This chapter contains sections titled: Names or Predicates? The Semantics of Ethnic‐Group Terms Nihilism about Ethnic‐Group Terms The Political Pragmatics of Ethnic‐Group Terms References Further Reading.

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...) many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today. (shrink)

Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true of (...) the other. I suggest that ‘i’ functions like a parameter in natural deduction systems. I gave an early version of this paper at a workshop on structuralism in mathematics and science, held in the Autumn of 2006, at Bristol University. Thanks to the organizers, particularly Hannes Leitgeb, James Ladyman, and Øystein Linnebo, to my commentator Richard Pettigrew, and to the audience there. The paper also benefited considerably from a preliminary session at the Arché Research Centre at the University of St Andrews. I am indebted to my colleagues Craige Roberts, for help with the linguistics literature, and Ben Caplan and Gabriel Uzquiano, for help with the metaphysics. Thanks also to Hannes Leitgeb and Jeffrey Ketland for reading an earlier version of the manuscript and making helpful suggestions. I also benefited from conversations with Richard Heck, John Mayberry, Kevin Scharp, and Jason Stanley. CiteULike Connotea Del.icio.us What's this? (shrink)

This paper uses neo-Fregean-style abstraction principles to develop the integers from the natural numbers (assuming Hume’s principle), the rational numbers from the integers, and the real numbers from the rationals. The first two are first-order abstractions that treat pairs of numbers: (DIF) INT(a,b)=INT(c,d) ≡ (a+d)=(b+c). (QUOT) Q(m,n)=Q(p,q) ≡ (n=0 & q=0) ∨ (n≠0 & q≠0 & m⋅q=n⋅p). The development of the real numbers is an adaption of the Dedekind program involving “cuts” of rational numbers. Let P be a property (of (...) rational numbers) and r a rational number. Say that r is an upper bound of P, written P≤r, if for any rational number s, if Ps then either s<r or s=r. In other words, P≤r if r is greater than or equal to any rational number that P applies to. Consider the Cut Abstraction Principle: (CP) ∀P∀Q(C(P)=C(Q) ≡ ∀r(P≤r ≡ Q≤r)). In other words, the cut of P is identical to the cut of Q if and only if P and Q share all of their upper bounds. The axioms of second-order real analysis can be derived from (CP), just as the axioms of second-order Peano arithmetic can be derived from Hume’s principle. The paper raises some of the philosophical issues connected with the neo-Fregean program, using the above abstraction principles as case studies. (shrink)

Graham Priest's In Contradiction (Dordrecht: Martinus Nijhoff Publishers, 1987, chapter 3) contains an argument concerning the intuitive, or ‘naïve’ notion of (arithmetic) proof, or provability. He argues that the intuitively provable arithmetic sentences constitute a recursively enumerable set, which has a Gödel sentence which is itself intuitively provable. The incompleteness theorem does not apply, since the set of provable arithmetic sentences is not consistent. The purpose of this article is to sharpen Priest's argument, avoiding reference to informal notions, consensus, or (...) Church's thesis. We add Priest's dialetheic semantics to ordinary Peano arithmetic PA, to produce a recursively axiomatized formal system PA★ that contains its own truth predicate. Whether one is a dialetheist or not, PA★ is a legitimate, rigorously defined formal system, and one can explore its proof‐theoretic properties. The system is inconsistent (but presumably non‐trivial), and it proves its own Gödel sentence as well as its own soundness. Although this much is perhaps welcome to the dialetheist, it has some untoward consequences. There are purely arithmetic (indeed, Π0) sentences that are both provable and refutable in PA★. So if the dialetheist maintains that PA★ is sound, then he must hold that there are true contradictions in the most elementary language of arithmetic. Moreover, the thorough dialetheist must hold that there is a number g which both is and is not the code of a derivation of the indicated Gödel sentence of PA★. For the thorough dialetheist, it follows ordinary PA and even Robinson arithmetic are themselves inconsistent theories. I argue that this is a bitter pill for the dialetheist to swallow. (shrink)

