This paper gives a semantics for schematic logic, proving soundness and completeness. The argument for soundness is carried out in ontologically innocent fashion, relying only on the existence of formulae which are actually written down in the course of a derivation in the logic. This makes the logic available to a nominalist, even a nominalist who does not wish to rely on modal notions, and who accepts the possibility that the universe may in fact be finite.

This paper puts forward a new account of rigorous mathematical proof and its epistemology. One novel feature is a focus on how the skill of reading and writing valid proofs is learnt, as a way of understanding what validity itself amounts to. The account is used to address two current questions in the literature: that of how mathematicians are so good at resolving disputes about validity, and that of whether rigorous proofs are necessarily formalizable.

This paper sketches an account of the standard of acceptable proof in mathematics—rigour—arguing that the key requirement of rigour in mathematics is that nontrivial inferences be provable in greater detail. This account is contrasted with a recent perspective put forward by De Toffoli and Giardino, who base their claims on a case study of an argument from knot theory. I argue that De Toffoli and Giardino’s conclusions are not supported by the case study they present, which instead is a very (...) good illustration of the kind of view of proof defended here. (shrink)

Although Peano arithmetic is necessarily incomplete, Isaacson argued that it is in a sense conceptually complete: proving a statement of the language of PA that is independent of PA will require conceptual resources beyond those needed to understand PA. This paper gives a test of Isaacon’s thesis. Understanding PA requires understanding the functions of addition and multiplication. It is argued that grasping these primitive recursive functions involves grasping the double ancestral, a generalized version of the ancestral operator. Thus, we can (...) test Isaacon’s thesis by seeing whether when we phrase arithmetic in a context with the double ancestral operator, the result is conservative over PA. This is a stronger version of the test given by Smith, who argued that understanding the predicate “natural number” requires understanding the ancestral operator, but did not investigate what is required to understand the arithmetic functions. (shrink)

Neo-Fregeanism aims to provide a possible route to knowledge of arithmetic via Hume’s principle, but this is of only limited significance if it cannot account for how the vast majority of arithmetic knowledge, accrued by ordinary people, is obtained. I argue that Hume’s principle does not capture what is ordinarily meant by numerical identity, but that we can do much better by buttressing plural logic with plural versions of the ancestral operator, obtaining natural and plausible characterizations of various key arithmetic (...) concepts, including finiteness, equinumerosity and addition and multiplication of cardinality—revealing these to be logical concepts, and obtaining much of ordinary arithmetic knowledge as logical knowledge. Supplementing this with an abstraction principle and a simple axiom of infinity (known either empirically or modally) we obtain a full interpretation of arithmetic. (shrink)

The initial motivating question for this thesis is what the standard of rigour in modern mathematics amounts to: what makes a proof rigorous, or fail to be rigorous? How is this judged? A new account of rigour is put forward, aiming to go some way to answering these questions. Some benefits of the norm of rigour on this account are discussed. The account is contrasted with other remarks that have been made about mathematical proof and its workings, and is tested (...) and illustrated by considering a case study discussed in the literature. On the view put forward here one can obtain a manner of informal, rigorous mathematics founded on any of a variety of proof systems. The latter part of the thesis is concerned with the question of how we should decide which of these competing proof systems we should base our mathematics on: i.e., the question of which proof system we should take as a foundation for our mathematics. A novel answer to this question is proposed, in which the key property we should require of a proof system is that for as many different kinds of structures as possible, when the proof system allows a generalization about that kind of structure to be proved, the generalization actually holds of all real examples of that kind of structure which exist. This is the requirement of soundness of the proof system. It is argued that the best way to establish the soundness of a proof system may be by giving an interpretation of its axioms on which they are established as true. As preparation for this discussion, the thesis first investigates the logical and conceptual basis of various arithmetic concepts, with the results obtained used in the final discussion of soundness. (shrink)

