Using Carnap’s concept explication, we propose a theory of concept formation in mathematics. This theory is then applied to the problem of how to understand the relation between the concepts formal proof and informal, mathematical proof.

St. Thomas’s commentary on the Book of Psalms, known as the Postilla super Psalmos, gives us a privileged insight into the mind and heart of a Dominican friar and theologian at work and at prayer. In this contribution I will elucidate these claims on the basis of elements found in his commentary and in particular in the areas of prayer and the liturgy, Christ, Mary and the Church, Sin and Mercy and Contemplation and Preaching.

Mathematical concepts are explications, in Carnap's sense, of vague or otherwise non-clear concepts; mathematical theories have an empirical and a deductive component. From this perspective, I argue that the empirical component of a mathematical theory may be tested together with the fruitfulness of its explications. Using these ideas, I furthermore give an argument for mathematical realism, based on the indispensability argument combined with a weakened version of confirmational holism.

In this paper I discuss possible ways of measuring the power of arithmetical theories, and the possiblity of making an explication in Carnap's sense of this concept. Chaitin formulates several suggestions how to construct measures, and these suggestions are reviewed together with some new and old critical arguments. I also briefly review a measure I have designed together with some shortcomings of this measure. The conclusion of the paper is that it is not possible to formulate an explication of the (...) concept. (shrink)

Recently Carrie S. Jenkins formulated an epistemology of mathematics, or rather arithmetic, respecting apriorism, empiricism, and realism. Central is an idea of concept grounding. The adequacy of this idea has been questioned e.g. concerning the grounding of the mathematically central concept of set (or class), and of composite concepts. In this paper we present a view of concept formation in mathematics, based on ideas from Carnap, leading to modifications of Jenkins’s epistemology that may solve some problematic issues with her ideas. (...) But we also present some further problems with her view, concerning the role of proof for mathematical knowledge. (shrink)

The initial purpose of this study is to provide an empirical validation of Victor and Cullen’s ethical-climate model (1987, Frederick (ed.), Research in Corporate Social Performance and Policy, Vol. 9, pp. 51–71; 1988, Administrative Science Quarterly 33, 101–125; 1990, Frederick and Preston (eds.), Business Ethics: Research Issues and Empirical Studies (JAI Press Inc., Greenwich, Connecticut), pp. 77–97). Testing the model on a sample of Danish firms, this study demonstrates that the empirical model as suggested by Victor and Cullen is much (...) stronger than suggested by previous research. Based on a confirmatory factor model, the results of this study suggest a revised ethical structure. Especially a sixth dimension – own interest – is separated from the original instrumental dimension. Further, this study suggests that the ethical-climate model can be enhanced with the dimension of autonomy deriving from Koys and DeCotiis’ (1991, Human Relations 44(3), 265–285.) dimensional psychological climate instrument. (shrink)

Child assent is recommended in addition to parental consent when enrolling children in clinical research; however, appreciation and relevance ascribed to these concepts vary in different contexts, and information on attitudes towards storage of biological samples for future research is limited, especially in developing countries. We assessed caregivers’ understanding and appreciation of consent and assent procedures, and their attitudes towards use of stored blood samples for future research prior to enrolling a child in clinical research. A total of 17 in-depth (...) interviews were conducted with primary caregivers of children at enrolment or on the immediate follow-up date. All caregivers recalled significant amount information from the study information sheet and were able to appropriately link such information to the consent process. While all participants confirmed information received prior to blood sampling as adequate, a few noted that the purpose was not sufficiently well communicated. Caregivers felt children were cognitively vulnerable, and prone to decisions that were not necessarily in their best interest. Nearly all caregivers felt it was their right and responsibility to overrule objections from their ward’s regarding enrolment into specific study or receipt of a therapeutic procedure. There were no objections or concerns regarding use of stored biological samples for future research purposes. There is thus, a need to improve understanding of caregivers on the information provided during the informed consent process. Context-specific studies on the age of assent in specific populations are needed. (shrink)

With this first part of the eleventh volume, Bruce Kirmmse et al.’s monumental task of translating Søren Kierkegaard’s journals and notebooks begins to draw to a close. The journals and notebooks t...

