The identification of an informal concept of ‘effective calculability’ with a rigorous mathematical notion like ‘recursiveness’ or ‘Turing computability’ is still viewed as problematic, and I think rightly so. I analyze three different and conflicting perspectives Gödel articulated in the three decades from 1934 to 1964. The significant shifts in Gödel's position underline the difficulties of the methodological issues surrounding the Church-Turing Thesis.
The concept of social capital helps to explain relations within and between companies but has not crystallized yet. As such, the nature, development, and effects of such relations remain elusive. How is social capital created, how is it put to use, and how is it maintained? Can it decline, and if so, how? We argue that the concept of social capital remains a black box as the mechanisms that constitute it remain underdeveloped and that it is a black hole as (...) many empirical phenomena are attributed to its presence. We use and develop the literature on gift exchange to provide a firmer theoretical basis for the concept of social capital. (shrink)
Originally published in 1913. Author: Henri Lichtenberger Language: English Keywords: History Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. Obscure Press are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.Keywords: English Keywords 1900s Language English Artwork.
It is argued that 'sustainable development' has been defined in such a way as to be either morally repugnant or logically redundant. 'Strong' sustainability, overriding all other considerations, is morally unacceptable as well as totally impractical; and 'weak' sustainability, in which compensation is made for resources consumed, offers nothing beyond traditional economic welfare maximisation. The 'sustainability' requirement that human well-being should never be allowed to decline is shown to be irrational. Welfare economics can accommodate distributional considerations, and, suitably defined, the (...) concept of welfare can include the subjective effects of changes in – as well as the levels of – well-being. Hence there is no reason why welfare maximisation should not remain an overriding policy objective. Nor can sustainability be regarded as a 'constraint' on welfare maximisation unless there is a clear conflict between the two – which has yet to be demonstrated. This is not to deny the importance of intergenerational justice, nor the need for economic incentives to correct market imperfections if the environment is to be managed in a socially optimal manner. Apart from a few small developing countries heavily dependent on minerals or other finite primary products, the measurement of some wider concept of 'sustainable' GNP is a waste of time and such estimates as have been made are virtually worthless. (shrink)
A recent review of his work describes Wilfred Carr as 'one of the most brilliant philosophers now working in the rich British tradition of educational philosophy ... His work is rigorous, refreshing and original ... and examines a number of fundamental issues with clarity and penetration'. In For Education Wilfred Carr provides a comprehensive justification for reconstructing educational theory and research as a form of critical inquiry. In doing this, he confronts a number of important philosophical questions. What (...) is educational theory? What is an educational practice? How are theory and practice related? What is the role of values in educational research? Is a genuinely educational science possible? By appealing to developments in critical theory, the philosophy of science and the philosophy of the social sciences, Wilfred Carr provides answers to these questions which vindicate the idea of an educational science that is not 'on' or 'about' education but 'for education' - a science genuinely committed to promoting educational values and ideals. (shrink)
The man or woman of faith living in today's pluralist world must have a theology that will do justice to his or her own faith, and also to the neighbours' - and to the differences between them. Similarly, humanists must have a theory that does justice to their own vision and also to the fact that for most of their fellows on earth the proper way of being human has been one or another of various `religious' ways. Any interpretation of (...) human history, both past and present, must take into serious account the self-consciousness of each major part, as well as the diversity and the dynamic of the whole. This exciting book, first published in 1981 and now also available in paperback, is perhaps our world's first serious endeavour towards a theology in global perspective. Here is a wrestling with the demands of an authentic theology of the comparative history of religion. (shrink)
This paper proceeds through four stages. First, it provides an account of the origins and evolution of the concept of educational theory. Second, it uses this historical narrative to show how what we now call 'educational theory' is deeply rooted in the foundationalist discourse of late nineteenth and early twentieth century modernity. Third, it outlines and defends a postfoundationalist critique of the foundationalist epistemological assumptions on which our understanding of educational theory has been erected. Finally, it argues that the only (...) conclusion to draw from this postfoundationalist critique is that educational theory has run its course and should now be brought to a dignified end. (shrink)
David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations.
