In 1941, Tarski published an abstract, finitely axiomatized version of the theory of binary relations, called the theory of relation algebras, He asked whether every model of his abstract theory could be represented as a concrete algebra of binary relations. He and Jonsson obtained some initial, positive results for special classes of abstract relation algebras. But Lyndon showed, in 1950, that in general the answer to Tarski's question is negative. Monk proved later that the answer remains negative even if one (...) adjoins finitely many new axioms to Tarski's system. In this paper we describe a far-reaching generalization of the positive results of Jonsson and Tarski, as well as of some later, related results of Maddux. We construct a class of concrete models of Tarski's axioms-called coset relation algebras-that are very close in spirit to algebras of binary relations, but are built using systems of groups and cosets instead of elements of a base set. The models include all algebras of binary relations, and many non-representable relation algebras as well, We prove that every atomic relation algebra satisfying a certain measurability condition-a condition generalizing the conditions imposed by Jonsson and Tarski-is essentially isomorphic to a coset relation algebra. The theorem raises the possibility of providing a positive solution to Tarski's problem by using coset relation algebras instead of the standard algebras of binary relations. (shrink)

An introduction to logic from the perspective of algebra.

It is shown that the automorphism group of a relation algebra ${\cal B}_P$ constructed from a projective geometry P is isomorphic to the collineation group of P. Also, the base automorphism group of a representation of ${\cal B}_P$ over an affine geometry D is isomorphic to the quotient of the collineation group of D by the dilatation subgroup. Consequently, the total number of inequivalent representations of ${\cal B}_P$ , for finite geometries P, is the sum of the numbers ${\mid Col(P)\mid\over (...) {\mid Col(D)\mid/\mid Dil(D)\mid}}$ where D ranges over a list of the non-isomorphic affine geometries having P as their geometry at infinity. This formula is used to compute the number of inequivalent representations of relation algebras constructed over projective lines of order at most 10. For instance, the relation algebra constructed over the projective line of order 9 has 56,700 mutually inequivalent representations. (shrink)

We investigate a notion called uniqueness in power κ that is akin to categoricity in power κ, but is based on the cardinality of the generating sets of models instead of on the cardinality of their universes. The notion is quite useful for formulating categoricity-like questions regarding powers below the cardinality of a theory. We prove, for universal theories T, that if T is κ-unique for one uncountable κ, then it is κ-unique for every uncountable κ; in particular, it is (...) categorical in powers greater than the cardinality of T. (shrink)

This paper is an edited form of a letter written by the two authors (in the name of Tarski) to Wolfram Schwabhäuser around 1978. It contains extended remarks about Tarski's system of foundations for Euclidean geometry, in particular its distinctive features, its historical evolution, the history of specific axioms, the questions of independence of axioms and primitive notions, and versions of the system suitable for the development of 1-dimensional geometry.

Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin, Monk and Tarski [13]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result (...) to other classes of algebras of logic, for example quasi-polyadic algebras and substitution-cylindrification algebras with and without equality, relation algebras, and special Boolean monoids. The results of op. cit. mentioned above are special cases of our general theorems. We point out an error in the proof of the Henkin-Monk-Tarski representation theorem for atomic, equality-free, quasi-polyadic algebras with rectangular atoms. The error consists in the implicit assumption of a property that does not, in general, hold. We then give a correct proof of their theorem. Henkin and Tarski also introduced the notion of a rich cylindric algebra and proved in op. cit. that every rich cylindric algebra of finite dimension satisfying certain special identities is representable. We introduce a modification of the notion of a rich algebra that, in our opinion, renders it more natural. In particular, under this modification richness becomes a density notion. Moreover, our notion of richness applies not only to algebras with equality, such as cylindric algebras, but also to algebras without equality. We show that a finite dimensional algebra is rich iff it is rectangularly dense and quasi-atomic; moreover, each of these conditions is also equivalent to a very natural condition of point density . As a consequence, every finite dimensional rich algebra of logic is representable. We do not have to assume the validity of any special identities to establish this representability. Not only does this give an improvement of the Henkin-Tarski representation theorem for rich cylindric algebras, it solves positively an open problem in op. cit. concerning the representability of finite dimensional rich quasi-polyadic algebras without equality. (shrink)

A series of nonrepresentable relation algebras is constructed from groups. We use them to prove that there are continuum many subvarieties between the variety of representable relation algebras and the variety of coset relation algebras. We present our main construction in terms of polygroupoids.

We shall show that certain natural and interesting intervals in the lattice of varieties of representable relation algebras embed the lattice of all subsets of the natural numbers, and therefore must have a very complicated lattice-theoretic structure.