1 Evidence-based policy requires researchers to provide the answers to ecological questions that are of interest to policy makers. To find out what those questions are in the UK, representatives from 28 organizations involved in policy, together with scientists from 10 academic institutions, were asked to generate a list of questions from their organizations. 2 During a 2-day workshop the initial list of 1003 questions generated from consulting at least 654 policy makers and academics was used as a basis for (...) generating a short list of 100 questions of significant policy relevance. Short-listing was decided on the basis of the preferences of the representatives from the policy-led organizations. 3 The areas covered included most major issues of environmental concern in the UK, including agriculture, marine fisheries, climate change, ecosystem function and land management. 4 The most striking outcome was the preference for general questions rather than narrow ones. The reason is that policy is driven by broad issues rather than specific ones. In contrast, scientists are frequently best equipped to answer specific questions. This means that it may be necessary to extract the underpinning specific question before researchers can proceed. 5 Synthesis and applications. Greater communication between policy makers and scientists is required in order to ensure that applied ecologists are dealing with issues in a way that can feed into policy. It is particularly important that applied ecologists emphasize the generic value of their work wherever possible. (shrink)

The adaptationist framework is necessary and sufficient for unifying the social and natural sciences. Gintis's “beliefs, preferences, and constraints” (BPC) model compares unfavorably to this framework because it lacks criteria for determining special design, incorrectly assumes that standard evolutionary theory predicts individual rationality maximisation, does not adequately recognize the impact of psychological mechanisms on culture, and is mute on the behavioural implications of intragenomic conflict. (Published Online April 27 2007).

Two extremely detailed accounts of temporal experience can be found in the work of C. D. Broad. These accounts have been subject to considerable criticism. I argue that, when we look more carefully at Broad’s work, we find that much of this criticism fails to find its target. I show that the objection that ultimately proves troubling for Broad stems from his commitment to two principles: i) the Thin-PSA, and ii) the ‘Overlap’ claim. I use this result to demonstrate that (...) we can learn two extremely important lessons from Broad’s work on temporal experience. -/- The first lesson is that there is a structural problem facing any account that commits to these two principles. This is significant given that a number of recent accounts of temporal experience are so committed. The second lesson is that the problem facing these accounts stems only from commitment to the Thin-PSA and ‘Overlap’, rather than to commitment to a particular conception of how experiences are to be individuated. This, I argue, gives us reason to reject Tye’s recent claim that the problems facing accounts of temporal experience can be dissolved simply by making stipulations about how experiences are to be individuated. (shrink)

We present evidence from neuroimaging and brain lesion studies that emotional contagion may not be a mechanism underlying musical emotions. Our brains distinguish voice from non-voice sounds early in processing, and dedicate more resources to such processing. We argue that super-expressive voice theory currently cannot account for evidence of the dissociation in processing musical emotion and voice prosody.

Whereas boson coherent states with complex parametrization provide an elegant, and intuitive representation, there is no counterpart for fermions using complex parametrization. However, a complex parametrization provides a valuable way to describe amplitude and phase of a coherent beam. Thus we pose the question of whether a fermionic beam can be described, even approximately, by a complex-parametrized coherent state and define, in a natural way, approximate complex-parametrized fermion coherent states. Then we identify four appealing properties of boson coherent states (eigenstate (...) of annihilation operator, displaced vacuum state, preservation of product states under linear coupling, and factorization of correlators) and show that these approximate complex fermion coherent states fail all four criteria. The inapplicability of complex parametrization supports the use of Grassman algebras as an appropriate alternative. (shrink)

It is argued that Minkowski space-time cannot serve as the deep structure within a ``constructive'' version of the special theory of relativity, contrary to widespread opinion in the philosophical community.

The purpose of this paper is to evaluate the `Lorentzian Pedagogy' defended by J.S. Bell in his essay ``How to teach special relativity'', and to explore its consistency with Einstein's thinking from 1905 to 1952. Some remarks are also made in this context on Weyl's philosophy of relativity and his 1918 gauge theory. Finally, it is argued that the Lorentzian pedagogy---which stresses the important connection between kinematics and dynamics---clarifies the role of rods and clocks in general relativity.