In this article it is argued that there are notable parallels between all of the different strands within ethics on the one hand, and accountancy on the other that, in teaching, can be drawn upon to enhance students’ understanding of the latter. Accountancy, part of economics, draws on utilitarian ethics, but not solely so. Accounting, in addition, draws on deontological and communitarian strands in ethics. The article suggests that the teaching of accounting – especially to non-economists – would benefit substantially (...) from highlighting and developing these parallels. (shrink)
This article concentrates on the Jacobs and Daly criticisms (Environmental Values, Spring 1994) of my earlier article in the same journal (Autumn 1994) criticising the concept of 'sustainable development'. Daly and Jacobs agreed with my criticisms of 'weak' sustainability, but defended 'strong' sustainability on the grounds that natural and manmade capital were 'complements' in the productive process and that economists are wrong, therefore, in assuming that they are infinitely substitutable. This article maintains that they are confusing different concepts of 'complementarity' (...) and 'substitutability'. It is also argued that, in fact, they do both sell crucial passes in their defence of strong sustainability without providing any clear criteria for their abandonment of it in certain cases. It is also denied that the fact that environmental services may provide different satisfactions from those obtained from other goods and services elevates it to the status of some over-riding moral value, or that discounting future costs and benefits is 'unfair' to future generations. (shrink)
The paper discusses some of the criticisms of contingent valuation (CV) and allied techniques for estimating the intensity of peoples' preferences for the environment. The weakness of orthodox utilitarian assumptions in economics concerning the commensurability of all items entering into peoples' choices is discussed. The concept of commensurability is explored as is the problem of rational choice between incommensurate alternatives. While the frequent claim that the environment has some unique moral intrinsic value is unsustainable, its preservation often raises ethical and (...) other motivations that are not commensurate with the values that people place on ordinary marketable goods. Nevertheless, CV is also claimed to have some advantages and it is concluded that little progress will be made in this area until both sides in the debate recognise what is valid in their opponents' arguments. (shrink)
The aim of this paper is to examine the role of methodology in action research. It begins by showing how, as a form of inquiry concerned with the development of practice, action research is nothing other than a modern 20th century manifestation of the pre‐modern tradition of practical philosophy. It then draws in Gadamer's powerful vindication of the contemporary relevance of practical philosophy in order to show how, by embracing the idea of ‘methodology’, action research functions to sustain a distorted (...) understanding of what practice is. The paper concludes by outlining a non‐methodological view of action research whose chief task is to promote the kind of historical self‐consciousness that the development of practice presupposes and requires. (shrink)
We establish by elementary proof-theoretic means the conservativeness of two subsystems of analysis over primitive recursive arithmetic. The one subsystem was introduced by Friedman , the other is a strengthened version of a theory of Minc ; each has been shown to be of considerable interest for both mathematical practice and metamathematical investigations. The foundational significance of such conservation results is clear: they provide a direct finitist justification of the part of mathematical practice formalizable in these subsystems. The results are (...) generalized to relate a hierarchy of subsystems, all contained in the theory of arithmetic properties, to a corresponding hierarchy of fragments of arithmetic. The proof theoretic tools employed there are used to re-establish in a uniform, elementary way relationships between various fragments of arithmetic due to Parsons, Paris and Kirby, and Friedman. (shrink)
Hilbert's finitist program was not created at the beginning of the twenties solely to counteract Brouwer's intuitionism, but rather emerged out of broad philosophical reflections on the foundations of mathematics and out of detailed logical work; that is evident from notes of lecture courses that were given by Hilbert and prepared in collaboration with Bernays during the period from 1917 to 1922. These notes reveal a dialectic progression from a critical logicism through a radical constructivism toward finitism; the progression has (...) to be seen against the background of the stunning presentation of mathematical logic in the lectures given during the winter term 1917/18. In this paper, I sketch the connection of Hilbert's considerations to issues in the foundations of mathematics during the second half of the 19th century, describe the work that laid the basis of modern mathematical logic, and analyze the first steps in the new subject of proof theory. A revision of the standard view of Hilbert's and Bernays's contributions to the foundational discussion in our century has long been overdue. It is almost scandalous that their carefully worked out notes have not been used yet to understand more accurately the evolution of modern logic in general and of Hilbert's Program in particular. One conclusion will be obvious: the dogmatic formalist Hilbert is a figment of historical (de)construction! Indeed, the study and analysis of these lectures reveal a depth of mathematical-logical achievement and of philosophical reflection that is remarkable. In the course of my presentation many questions are raised and many more can be explored; thus, I hope this paper will stimulate interest for new historical and systematic work. (shrink)
Natural Formalization proposes a concrete way of expanding proof theory from the meta-mathematical investigation of formal theories to an examination of “the concept of the specifically mathematical proof.” Formal proofs play a role for this examination in as much as they reflect the essential structure and systematic construction of mathematical proofs. We emphasize three crucial features of our formal inference mechanism: (1) the underlying logical calculus is built for reasoning with gaps and for providing strategic directions, (2) the mathematical frame (...) is a definitional extension of Zermelo–Fraenkel set theory and has a hierarchically organized structure of concepts and operations, and (3) the construction of formal proofs is deeply connected to the frame through rules for definitions and lemmas. To bring these general ideas to life, we examine, as a case study, proofs of the Cantor–Bernstein Theorem that do not appeal to the principle of choice. A thorough analysis of the multitude of “different” informal proofs seems to reduce them to exactly one. The natural formalization confirms that there is one proof, but that it comes in two variants due to Dedekind and Zermelo, respectively. In this way it enhances the conceptual understanding of the represented informal proofs. The formal, computational work is carried out with the proof search system AProS that serves as a proof assistant and implements the above inference mechanism; it can be fully inspected at (see link below). (shrink)