§1. Overview. Philosophers and mathematicians have drawn lots of conclusions from Gödel's incompleteness theorems, and related results from mathematical logic. Languages, minds, and machines figure prominently in the discussion. Gödel's theorems surely tell us something about these important matters. But what?A descriptive title for this paper would be “Gödel, Lucas, Penrose, Turing, Feferman, Dummett, mechanism, optimism, reflection, and indefinite extensibility”. Adding “God and the Devil” would probably be redundant. Despite the breath-taking, whirlwind tour, I have the modest aim of forging (...) connections between different parts of this literature and clearing up some confusions, together with the less modest aim of not introducing any more confusions.I propose to focus on three spheres within the literature on incompleteness. The first, and primary, one concerns arguments that Gödel's theorem refutes the mechanistic thesis that the human mind is, or can be accurately modeled as, a digital computer or a Turing machine. The most famous instance is the much reprinted J. R. Lucas [18]. To summarize, suppose that a mechanist provides plans for a machine,M, and claims that the output ofMconsists of all and only the arithmetic truths that a human, or the totality of human mathematicians, will ever or can ever know. We assume that the output ofMis consistent. (shrink)

We prove that there is no maximal low d.c.e degree.

A paper in this journal by Fraser MacBride, ‘Can Ante Rem Structuralism Solve the Access Problem?’, raises important issues concerning the epistemological goals and burdens of contemporary philosophy of mathematics, and perhaps philosophy of science and other disciplines as well. I use a response to MacBride's paper as a framework for developing a broadly holistic framework for these issues, and I attempt to steer a middle course between reductive foundationalism and extreme naturalistic quietism. For this purpose the notion of entitlement (...) is invoked along the way, suitably modified for the present anti-foundationalist setting. (shrink)

Among the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics. - The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise classical contexts and represents the formalization of important intensional aspects of mathematical practice. - The direct formalization of intensional concepts (such as computability) in a mixed constructive/classical context.

It has long been known that (classical) Peano arithmetic is, in some strong sense, “equivalent” to the variant of (classical) Zermelo–Fraenkel set theory (including choice) in which the axiom of infinity is replaced by its negation. The intended model of the latter is the set of hereditarily finite sets. The connection between the theories is so tight that they may be taken as notational variants of each other. Our purpose here is to develop and establish a constructive version of this. (...) We present an intuitionistic theory of the hereditarily finite sets, and show that it is definitionally equivalent to Heyting Arithmetic, in a sense to be made precise. Our main target theory, the intuitionistic small set theory is remarkably simple, and intuitive. It has just one non-logical primitive, for membership, and three straightforward axioms plus one axiom scheme. We locate our theory within intuitionistic mathematics generally. (shrink)

The Evolution of Animal Communication is a detailed examination of a wide variety of animal signalling systems. The main focus of the book is explaining how such signalling systems remain reliable when there is apparent evolutionary pressure to deceive. The principle strategy is to appeal to signal costs: signals remain reliable because the potential benefits of deceit are outweighed by the costs of producing the deceptive signal. In this review I show just how difficult this idea is to test, even (...) in the simplest cases. (shrink)

We show the existence of noncomputable oracles which are low for Demuth randomness, answering a question in [15] (also Problem 5.5.19 in [34]). We fully characterize lowness for Demuth randomness using an appropriate notion of traceability. Central to this characterization is a partial relativization of Demuth randomness, which may be more natural than the fully relativized version. We also show that an oracle is low for weak Demuth randomness if and only if it is computable.

Several papers (e.g. [7, 23, 42]) have recently sought to give general frameworks for online structures and algorithms ([4]), and seeking to connect, if only by analogy, online and computable structure theory. These initiatives build on earlier work on online colouring and other combinatorial algorithms by Bean [10], Kierstead, Trotter et al. [48, 54, 57] and others, as we discuss below. In this paper we will look at such frameworks and illustrate them with examples from the first author’s MSc Thesis (...) ([58]). In this thesis, Askes looks at online, adversarial online and strongly online algorithms and structures. Additionally, we prove some new theorems about online algorithms on graphs of bounded pathwidth as well as some new results on punctually 1-decidable structures. (shrink)

_A look at the philosophical underpinnings of the hit TV show, _Mad Men__ With its swirling cigarette smoke, martini lunches, skinny ties, and tight pencil skirts, Mad Men is unquestionably one of the most stylish, sexy, and irresistible shows on television. But the series becomes even more absorbing once you dig deeper into its portrayal of the changing social and political mores of 1960s America and explore the philosophical complexities of its key characters and themes. From Socrates, Plato, and Aristotle (...) to John Kenneth Galbraith, Milton Friedman, and Ayn Rand, Mad Men and Philosophy brings the thinking of some of history's most powerful minds to bear on the world of Don Draper and the Sterling Cooper ad agency. You'll gain insights into a host of compelling Mad Men questions and issues, including happiness, freedom, authenticity, feminism, Don Draper's identity, and more. Takes an unprecedented look at the philosophical issues and themes behind AMC's Emmy Award-winning show, Mad Men Explores issues ranging from identity to authenticity to feminism, and more Offers new insights on your favorite Mad Men characters, themes, and storylines Mad Men and Philosophy will give _Mad Men_ fans everywhere something new to talk about around the water cooler. (shrink)

