In 1999, Jeffrey Ketland published a paper which posed a series of technical problems for deflationary theories of truth. Ketland argued that deflationism is incompatible with standard mathematical formalizations of truth, and he claimed that alternate deflationary formalizations are unable to explain some central uses of the truth predicate in mathematics. He also used Beth’s definability theorem to argue that, contrary to deflationists’ claims, the T-schema cannot provide an ‘implicit definition’ of truth. In this article, I want to challenge (...) this final argument. Whatever other faults deflationism may have, the T-schema does provide an implicit definition of the truth predicate. Or so, at any rate, I shall argue. (shrink)
Is the restricted, consistent, version of the T-scheme sufficient for an ‘implicit definition’ of truth? In a sense, the answer is yes (Haack 1978 , Quine 1953 ). Section 4 of Ketland 1999 mentions this but gives a result saying that the T-scheme does not implicitly define truth in the stronger sense relevant for Beth’s Definability Theorem. This insinuates that the T-scheme fares worse than the compositional truth theory as an implicit definition. However, the insinuation is mistaken. For, as (...) Bays rightly points out, the result given extends to the compositional truth theory also. So, as regards implicit definability, both kinds of truth theory are equivalent. Some further discussion of this topic is mentioned (Gupta 2008 , Ketland 2003 , McGee 1991 ), all in agreement with Bays’s analysis. (shrink)
This paper will articulate an underappreciated side of the psychoanalytical Deleuze: his relation to Melanie Klein, particularly as it appears in The Logic of Sense. Deleuze's engagement with Klein largely follows his familiar strategy of re-reading a thinker off of a twist in one or two of that thinker's key concepts. With Klein, this twist involves re-reading her story of psychic development on the basis of disjunction rather than negation, so that the psychic surface that emerges generates a persistent (...) non-correspondence between self and other and between concept and thing. Deleuze thereby makes Klein a central figure in his ontology of sense and his analysis of how the physical surface of bodies generates a metaphysical surface of thought. However, Deleuze's ultimate turn is a Nietzschean one towards overcoming, the thought of eternal return, and the demolition of the Oedipal Law. As this final turn makes clear, even in his early writings that engaged more directly and affirmatively with psychoanalytical thought, Deleuze was already on an anti-Oedipal path. (shrink)
On the difficulty of extracting the logical form of a seemingly simple sentence such as ‘If Andy went to the movie then Beth went too, but only if she found a taxi cab’, with some morals and questions on the nature of the difficulty.
This paper examines E. W. Beth’s work in the philosophy of physics, both from a historical and a systematic point of view. Beth saw the philosophy of physics first of all as an opportunity to illustrate and promulgate a new and modern general approach to the philosophy of nature and to philosophy tout court: an approach characterized negatively by its rejection of all traditional metaphysics and positively by its firm orientation towards science. Beth was successful in defending (...) this new ideology, and became its leading Dutch representative in the first two decades after the second world war. Beth also contributed importantly to the method of the philosophy of physics in a narrower sense, by proposing and promoting the semantic approach in the formal analysis of physical theories. Finally, he worked on several specific foundational questions; but he was probably too much of a logician to leave his mark in this area. (shrink)
This paper studies definability within the theory of institutions, a version of abstract model theory that emerged in computing science studies of software specification and semantics. We generalise the concept of definability to arbitrary logics, formalised as institutions, and we develop three general definability results. One generalises the classical Beth theorem by relying on the interpolation properties of the institution. Another relies on a meta Birkhoff axiomatizability property of the institution and constitutes a source for many new actual definability (...) results, including definability in (fragments of) classical model theory. The third one gives a set of sufficient conditions for 'borrowing' definability properties from another institution via an 'adequate' encoding between institutions. The power of our general definability results is illustrated with several applications to (many-sorted) classical model theory and partial algebra, leading for example to definability results for (quasi-)varieties of models or partial algebras. Many other applications are expected for the multitude of logical systems formalised as institutions from computing science and logic. (shrink)
The present paper is a study in abstract algebraic logic. We investigate the correspondence between the metalogical Beth property and the algebraic property of surjectivity of epimorphisms. It will be shown that this correspondence holds for the large class of equivalential logics. We apply our characterization theorem to relevance logics and many-valued logics.