This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the (...) authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. They provide researchers in algebra and logic with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic. (shrink)

It is shown that Tarski’s set of ten axioms for the calculus of relations is independent in the sense that no axiom can be derived from the remaining axioms. It is also shown that by modifying one of Tarski’s axioms slightly, and in fact by replacing the right-hand distributive law for relative multiplication with its left-hand version, we arrive at an equivalent set of axioms which is redundant in the sense that one of the axioms, namely the second involution law, (...) is derivable from the other axioms. The set of remaining axioms is independent. Finally, it is shown that if both the left-hand and right-hand distributive laws for relative multiplication are included in the set of axioms, then two of Tarski’s other axioms become redundant, namely the second involution law and the distributive law for converse. The set of remaining axioms is independent and equivalent to Tarski’s axiom system. (shrink)

Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but most of the Aristotelian corpus is not about logic, whereas (...) virtually everything written by Tarski concerns logic more or less directly. There is no doubt that Tarski wrote more on logic than any other author; he started publishing on logic in 1921 at the age of 20 and continued until his death at the age of 82. Two of his works appeared posthumously [Hist. Philos. Logic 7 (1986), no. 2, 143--154; MR0868748 (88b:03010); Tarski and Givant, A formalization of set theory without variables, Amer. Math. Soc., Providence, RI, 1987; MR0920815 (89g:03012)]. Tarski's voluminous writings were widely scattered in numerous journals, some quite rare. It has been extremely difficult to study the development of Tarski's thought and to trace the interconnections and interdependence of his various papers. Thanks to the present collection all this has changed, and it is likely that the increased accessibility of Tarski's papers will have the effect of increasing Tarski's already enormous influence. (shrink)

Weinberg's 1972 work, in his description, had two purposes. The first was practical to bring together and assess the wealth of data provided over the previous decade while realizing that newer data would come in even as the book was being printed. He hoped the comprehensive picture would prepare the reader and himself to that new data as it emerged. The second was to produce a textbook about general relativity in which geometric ideas were not given a starring role for (...) (in his words) too great an emphasis on geometry can only obscure the deep connections between gravitation and the rest of physics. (shrink)

This paper presents a way of thinking about how to respond to the pluralism of modern societies that avoids any commitment to contractualist norms of political justification. The argument developed appeals to the notion of a constitutional settlement. Constitutional settlements are complex on-going social practices that both express certain values to which political societies are committed and establish procedures for resolving disputes among members of these societies. As such, they are a product of both moral commitment and the balance of (...) power. The paper shows how constitutional settlements relate to issues of stability and non-subjugation in politics, and explains how they can ground a distinction between justice and legitimacy. (shrink)

In the only two articles on the topic of which I am aware, Chad Carlson and Scott Aikin have leveled three objections against fantasy sports—namely, that participation in fantasy sports elicits...

In this paper, I build on Wittgenstein’s metaphor of a toolbox to introduce the metaphor of ‘tool confusion’ – how differing conceptual constructs may be applied, or misapplied, to one another and the effect that such applications have on the advancement of management theory. Moving beyond metaphor, I investigate a theory of management through two specific philosophical lenses (Popper and Lyotard). This analysis tests both the theory and the philosophies with regard to how each philosophy may be applied as a (...) tool to advance theory towards more effective application. Preliminary conclusions confirm that the application of partial philosophies is not as useful as the application of complete philosophies. Deeper contemplation, however, suggests that there is no upper limit to the completeness of philosophies. Thus, the problem of completeness is inescapable. In place of completeness, I explore the use of perceptual tools that are more specific, foundational and concise. Engaging in a second investigation, I use structures of logic (circular, linear, branching and co-causal) to investigate the subject theory. This investigation suggests at least two important insights relating to the structure of theory and the fuzziness of theory. Combined, these investigations and related conversations suggest rigorous methods for advancing theories and a more normative role for the philosophy of management that will support the accelerated advancement of management theory and practice. (shrink)

This paper articulates and defends a novel hybrid account of well-being. We will call our view a Robust Hybrid. We call it robust because it grants a broad and not subservient role to both objective and subjective values. In this paper we assume, we think plausibly but without argument, that there is a significant objective component to well-being. Here we clarify what it takes for an account of well-being to have a subjective component. Roughly, we argue, it must allow that (...) favoring attitudes that are not warranted by the lights of objective values can ground benefits. Given this understanding, we show that there is an important and unrecognized expansion in the resources available to fully objectivist views: namely that such views can help themselves to the value of warranted love of objective goods. Such a move by the objectivist can help them respond to concerns that, on their view, a person’s well-being can be too alien to them. We next argue that, nonetheless, such objectivist views are still unconvincing due to their lack of a subjective component. This motivates a move from fully objective accounts to hybrid accounts. We show that many prominent hybrid theories in the literature are inadequate because they implausibly minimize the subjective component. This motivates a move to a robust hybrid view that has an expanded subjectivist component. We conclude with some remarks about the interrelation between the subjective and objective components in the hybrid account that we favor and a role for resonance in a theory of well-being other than serving as a hard constraint on any benefit. (shrink)

