A subspace V of an infinite dimensional fully effective vector space V ∞ is called decidable if V is r.e. and there exists an r.e. W such that $V \oplus W = V_\infty$ . These subspaces of V ∞ are natural analogues of recursive subsets of ω. The set of r.e. subspaces forms a lattice L(V ∞ ) and the set of decidable subspaces forms a lower semilattice S(V ∞ ). We analyse S(V ∞ ) and its relationship with L(V (...) ∞ ). We show: Proposition. Let U, V, W ∈ L(V ∞ ) where U is infinite dimensional and $U \oplus V = W$ . Then there exists a decidable subspace D such that U |oplus D = W. Corollary. Any r.e. subspace can be expressed as the direct sum of two decidable subspaces. These results allow us to show: Proposition. The first order theory of the lower semilattice of decidable subspaces, Th(S(V ∞ )), is undecidable. This contrasts sharply with the result for recursive sets. Finally we examine various generalizations of our results. In particular we analyse S * (V ∞ ), that is, S(V ∞ ) modulo finite dimensional subspaces. We show S * (V ∞ ) is not a lattice. (shrink)

In this article we show that it is possible to completely classify the degrees of r.e. bases of r.e. vector spaces in terms of weak truth table degrees. The ideas extend to classify the degrees of complements and splittings. Several ramifications of the classification are discussed, together with an analysis of the structure of the degrees of pairs of r.e. summands of r.e. spaces.

Schnorr randomness is a notion of algorithmic randomness for real numbers closely related to Martin-Löf randomness. After its initial development in the 1970s the notion received considerably less attention than Martin-Löf randomness, but recently interest has increased in a range of randomness concepts. In this article, we explore the properties of Schnorr random reals, and in particular the c.e. Schnorr random reals. We show that there are c.e. reals that are Schnorr random but not Martin-Löf random, and provide a new (...) characterization of Schnorr random real numbers in terms of prefix-free machines. We prove that unlike Martin-Löf random c.e. reals, not all Schnorr random c.e. reals are Turing complete, though all are in high Turing degrees. We use the machine characterization to define a notion of "Schnorr reducibility" which allows us to calibrate the Schnorr complexity of reals. We define the class of "Schnorr trivial" reals, which are ones whose initial segment complexity is identical with the computable reals, and demonstrate that this class has non-computable members. (shrink)

BackgroundPeople with upper extremity amputations report receiving insufficient information about treatment options. Furthermore, patients commonly report not knowing what questions to ask providers. A question prompt sheet, or list of questions, can support patient-centered care by empowering patients to ask questions important to them, promoting patient-provider communication, and increasing patient knowledge. This study assessed information needs among people with UE amputations about UE vascularized composite allotransplantation and developed a UE VCA-QPS.MethodsThis multi-site, cross-sectional, mixed-methods study involved in-depth and semi-structured interviews with (...) people with UE amputations to assess information needs and develop a UE VCA-QPS. Qualitative data were analyzed by thematic analysis; quantitative data were analyzed by descriptive statistics. The initial UE VCA-QPS included 130 items across 18 topics.ResultsEighty-nine people with UE amputations participated. Most were male, had a mean age of 46 years, and had a unilateral and below-elbow amputation. Participants desired information about UE VCA eligibility, evaluation process, surgery, risks, rehabilitation, and functional outcomes. After refinement, the final UE VCA-QPS included 35 items, across 9 topics. All items were written at a ≤ 6th grade reading level. Most semi-structured interview participants reported being ‘completely’ or ‘very’ likely to use a UE VCA-QPS.ConclusionPeople with UE amputations have extensive information needs about UE VCA. The UE VCA-QPS aims to address patients’ information needs and foster patient-centered care. Future research should assess whether the UE VCA-QPS facilitates patient-provider discussion and informed decision-making for UE VCA. (shrink)