The pathway from scientific knowledge (based on data, models, and forecasts) to societal implications and policy advice is a perilous one. The shift from "is" to "ought" may be slippery in terms of climate, biodiversity, regulations, and business. Yet, what is to be done if one's research discloses that fellow humans are unwittingly carrying out destructive actions on a large scale? If they are unaware of the dynamics within which they are (or are in danger of becoming) imprisoned, is there (...) then not an ethical obligation to respond beyond the scope of one's given role? This dilemma lies at the core of the issue of science-based activism, which the life and work of Jorgen Randers in many ways epitomizes. The best means of understanding science-based activism can be found in exploring Randers' steps, as this festschrift does. [Jorgen Randers (born 1945) co-authored The Limits to Growth in 1972 and its sequels in 1992 and 2004. He is a Professor of Climate Strategy at the Norwegian Business School in Oslo where he works on climate and energy issues, system dynamics, and green growth. Randers was President of the Norwegian Business School/BI 1981-89, and Deputy Director General of WWF International 1994-99. He chaired the Norwegian Commission on a Low-Emission Society which reported in 2006. In 2012, his work 2052 - A Global Forecast for the Next Forty Years was published.] [Subject: Science, Ethics, Environmental Studies]. (shrink)

Jörgen Jörgensen (1938) asks why there should not be a valid deduction even though the premises are imperatives (“Jörgensen’s Dilemma”). Robert Walter (1996; 9 Ratio Juris 168), following Hans Kelsen, thinks that there can be a valid deduction if the premises, although in prescriptive (including imperative) language, are actually descriptions of prescriptions. It is suggested that Walter then has his own dilemma: the more possible it is, for such descriptions to be valid, the less likely it is, that the prescriptions (...) described are illogical; Walter’s Dilemma is a species of Jörgensen’s. (shrink)

"Practice in Christianity is the second volume in what could be called the "collected Works" of "Anti-Climacus," Kierkegaard's new pseudonym. Anti-Climacus's first volume, The Sickness Unto Death, appeared just a year earlier in 1849. The use of a pseudonym is consistent with Kierkegaard's usual practice when presenting an idealized statement of his subject, be it sexual seduction or Christian theology. Anti-Climacus argues the conceptual content of Christianity against the "leading thought of the times" and also against the ethical and social (...) import of the comforts and consolations of bourgeois culture and religion which he called "Christendom." In his own mind at least, Kierkegaards presents Christianity as it must be thought and lived if it is to be authentic. The Sickness unto Death and Practice in Christianity can be and are read quite independently, but jointly they provide the basis of Kierkegaard's devastating critique of a secularized, culturally homogenized, and tame Christianity. The authors of the studies in this present volume, Merold Westphal, Paul R. Sponheim, Murray A. Rae, Niels Jorgen Cappelorn, Sylvia Walsh, David D. Possen, Andrew J. Burgess, Christian Fink Tolstrup, Robert L. Perkins, and Wanda Warren Berry, raise a wide spectrum of issues regarding Practice in Christianity, its theology, its moral and religious psychology, and its cultural, social, and political world" --. (shrink)

David Lewis is widely credited with the first formulation of common knowledge and the first rigorous analysis of convention. However, common knowledge and convention entered mainstream game theory only when they were formulated, later and independently, by other theorists. As a result, some of the most distinctive and valuable features of Lewis' game theory have been overlooked. We re-examine this theory by reconstructing key parts in a more formal way, extending it, and showing how it differs from more recent game (...) theory. In contrast to current theories of common knowledge, Lewis' theory is based on an explicit analysis of the modes of reasoning that are accessible to rational individuals and so can be used to analyse the genesis of common knowledge. Lewis' analysis of convention emphasises the role of inductive reasoning and of salience in the maintenance of conventions over time. Footnotes Earlier versions of this paper were presented at the 13th Amsterdam Colloquium at the University of Amsterdam, at a workshop on social norms at Wissenschaftskolleg zu Berlin, and at seminars at Tilburg University and the University of Bristol. We are grateful for comments from participants at those meetings, from two anonymous referees, and from Michael Bacharach, Nick Bardsley, Cristina Bicchieri, Luc Bovens, Simon Grant, David McCarthy, Shepley Orr, Brian Skyrms, Peter Vanderschraaf, Peter Wakker and Jörgen Weibull. Robert Sugden's work was supported by the Leverhulme Trust. (shrink)