A basic aim of E. Beth's work in philosophy of science was to explore the use of formal semantic methods in the analysis of physical theories. We hope to show that a general framework for Beth's semantic analysis is provided by the theory of semi-interpreted languages, introduced in a previous paper. After developing Beth's analysis of nonrelativistic physical theories in a more general form, we turn to the notion of the 'logic' of a physical theory. Here we (...) prove a result concerning the conditions under which semantic entailment in such a theory is finitary. We argue, finally, that Beth's approach provides a characterization of physical theory which is more faithful to current practice in foundational research in the sciences than the familiar picture of a partly interpreted axiomatic theory. (shrink)
All extensions of the modal Grzegorczyk logic Grz possessing projective Beth's property PB2 are described. It is proved that there are exactly 13 logics over Grz with PB2. All of them are finitely axiomatizable and have the finite model property. It is shown that PB2 is strongly decidable over Grz, i.e. there is an algorithm which, for any finite system Rul of additional axiom schemes and rules of inference, decides if the calculus Grz+Rul has the projective Beth property.
A few results generalizing well-known classical model theory ones have been obtained in institution theory these last two decades (e.g. Craig interpolation, ultraproduct, elementary diagrams). In this paper, we propose a generalized institution-independent version of the Beth definability theorem.
We prove that if ℵα is uncountable and regular, then the Beth-closure of Lωω(Qα) is not a sublogic of L∞ω(Qn), where Qn is the class of all n-ary generalized quantifiers. In particular, B(Lωω(Qα)) is not a sublogic of any finitely generated logic; i.e., there does not exist a finite set Q of Lindstrom quantifiers such that B(Lωω(Qα)) ≤ Lωω(Q).
Though E. W. Beth is famous for his contributions to logic aspects of his philosophical reflections and details of its development are almost unknown. In his work four periods can be distinguished: the neo-kantian, the anti-kantian, the anti-irrationalist and the logical one. Within this framework it is possible to individuate a core around which Beth developed his reflections: it is the interplay between philosophy and the sciences. His philosophy was always linked to the sciences in two ways: He (...) steadily checked his philosophical ideas against the current situation in foundational research and he occupied himself with the general question of the relationship between philosophy and the sciences. (shrink)
In this paper it will be shown that the Beth definability property corresponds to surjectiveness of epimorphisms in abstract algebraic logic. This generalizes a result by I. Németi (cf. [11, Theorem 5.6.10]). Moreover, an equally general characterization of the weak Beth property will be given. This gives a solution to Problem 14 in . Finally, the characterization of the projective Beth property for varieties of modal algebras by L. Maksimova (see ) will be shown to hold for (...) the larger class of semantically algebraizable logics. (shrink)
What is the meaning of reason in our postmodern society today? Is reason a weapon of domination, or can it also serve as a means for emancipation? Is it possible for reason to understand its "other"--what it is not? Confronting such questions, Bounds of Reason is a compelling discussion of the limits and meaning of rationality as a tool for understanding the ideas of truth, justice and freedom. Emilia Steuerman explores the modernist and postmodernist controversy between Habermas and Lyotard to (...) highlight the problems encountered both by a defense of reason and by the lack of meaning that haunts a world without it. Using Kleinian theory to examine the debate as it is manifested in the main philosophical themes of this century, Steuerman argues that a rational and ethical theory of justice must take into account that which is not rational, symmetrical or transparent--namely a primitive world of love and hatred which colors and shapes our perceptions. (shrink)
: Through a close reading of Klein and Irigaray's work on the mother-daughter relationship via the Electra myth, Jacobs diagnoses what she considers a fundamental problem in psychoanalytic and feminist psychoanalytic theory. She shows that neither thinker is able to theorize the mother-daughter relationship on a structural level but is only able to describe its symptoms. Jacobs makes a crucial distinction between description and theory and argues that the need to go beyond description and phenomenology toward the creation of a (...) structural theory is the only way that feminist philosophy and psychoanalysis can avoid reproducing the terms of the male imaginary. The essay concludes by arguing that theorization of the mother-daughter relationship can only be achieved if we analyze manifestations of the mother-daughter relationship in clinical, cultural, and mythical material through the framework of a foreclosed or absent underlying maternal law. (shrink)
