The purpose of this paper is to study an analogue of Hilbert's seventeenth problem for functions over a valued field which are integral definite on some definable set; that is, that map the given set into the valuation ring. We use model theory to exhibit a uniform method, on various theories of valued fields, for deriving an algebraic characterization of such functions. As part of this method we refine the concept of a function being integral (...) at a point, and make it dependent on the relevant class of valued fields. We apply our framework to algebraically closed valued fields, model complete theories of difference and differential valued fields, and real closed valued fields. (shrink)

The notion of a D-ring, generalizing that of a differential or a difference ring, is introduced. Quantifier elimination and a version of the Ax-Kochen-Eršov principle is proven for a theory of valued D-fields of residual characteristic zero.

The notion of a D-ring, generalizing that of a differential or a difference ring, is introduced. Quantifier elimination and a version of the Ax-Kochen-Ersov principle is proven for a theory of valued D-fields of residual characteristic zero.

Religious therapeutics is the term I use to designate relations between health and spirituality, and medicine and religion. Dimensions of religious therapeutics include religious meanings that inform medical theory, religious means of healing, health as part of religious life, and religion as a remedy for human suffering. Classical Yoga is analyzed to establish an initial matrix of religious therapeutics with 5 branches: philosophical foundations, soteriology, value theory, physical practice, and cultivation of consciousness. Through comparative criticism of classical Yoga, (...) the study presents a heuristic of religious therapeutics: a model for interpreting relations among healing and liberative functions in world religions. ;Body and health are of instrumental but not ultimate value in classical Yoga: the body is used to transcend itself for attainment of Yoga's soteriological goal, realization of self as pure consciousness. Yoga's Samkhya-based metaphysics contains an unreconciled dualism, and while practice of Yoga is paradigmatic of mind/body holism, Yoga prescribes realization of a spiritual self, independent of material and psychological nature. The study rehabilitates the body in respect of the compatibility of embodiedness with religiousness. ;Other Indian and world traditions suggest dimensions of religious therapeutics both resonant with classical Yoga and lacking from it. India's Ayurvedic medicine represents the sixth branch of religious therapeutics: medical therapeutics. I distill from Ayurvedic and Western sources a set of determinants of health: biological, medical/psychological, cultural, and metaphysical. Significant determinants of health are wholeness, self-identity, and freedom; these are incorporated in discussion of the complementary functions of medicine and religion, grounding the claim that in classical Yoga, liberation is healing in an ultimate sense. ;Tantric yogas utilize material nature for human spiritual progress, and unlike classical Yoga, esteem nature, body/mind, the feminine, and relationality. Tantra provides another branch of religious therapeutics: aesthetic therapeutics. The study anticipates elements of health/medicine in western religions, Buddhism, and Lakota religious philosophy. Sacred speech and song are explored to demonstrate comparative inquiry into religious therapeutics; some Native American Indian and Hindu applications of sacred language are considered. Finally, the model of religious therapeutics is supplemented with community, embracing ecological, social, and religious relationality and communication. (shrink)

Model theorists have been studying analytic functions since the late 1970s. Highlights include the seminal work of Denef and van den Dries on the theory of the p-adics with restricted analytic functions, Wilkie's proof of o-minimality of the theory of the reals with the exponential function, and the formulation of Zilber's conjecture for the complex exponential. My goal in this talk is to survey these main developments and to reflect on today's open problems, in particular for theories (...) of valued fields. (shrink)