Introduction by Ralph McInerny The essays in this volume, indebted in great part to Jacques Maritain and to other Neo-Thomists, represent a contribution to an understanding of beauty and the arts within the Aristotelian-Thomistic tradition. As such they constitute a different voice in present-day discussions on beauty and aesthetics, a voice which nonetheless shares with many of its contemporaries concern over questions such as the relationship between beauty and morality, public funding of the arts and their educational role, objective and (...) universal standards of what is beautiful. In the tradition in which the contributors of this volume reflect, beauty manifests itself in the order of the universe, an order that provides human reason with a window onto the transcendent. For Aristotle and Aquinas the natural order grounds both art and morality, and yet it is this very order which has been called into question by modern science and philosophy. Instead of pointing us to a suprahuman order, the beautiful then points to the order of human freedom and creativity. Reflection on the beautiful since the modern philosopher Immanuel Kant has thus often taken a subjectivistic turn. Because of the importance of beauty and art in human existence, in man's education and life as a moral and political being, an alternative should be sought to any reduction of the beautiful to a purely subjective experience or cultural construct. The Aristotelian-Thomistic tradition, in dialogue with modern and contemporary conceptions of the beautiful, provides us with just that alternative, and thus the essays herein represent a decisive step in the "journey for Thomistic aesthetics." THE CONTRIBUTORS: In addition to the editor, the contributors to the volume are: Brian J. Braman, Matthew Cuddeback, Christopher M. Cullen, S.J., Patrick Downey, Desmond J. FitzGerald, Donald Haggerty, Wayne H. Harter, Jeanne M. Heffernan, Thomas S. Hibbs, Gregory J. Kerr, Joseph W. Koterski, S.J., Daniel McInerny, Ralph McInerny, James P. Mesa, John F. Morris, Ralph Nelson, Katherine Anne Osenga, Carrie Rehak, Stephen Schloesser, S.J., Francis Slade, John G. Trapani, Jr., and Henk E. S. Woldring. ABOUT THE EDITOR: Alice Ramos is associate professor of philosophy at St. John's University. (shrink)

The people and the value of their experience, by N. T. Pratt.--From kingship to democracy, by J. P. Harland.--Democracy at Athens, by G. M. Harper.--Athens and the Delian League, by B. D. Meritt.--Socialism at Sparta, by P. R. Coleman-Norton.--Tyranny, by M. Mac Laren.--Federal unions, by C. A. Robinson.--Alexander and the world state, by O. W. Reinmuth.--The Antigonids, by J. V. A. Fine.--Ptolemaic Egypt: a planned economy, by S. L. Wallace.--The Seleucids: the theory of monarchy, by G. Downey.--The political status (...) of the independent cities of Asia Minor in the Hellenistic period, by D. Magie.--The ideal states of Plato and Aristotle, by W. J. Oates.--Epilogue, by A. C. Johnson.--Bibliography (p. 225-233).--Index, by H. V. M. Dennis, III. (shrink)

Since Leibniz's time, Cartesian mental causation has been criticized for violating the conservation of energy and momentum. Many dualist responses clearly fail. But conservation laws have important neglected features generally undermining the objection. Conservation is _local_, holding first not for the universe, but for everywhere separately. The energy in any volume changes only due to what flows through the boundaries. Constant total energy holds if the global summing-up of local conservation laws converges; it probably doesn't in reality. Energy conservation holds (...) if there is symmetry, the sameness of the laws over time. Thus, if there are time-places where symmetries fail due to nonphysical influence, conservation laws fail there and then, while holding elsewhere, such as refrigerators and stars. Noether's converse first theorem shows that conservation laws imply symmetries. Thus conservation trivially nearly entails the causal closure of the physical. But expecting conservation to hold in the brain simply assumes the falsehood of Cartesianism. Hence Leibniz's objection begs the question. Empirical neuroscience is another matter. So is Einstein's General Relativity: far from providing a loophole, General Relativity makes mental causation _harder_. (shrink)

ABSTRACTThe seminal work of David Marr, popularized in his classic work Vision, continues to exert a major influence on both cognitive science and philosophy. The interpretation of his work also co...

