We discuss saturating ultrafilters on N, relating them to other types of nonprincipal ultrafilter. (a) There is an (ω,c)-saturating ultrafilter on $\mathbf{N} \operatorname{iff} 2^\lambda \leq \mathfrak{c}$ for every $\lambda and there is no cover of R by fewer than c nowhere dense sets. (b) Assume Martin's axiom. Then, for any cardinal κ, a nonprincipal ultrafilter on N is (ω,κ)-saturating iff it is almost κ-good. In particular, (i) p(κ)-point ultrafilters are (ω,κ)-saturating, and (ii) the set of (ω,κ)-saturating ultrafilters is invariant under (...) homeomorphisms of $\beta\mathbf{N\backslash N}$ . (c) It is relatively consistent with ZFC to suppose that there is a Ramsey p(c)-point ultrafilter which is not (ω,c)-saturating. (shrink)

Reviewed Works:Andreas Blass, Saharon Shelah, Ultrafilters with Small Generating Sets.Andreas Blass, Saharon Shelah, There May Be Simple $P_{\aleph_1}$- and $P_{\aleph_2}$-Points and the Rudin-Keisler ordering may be downward directed.Andreas Blass, Near Coherence of Filters. II: Applications to Operator Ideals, the Stone- Cech Remainder of a Half-Line, Order Ideals of Sequences, and the Slenderness of Groups.Andreas Blass, Saharon Shelah, Near Coherence of Filters III: A Simplified Consistency Proof.Andreas Blass, Claude Laflamme, Consistency Results About Filters and the Number of Inequivalent Growth Types.Andreas Blass, (...) J. Steprans, S. Watson, Applications of Superperfect Forcing and Its Relatives.Andreas Blass, Saharon Shelah, Ultrafilters with Small Generating Sets. (shrink)

Critically discussing the causal social ontologies presented by Dave Elder-Vass and John Searle, the article argues that these views implausibly identify the causal ontological source of human sociality in collectively known, recognized and accepted statuses, criteria, norms and the like. This is implausible, for it ignores human sociality as occurring in temporally and spatially dispersed on-going processes of human interaction of differently placed, often unequal, and thus epistemically differently equipped actors in division of labour. Human scientific concepts are best seen (...) as picking out (aspects of) such complex and heterogeneous processes, not what the participating actors allegedly collectively know, accept or recognize about them. The article observes that similar appeals to collective recognition are also common in Wittgensteinian literature that, however, have claimed to reject the causal ontological view. It is argued that the ultimate value in rejecting the causal ontological view, and the accompanying idea of collective recognition, resides in that we thereby avoid epistemically homogenizing and over-intellectualizing the diverse mass of dispersed, often unequal, but interacting actors. (shrink)

Distributed Leadership (DL) is a feature of education in many jurisdictions. Similarly, in Ireland the principles of DL have been adopted as part of a quality framework to underpin a system that provides high quality student care, learning and teaching. This model necessitates an alignment of senior leaders (SLs) and middle leaders (MLs) whose actions are informed by the needs and priorities of their particular school. The traditional notion of the ML position as a management position is changing. The evolution (...) requires a reconceptualisation, a transformation of the role and how we support and develop it to ensure that MLs are an integral part of the leadership structure of the school. This pragmatic research explored the PD needs of MLs in Irish, Education and Training Board (ETB) post-primary schools. It involved a mixed-methods, exploratory sequential study. Stage one involved a set of five semi structured interviews with AP I post holders. These were used as an instrument to develop the online surveys. Stage two involved quantitative research. Online surveys were distributed to all ETB schools in the republic of Ireland. In stage three a summary of the findings of the survey were shared with ten AP Is who were subsequently interviewed to gain further insights. The study illustrated that the development of MLs requires the support of SLs, skills development, a supportive school culture and combined training for senior and middle leaders which should be facilitated by an independent person. (shrink)

Cartesian representationalism and the Enlightenment heritage more broadly continue to play a pivotal role in shaping the 21st-century human scientific theory and practice. This introduction to a special section on the topic surveys some aspects of that heritage.

Miracle and miracle narrative against the background of myth and demythologizing.Religio-scientific perspectives on communication, language, reality conception, myth and the world of the sacred, as well as a different angle on demythologizing, are utilised in formulating a broad theological view of miracles, miracle experiences and miracle narratives.

Between 1787, and the end of his life in 1832, Bentham turned his attention to the development and application of economic ideas and principles within the general structure of his legislative project. For seventeen years this interest was manifested through a number of books and pamphlets, most of which remained in manuscript form, that develop a distinctive approach to economic questions. Although Bentham was influenced by Adam Smith's An Inquiry into the Nature and Causes of the Wealth of Nations, he (...) neither adopted a Smithian vocabulary for addressing questions of economic principle and policy, nor did he accept many of the distinctive features of Smith's economic theory. One consequence of this was that Bentham played almost no part in the development of the emerging science of political economy in the early nineteenth century. The standard histories of economics all emphasize how little he contributed to the mainstream of late eighteenth and early nineteenth-century debate by concentrating attention on his utilitarianism and the psychology of hedonism on which it is premised. Others have argued that the calculating nature of his theory of practical reason reduced the whole legislative project to a crude attempt to apply economics to all aspects of social and political life. Put at its simplest this argument amounts to the erroneous claim that Bentham's science of legislation is reducible to the science of political economy. A different but equally dangerous error would be to argue that because Bentham's conception of the science of legislation comprehends all the basic forms of social relationships, there can be no science of political economy as there is no autonomous sphere of activity governed by the principles of economics. This approach is no doubt attractive from an historical point of view given that the major premise of this argument is true, and that many of Bentham's ‘economic’ arguments are couched in terms of his theory of legislation. Yet it fails to account for the undoubted importance of political economy within Bentham's writings, not just on finance, economic policy, colonies and preventive police, but also in other aspects of his utilitarian public policy such as prison reform, pauper management, and even constitutional reform. All of these works reflect a conception of political economy in its broadest terms. However, this conception of political economy differs in many respects from that of Bentham's contemporaries, and for this reason Bentham's distinctive approach to problems of economics and political economy has largely been misunderstood. (shrink)

In his paper ‘Has the Ontological Argument Been Refuted?’, 97–110) William F. Vallicella argues that my attempt to show that the Ontological Argument begs the question is unsuccessful. 1 I believe he is wrong about this, but before endeavouring to vindicate my position I must first make clear what precisely is the point at issue between us. The Ontological Argument is not a single argument, but a family of arguments. Newly devised formulations of the argument are frequently put forward by (...) philosophers in an effort to avoid difficulties that have been pointed out in previous versions. As a consequence there is no possibility of a conclusive proof that every form of the argument embodies the same fallacy. Nevertheless, one can, I believe, prove that all the standard versions of the argument embody a certain fallacy and that, given the nature of the argument, it is therefore unlikely that the argument can be formulated in such a way as to avoid this difficulty. What I tried to show in my paper is that the six best-known versions of the argument all beg the question and that they do so at the same point in the argument, namely when it is asserted that it is possible that an absolutely perfect being exists. It is difficult to see how an ontological argument could be formulated without including this claim as one of its premises, since the distinguishing badge of the argument is the inference from the possibility of an absolutely perfect being to its actuality. It must be unlikely then, if my criticism of these six versions is correct, that there is any way of formulating the argument that avoids this fallacy. (shrink)