The concept of general equilibrium, one of the central components of economic theory, explains the behavior of supply, demand, and prices by showing that supply and demand exist in balance through pricing mechanisms. The mathematical tools and properties for this theory have developed over time to accommodate and incorporate developments in economic theory, from multiple markets and economic agents to theories of production.Yves Balasko offers an extensive, up-to-date look at the standard theory of general equilibrium, to (...) which he has been a major contributor. This book explains how the equilibrium manifold approach can be usefully applied to the general equilibrium model, from basic consumer theory and exchange economies to models with private ownership of production. Balasko examines properties of the standard general equilibrium model that are beyond traditional existence and optimality. He applies the theory of smooth manifolds and mappings to the multiplicity of equilibrium solutions and related discontinuities of market prices. The economic concepts and differential topology methods presented in this book are accessible, clear, and relevant, and no prior knowledge of economic theory is necessary.General Equilibrium Theory of Value offers a comprehensive foundation for the most current models of economic theory and is ideally suited for graduate economics students, advanced undergraduates in mathematics, and researchers in the field. (shrink)

A prominent member of the second generation of Cambridge Keynesians, Luigi Pasinetti has been a key player in the development of neo-Ricardian economics as well. Having studied under Piero Sraffa at Cambridge, he developed a mathematical representation of Ricardo's theory of value and distribution, as well as the reswitching problem in neoclassical capital theory: thus making him a leader of the British Cambridge side during the Cambridge Capital Controversy. Since leaving Cambridge for Rome, he has become particularly interested (...) in structural change, i.e. the responses of multi-sectoral models of the economy to technical changes. This book draws together Pasinetti's main contributions in the field of value theory. (shrink)

We study the model theory of fields k carrying a henselian valuation with real closed residue field. We give a criteria for elementary equivalence and elementary inclusion of such fields involving the value group of a not necessarily definable valuation. This allows us to translate theories of such fields to theories of ordered abelian groups, and we study the properties of this translation. We also characterize the first-order definable convex subgroups of a given ordered abelian (...) group and prove that the definable real valuation rings of k are in correspondence with the definable convex subgroups of the value group of a certain real valuation of k. (shrink)

We give a survey of results obtained in the model theory of finite and pseudo-finite fields.

Let G be a finite group. We explore the model-theoretic properties of the class of differential fields of characteristic zero in m commuting derivations equipped with a G-action by differential fie...

Is logic normative for belief? A standard approach to answering this question has been to investigate bridge principles relating claims of logical consequence to norms for belief. Although the question is naturally an epistemic one, bridge principles have typically been investigated in isolation from epistemic debates over the correct norms for belief. In this paper we tackle the question of whether logic is normative for belief by proposing a Kripkean model theory accounting for the interaction between logical, doxastic, (...) epistemic and deontic notions and using this model theory to show which bridge principles are implied by epistemic norms that we have independent reason to accept, for example, the knowledge norm and the truth norm. We propose a preliminary theory of the interaction between logical, doxastic, epistemic and deontic notions that has among its commitments bridge principles expressing how logic is normative for belief. We also show how our framework suggests that logic is exceptionally normative. (shrink)

If properties are to play a useful role in semantics, it is hard to avoid assuming the naïve theory of properties: for any predicate Θ(x), there is a property such that an object o has it if and only if Θ(o). Yet this appears to lead to various paradoxes. I show that no paradoxes arise as long as the logic is weakened appropriately; the main difficulty is finding a semantics that can handle a conditional obeying reasonable laws without engendering (...) paradox. I employ a semantics which is infinite-valued, with the values only partially ordered. Can the solution be adapted to naïve set theory? Probably not, but limiting naïve comprehension in set theory is perfectly satisfactory, whereas this is not so in a property theory used for semantics. (shrink)

When [Formula: see text] is a finite field, [J. Becker, J. Denef and L. Lipshitz, Further remarks on the elementary theory of formal power series rings, in Model Theory of Algebra and Arithmetic, Proceedings Karpacz, Poland, Lecture Notes in Mathematics, Vol. 834 (Springer, Berlin, 1979)] observed that the total residue map [Formula: see text], which picks out the constant term of the Laurent series, is definable in the language of rings with a parameter for [Formula: see text]. (...) Driven by this observation, we study the theory [Formula: see text] of valued fields equipped with a linear form [Formula: see text] which restricts to the residue map on the valuation ring. We prove that [Formula: see text] does not admit a model companion. In addition, we show that [Formula: see text] is undecidable whenever [Formula: see text] is an infinite field. As a consequence, we get that [Formula: see text] is undecidable, where [Formula: see text] maps [Formula: see text] to its complex residue at [Formula: see text]. (shrink)