In the year 2002, I came across a manuscript by Jean-Pierre Dupuy that linked the work of Ivan Illich with that of René Girard. I immediately set about translating the text, which was published in Spanish as part of the essay collection The Other Titan: Ivan Illich.1 The original “Detour and Sacrifice” can be found in two books that pay tribute to the authors. The first was compiled by Lee Hoinacki and Carl Mitcham, Illich’s disciples;2 the second is a book (...) edited by Sandor Goodhart, Jorgen Jorgensen, Tom Ryba, and James G. Williams that celebrates Girard’s work.3The genesis of Dupuy’s text actually goes back to 1996 and was inspired by Ivan Illich’s seventieth birthday, which was celebrated with a series of... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Converging Ways? Conversion and Belonging in Buddhism and ChrisitanityCatherine CornilleConverging Ways? Conversion and Belonging in Buddhism and Chrisitanity. By John D’Arcy May. Sankt Ottilien: EOS Klosterverlag, 2007. 207 pp.In the course of the past seven years, the European Network of Buddhist-Christian Studies has established itself as a locus of serious dialogue and creative religious reflection. This volume, which emerged out of the sixth conference (in 2005) at the (...) Benedictine Abbey of St. Ottilien in Germany, combines a diversity of contributions on various issues relating to conversion, religious belonging, and multiple religious belonging. At the heart of the volume are two responses (by Christian theologian Perry Schmidt-Leukel and Buddhist theologian José Cabezón) to the highly publicized conversion of Paul Williams from Tantric Buddhism to Roman Catholicism, followed by a reply by Williams himself. These three articles represent a powerful demonstration of religious apologetics at its best. Each offers their critique of the other from a clearly defined religious position, displaying a clear understanding of the views of the other, but arguing unabashedly for the validity or superiority of their own position or theological convictions. Somewhat missing in the reading is an account of Williams’s conversion story, which he developed in An Unexpected Way. But each of the discussants offers a clear enough account of the other so that even those who have not read the book are able to reconstruct the main points of Williams’s narrative and arguments. Against Williams, who juxtaposes Buddhist atheism with Christian theism, Schmidt-Leukel proposes a conception of the absolute which he believes is amenable to both, but which—as Williams later argues—may be representative of neither. Cabezón, for his part, focuses not only on Williams’s theological arguments, but also on his ethical arguments for the superiority of Christianity, objecting that the black-and-white picture presented in a conversion narrative often entails a distortion or oversimplification of the tradition left behind, and pointing to the importance of interconnection and love in Buddhist texts and traditions. While conceding the latter, Williams, in his retort, passionately and eloquently reiterates his arguments for the plausibility of the Christian conception of God, countering one by one the points raised by his respondents. In this, he draws almost exclusively on Thomas Aquinas, which gives power and focus to his arguments but also seems to ignore the presence of other theological voices within the Christian and Roman Catholic tradition. This exercise in apologetics is interesting, not only because of the contents of the arguments, but also because of the tone. While Williams pays heed to Cabezón, [End Page 161] who approaches his conversion from a clearly defined Buddhist perspective, he seems less respectful of the position of Schmidt-Leukel, who attempts to reconcile Buddhist and Christian views of God. The reasons why such reconciliations are unappealing for someone who has converted from the one religion to the other may be many. But it certainly points to the tensions between clear commitment and belonging to a particular religious and theological tradition and the rhetoric of multiple religious belonging.This brings us to some of the other articles collected in this volume. Some focus on the lived reality of multiple belonging in Korea (Thomas Timpte) or in Sweden (Kajsa Ahlstrand) while others focus on personal experience (Thomas Josef Gotz and Ruben Habito) or on the religious or theological grounds for multiple religious belonging (Jorgen Skov Sorensen and Michael von Bruck). All of these contributions point to the reality or the ideality of belonging to more than one religious tradition. It would appear that in the context of religious diversity, such multiple belonging is all but unavoidable. While some point to the false construction of religious boundaries, others dismiss all notions of religious and theological superiority as well as the centrality of truth in religion. In contrast with this, the robust theological debate on matters of truth and difference at the heart of this volume offers a healthy counterbalance and a welcome reminder of the categorical and at times conflicting claims to truth in religion. If religions are taken seriously, multiple religious identity is less evident than sociological data... (shrink)

Sally Sedgwick presents a fresh account of Hegel's critique of Kant's theoretical philosophy. She argues that Hegel offers a compelling critique of and alternative to the conception of cognition that Kant defended in his 'Critical' period, and explores Hegel's claim to derive from Kantian doctrines clues to a superior form of idealism.

