthetic value for the age of remix, going beyond the usual debates over originality and appropriation. Remix—or the practice of recombining preexisting content—has proliferated across media both digital and analog. Fans celebrate it as a revolutionary new creative practice; critics characterize it as a lazy and cheap (and often illegal) recycling of other people's work. In Of Remixology, David Gunkel argues that to understand remix, we need to change the terms of the debate. The (...) two sides of the remix controversy, Gunkel contends, share certain underlying values—originality, innovation, artistic integrity. And each side seeks to protect these values from the threat that is represented by the other. In reevaluating these shared philosophical assumptions, Gunkel not only provides a new way to understand remix, he also offers an innovative theory of moral and aesthetic value for the twenty-first century. In a section called “Premix,” Gunkel examines the terminology of remix (including “collage,” “sample,” “bootleg,” and “mashup”) and its material preconditions, the technology of recording. In “Remix,” he takes on the distinction between original and copy; makes a case for repetition; and considers the question of authorship in a world of seemingly endless recompiled and repurposed content. Finally, in “Postmix,” Gunkel outlines a new theory of moral and aesthetic value that can accommodate remix and its cultural significance, remixing—or reconfiguring and recombining—traditional philosophical approaches in the process. (shrink)

I attempt to get as clear as possible on the chain of reasoning by which irreversible macrodynamics is derivable from time-reversible microphysics, and in particular to clarify just what kinds of assumptions about the initial state of the universe, and about the nature of the microdynamics, are needed in these derivations. I conclude that while a “Past Hypothesis” about the early Universe does seem necessary to carry out such derivations, that Hypothesis is not correctly understood as a constraint on the (...) early Universe’s entropy. (shrink)

We start by presenting three different views that jointly imply that every person has many conscious beings in their immediate vicinity, and that the number greatly varies from person to person. We then present and assess an argument to the conclusion that how confident someone should be in these views should sensitively depend on how massive they happen to be. According to the argument, sometimes irreducibly de se observations can be powerful evidence for or against believing in metaphysical theories.

Worries about mental causation are prominent in contemporary discussions of the mind and human agency. Originally, the problem of mental causation was that of understanding how a mental substance (thought to be immaterial) could interact with a material substance, a body. Most philosophers nowadays repudiate immaterial minds, but the problem of mental causation has not gone away. Instead, focus has shifted to mental properties. How could mental properties be causally relevant to bodily behavior? How could something mental qua mental cause (...) what it does? After looking at the traditional Problem of Interaction, we survey various versions of the property-based problem and look at proposed solutions to them. (shrink)

Unprecedented advances in medicine, genetic engineering, and demographic forecasting raise new questions that strain the categories and assumptions of traditional ethical theories. Heyd's approach resolves many paradoxes in intergenerational justice, while offering a major test case for the profound problems of the limits of ethics and the nature of value. This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and (...) impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1992. (shrink)

The mystery of existence and our place in that mystery--as expressed in a single Chinese landscape painting: a new work of meditative philosophy by the renowned translator of the Chinese classics and author of Hunger Mountain. Join David Hinton, the premier modern translator of the Chinese classics, as he stands before a single landscape painting, discovering in it the wondrous story of existence—and as part of that story, the magical nature of consciousness. What he coaxes from the image is nothing (...) less than a revelation: the dynamic interweaving of mind and Cosmos, and the glorious dance of Absence and Presence that is the secret of that Cosmos. The painting called Peaceful-Distance Pavilion by Shih-t'ao (1642-1707) is, like other paintings in that genre, mostly space: one tiny figure, accompanied by an attendant, looks out over a vast landscape of mountains and clouds. But start looking into that space and, with the right guidance, what you end up seeing is profound. David Hinton is the perfect guide. He uses his knowledge of Chinese philosophy, poetry, art, language, and writing system to illuminate this painting's message, which is ultimately the story of the glorious dance between nothing and everything, between emptiness and existence. It's an enthralling journey that can change the way you look at the world, a journey for which David is a wise and eloquent guide. (shrink)