Many writers claim that democratic government rests on a principled commitment to the ideal of political equality. The ideal of political equality holds that political institutions ought to be arranged so that they distribute political standing equally to all citizens. I reject this common view. I argue that the ideal of political equality, under its most plausible characterizations, lacks independent justificatory force. By casting doubt on the ideal of political equality, I provide indirect support for the claim that democratic government (...) is only instrumentally justified. (shrink)

Purpose – The purpose of this paper is to investigate the internal structure of Gandhi's ethics as a way to determine opportunities for improving that system's ability to influence behavior. In this paper, the author aims to work under the idea that a system of ethics is a guide for social responsibility. -/- Design/methodology/approach – The data source is Gandhi's set of ethics as described by Naess. These simple (primarily quantitative) studies compare the concepts within the code of ethics, and (...) their relationships to one another. -/- Findings – Gandhi's ethics are robust at the 0.25 level (the scale is zero to one – zero is lowest). This is consistent with theories of the social sciences (that do not work well in practice). Gandhi's success might be ascribed to his leadership ability. -/- Research limitations/implications – Some suggest this approach is reductionist because of its superficial similarity to approaches of physical science. The implications for research are profound. First, this approach provides an objective method for comparing (and so, advancing) systems of ethics. Second, this paper suggests the opportunity to compare the internal structure of ethics with “external” aspects – the implementation of ethical systems. -/- Practical implications – By itself, Gandhi's system of ethics cannot be reliably applied in practice - it cannot be expected to change behavior more than any other system of ethics. This raises concerns about other ethical codes as well. The practical implications of the form of analysis presented in this paper are immense because it provides a way for practitioners to objectively compare two codes of ethics and determine which one will be more effective. -/- Originality/value – The approach documented in the paper has never been applied to the field of ethics. It is unique in that it addresses the “internal” structure of a system of ethics (compared to the “external”, or application, of ethical systems). (shrink)

When creating theory to understand or implement change at the social and/or organizational level, it is generally accepted that part of the theory building process includes a process of abstraction. While the process of abstraction is well understood, it is not so well understood how abstractions “fit” together to enable the creation of better theory. Starting with a few simple ideas, this paper explores one way we work with abstractions. This exploration challenges the traditionally held importance of abstracting concepts from (...) experience. That traditional focus has been one-sided—pushing science toward the discovery of data without the balancing process that occurs with the integration of the data. Without such balance, the sciences have been pushed toward fragmentation. Instead, in the present paper, new emphasis is placed on the relationship between abstract concepts. Specifically, this paper suggests that a better theory is one that is constructed of concepts that exist on a similar level of abstraction. Suggestions are made for quantifying this claim and using the insights to enable scholars and practitioners to create more effective theory. (shrink)

Why do policies fail? How can we objectively choose the best policy from two (or more) competing alternatives? How can we create better policies? To answer these critical questions this book presents an innovative yet workable approach. Avoiding Policy Failure uses emerging metapolicy methodologies in case studies that compare successful policies with ones that have failed. Those studies investigate the systemic nature of each policy text to gain new insights into why policies fail. -/- In addition to providing intriguing directions (...) for research, this book also suggests a bold new standard for evaluating policies. While this method is broadly generalizable, specific examples are provided showing how to develop better Economic Policy, Military Policy, and Constitutional Organizations. This book shows scholars, researchers, and policy analysts how to develop more effective policies so that we may achieve our highest aspirations and avoid the horrendous failures of the past. (shrink)

The rapid development of quantum technologies, such as quantum computing, quantum internet, and quantum sensing, has led to a growing awareness of the ethical issues surrounding these technologies. This literature review aims to analyze the existing research on these ethical issues using the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) literature review approach. The literature search was conducted using the following databases: Scopus ArXiv, and IEEE Xplore, and the search terms used were “quantum computing,” “quantum internet,” “quantum sensing,” (...) “quantum technology,” AND “ethics.” Inclusion criteria were: (1) articles that addressed ethical issues related to quantum technologies and (2) articles that were written in English. A total of 14 articles were included in the review. The majority of the articles (64 percent) were published in the last 5 years. The majority of the articles (78 percent) focused on the potential impact of quantum technologies on privacy and security, with a particular emphasis on the potential for quantum computers to break encryption and the subsequent impact on privacy and security. Approximately 50 percent of the articles focused on the accessibility and responsibility dimensions of quantum technologies. This scoping review has demonstrated that there is a growing awareness of the ethical issues surrounding quantum technologies and an increasing number of researchers, policymakers, and industry leaders working to address them. Future research should continue to explore these ethical issues in more depth and develop recommendations for addressing them. (shrink)

In a number of publications, Gerald Gaus has presented an ambitious account of political morality that gives the ideal of public justification pride of place. This article critically discusses Gaus’s characterization and defense of the ideal of public justification in politics. It also presents an account and an argument in support of first-person political justification.

