Volume I provides a detailed analysis of cylindric algebras, starting with a formulation of their axioms and a development of their elementary properties, and proceeding to a deeper study of their interrelationships by means of general algebraic notions such as subalgebras, homomorphisms, direct products, free algebras, reducts and relativized algebras.

Building on the seminal work of Kit Fine in the 1980s, Leon Horsten here develops a new theory of arbitrary entities. He connects this theory to issues and debates in metaphysics, logic, and contemporary philosophy of mathematics, investigating the relation between specific and arbitrary objects and between specific and arbitrary systems of objects. His book shows how this innovative theory is highly applicable to problems in the philosophy of arithmetic, and explores in particular how arbitrary objects can engage with (...) the nineteenth-century concept of variable mathematical quantities, how they are relevant for debates around mathematical structuralism, and how they can help our understanding of the concept of random variables in statistics. This fully worked through theory will open up new avenues within philosophy of mathematics, bringing in the work of other philosophers such as Saul Kripke, and providing new insights into the development of the foundations of mathematics from the eighteenth century to the present day. (shrink)

A collection of papers dealing with history as a way of knowing, not a mode of discourse.

§1. Introduction. This paper deals with aspects of my doctoral dissertation which contributed to the early development of model theory. What was of use to later workers was less the results of my thesis, than the method by which I proved the completeness of first-order logic—a result established by Kurt Gödel in his doctoral thesis 18 years before.The ideas that fed my discovery of this proof were mostly those I found in the teachings and writings of Alonzo Church. This may (...) seem curious, as his work in logic, and his teaching, gave great emphasis to the constructive character of mathematical logic, while the model theory to which I contributed is filled with theorems about very large classes of mathematical structures, whose proofs often by-pass constructive methods.Another curious thing about my discovery of a new proof of Gödel's completeness theorem, is that it arrived in the midst of my efforts to prove an entirely different result. Such “accidental” discoveries arise in many parts of scientific work. Perhaps there are regularities in the conditions under which such “accidents” occur which would interest some historians, so I shall try to describe in some detail the accident which befell me.A mathematical discovery is an idea, or a complex of ideas, which have been found and set forth under certain circumstances. The process of discovery consists in selecting certain input ideas and somehow combining and transforming them to produce the new output ideas. The process that produces a particular discovery may thus be represented by a diagram such as one sees in many parts of science; a “black box” with lines coming in from the left to represent the input ideas, and lines going out to the right representing the output. To describe that discovery one must explain what occurs inside the box, i.e., how the outputs were obtained from the inputs. (shrink)

Excerpt from La Théorie Platonicienne des Idées Et des Nombres d'Après Aristote: Étude Historique Et Critique La théorie phtonioionno de l'amour. Vol. Ia-8 de la Collection historique des grands philosophes 3 fr. 75. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the (...) aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

In his book The future of human nature, Jürgen Habermas argues against a scenario of liberal eugenics, in which parents are free to prenatally manipulate their children’s genetic constitution via germline interventions. In this paper, I draw attention to the fact that his species‐ethical line of argument is pervaded by a substantial ambiguity between an argument from actual intervention (AAI) and an argument from mere controllability (AMC). Whereas the first argument focuses on threats for the autonomy and equality of prenatally (...) modified persons, the second argument takes all human beings, whether they have been modified or not, into account. Hence, when invoking Habermas in these debates, bioethicists need to consider carefully which argument they are referring to. (shrink)

The role played by witnesses of bullying in nursing settings remains little studied, despite their potential relevance in explaining the onset and development of bullying. The objective of this study was to develop a model to account for witnesses’ intention to help and helping behaviour in response to bullying in a nursing setting. Three hundred and thirty‐seven witnesses completed self‐report measures of variables predicting intention to help and helping behaviour. A full structural model was constructed using structural equation modelling. The (...) intention to help victims was elicited by tension, group identity, support to peers’ initiative to intervene and absence of fear of retaliation. However, engagement in helping behaviour was only predicted by the absence of fear of retaliation. This study shows that witnesses of bullying in nursing settings do not remain impassive, but their experienced discomfort and intention to help victims is not sufficient to predict helping behaviour. Fear of possible retaliation if intervening in favour of victims constitutes a crucial factor explaining witnesses’ hesitation to help victims. Several implications for the implementation of policies directed at eradicating bullying in nursing settings are discussed. (shrink)

Over the course of the last four decades, William Leon McBride has distinguished himself as one of the most esteemed and accomplished philosophers of his generation. This volume—which celebrates the occasion of his seventy-fifth birthday—includes contributions from colleagues, friends, and formers students and pays tribute to McBride’s considerable achievements as a teacher, mentor, and scholar.

In a contribution to a symposium on “Causality in the Social Sciences,” Lewis Feuer remarks in passing that “Functionalism, in the form which Malinowski gave it, affirms that culture is an ‘organic unity’; it is the principle that in every culture, each custom, belief, and behavioral form ‘represents an indespensible part within a working whole.’” That culture is an integrated and organic unity is a view found quite often in the writings of Malinowski, though he does not maintain it with (...) full consistency. Sometimes he seems to say that a culture is made up of a number of grand institutions, each of which is an integrated unity, though the totality need not be. But whether affirmed or denied this thesis is not the doctrine, characteristic of almost every attempt made by Malinowski to explain cultural phenomena during the last quarter century of his life, which may be properly called “Malinowskian functionalism.” And that the doctrine cited by Feurer is sometimes formulated in such a way that the term “functional” or some variant is used, as in “culture is a functionally integrated organic unity,” makes no difference to my claim. I am not at all certain that the addition of the word “functionally” does anything for the view in question; it surely makes no difference to its scientific sterility. But that apart, the point I wish to make here is that a good many scholars who make references to Malinowski's functionalism have never bothered to discover just what in the world this is. They have been all too ready to cite the vague programmatic pronouncements in which Malinowski's writings abound, while seemingly oblivious to the fact that with rare exception every major attempt by Malinowski to account systematically for some kind of sociocultural phenomena reveals one and the same pattern of explanation. And it is this pattern alone which may be spoken of as Malinowski's method of functional analysis. (shrink)

The chief aim of the paper is to extend the calculusDSC 1 (see [4]) in such a way as to satisfy all the requirements listed in [4] as well as a further stipulation — called the principle of uninvolvement — to the effect that neither deontic compatibility nor deontic incompatibility of codes (see [2]) should be presupposed in deontic logic.

Some requirements concerning deontic logic are formulated and discussed. Stress is laid on the need to distinguish between theories and deductive systems. It is argued that deontic theories need not be closed under the rule of detachment. Two deontic calculi, called DSC1, DSC2, are presented and talked over.

Trust, as a philosophical concept in education, seems largely taken for granted, either because it is embedded in other discourses, or is self-evidently assumed to be one on which there is general agreement and understanding. Its associated notions, such as confidence and belief, have counters in such concepts as disappointment and betrayal. These various notions come to the fore in interpersonal relations that require openness and self-critique. Critically reflective practice in professional teaching contexts is one such example, where openness means (...) that people involved may experience vulnerability. I will argue that the development of critically reflective practice is impossible in the absence of trust, and will take the position that trust requires the trustor to be vulnerable to betrayal. I draw on some findings of an ongoing research study in a selection of New Zealand schools, during which I have found that many participants attempt to connect reflective practice to appraisal, a move which, in light of what I present in relation to trust, I argue should be resisted. (shrink)