In response to Mader's and Deutscher's questions, the author defends her approach to reading Irigaray and Butler, which entails extending the ideas of these thinkers into areas of thought with which they do not engage directly themselves. This involves relating Irigaray's ideas to the tradition of the philosophy of nature and interpreting Butler as offering, in spite of her focus on the genealogy of claims about sex, also a theory of sex itself, a theory of sex as an effect entirely (...) of gender. This approach to reading differs from Irigaray's own reading method of expanding and transforming philosophies in light of their constitutive exclusions. An example of this, explored here, is Irigaray's expansion and transformation of Merleau-Ponty's late ontology of flesh in light of its constitutive exclusion, the "maternal sojourn." This article also asks whether rhythmic sexual difference, which the author has attempted to differentiate from biological sex difference, ultimately remains tied to biological sex difference. This commentary suggests that it does but that reference to biological sex difference need not be politically problematic. Finally, the author asks whether the metaphysics of potentials and tendencies that she attributes to Irigaray impedes social change by inevitably reinstalling the actual as the horizon of possibility. Irigaray's strategy of reading texts and cultures for their constitutive exclusions offers a solution to this problem. (shrink)
Infants apparently start to understand their experience via the linked concepts of numerical identity and spatio-temporally continuous objects during the forth month of life. As described by Piaget and Klein, this development requires them to synthesise their experience in a new ways: in particular they must start to acknowledge that the main target of their anger at frustration and the main target of their gratitude and love are the same person, who is unique and irreplaceable. This seems to have an (...) immediate consequence in the onset of separation distress and stranger anxiety, and apparently has far-reaching psychological consequences later. (shrink)
What enables individually simple insects like ants to act with such precision and purpose as a group? How do trillions of individual neurons produce something as extraordinarily complex as consciousness? What is it that guides self-organizing structures like the immune system, the World Wide Web, the global economy, and the human genome? These are just a few of the fascinating and elusive questions that the science of complexity seeks to answer. In this remarkably accessible and companionable book, leading complex systems (...) scientist Melanie Mitchell provides an intimate, detailed tour of the sciences of complexity, a broad set of efforts that seek to explain how large-scale complex, organized, and adaptive behavior can emerge from simple interactions among myriad individuals. Comprehending such systems requires a wholly new approach, one that goes beyond traditional scientific reductionism and that re-maps long-standing disciplinary boundaries. Based on her work at the Santa Fe Institute and drawing on its interdisciplinary strategies, Mitchell brings clarity to the workings of complexity across a broad range of biological, technological, and social phenomena, seeking out the general principles or laws that apply to all of them. She explores as well the relationship between complexity and evolution, artificial intelligence, computation, genetics, information processing, and many other fields. Richly illustrated and vividly written, Complexity: A Guided Tour offers a comprehensive and eminently comprehensible overview of the ideas underlying complex systems science, the current research at the forefront of this field, and the prospects for the field's contribution to solving some of the most important scientific questions of our time. (shrink)
The debate over foundationalism, the viewpoint that there exists some secure foundation upon which to build a system of knowledge, appears to have been resolved and the antifoundationalists have at least temporarily prevailed. From a firmly historical approach, the book traces the foundationalism/antifoundationalism controversy in the work of many important figures Animaxander, Aristotle and Plato, Augustine, Descartes, Hegel and Nietzsche, Habermas and Chisholm, and others throughout the history of philosophy. The contributors, Joseph Margolis, Ronald Polansky, Gary Calore, Fred and Emily (...) Michael, William Wurzer, Charlene Haddock Siegfried, Sandra B. Rosenthal, Kathleen Wallace, and the editors present well the diversity, interest, and roots of antifoundationalism. Tom Rockmore is Professor and Chairman in the Department of Philosophy at Duquesne University. Beth J. Singer is Professor of Philosophy at Brooklyn College of the City University of New York. (shrink)
Theoretical and Applied Issues Edited by Andrew Ortony Jon Slack Oliviero Stock NATO ASI Series Series F: Computer and Systems Sciences, Vol. 100 Communication from an Artificial Intelligence Perspective NATO ASI Series Advanced ...