AbstractAgroecosystems in the Midwestern United States are undergoing changes that pressure farmers to adapt their farming practices. Because farmers decide what practices to implement on their land, there are needs to understand how they adapt to competing demands of changes in global markets, technology, farm sizes, and decreasing rural populations. Increased understanding of farmer decision-making can also inform agricultural policy in ways that encourage farmer adoption of sustainable practices. In this research we adopt a grounded view of farmers by interpreting (...) their decision-making through their stories of everyday life. We use a narrative analysis to identify recurrent themes that characterize farmer decisions as active negotiations between the demands of efficiency in maximizing crop yields with a desire to steward land through past, present, and future generations. Together these narratives portray farmer decisions as a place-making process that seeks compatibility among distinct aspirations for their land. (shrink)

Inhibition, an executive function, is critical for achieving goals that require suppressing unwanted behaviours, thoughts, or distractions. One hypothesis of the emotion and goal compatibility theory is that emotions of sadness and fear enhance inhibitory control. Across Experiments 1–4, we tested this hypothesis by inducing a happy, sad, fearful, and neutral emotional state prior to completing an inhibition task that indexed a specific facet of inhibition (oculomotor, resisting interference, behavioural, and cognitive). In Experiment 4, we included an anger induction to (...) examine whether valence or motivational-orientation best-predicted performance. We found support that fear and sadness enhanced inhibition except when inhibition required resisting interference. We argue that sadness and fear enhance inhibitory control aiding the detection and analysis of problems (i.e. sadness) or threats (i.e. fear) within one’s environment. In sum, this work highlights the importance of identifying how negative emotions can be beneficial for and interact with specific executive functions influencing down-stream processing including attention, cognition, and memory. (shrink)

Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- List of Contributors -- Preface -- Acknowledgements -- List of Abbreviations -- Giorgio Agamben: State of Exception -- Hannah Arendt: Religion, Politics and the Influence of Kierkegaard -- Alain Badiou: Thinking the Subject after the Death of God -- Judith Butler: Kierkegaard as Her Early Teacher in Rhetoric and Parody -- Jürgen Habermas: Social Selfhood, Religion, and Kierkegaard -- Martin Luther King, Jr.: Kierkegaard's Works of (...) Love, King's Strength to Love. (shrink)

René Girard: From Mimetic Desire to Anonymous Masses -- Carl Gustav Jung: A Missed Connection -- Julia Kristeva: Tales of Horror and Love -- Jacques Lacan: Kierkegaard as a Freudian Questioner of the Soul avant la lettre -- Rollo May: Existential Psychology -- Carl R. Rogers: "To Be That Self Which One Truly Is"--Max Weber: Weber'S Existential Choice -- Irvin Yalom: The "Throw-Ins" of Psychotherapy -- Slavoj ŽIžek: Mirroring the Absent God -- Index of Persons -- Index of Subjects.

Tome I covers the reception of Kierkegaard in Northern and Western Europe. The articles on Denmark, Norway, Sweden, Finland and Iceland can be said to trace Kierkegaard's influence in its more or less native Nordic Protestant context. Since the authors in these countries were not dependent on translations or other intermediaries, this represents the earliest tradition of Kierkegaard reception. The early German translations of his works opened the door for the next phase of the reception which expanded beyond the borders (...) of the Nordic countries. The articles in the section on Western Europe trace his influence in Great Britain, the Netherlands and Flanders, Germany and Austria, and France. All of these countries and linguistic groups have their own extensive tradition of Kierkegaard reception. (shrink)

Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- List of Contributors -- List of Abbreviations -- Hans Christian Andersen: Andersen was Just an Excuse -- Jens Baggesen: Kierkegaard and His Master's Voice -- Steen Steensen Blicher: The Melancholy Poet of the Jutland Heath -- August Bournonville: Kierkegaard's Leap of Faith and the "Noble Art of Terpsichore"--Mathilde Fibiger: Kierkegaard and the Emancipation of Women -- Meïr Goldschmidt: The Cross-Eyed Hunchback -- Thomasine Gyllembourg: Kierkegaard's Appreciation (...) of the Everyday Stories and Two Ages. (shrink)