In this paper we set out the basic model theory of differential fields of characteristic 0, which have finitely many commuting derivations. We give axioms for the theory of differentially closed differential fields with m derivations and show that this theory is ω-stable, model complete, and quantifier-eliminable, and that it admits elimination of imaginaries. We give a characterization of forking and compute the rank of this theory to be ω m + 1.

We extend the characterization of extremal valued fields given in [2] to the missing case of valued fields of mixed characteristic with perfect residue field. This leads to a complete characterization of the tame valued fields that are extremal. The key to the proof is a model theoretic result about tame valued fields in mixed characteristic. Further, we prove that in an extremal valued field of finitep-degree, the images of all (...) additive polynomials have the optimal approximation property. This fact can be used to improve the axiom system that is suggested in [8] for the elementary theory of Laurent series fields over finite fields. Finally we give examples that demonstrate the problems we are facing when we try to characterize the extremal valued fields with imperfect residue fields. To this end, we describe several ways of constructing extremal valued fields; in particular, we show that in every ℵ1saturated valued field the valuation is a composition of extremal valuations of rank 1. (shrink)

In his Ph.D. thesis [7], L. van den Dries studied the model theory of fields with finitely many orderings and valuations where all open sets according to the topology defined by an order or a valuation is globally dense according with all other orderings and valuations. Van den Dries proved that the theory of these fields is companionable and that the theory of the companion is decidable .In this paper we study the case where (...) the fields are expanded with finitely many orderings and an independent derivation. We show that the theory of these fields still admits a model companion in the language Lequation image = {+, –, ·, D, <1, …, model companion by CODFm and give a geometric axiomatization of this theory which uses basic notions of algebraic geometry and some generalized open subsets which appear naturally in this context. This axiomatization allows to recover the one given in [4] for the theory CODF of closed ordered differential fields. Most of the technics we use here are already present in [2] and [4].Finally, we prove that it is possible to describe the completions of CODFm and to obtain quantifier elimination in a slightly enriched language. This generalizes van den Dries' results in the “derivation free” case. (shrink)

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative Hasse–Schmidt derivations [13] and about Galois actions [14]. As an application of our methods, we obtain a new model complete theory of actions of a finite group on fields of finite imperfection degree.

This monograph is a follow up to the author's classic text Boolean-Valued Models and Independence Proofs in Set Theory, providing an exposition of some of the most important results in set theory obtained in the 20th century--the independence of the continuum hypothesis and the axiom of choice. Aimed at research students and academics in mathematics, mathematical logic, philosophy, and computer science, the text has been extensively updated with expanded introductory material, new chapters, and a new appendix on (...) category theory, and includes recent developments in the field. Numerous exercises, along with the enlarged and entirely updated background material, make this an ideal text for students in logic and set theory. (shrink)

A number of philosophers :171–187, 2011; Arnold 2011, in Ethics Politics XV:101–138, 2013) have argued that agent-based, evolutionary game theory models of the evolution of cooperation fail to provide satisfying explanations of cooperation because they are too disconnected from actual biology. I show how these criticisms can be answered by employing modeling approaches from the situated cognition research program that allow for more biologically detailed models. Using cases drawn from recent situated cognition modeling research, I show how agent-based models (...) of the evolution of cooperation can become more empirically-informed and relevant to explaining the evolution of cooperation in real populations. I argue that because situated cognition models allow for more detailed representations of not just agents’ brains but bodies and environments as well, they can be informed by a much wider breadth of empirical research than traditional agent-based models. Moreover, because the simulated bodies of these agents exhibit particular behaviors, they can be more readily compared to the behaviors of actual organisms. I conclude that employing situated cognition approaches to modeling the evolution of cooperation is a more promising way to investigate the evolution of cooperation than more traditional agent-based evolutionary game theory models. (shrink)

