In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses ofDirichlet characters in presentations of Dirichlet’s proof in the nineteenth and early twentieth centuries, with an eye toward understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method.

In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. Modern presentations of the proof are explicitly higher-order, in that they involve quantifying over and summing over Dirichlet characters, which are certain types of functions. The notion of a character is only implicit in Dirichlet’s original proof, and the subsequent history shows a very gradual transition to the modern mode of presentation. In this essay, we (...) describe an approach to the philosophy of mathematics in which it is an important task to understand the roles of our ontological posits and assess the extent to which they enable us to achieve our mathematical goals. We use the history of Dirichlet’s theorem to understand some of the reasons that functions are treated as ordinary objects in contemporary mathematics, as well as some of the reasons one might want to resist such treatment. We also use these considerations to illuminate the formal treatment of functions and objects in Frege’s logical foundation, and we argue that his philosophical and logical decisions were influenced by many of the same factors. (shrink)

The prevailing notion that the problem of essential indexicals must be solved through the theory of meaning of attitude ascriptions is incorrect. Well-known attempts to solve the problem along those lines, e.g., the proposals of Lewis and Perry , have rested on the overly optimistic assumption that there is no limit in principle to the access one may have to the contents of someone else’s thoughts, including their knowledge. That assumption is challenged in this essay. The hazards associated with limited (...) accessibility can be and indeed must be alleviated by an epistemological theory in such a way that allows for a new nonsemantic approach to the problem. The following is an outline of the arguments in favor of this approach. In the first part, the problem of essential indexicals and the familiar corollary thesis that such indexicals are not reducible to nonindexicals is briefly reviewed. In the second part, indexical irreducibility is shown to hold for a range of explanations of theoretical rationality in addition to the basic explanations of action in which the irreducibility is typically illustrated. (shrink)

Self-defeating and self-justifying expressions are reflexive insofar as they pertain to themselves. However, the reflexivity involved is often pragmatic, i.e., does not entirely depend upon the logical properties of what is expressed but also upon the expressive act. In this paper I present a general account of pragmatic reflexivity and apply it to some familiar self-defeating and self-justifying expressions in epistemology. This application indicates some important, if often neglected features of the epistemological issues involved. The account I defend suggests that (...) epistemology is particularly sensitive to pragmatic reflexivity since what epistemologists do, i.e., inquire, theorize, and defend theories, is also the subject of the inquiry and resultant theories. (shrink)

The development of possible worlds semantics for modal claims has led to a more general application of that theory as a complete semantics for various formal and natural languages, and this view is widely held to be an adequate (philosophical) interpretation of the model theory for such languages. We argue here that this view generates a self-referential inconsistency that indicates either the falsity or the incompleteness of PWS.

In this paper it is argued that the conjunction of linguistic ersatzism, the ontologically deflationary view that possible worlds are maximal and consistent sets of sentences, and possible world semantics, the view that the meaning of a sentence is the set of possible worlds at which it is true, implies that no actual speaker can effectively use virtually any language to successfully communicate information. This result is based on complexity issues that relate to our finite computational ability to deal with (...) large bodies of information and a strong, but well motivated, assumption about the cognitive accessibility of meanings of sentences ersatzers seem to be implicitly committed to. It follows that linguistic ersatzism, possible world semantics, or both must be rejected. (shrink)

In practice, mathematical proofs are most often the result of careful planning by the agents who produced them. As a consequence, each mathematical proof inherits a plan in virtue of the way it is produced, a plan which underlies its “architecture” or “unity”. This paper provides an account of plans and planning in the context of mathematical proofs. The approach adopted here consists in looking for these notions not in mathematical proofs themselves, but in the agents who produced them. The (...) starting point is to recognize that to each mathematical proof corresponds a proof activity which consists of a sequence of deductive inferences—i.e., a sequence of epistemic actions—and that any written mathematical proof is only a report of its corresponding proof activity. The main idea to be developed is that the plan of a mathematical proof is to be conceived and analyzed as the plan of the agent(s) who carried out the corresponding proof activity. The core of the paper is thus devoted to the development of an account of plans and planning in the context of proof activities. The account is based on the theory of planning agency developed by Michael Bratman in the philosophy of action. It is fleshed out by providing an analysis of the notions of intention—the elementary components of plans—and practical reasoning—the process by which plans are constructed—in the context of proof activities. These two notions are then used to offer a precise characterization of the desired notion of plan for proof activities. A fruitful connection can then be established between the resulting framework and the recent theme of modularity in mathematics introduced by Jeremy Avigad. This connection is exploited to yield the concept of modular presentations of mathematical proofs which has direct implications for how to write and present mathematical proofs so as to deliver various epistemic benefits. The account is finally compared to the technique of proof planning developed by Alan Bundy and colleagues in the field of automated theorem proving. The paper concludes with some remarks on how the framework can be used to provide an analysis of understanding and explanation in the context of mathematical proofs. (shrink)