The implications for the substantivalist–relationalist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the context of Newtonian mechanics, the Machian framework provides a genuinely relational interpretation of dynamics and that it is more explanatory than the conventional, substantival interpretation. In a companion paper (Pooley [2002a]), the viability of the Machian framework as an interpretation of relativistic physics is explored. 1 Introduction 2 Newton versus Leibniz 3 Absolute space versus (...) an affine connection 4 Anti-relationalist arguments 5 Rehabilitating relationalism 6 Dynamics on the relative configuration space 7 Intrinsic particle dynamics 8 Conclusion. (shrink)

Originally published in 1966 and now recognized as a classic, Norman O. Brown's meditation on the condition of humanity and its long fall from the grace of a natural, instinctual innocence is available once more for a new generation of readers. Love's Body is a continuation of the explorations begun in Brown's famous Life Against Death . Rounding out the trilogy is Brown's brilliant Apocalypse and/or Metamorphosis.

It is argued that Minkowski space-time cannot serve as the deep structure within a ``constructive'' version of the special theory of relativity, contrary to widespread opinion in the philosophical community.

Here is the final volume of Norman O. Brown's trilogy on civilization and its discontents, on humanity's long struggle to master its instincts and the perils that attend that denial of human nature. Following on his famous books _Life Against Death_ and _Love's Body_, this collection of eleven essays brings Brown's thinking up to 1990 and the fall of Communism in Eastern Europe. Brown writes that "the prophetic tradition is an attempt to give direction to the social (...) structure precipitated by the urban revolution; to resolve its inherent contradictions; to put an end to its injustice, inequality, anomie, the state of war... that has been its history from start to finish." Affiliating himself with prophets from Muhammad to Blake and Emerson, Brown offers further meditations on what's wrong with Western civilization and what we might do about it. Thus the duality in his title: crisis and the hope for change. In pieces both poetic and philosophical, Brown's attention ranges over Greek mythology, Islam, Spinoza, and _Finnegan's Wake_. The collection includes an autobiographical essay musing on Brown's own intellectual development. The final piece, "Dionysus in 1990," draws on Freud and the work of Georges Bataille to link the recent changes in the world's economies with mankind's primordial drive to accumulation, waste, and death. (shrink)

Umbilical cord blood has become the focus of intense efforts to collect, screen and bank haematopoietic stem cells in hundreds of repositories around the world. UCB banking has developed through a broad spectrum of overlapping banking practices, sectors and institutional forms. Superficially at least, these sectors have been widely distinguished in bioethical and policy literature between notions of the ‘public’ and the ‘private’, the commons and the market respectively. Our purpose in this paper is to reflect more critically on these (...) distinctions and to articulate the complex practical and hybrid nature of cord blood as a ‘bio-object’ that straddles binary conceptions of the blood economies. The paper draws upon Roberto Esposito’s reflections on biopolitics and his attempt to transcend the dualistic polarisations of immunity and community, or the private and the public. We suggest that his thoughts on immunitary hospitality resonate with many of the actual features and realpolitik of a necessarily internationalised and globally distributed UCB ‘immunitary regime’. (shrink)

The UN Global Compact is a voluntary initiative designed to help fashion a more humane world by enlisting business to follow ten principles concerning human rights, labor, the environment, and corruption. Although the four-year-old Compact is a relatively successful initiative, having signed up over eleven hundred companies and more than two hundred of the large multinationals, and having begun some important projects on globalization issues, there is a serious problem in that very few of the major U.S. companies have joined. (...) While the premier U.S. companies are interested in meeting the legitimate expectations of society, there is concerncentering around accountability issues. The accountability issues are in four major areas: 1. Accountability showing that the globalization of the economy actually helps the poor. 2. Accountability showing the corporate performance matches rhetoric. 3. Accountability that provides legitimacy to a two-tier pricing system and other measures that are designed to assist the poor in developing countries. 4. Accountability in the human rights area; what societal expectations are multinational companies accountablefor? The article outlines the problems that the Compact brings to the fore and offers some insight from the ethical literature that may address U.S. company concerns or provide new ways of thinking about the issues. It further argues that the forum provided by the Compact may be the most effective means to gain consensus of the role of business in society. (shrink)

Originally published in 1966 and now recognized as a classic, Norman O. Brown's meditation on the condition of humanity and its long fall from the grace of a natural, instinctual innocence is available once more for a new generation of readers. _Love's Body_ is a continuation of the explorations begun in Brown's famous _Life Against Death_. Rounding out the trilogy is Brown's brilliant _Apocalypse and/or Metamorphosis_.

