This paper introduces the notion of syntactic feature to provide a unified treatment of earlier model theoretic proofs of both the compactness and interpolation theorems for a variety of two valued logics including sentential logic, first order logic, and a family of modal sentential logic includingM,B,S 4 andS 5. The compactness papers focused on providing a proof of the consequence formulation which exhibited the appropriate finite subset. A unified presentation of these proofs is given by isolating their essential feature and (...) presenting it as an abstract principle about syntactic features. The interpolation papers focused on exhibiting the interpolant. A unified presentation of these proofs is given by isolating their essential feature and presenting it as a second abstract principle about syntactic features. This second principle reduces the problem of exhibiting the interpolant to that of establishing the existence of a family of syntactic features satisfying certain conditions. The existence of such features is established for a variety of logics (including those mentioned above) by purely combinatorial arguments. (shrink)
A Dedekind algebra is an ordered pair (B, h), where B is a non-empty set and h is a similarity transformation on B. Among the Dedekind algebras is the sequence of the positive integers. From a contemporary perspective, Dedekind established that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable. The purpose here is to show that this seemingly isolated result is a consequence of more general results in the model theory of second-order languages. (...) Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are ?0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on ? called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type that occurs in the decomposition of the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. The second-order theory of any countably infinite Dedekind algebra is categorical, and there are countably infinite Dedekind algebras whose second-order theories are not finitely axiomatizable. It is shown that there is a condition on configuration signatures necessary and sufficient for the second-order theory of a Dedekind algebra to be finitely axiomatizable. It follows that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable. (shrink)
A Dedekind Algebra is an ordered pair (B,h) where B is a non-empty set and h is an injective unary function on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called configurations of the Dedekind algebra. There are N0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on omega called its configuration signature. The configuration signature of a Dedekind algebra counts the number of configurations in the decomposition of the (...) algebra in each isomorphism type.The configuration signature of a Dedekind algebra encodes the structure of that algebra in the sense that two Dedekind algebras are isomorphic iff their configuration signatures are identical. Configuration signatures are used to establish various results in the first-order model theory of Dedekind algebras. These include categoricity results for the first-order theories of Dedekind algebras and existence and uniqueness results for homogeneous, universal and saturated Dedekind algebras. Fundamental to these results is a condition on configuration signatures that is necessary and sufficient for elementary equivalence. (shrink)
Much of the inspiration for structuralist approaches to mathematics can be found in the late nineteenth- and early twentieth-century program of characterizing various mathematical systems upto isomorphism. From the perspective of this program, differences between isomorphic systems are irrelevant. It is argued that a different view of the import of the differences between isomorphic systems can be obtained from the perspective of contemporary discussions of representation theorems and that from this perspective both the identification of isomorphic systems and the reduction (...) to abstract structures or patterns should be resisted. (shrink)
After an introduction which demonstrates the failure of the equational analogue of Beth?s definability theorem, the first two sections of this paper are devoted to an elementary exposition of a proof that a functional constant is equationally definable in an equational theory iff every model of the set of those consequences of the theory that do not contain the functional constant is uniquely extendible to a model of the theory itself.Sections three, four and five are devoted to applications and extensions (...) of this result.Topics considered here include equational definability in first order logic, an extended notion of definability in equational logic and the synonymy of equational theories.The final two sections briefly review some of the history of equational logic. (shrink)
Senior managers are important to the successful management of ethics in organizations. Therefore, their perceptions of organizational ethics are important. In this study, we propose that senior managers are likely to have a more positive perception of organizational ethics than lower level employees do largely because of their managerial role and their corresponding identification with the organization and need to protect the organization’s image as well as their own identity. Bycontrast, lower level employees are more likely to be cynical about (...) the organization’s ethics. In order to compare senior managers’ and lower level employees’ perceptions of ethics in the organization, we surveyed randomly selected senior managers and lower level employees in three firms. We found that perceptions of ethics in the organization differed predictably across levels, with senior managers’ perceptions being significantly more positive and lower level employees’ perceptions being more negative. Implications for practice and research are discussed. (shrink)
A Dedekind algebra is an order pair (B, h) where B is a non-empty set and h is a similarity transformation on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are 0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type which occur in the decomposition of (...) the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. It is shown that configuration signatures can be used to characterize the homogeneous, universal and homogeneous-universal Dedekind algebras. This characterization is used to prove various results about these subclasses of Dedekind algebras. (shrink)
Among the complete 0-categorical theories with finite non-logical vocabularies, we distinguish three classes. The classification is obtained by looking at the number of bound variables needed to isolated complete types. In classI theories, all types are isolated by quantifier free formulas; in classII theories, there is a leastm, greater than zero, s.t. all types are isolated by formulas in no more thanm bound variables: and in classIII theories, for eachm there is a type which cannot be isolated inm or fewer (...) bound variables. ClassII theories are further subclassified according to whether or not they can be extended to classI theories by the addition of finitely many new predicates. Alternative characterizations are given in terms of quantifier elimination and homogeneous models. It is shown that for each primep, the theory of infinite Abelian groups all of whose elements are of orderp is classI when formulated in functional constants, and classIII when formulated in relational constants. (shrink)
Clark and Krauss [1977] presents a classification of complete, satisfiable and o-categorical theories in first order languages with finite non-logical vocabularies. In 1988 the first author modified this classification and raised three questions about the distribution of finitely axiomatizable theories. This paper answers two of those questions.