Available in English for the first time, _Hegel and the Freedom of Moderns_ revives discussion of the major political and philosophical tenets underlying contemporary liberalism through a revolutionary interpretation of G. W. F. Hegel’s thought. Domenico Losurdo,_ _one of the world’s leading Hegelians, reveals that the philosopher was fully engaged with the political controversies of his time. In so doing, he shows how the issues addressed by Hegel in the nineteenth century resonate with many of the central political concerns of (...) today, among them questions of community, nation, liberalism, and freedom. Based on an examination of Hegel’s entire corpus—including manuscripts, lecture notes, different versions of texts, and letters—Losurdo locates the philosopher’s works within the historical contexts and political situations in which they were composed. _Hegel and the Freedom of Moderns_ persuasively argues that the tug of war between “conservative” and “liberal” interpretations of Hegel has obscured and distorted the most important aspects of his political thought. Losurdo unravels this misleading dualism and provides an illuminating discussion of the relation between Hegel’s political philosophy and the thinking of Karl Marx and Friedrich Engels. He also discusses Hegel’s ideas in relation to the pertinent writings of other major figures of modern political philosophy such as Jean-Jacques Rousseau, John Locke, Edmund Burke, John Stuart Mill, Jeremy Bentham, Karl Popper, Norberto Bobbio, and Friedrich Hayek. (shrink)

Due to the ethical breaches of tobacco companies over a 50-year period, a U.S. Court ruled in United States v. Philip Morris USA, Inc. that major U.S. tobacco companies had misled consumers and the government about tobacco’s addictiveness, effects of environmental smoke, marketing targeted at adolescents, and deceptive practices related to harmfulness of smoking. We address the actions of the tobacco companies based on the consumer’s right to be informed and values for ethical corporate behavior, and we draw from (...) psychological theories and the smoking literature to develop our conceptual framework and test the effectiveness of the ensuing corrective advertising campaign mandated in the Court decision. We use a quota sample of 470 smokers and non-smoker participants in a longitudinal study to test the impact of the corrective advertising campaign on key antismoking beliefs from the campaign. Results reveal that the corrective ad campaign has not been successful in affecting smokers’ or non-smokers’ antismoking beliefs. However, differences are found between smokers’ and non-smokers’ beliefs about the adverse health effects of smoking, effects of secondhand smoke, and tobacco company deceptiveness, with these beliefs being stronger for non-smokers. Smokers’ weaker beliefs about the effects of secondhand smoke are viewed as particularly problematic, given the established health risks. We address the implications of the ethical breaches and the corrective advertising attempt to address the deception identified by the Court. (shrink)

We become ill in ways our parents and grandparents did not, with diseases unheard of and treatments undreamed of generations ago. This text tells the story of the modern experience of illness, linking ideas of illness, health, and postmodernism.

Principles of legislation.--Principles of the civil code.--Principles of the penal code.

Jeremy Sherman distills Terrence Deacon's breakthrough natural science hypothesis for the emergence of agents and agency, selves and aims in an otherwise aimless universe. The theory cuts a new path through the dualistic spirit vs. mechanism debate, unifying the hard and soft sciences and suggesting new solutions to philosophical mysteries.