Sethi and Schepers have identified an important issue for the global economy: Providing some mechanism for requiring assurance that environmental, social, and corporate governance information provided by a business is accurate and objective. Where they have gone wrong is in trying to change the mission of the United Nations Global Compact. From its inception, the UNGC has been clear that its mission is not to provide such assurance. This article first outlines the background for the historic announcement of the UNGC (...) by the then Secretary-General of the UN, Kofi Annan. Then a summary of the major criticisms of the initiative is provided with a focus on the Sethi–Schepers article. Finally, I argue that the mission of the UNGC, to gain consensus in the global community on the shared values and moral norms that will guide the global economy, is being accomplished, although it is a work in progress. (shrink)

Exploring what a scientific metaphysics grounded in biological practices could look like and how it might impact the way we investigate the world around us, the contributors to From Biological Practice to Scientific Metaphysics review and discuss long-held objections to metaphysics by natural scientists. They illuminate how, in order to learn about the world as it truly is, we must look not only at what scientists say but also what they do.

North Korea is under strict UN economic sanctions because it violated UN policy in its development of nuclear weapons and long range missiles as well as for its militant rhetoric. South Korea and Japan, as close allies of the USA, are unsure of the future. Is there a way to bring some peace and stability to the Korean peninsula? Some argue that this is a hopeless task as long as the current leadership of North Korea is in power. This article (...) takes a more positive stance and outlines a possible way forward. The study, following the position of the Heidelberg Institute for International Conflict Research, assumes that the conflict is at root one over ideology and power. The leadership of North Korea understands itself as “a revolutionary and socialist state” and is determined to continue to control the country through a rigorous and sometimes brutal government oversight of the culture. Although poverty and hunger are widespread, the people have little opportunity to be heard. What if the leaders of North Korea were persuaded that they could gain legitimacy through developing a dynamic economy that brought flourishing to their people and respect by fellow-nations in the global village? The article proposes to start this new adventure by developing enterprise zones in the North that would bring jobs and food to hundreds of thousands of North Koreans. To begin this project, there would need to be dramatic steps toward denuclearization on the part of the North in order to relax the UN economic sanctions. Is it possible? The article outlines a way forward. (shrink)

Catholic Social Teaching has taken a remarkable turn with the May 1991 document on economic ethics,Centesimus Annus. During their one hundred year history, church documents were notable for their courageous championing of the rights of the least advantaged; they were much less distinguished for their understanding of how markets and incentives function in capitalism. Most business leaders admired church teaching for its compassion but had little respect for its competence. With this most recent document, however, there is a growing conviction (...) that the church may have come of age in economic ethics. Even theWall Street Journal has celebratedCentesimus Annus. The article outlines the highlights of the document and its points of continuity with the tradition. Responses from business and the academy are also briefly considered. (shrink)

The work of philosophers in business ethics has been important in providing a systematic framework to analyze moral obligations of corporations and their many stakeholders. Yet the field of ethics as defined by the philosophers of the past two centuries is too narrow to do justice to what is at stake in the business world. Ethics in the theological perspective is not primarily concerned with analyzing situations so that one can make right decisions, but rather with reflecting on what is (...) constitutive of the good life. Theological business ethics can apply a crucial corrective to the business ethics of philosophers by broadening the endeavor to include a vision of what constitutes a good life — of the kind of persons we want to be and the kind of communities we want to form. (shrink)