Even if there were widespread cross-cultural agreement on the normative issues of business ethics, corporate ethics management initiatives (e.g., codes of conduct, ethics telephone lines, ethics offices) which are appropriate in one cultural setting still could fail to mesh with the management practices and cultural characteristics of a different setting. By uncritically adopting widely promoted American practices for managing corporate ethics, multinational businesses risk failure in pursuing the ostensible goals of corporate ethics initiatives. Pursuing shared ethical goals by means of (...) culturally inappropriate management practices, in short, can undermine the effectiveness of ethics management efforts. This article explicates how several important dimensions of culture can influence the effectiveness of common ethics initiatives, and recommends the development and application of a culture-structure contingency analysis in the task of encouraging ethical behavior in global businesses. (shrink)
This empirical study of Fortune 1000 firms assesses the degree to which those firms have adopted various practices associated with corporate ethics programs. The study examines the following aspects of formalized corporate ethics activity: ethics-oriented policy statements; formalization of management responsibilities for ethics; free-standing ethics offices; ethics and compliance telephone reporting/advice systems; top management and departmental involvement in ethics activities; usage of ethics training and other ethics awareness activities; investigatory functions; and evaluation of ethics program activities. Results show a high (...) degree of corporate adoption of ethics policies, but wide variability in the extent to which these policies are implemented by various supporting structures and managerial activities. In effect, the vast majority of firms have committed to the low cost, possibly symbolic side of ethics management (e.g., adoption of ethics codes and policies, etc.). But firms differ substantially in their efforts to see that those policies or codes actually are put into practice. (shrink)
Sodium monofluoroacetate (1080) is a mammalian pesticide used in different parts of the world for the control of mammalian pest species. In New Zealand it is used extensively and very successfully as a conservation management tool for the control of brushtail possums (Trichosurus vulpecula) – an introduced marsupial that has become a substantial agricultural and conservation management pest. Possums pose a threat to cattle farming in New Zealand as they are a vector for bovine tuberculosis. In protected natural areas, possum (...) browsing is responsible for large scale defoliation of native vegetation. As with many other pesticides, there has been some degree of popular concern about the use of this toxin and its safety, with particular reference to non-target effects. These concerns have been associated with potential non-target effects on human health, and the health of animals of recreational value (e.g., hunting dogs and game animals). This has led to the development of a strong “anti-1080” lobby in New Zealand. In contrast, this study encompasses a science-based risk analysis focusing on the potential risks to non-target native wildlife with a particular focus on chronic toxicity. It finds that there is evidence that 1080 may have endocrine disrupting capabilities (with potential relevance for non-target wildlife) but that this still needs more detailed investigation. This can be clarified by further targeted research. Further research is also needed to test the degradation rates of 1080 and its breakdown products at ecologically-relevant temperatures (i.e., winter stream temperatures – below 11 °C). Such research may demonstrate that some adjustment to 1080 risk management is warranted in New Zealand, or it may help to put to rest the current controversy over the use of this cost effective conservation management tool. (shrink)
This article examines perceptions of tax partners and non-partner tax practitioners regarding their CPA firms’ ethical environment, as well as experiences with ethical dilemmas. Prior research emphasizes the importance of executive leadership in creating an ethical climate (e.g., Weaver et al., Acad Manage Rev 42(1):41–57, 1999 ; Trevino et al., Hum Relat 56(1):5–37, 2003 ; Schminke et al., Organ Dyn 36(2):171–186, 2007 ). Thus, it is important to consider whether firm partners and other employees have congruent perceptions and (...) experiences. Based on the responses of 144 tax practitioners employed at CPA firms, the results show that tax partners rate the ethical environment of their firms as stronger than non-partner tax practitioners, particularly among those who describe a self-identified ethical dilemma. Tax partners also report having encountered more of the common examples of researcher-provided ethical dilemmas than non-partner tax practitioners, although non-partners perceive that certain ethical dilemmas occur at a higher rate than partners do. Overall, this study provides evidence of a disconnect between tax partners and non-partner tax practitioners with respect to perceptions of organizational ethics. Suggestions for potential remedies are offered. (shrink)