We characterize a type of functional explanation that addresses why a homologous trait originating deep in the evolutionary history of a group remains widespread and largely unchanged across the group’s lineages. We argue that biologists regularly provide this type of explanation when they attribute conserved functions to phenotypic and genetic traits. The concept of conserved function applies broadly to many biological domains, and we illustrate its importance using examples of molecular sequence alignments at the intersection of evolution and cell biology. (...) We use these examples to show how the study of conserved functions can integrate knowledge of a trait’s causal effects on fitness and its history of natural selection without invoking adaptation. We also show how conserved function provides a novel basis for addressing objections against evolutionary functions raised by Robert Cummins. (shrink)

Although the pedagogy literature indicates significant relationships between cheating intentions and both personal and situational factors, no published research has examined the joint effect of personal moral philosophy and perceived moral intensity components on students’ cheating intentions. Hence, a structural equation model that relates magnitude of consequences, relativism, and idealism to willingness to cheat, is developed and tested. Using data from undergraduate business students, the empirical results provide insight into these relationships and evidence of mediation for magnitude of consequences on (...) idealism and students’ cheating intentions. Implications for educators are offered. (shrink)

Science and the End of Ethics examines some of the most important positive and negative implications that science has for ethics. Addressing the negative implications first, author Stephen Morris discusses how contemporary science provides significant challenges to moral realism. One threat against moral realism comes from evolutionary theory, which suggests that our moral beliefs are unconnected to any facts that would make them true. Ironically, many of the same areas of science (e.g. evolutionary biology, neuroscience, psychology) that present difficulties (...) for moral realism point to a new ethical approach that focuses on achieving some of the key practical goals shared by ethicists. Chief among these is how to increase amicable behavior among people. (shrink)

In considering the debate about the meaning of ‘disease’, the positions are generally presented as falling into two categories: naturalist, e.g., Boorse, and normativist, e.g., Engelhardt and many others. This division is too coarse, and obscures much of what is going on in this debate. I therefore propose that accounts of the meaning of ‘disease’ be assessed according to Hare’s (1997) taxonomy of evaluative terms. Such an analysis will allow us to better understand both individual positions and their inter-relationships. Most (...) importantly, it will show that it is unlikely that there is a single unique disease-concept at issue. Rather, different authors are, for the most part, considering different concepts. (shrink)

Many philosophers think that free will requires alternative possibilities. Other philosophers deny this. There are plenty of philosophical arguments on both sides of this debate, but here I want to highlight various theological pressures that might push Christians into rejecting the principle of alternative possibilities. In this paper, I explore six cases that might push Christians in that direction: the case of divine foreknowledge, the case of prophecy, the case of the blessed in heaven, the case of Christ's human freedom, (...) the case of Mary's fiat in light of her immaculate conception, and the case of prayers for the past. As I will argue, in each of these cases, given certain other standard theological commitments, it seems that Christians are pushed to admit that the agent in question does indeed act freely but also that he or she did not possess alternative possibilities at the moment of decision. (shrink)

A rigorous, authoritative new anthology which brings together some of the most significant contemporary scholarship on the theory of knowledge Carefully-calibrated and judiciously-curated, this strong and contemporary new anthology builds upon Epistemology: An Anthology, Second Edition (Wiley Blackwell, 2008) by drawing a concise and well-balanced selection of higher-level readings from a large, diverse, and evolving body of research. Includes 17 readings that represent a broad and vital part of contemporary epistemology, including articles by female philosophers and emerging thought leaders Organized (...) into seven thoughtful and distinct sections, including virtue epistemology, practical reasons for belief, and epistemic dysfunctions among others Designed to sit alongside the highly-successful anthology of canonical essays, Epistemology: An Anthology, Second Edition (Wiley Blackwell, 2008) Edited by a distinguished editorial team, including Ernie Sosa, one of the most influential active epistemologists Highlights cutting edge methodologies and contemporary topics for advanced students, instructors, and researchers. (shrink)

"Arguing that debates over legitimacy, political violence, freedom, and justice would benefit greatly from cross-tradition theorizing, this book shows how putting analytic and continental political theory in conversation would help us to overcome these intractable problems"--.