Leadership has been shown to be a fundamental factor influencing the performance of sport teams. Within these teams, leadership can be provided by coaches, formal athlete leaders, such as team captains, and other ‘informal’ athlete leaders. The role of the athlete leader in a team, either formal or informal, has been consistently reported over the last 10 years to have a significant impact upon a teams’ functioning and effectiveness, as well as teammates’ general health and mental wellbeing. As such, cultivating (...) the provision of this leadership within a team has emerged as an important focus for managers, coaches, sport psychologists and scholars alike. While the recognition of the importance of athlete leadership is well established, there has been a lag in the development of systematic approaches to enhance and develop the leadership skills and capabilities of the athletes within sport teams. As a result, this paper seeks to review contemporary examples and current understanding of approaches to athlete leadership development. The paper will also highlight future areas for research and applied practice development. (shrink)

From ancient Greece to the present, philosophers have variously emphasized either the similarities or the differences between humans and nonhuman animals as a basis for ethical conclusions. Thus animal ethics has traditionally involved both factual claims, usually about animals’ mental states and capacities, and ethical claims about their moral standing. However, even in modern animal ethics the factual claims are often scientifically uninformed, involve broad generalizations about diverse taxonomic groups, and show little agreement about how to resolve the contradictions. Research (...) in cognitive ethology and animal welfare science provides empirical material and a set of emerging methods for testing the plausibility of claims about animal mentation and thus for clarifying the interests and needs of animals. We suggest that progress in animal ethics requires both philosophically informed science to provide an empirically grounded understanding of animals, and scientifically informed philosophy to explore the ethical implications that follow. (shrink)

It is natural to wish to study miniaturisations of Cohen forcing suitable to sets of low arithmetic complexity. We consider extensions of the work of Schaeffer [9] and Jockusch and Posner [6] by looking at genericity notions within the Δ2 sets. Different equivalent characterisations of 1-genericity suggest different ways in which the definition might be generalised. There are two natural ways of casting the notion of 1-genericity: in terms of sets of strings and in terms of density functions, as we (...) will see here. While these definitions coincide at the first level of the difference hierarchy, they turn out to differ at other levels. Furthermore, these differences remain when the remainder of the Δ02 sets are considered. While the string characterization of 1-genericity collapses at the second level of the difference hierarchy to 2-genericity, the density function definition gives a very interesting hierarchy at level w and above. Both of these results point towards the deep similarities exhibited by the n-c.e. degrees for n ≥ 2. (shrink)

Recent theologically grounded contributions to business ethics, though innovative and promising, are flawed by an unrealistic conception of human agency in corporate settings. By drawing upon the resources of organization theory, we can construct a more reliable descriptive anthropology as a foundation for prescriptive judgments. By bringing this reconstructed knowledge into connection with the normative moral arguments of H. Richard Niebuhr, we can develop a corporate ethics of trust building that both takes organizational realities seriously and also guides their transformation.

Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall with respect to professionalbasketball players. The main feature (...) of Shapiro's account is that the extensions of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis is that in some cases, a competent speaker ofthe language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts. Shapiro calls this open texture, borrowing the term from Friedrich Waismann.The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of 'determinacy' and 'borderline' - and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems.As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are. There is no need to blame the phenomenon on any one of those aspects. (shrink)

Dugald Stewart is usually thought of as the final major figure of the Scottish Enlightenment. But though his name is a recognisable one among intellectual historians, few would probably be able to...

In his Enquiry concerning the Principles of Morals David Hume said that a group of earlier modern philosophers, beginning with Malebranche, held that morality was founded on relations. In this paper I follow up on that suggestion by investigating pre-Humean views in moral philosophy according to which morality is founded on relations. I do that by looking at the work of Nicolas Malebranche, John Locke, and Samuel Clarke. Each of them talked prominently about relations in their accounts of basic aspects (...) of morality. Beyond that, each of them turns out to have held both metaphysical and epistemological views that might be described as founding morality on relations. Despite the definite differences between the three philosophers’ approaches, Hume does seem to have noticed a genuine connection here—even though he himself tended to ignore significant versions of this approach when criticizing it. (shrink)

A step-by-step guide to develop your idea from the first spark to the finished product, with charming illustrations recalling the whimsy and imagination of childhood.

There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalised Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here, we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalised Odds in non-trivial scenarios. We show that it is not, thereby establishing (...) an even more general impossibility theorem. (shrink)