This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics has been completely revised for this second edition. Brouwer's proof of the Bar Theorem has been reworked, the account of valuation systems simplified, and the treatment of generalized Beth Trees and the completeness of intuitionistic first-order logic rewritten. (...) Readers are assumed to have some knowledge of classical formal logic and a general awareness of the history of intuitionism. (shrink)
This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The companion paper analyses the situation in physics, especially limiting relations between physical theories. I shall take emergence as behaviour that is novel and robust relative to some comparison class. I shall take reduction as deduction using appropriate auxiliary definitions. And I shall take supervenience as a weakening of reduction, viz. to allow infinitely long definitions. The overall claim (...) of this paper will be that emergence is logically independent both of reduction and of supervenience. In particular, one can have emergence with reduction, as well as without it; and emergence without supervenience, as well as with it. Of the subsidiary claims, the four main ones (each shared with some other authors) are: (i): I defend the traditional Nagelian conception of reduction (Section 3}); (ii): I deny that the multiple realizability argument causes trouble for reductions, or ``reductionism'' (Section 4); (iii): I stress the collapse of supervenience into deduction via Beth's theorem (Section 5.1); (iv): I adapt some examples already in the literature to show supervenience without emergence and vice versa (Section 5.2). (shrink)
Function theorists routinely speculate that a viable function theory will be equally applicable to biological traits and artifacts. However, artifact function has received only the most cursory scrutiny in its own right. Closer scrutiny reveals that only a pluralist theory comprising two distinct notions of function--proper function and system function--will serve as an adequate general theory. The first section describes these two notions of function. The second section shows why both notions are necessary, by showing that attempts to do away (...) with one of them fail. This demonstration draws on examples from the artifactual realm to motivate major points of the argument. The third section is an outline of artifact function. It confirms the conclusions of the second section, and also begins the task of describing some of the special features of artifact function needing accommodation within the general theory. (shrink)
Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora . These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science . In this paper we will do two things. First of all, we will (...) propose a general and systematized account of the Classical Model of Science. Secondly, we will offer an analysis of the philosophical significance of this model at different historical junctures by giving an overview of the connections it has had with a number of important topics. The latter include the analytic-synthetic distinction, the axiomatic method, the hierarchical order of sciences and the status of logic as a science. Our claim is that particularly fruitful insights are gained by seeing themes such as these against the background of the Classical Model of Science. In an appendix we deal with the historiographical background of this model by considering the systematizations of Aristotle’s theory of science offered by Heinrich Scholz, and in his footsteps by Evert W. Beth. (shrink)
The article argues for an alliance of the capability approach developed by Amartya Sen with ideas from critical pedagogy for undergraduate university education which develops student agency and well being on the one hand, and social change towards greater justice on the other. The purposes of a university education in this article are taken to include both intrinsic and instrumental purposes and to therefore include personal development, economic opportunities and becoming educated citizens. Core ideas from the capability approach are outlined, (...) with examples, before possible articulations of capability and Sen's notion of process freedom with critical pedagogy are investigated. It is argued that each approach has something to offer when brought alongside as ‘critical capability pedagogies’, which seek to enhance and expand student experiences of learning and their ‘valuable beings and doings’. Finally core capabilities in a university education are considered and some of the problems of domesticating the capability approach addressed. (shrink)
Various explanations are offered to explain why employees increasingly work longer hours: the combined effects of technology and globalization; people are caught up in consumerism; and the "ideal worker norm," when professionals expect themselves and others to work longer hours. In this article, we propose that the processes of employer recruitment and selection, employee self-selection, cultural socialization, and reward systems help create extended work hours cultures (EWHC) that reinforce these trends. Moreover, we argue that EWHC organizations are becoming more prevalent (...) and that organizations in which long hours have become the norm may recruit for and reinforce workaholic tendencies. Next, we offer spiritual leadership as a paradigm for organizational transformation and recovery from the negative aspects of EWHC to enhance employee wellbeing and corporate social responsibility without sacrificing profitability, revenue growth, and other indicators of financial performance. Finally, we will offer suggestions for future theory, research, and practice. (shrink)
: Recent work in the area of ethics and animals suggests that it is philosophically legitimate to ascribe emotions to nonhuman animals. Furthermore, it is sometimes argued that emotionality is a morally relevant psychological state shared by humans and nonhumans. What is missing from the philosophical literature that makes reference to emotions in nonhuman animals is an attempt to clarify and defend some particular account of the nature of emotion, and the role that emotions play in a characterization of human (...) nature. I argue in this paper that some analyses of emotion are more credible than others. Because this is so, the thesis that humans and nonhumans share emotions may well be a more difficult case to make than has been recognized thus far. (shrink)