This paper offers a realist critique of socialresearch on health inequalities. A conspectus of thefield of health inequalities research identifies twomain research approaches: the positivist quantitativesurvey and the interpretivist qualitative `casestudy'. We argue that both approaches suffer fromserious philosophical limitations. We suggest that aturn to realism offers a productive `third way' bothfor the development of health inequality research inparticular and for the social scientific understandingof the complexities of the social world in general.

When creating theory to understand or implement change at the social and/or organizational level, it is generally accepted that part of the theory building process includes a process of abstraction. While the process of abstraction is well understood, it is not so well understood how abstractions “fit” together to enable the creation of better theory. Starting with a few simple ideas, this paper explores one way we work with abstractions. This exploration challenges the traditionally held importance of abstracting concepts from (...) experience. That traditional focus has been one-sided—pushing science toward the discovery of data without the balancing process that occurs with the integration of the data. Without such balance, the sciences have been pushed toward fragmentation. Instead, in the present paper, new emphasis is placed on the relationship between abstract concepts. Specifically, this paper suggests that a better theory is one that is constructed of concepts that exist on a similar level of abstraction. Suggestions are made for quantifying this claim and using the insights to enable scholars and practitioners to create more effective theory. (shrink)

Are liberalism and perfectionism compatible? In this study Steven Wall presents and defends a perfectionist account of political morality that takes issue with many currently fashionable liberal ideas but retains the strong liberal commitment to the ideal of personal autonomy. He begins by critically discussing the most influential version of anti-perfectionist liberalism, examining the main arguments that have been offered in its defence. He then clarifies the ideal of personal autonomy, presents an account of its value and shows that (...) a strong commitment to personal autonomy is fully compatible with an endorsement of perfectionist political action designed to promote valuable pursuits and discourage base ones. (shrink)

Seminari a càrrec del Dr. Steven Wall de la University of Arizona sobre l'Autonomia com una perfecció.

While examining the important role of imagination in making moral judgments, John Dewey and Moral Imagination focuses new attention on the relationship between American pragmatism and ethics. Steven Fesmire takes up threads of Dewey's thought that have been largely unexplored and elaborates pragmatism's distinctive contribution to understandings of moral experience, inquiry, and judgment. Building on two Deweyan notions—that moral character, belief, and reasoning are part of a social and historical context and that moral deliberation is an imaginative, dramatic rehearsal (...) of possibilities—Fesmire shows that moral imagination can be conceived as a process of aesthetic perception and artistic creativity. Fesmire's original readings of Dewey shed new light on the imaginative process, human emotional make-up and expression, and the nature of moral judgment. This original book presents a robust and distinctly pragmatic approach to ethics, politics, moral education, and moral conduct. [The downloadable sample is Chapter Seven, "The Moral Artist."]. (shrink)

In ancient times, when persuasion played the role of public force, eloquence was necessary. Of what use would it be today, when public force has replaced persuasion. One needs neither art nor metaphor to say such is my pleasure. Jean Jacques Rousseau.

Robotization is an increasingly pervasive feature of our lives. Robots with high degrees of autonomy may cause harm, yet in sufciently complex systems neither the robots nor the human developers may be candidates for moral blame. John Danaher has recently argued that this may lead to a retribution gap, where the human desire for retribution faces a lack of appropriate subjects for retributive blame. The potential social and moral implications of a retribution gap are considerable. I argue that the retributive (...) intuitions that feed into retribution gaps are best understood as deontological intuitions. I apply a debunking argument for deontological intuitions in order to show that retributive intuitions cannot be used to justify retributive punishment in cases of robot harm without clear candidates for blame. The fundamental moral question thus becomes what we ought to do with these retributive intuitions, given that they do not justify retribution. I draw a parallel from recent work on implicit biases to make a case for taking moral responsibility for retributive intuitions. In the same way that we can exert some form of control over our unwanted implicit biases, we can and should do so for unjustifed retributive intuitions in cases of robot harm. (shrink)