The medial prefrontal cortex (mPFC) has been the subject of intense interest as a locus of cognitive control. Several computational models have been proposed to account for a range of effects, including error detection, conflict monitoring, error likelihood prediction, and numerous other effects observed with single-unit neurophysiology, fMRI, and lesion studies. Here, we review the state of computational models of cognitive control and offer a new theoretical synthesis of the mPFC as signaling response–outcome predictions. This new synthesis has two interacting (...) components. The first component learns to predict the various possible outcomes of a planned action, and the second component detects discrepancies between the actual and intended responses; the detected discrepancies in turn update the outcome predictions. This single construct is consistent with a wide array of performance monitoring effects in mPFC and suggests a unifying account of the cognitive role of medial PFC in performance monitoring. (shrink)

In the past two decades, reinforcement learning has become a popular framework for understanding brain function. A key component of RL models, prediction error, has been associated with neural signals throughout the brain, including subcortical nuclei, primary sensory cortices, and prefrontal cortex. Depending on the location in which activity is observed, the functional interpretation of prediction error may change: Prediction errors may reflect a discrepancy in the anticipated and actual value of reward, a signal indicating the salience or novelty of (...) a stimulus, and many other interpretations. Anterior cingulate cortex has long been recognized as a region involved in processing behavioral error, and recent computational models of the region have expanded this interpretation to include a more general role for the region in predicting likely events, broadly construed, and signaling deviations between expected and observed events. Ongoing modeling work investigating the interaction between ACC and additional regions involved in cognitive control suggests an even broader role for cingulate in computing a hierarchically structured surprise signal critical for learning models of the environment. The result is a predictive coding model of the frontal lobes, suggesting that predictive coding may be a unifying computational principle across the neocortex. (shrink)

For business to flourish, society must flourish. In today's global economy, business serves the common good not only by producing goods and services but also by reaching out to the many who are not even in the market because they lack marketable skills and the resources to acquire them. _Sustainable Development: The UN Millennium Development Goals, the UN Global Compact, and the Common Good_ contains twenty-two essays that document the work of Western companies, working through the UN Global Compact and (...) its Principles of Responsible Investment and the Principles for Responsible Management Education, to shape more peaceful and just societies. Seven case studies by leading businesses and private-public partnerships—including Microsoft, Merck, Sumitomo Chemical, Nestlé, Coca-Cola, Novartis, and Levi Strauss—outline their projects, especially those advancing the MDGs designed to alleviate dire poverty. Twelve chapters reflect on some of the conceptual issues involved with the MDGs, and the three concluding essays examine the future of the UN Global Compact, of the Millennium Development Goals, and of the role of business enterprise in society._ "The United Nations Global Compact is a major initiative in the worldwide effort to ensure the fair distribution of the enormous wealth generated by the globalization of corporate capitalism, an initiative of interest to all nations, corporations public and private, and the present and future citizens of the world. This volume comprises original contributions from the foremost scholars in the field. These papers are the state of the art in the scholarly examination of the international efforts on the part of private enterprise to assist in economic development and forging peace." — Lisa H. Newton, Fairfield University_. (shrink)

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Numerous scholarly works focus solely on scientific metaphysics or biological practice, but few attempt to bridge the two subjects. This volume, the latest in the Minnesota Studies in the Philosophy of Science series, explores what a scientific metaphysics grounded in biological practices could look like and how it might impact the way we investigate the world around us. From Biological Practice to Scientific Metaphysics examines how to reconcile the methods of biological practice with the methods of metaphysical cosmology, notably regarding (...) the origins of life. The contributors take up a wide range of traditional metaphysics and philosophy of science topics, including natural kinds, medicine, ecology, genetics, scientific pluralism, reductionism, operationalism, mechanisms, the nature of information, and more. Many of the chapters represent the first philosophical treatments of significant biological practices. From causality and complexity to niche constructions and inference, the contributors review and discuss long-held objections to metaphysics by natural scientists. They illuminate how, in order to learn about the world as it truly is, we must look not only at what scientists say but also what they do: for ontology cannot be read directly from scientific claims. (shrink)