The epsilon calculus is a logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics. The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. Specifically, in the calculus, a term εx A denotes some x satisfying A(x), if there is one. In Hilbert's Program, the epsilon terms play the role of ideal elements; the aim of Hilbert's finitistic consistency proofs is to give a procedure which removes such terms (...) from a formal proof. The procedures by which this is to be carried out are based on Hilbert's epsilon substitution method. The epsilon calculus, however, has applications in other contexts as well. The first general application of the epsilon calculus was in Hilbert's epsilon theorems, which in turn provide the basis for the first correct proof of Herbrand's theorem. More recently, variants of the epsilon operator have been applied in linguistics and linguistic philosophy to deal with anaphoric pronouns. (shrink)

We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites. Our motivation is that renormalization is undoubtedly one of the great ideas—and great successes--of twentieth-century physics. Also it has strongly influenced in diverse ways, how physicists conceive of physical theories. So it is of considerable philosophical interest. Second, we will briefly relate renormalization to Ernest Nagel's account of inter-theoretic relations, especially reduction. One theme will be a contrast between (...) two approaches to renormalization. The old approach, which prevailed from ca. 1945 to 1970, treated renormalizability as a necessary condition for being an acceptable quantum field theory. On this approach, it is a piece of great good fortune that high energy physicists can formulate renormalizable quantum field theories that are so empirically successful. But the new approach to renormalization explains why the phenomena we see, at the energies we can access in our particle accelerators, are described by a renormalizable quantum field theory. For whatever non-renormalizable interactions may occur at yet higher energies, they are insignificant at accessible energies. Thus the new approach explains why our best fundamental theories have a feature, viz. renormalizability, which the old approach treated as a selection principle for theories. That is worth saying since philosophers tend to think of scientific explanation as only explaining an individual event, or perhaps a single law, or at most deducing one theory as a special case of another. Here we see a framework in which there is a space of theories. And this framework is powerful enough to deduce that what seemed “manna from heaven” is to be expected: the good fortune is generic. We also maintain that universality, a concept stressed in renormalization theory, is essentially the familiar philosophical idea of multiple realizability; and that it causes no problems for reductions of a Nagelian kind. (shrink)

This essay develops a framework for understanding what I call the ethics of reflexivity, that is, the norms that govern attitudes and actions with respect to one’s own worth. I distinguish five central aspects of the reflexive commitment to living in accordance with one’s personal ideals: the extent to which and manner in which one regards oneself from an evaluative point of view, the extent to which one cares about receiving the respect of others, the degree to which one interprets (...) one’s personal ideals in an individualistic or collective manner, the degree to which one’s commitment to living in accordance with one’s personal ideals is rigid or flexible, and the worthiness of one’s personal ideals. This framework, I argue, illuminates the nature and moral significance of virtuous and vicious forms of the character trait of pride. (shrink)

Although the concept of HAPPINESS plays a central role in ethics, contemporary philosophers have generally given little attention to providing a robust account of what this concept entails. In a recent paper, Dan Haybron sets out to accomplish two main tasks: the first is to underscore the importance of conducting philosophical inquiry into the concept of HAPPINESS; the second is to defend a particular account of happiness—which he calls the ‘emotional state conception of happiness’—while pointing out weaknesses in the primary (...) competing accounts of happiness, including the hedonistic account. I argue against his claim that the emotional state conception of happiness is superior to the hedonistic conception of happiness. In the course of defending the hedonistic account of happiness against Haybron's attacks, I provide my own explanation for why the study of happiness is important to ethics. (shrink)

Eros and Illness explores the place of desire in illness. We urgently need such an exploration because illness is no longer simply a natural feature of the human condition. Most people fall ill, but illness now falls under the supervision of biomedicine, a science-based, state-regulated system dominated by the new molecular gaze. The use of a person's distinctive genetic data to guide treatment and to forestall disease--called "personalized medicine"-- reflects how the molecular gaze can produce valuable advances in biomedical healthcare. (...) What does this indispensable super-vision, however, tend to overlook? Eros and Illness proposes that biomedicine ignores, in clinical practice and in bench science, the powerful role of desire in illness. Desire, always double-edged, requires attention because it can do both great harm and great good. Patients, caregivers, family members, and physicians, as they recognize the role of desire, gain access to a power that can make the passage through illness much less onerous and far more healing: truly "personalized. (shrink)

This work examines the concept of the "philosophical life" by looking at Socrates and his relationships to his interlocutors.