Seeing, really seeing, is like meditation. In a world filled with distraction, seeing mindfully is a way to pay attention, to hit pause and find calm by focusing on what’s directly in front of us. See Your Way to Mindfulness is a gift book of inspiration and instruction to help readers open their eyes—and their “I’s.” Written by David Schiller, author of the national bestseller The Little Zen Companion, it’s a collection of quotes, prompts, exercises, meditations—married with photographs and drawings (...) that bring the words to life. The quotes are from artists, Buddhists, philosophers, poets, and more, all centered on the theme of how “The real voyage of discovery consists not in seeking new landscapes, but in having new eyes” (Marcel Proust). The short, playful exercises and prompts—like Seeing in the Rain, Eye Spy with My Open I, Spend 30 Minutes Taking a Five-Minute Walk, Get Lost—are designed to disrupt routine and inspire readers to see for themselves. Some of the exercises involve drawing, writing, and taking photographs, opening a path to creativity as well as showing how to engage in the moment. Think of it as the Zen of seeing—a new way to look at the world afresh and rediscover joy in the everyday. (shrink)

Our aim in this entry is to articulate the state of the art in the moral psychology of personal identity. We begin by discussing the major philosophical theories of personal identity, including their shortcomings. We then turn to recent psychological work on personal identity and the self, investigations that often illuminate our person-related normative concerns. We conclude by discussing the implications of this psychological work for some contemporary philosophical theories and suggesting fruitful areas for future work on personal identity.

Om den menneskelige erkendelses udvikling fra oldtiden til i dag - med fokus på især naturvidenskabens opdagelser.

What is the Bible? -- What is religion? -- Enlightenment theology -- Covenant theology -- Jesus the teacher of nothingness -- Creating God in 325 -- Meet the new Jesus, a Christian Avatar -- When God stopped working -- Religion and the God who almost is -- Saving apocalypticism -- Theology and the opening of time.

Nietzsche and the theater -- Zukunftstheater! -- How to theatricalize with a hammer -- Nietzsche contra Nietzsche -- The theater and Nietzsche -- Ecce Strindberg -- The genealogy of Shaw -- Thus spake O'Neill -- Epilogue: Centaurs.

Tout oppose les œuvres de William et Henry James, le philosophe américain fondateur du pragmatisme et le romancier, auteur de Portrait de femme et des Ailes de la colombe. L'un se présente comme le philosophe des vérités concrètes, l'inventeur d'un empirisme " radical ", résolument tourné vers une pensée pratique sans cesse reconduite vers l'expérience directe des réalités sensibles ; l'autre se présente au contraire comme le romancier de l'indirect et dresse le portrait de consciences qui ne cessent de s'interpréter (...) les unes les autres en s'éloignant toujours davantage du socle des certitudes sensibles. Mais s'agit-il d'une opposition? N'a-t-on pas en réalité affaire à une sorte d'échange ou de vol mutuel? L'un fait de la philosophie une sorte de roman d'aventures tandis que l'autre fait du roman la forme réfléchie par excellence, le récit du mental et de ses modes de raisonnement. L'un fait de l'action le nouveau centre de gravité de la philosophie ; l'autre fait de la pensée le nouveau sujet du roman, comme si chacun volait à l'autre ce qui jusqu'alors lui revenait de droit. C'est de ce vol ou cet échange dont il s'agit de faire le récit conceptuel. (shrink)

A personalist account of persons -- Persons as beyond good and evil -- Reality transcends itself in persons -- God as the seal of the personal -- Art as the radiance of persons in reality -- History as the memory of persons -- Politics of the person.

Perceptualists say that having a pain in a body part consists in perceiving the part as instantiating some property. I argue that perceptualism makes better sense of the connections between pain location and the experiences undergone by people in pain than three alternative accounts that dispense with perception. Turning to fellow perceptualists, I also reject ways in which David Armstrong and Michael Tye understand and motivate perceptualism, and I propose an alternative interpretation, one that vitiates a pair of objections—due to (...) John Hyman—concerning the meaning of ‘Amy has a pain in her foot’ and the idea of bodily sensitivity. Perceptualism, I conclude, remains our best account of the location of pains. (shrink)