The relationship of man himself to his environment is an inseparable part of ecology; for he also is an organism and other organisms are a part of his environment. Ecology, therefore, broadly conceived and rightly understood, instead of being an academic science merely, out of touch with humanistic interests, is really that part of every other biological science which brings it into immediate relation to human kind. The proper place of humans in ecological study has been a recurring issue for (...) ecology. Of course humans are part of Nature writ large, but are they part of the ecologist's nature? The question bothered biologists even before the discipline of ecology was firmly institutionalized.... (shrink)

According to Aristotle, Metaphysics 2.3, 995a7–8, there are people who will take seriously the arguments of a speaker only if a poet can be cited as a ‘witness’ in support of them. Aristotle's passing observation sharply reminds us that Greek philosophy had developed within, and was surrounded by, a culture which extensively valued the authority of the poetic word and the poet's ‘voice’ from which it emanated. The currency of ideas, values, and images disseminated through familiarity with poetry had always (...) been a force with which philosophy, in its various manifestations, needed to reckon. As a mode of thought and discourse which proclaimed its aspiration to wisdom, philosophy could not easily eschew some degree of dialogue with an art whose practitioners had traditionally been ranked prominently among the sophoi. Even Aristotle, who keeps aloof from the assumption that philosophical contentions stand in need of poetic support, cites and quotes poetry regularly in his own writings in ways which indicate the influence on him of a prevailing mentality that regarded poets and philosophers as pursuers, up to a point at least, of a common wisdom. (shrink)

The codex Cromwellianus 12 , one of the most interesting astrological manuscripts of the Bodleian Library in Oxford, contains on p. 450 f., under the heading 'Ιμβρασίου 'Εεσίου περί ρρώστων, the first part of the first part of Ps.-Galen's περι κατακλίσεως νοσούντων, which is, together with a work of Hermes Trismegistos, our principal source for iatromathematics, that is, for diagnosis and prognosis based on certain constellations, above all on the Moon's position in a particular sign of the zodiac. It is (...) not the text itself that calls for notice—since we possess older and better manuscripts of it—but the mention of the author, Imbrasios of Ephesus, which only occurs here. (shrink)

It is Frege's third contribution that makes the point of departure for the present paper. Not merely did Frege show how to manipulate symbols more exactly; he also gave a searching account of what these symbols mean. Consider a philosophical problem that arises out of the simplest arithmetic. When we say that 5 = 2 + 3, what do we mean? Do we mean that 5 is identical with 2 + 3? But in some ways 5 and 2 + 3 (...) are obviously different. Or do we mean that 5 and 2 + 3 are equal but not identical, equality being a relation that falls short of complete identity? But in that case, some ordinary ways of speaking in mathematics must be false. Suppose a pupil is asked for the positive square root of 25. The phrasing of the question implies that there is one and only one. No doubt he may answer, '5'. But then it follows that the answer '2 + 3' is not allowable, since ex hypothesi 5 and 2 + 3, though equal, are not identical. Yet ordinarily the answer '2 + 3' would be regarded as strange but not as wrong. (shrink)

Frank Ebersole's extraordinary investigations of certain key philosophical ideas behind problems in epistemology and metaphysics are the subject of this article-review. I have resisted providing what many readers will expect me to provide, namely, a critical examination of his philosophical methodology. I do question his unwilligness to say why his investigations only yield I negative results, and I do have something to say about classifying him as an ordinary language philosopher. However, my main focus is on trying to engage critically (...) with what he actually does in his work. To this end, I provide a narrative of the investigation he carries out into the possibility of comparing the objects of perception and dreams, and I cite other works of his in support of my understanding of that investigation. Although one of his lengthiest essays seems to be devoted to an anticipation of an objection to his approach, I explain why even there he is not concerned with the question of why he always seems to get negative results. After suggesting why some of his later essays seem to be so hard to read, I conclude by saying something about what I take to be his achievement. (shrink)

David Bohm's interpretation of quantum mechanics yields a quantum potential, Q. In his early work, the effects of Q are understood in causal terms as acting through a real (quantum) field which pushes particles around. In his later work (with Basil Hiley), the causal understanding of Q appears to have been abandoned. The purpose of this paper is to understand how the use of certain metaphors leads Bohm away from a causal treatment of Q, and to evaluate the use of (...) those metaphors. (shrink)

This is a short paper covering my own views on the methods and reasons behind the teaching of medical ethics. All the whys and wherefores are discussed and some conclusions reached. This paper is given from a junior doctor's viewpoint but could equally apply to many others.

Robert Kilwardby occupies an important place in the history of logic, and the history of western thought more generally. Perhaps best known to scholars for his Oxford condemnations of 1277...