One of the most important philosophical topics in the early twentieth century and a topic that was seminal in the emergence of analytic philosophy was the relationship between Kantian philosophy and modern geometry. This paper discusses how this question was tackled by the Neo-Kantian trained philosopher Ernst Cassirer. Surprisingly, Cassirer does not affirm the theses that contemporary philosophers often associate with Kantian philosophy of mathematics. He does not defend the necessary truth of Euclidean geometry but instead develops a kind of (...) logicism modeled on Richard Dedekind's foundations of arithmetic. Further, because he shared with other Neo-Kantians an appreciation of the developmental and historical nature of mathematics, Cassirer developed a philosophical account of the unity and methodology of mathematics over time. With its impressive attention to the detail of contemporary mathematics and its exploration of philosophical questions to which other philosophers paid scant attention, Cassirer's philosophy of mathematics surely deserves a place among the classic works of twentieth century philosophy of mathematics. Though focused on Cassirer's philosophy of geometry, this paper also addresses both Cassirer's general philosophical orientation and his reading of Kant. (shrink)

As our civilization careens toward climate breakdown, ecological destruction, and gaping inequality, people are losing their existential moorings. The dominant worldview of disconnection, which tells us we are split between mind and body, separate from each other, and at odds with the natural world, has been invalidated by modern science. Award-winning author, Jeremy Lent, investigates humanity's age-old questions -- Who am I? Why am I? How should I live? -- from a fresh perspective, weaving together findings from modern systems (...) thinking, evolutionary biology, and cognitive neuroscience with insights from Buddhism, Taoism, and Indigenous wisdom. The result is a breathtaking accomplishment: a rich, coherent worldview based on a deep recognition of connectedness within ourselves, between each other, and with the entire natural world. It offers a compelling foundation for a new philosophical framework that could enable humanity to thrive sustainably on a flourishing Earth. The Web of Meaning is for everyone looking for deep and coherent answers to the crisis of civilization. -- Amazon. (shrink)

This chapter contains section titled: The ‘Essence’ of a Philosophical Prejudice One Philosophical Task or Two? Techniques for Ridding People of Philosophical Prejudices.

Quizás sea lícito decir que este Tratado de los Sofismas Políticos es, en alguna medida, el libro síntesis de toda la obra de Jeremías Bentham, porque con demoledora lógica se aplica a mostrar las inconsistencias y falacias de los opositores a la deliberación política, vale decir, al ejercicio de la democracia, en última instancia. Bentham es una figura que espera el reconocimiento de los americanos todos, en la medida en que impulsó con su racionalismo revolucionario (valga la contradicción), la capacidad (...) de todo el continente americano para constituirse como un ámbito de libertad, frente a la opresión colonial europea. Es conocida su correspondencia con grandes figuras de la emancipación americana, y con Bernardino Rivadavia entre nosotros. Todavía no lo hemos ubicado suficientemente en nuestra conciencia ideológica. (shrink)

Physicians place significant weight on the distinction between acts and omissions. Most believe that autonomous refusals for procedures, such as blood transfusions and resuscitation, ought to be respected, but they feel no similar obligation to accede to requests for treatment that will, in the physician’s opinion, harm the patient (e.g., assisted death). Thus, there is an asymmetry. In this paper, we challenge the strength of this distinction by arguing that the ordering of values should be the same in both cases. (...) The reason for respecting refusals is that, in such cases, autonomy outweighs well-being. We argue that the same should be true in request cases, which means that requests should not be denied only due to the treatment being too harmful in the physician’s opinion. Our strategy is to consider and reject a number of arguments for the asymmetrical view, including an appeal to the doing–allowing distinction and positive and negative rights. The duty to respect refusals is still greater than the duty to grant requests on our view, but, by arguing that the ordering of values is the same in both cases, we show that there is less of a distinction in healthcare between requests and refusals than many currently believe. (shrink)

This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it is then shown how we can use pure higher-order logic to (...) ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)