This article sketches a theory of time-binding communication, which is to say communication that unifies widely separated times much as space-binding communication unifies widely separated places. Drawing from the work of Harold Innis, it first describes the function and character of time-binding communication as a means to social continuity. Then, following Alasdair MacIntyre and Michael Oakshott, it explains the nature and necessary circumstances of this sort of time-binding communication, or tradition. It discusses the character, consequences, and causes of decadence - (...) radical discontinuity - as these have been described by Richard Weaver, C. E. M. Joad, and Jacques Barzun. Finally, it turns to David Lowenthal's notion of the past as a 'foreign country' in an effort to explain the relations between modernity and both tradition and decadence, as well as the geography of tradition and decadence in the modern world. (shrink)
Reductionism--understanding complex processes by breaking them into simpler elements--dominates scientific thinking around the world and has certainly proved a powerful tool, leading to major discoveries in every field of science. But reductionism can be taken too far, especially in the life sciences, where sociobiological thinking has bordered on biological determinism. Thus popular science writers such as Richard Dawkins, author of the highly influential The Selfish Gene, can write that human beings are just "robot vehicles blindly programmed to preserve the selfish (...) molecules known as genes." Indeed, for many in science, genes have become the fundamental unit for understanding human existence: genes determine every aspect of our lives, from personal success to existential despair: genes for health and illness, genes for criminality, violence, and sexual orientation. Others would say that this is reductionism with a vengeance. In Lifelines, biologist Steven Rose offers a powerful alternative to the ultradarwinist claims of Dawkins, E.O. Wilson, Daniel Dennett and others. Rose argues against an extreme reductionist approach that would make the gene the key to understanding human nature, in favor of a more complex and richer vision of life. He urges instead that we focus on the organism and in particular on the organism's lifeline: the trajectory it takes through time and space. Our personal lifeline, Rose points out, is unique--even identical twins, with identical genes at birth, will differ over time. These differences are obviously not embedded in our genes, but come about through our developmental trajectory in which genes, as part of the biochemical orchestra of trillions of cells in each human body, have an important part--but only a part--to play. To illustrate this idea, Rose examines recent research in modern biology, and especially two disciplines--genetics (which looks at the impact of genes on form) and developmental biology (which examines the interaction between the organism and the environment)--and he explores new ideas on biological complexity proposed by scientists such as Stuart Kauffman. He shows how our lifelines are constructed through the interplay of physical forces--such as the intrinsic chemistry of lipids and proteins, and the self-organizing and stabilizing properties of complex metabolic webs--and he reaches a startling conclusion: that organisms are active players in their own fate, not simply the playthings of the gods, nature, or the inevitable workings out of gene-driven natural selection. The organism is both the weaver and the pattern it weaves. Lifelines will be a rallying point for all who seek an alternative to the currently fashionable, deeply determinist accounts which dominate popular science writing and, in fact, crowd the pages of some of the major scientific journals. Based on solid, state-of-the-art research, it not only makes important contributions to our understanding of Darwin and natural selection, but will swing the pendulum back to a richer, more complex view of human nature and of life. (shrink)
Fred Dretske's "Knowledge and the Flow of Information" is an extended attempt to develop a philosophically useful theory of information. Dretske adapts central ideas from Shannon and Weaver's mathematical theory of communication, and applies them to some traditional problems in epistemology. In doing so, he succeeds in building for philosophers a much-needed bridge to important work in cognitive science. The pay-off for epistemologists is that Dretske promises a way out of a long-standing impasse -- the Gettier problem. He offers (...) an alternative model of knowledge as information-based belief, which purports to avoid the problems justificatory accounts face. This essay looks closely at Dretske's theory. I argue that while the information-theoretic framework is attractive, it does not provide an adequate account of knowledge. And there seems to be no way of tightening the theory without introducing some version of a theory of justification -- the very notion Dretske's theory was designed to avoid. (shrink)