Part intellectual autobiography and part exposition of complex yet contemporary economic ideas, this lively conversation with renowned scholar and public intellectual Kenneth J. Arrow focuses on economics and politics in light of history, current events, and philosophy as well. Reminding readers that economics is about redistribution and thus about how we treat each other, Arrow shows that the intersection of economics and ethics is of concern not just to economists but for the public more broadly. With a foreword by Amartya (...) Sen, this book highlights the belief that government can be a powerful force for good, and is particularly relevant in the current political climate and to the lay reader as well as the economist. (shrink)

Measurement realism, the view that measurement targets quantitative attributes and that not all attributes are quantitative, has come under attack both from metrologists and philosophers. In this paper, I take a close look at two influential arguments against measurement realism: the argument from obsolescence and the argument from coordination. I concede that these arguments do challenge the epistemological position traditionally taken by measurement realists, but argue that the metaphysical core of measurement realism survives the challenge posed by these arguments. This (...) metaphysical core is vital to maintaining a clear and ambitious standard for successful measurement. (shrink)

Gaston Fessard employs Hegel’s dialectical logic to clarify how St. Ignatius’s _Spiritual Exercises_ envisage and prepare the decisions and choices between contrasting options or major turning points in spiritual life, in moments of what Ignatius would call _Election_.

In focusing on the story of Darwin's religious doubts, scholars too often overlook Darwin's positive contribution to the study of religion. J. David Pleins traces Darwin's journey in five steps. He begins with Darwin's global voyage, where his encounter with religious and cultural diversity transformed his understanding of religion. Surprisingly, Darwin wrestles with serious theological questions even as he uncovers the evolutionary layers of religion from savage roots. Next, we follow Darwin as his doubts about traditional biblical religion take root, (...) affecting his career choice and marriage to Emma Wedgwood. Pleins then examines Darwin's secret notebooks as he searches for a materialist theory of religion. Again, other surprises loom as Darwin's reading of Comte's three stages of religion's development actually predate his reading of Malthus. Pleins explores how Darwin applied his discovery to the realm of ethics by formulating an evolutionary view of the "Golden Rule" in his Descent of Man. Finally, he considers Darwin's later reflections on the religion question, as he wrestled with whether his views led to atheism, agnosticism, or a new kind of theism. The Evolving God concludes by looking at some of the current religious debates surrounding Darwin and suggests the need for a deeper appreciation for Darwin as a religious thinker. Though he grew skeptical of traditional Christian dogma, Darwin made key discoveries concerning the role and function of religion as a natural evolutionary phenomenon. (shrink)

Background: The American Medical Association, the British Medical Association and the Canadian Medical Association have guidelines that specifically discourage physicians from self-prescribing or prescribing to family members, but only the BMA addresses informal prescription requests between colleagues. Objective: To examine the practices of paediatric providers regarding self-prescribing, curbsiding colleagues, and prescribing and refusing to prescribe to friends and family. Methods: 1086 paediatricians listed from the American Academy of Paediatrics 2007 web-based directory were surveyed. Results: 44% of eligible survey respondents returned (...) usable surveys. Almost half of respondents had prescribed for themselves. An equal number had informally requested a prescription from a colleague. Three-quarters stated they had been asked to prescribe a prescription drug for a first-degree or second-degree relative, and 51% had been asked by their spouse. Eighty-six per cent stated that they had refused to write a prescription on at least one occasion for a friend or family member. The following reasons “strongly influenced” their decision to refuse a prescription request: outside of provider’s expertise ; patient’s need for his or her own physician ; not medically indicated ; need for a physical examination. Conclusion: These data confirm that most physicians have engaged in self-prescribing or curbside requests for prescriptions. It can be argued that curbsiding is more morally problematic than self-prescribing because it implicates a third party, and should be discouraged regardless of whether the requester is a colleague, family member or friend. (shrink)

There are five main claims that may be made about life after death: We are reincarnated in the self-same body we had in life. We are reincarnated in another body. We are revived, or continue to live in a disembodied form.

ABSTRACT On 19 July 2019, Agnes Heller died whilst swimming in Lake Balaton outside Budapest. With her passing, the culture of humanity lost one of its most remarkable representatives. So too, contemporary critique lost a philosophical sensibility that is, today, within the neoliberal university, increasingly rare. It is this philosophical sensibility with which this essay is concerned. Through a critical reconstruction of Heller’s reading of three key figures from the philosophical tradition (Marx, Pascal and Kierkegaard), this essay both charts the (...) changes and continuities in Heller’s philosophy of concrete subjectivity and makes a case for its continuing relevance to the cultural project of philosophy. (shrink)