The term ‘social capital’ is a way of defining the intangible resources of community, shared values and trust upon which we draw in daily life. It has achieved considerable international currency across the social sciences through the very different work of Pierre Bourdieu in France and James Coleman and Robert Putnam in the United States, and has been widely taken up within politics and sociology as an explanation for the decline in social cohesion and community values in western societies. It (...) has also been adopted by policy makers, particularly in international governmental bodies such as the World Bank. (shrink)

_The VaKE Handbook: Theory and Practice of Values and Knowledge Education_ presents a theoretical model and many examples in various fields of education and training for the realization of the principle "Values without knowledge are blind, while knowledge without values is irresponsible".

Generalizing and unifying the known theorems for difference and differential fields, it is shown that for every finite free algebra scheme.

Is logic normative for belief? A standard approach to answering this question has been to investigate bridge principles relating claims of logical consequence to norms for belief. Although the question is naturally an epistemic one, bridge principles have typically been investigated in isolation from epistemic debates over the correct norms for belief. In this paper we tackle the question of whether logic is normative for belief by proposing a Kripkean model theory accounting for the interaction between logical, doxastic, (...) epistemic and deontic notions and using this model theory to show which bridge principles are implied by epistemic norms that we have independent reason to accept, for example, theknowledge normand thetruth norm. We propose a preliminary theory of the interaction between logical, doxastic, epistemic and deontic notions that has among its commitments bridge principles expressing how logic is normative for belief. We also show how our framework suggests that logic is exceptionally normative. (shrink)

The paper shows how we can add a truth predicate to arithmetic (or formalized syntactic theory), and keep the usual truth schema Tr( ) ↔ A (understood as the conjunction of Tr( ) → A and A → Tr( )). We also keep the full intersubstitutivity of Tr(>A>)) with A in all contexts, even inside of an →. Keeping these things requires a weakening of classical logic; I suggest a logic based on the strong Kleene truth tables, but with (...) → as an additional connective, and where the effect of classical logic is preserved in the arithmetic or formal syntax itself. Section 1 is an introduction to the problem and some of the difficulties that must be faced, in particular as to the logic of the →; Section 2 gives a construction of an arithmetically standard model of a truth theory; Section 3 investigates the logical laws that result from this; and Section 4 provides some philosophical commentary. (shrink)

Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector spaces over algebraically closed (...) fields is the model-completion of the theory of vector spaces. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Commentary on “Sanity and Irresponsibility”Lloyd Fields (bio)AbstractI make two criticisms of Wilson’s proposal to dispense with a loaded axiological criterion of sanity. First, Edwards’s axiological criterion of sanity, which Wilson accepts, involves the requirement of impartiality, which at least excludes some standards of right and wrong. Second, value pluralism applies only to morally acceptable forms of life and thus presupposes a standard of right and wrong. I conclude (...) by noting that mental illnesses are not sufficiently characterised by extreme and persistent deviance from practical rationality, as conceived by Edwards and Wilson.KeywordsSanity, responsibility, mental illness, value pluralismWilson’s paper is set in an important tradition of which Susan Wolf is a notable exemplar. He tackles the crucially important issue of how practical rationality is related to mental health and of how certain forms of irrationality are connected with mental illness. This issue must be taken into account in order to avoid infecting the criteria of sanity with “idiosyncratic or culturally biased norms.” Like Wolf (1989, 137–151), Wilson holds that sanity is a necessary condition of responsibility. But Wilson rejects the second of Wolf’s two criteria of sanity on the grounds that it invokes a definite normative theory of right and wrong. He proposes instead that whether an agent is sane should be decided on the basis of whether s/he displays practical rationality, as defined by Edwards’s list of seven items. Following Edwards, Wilson implicitly equates “sanity” with “mental health” and “insanity” with “mental illness.” By rejecting an axiological criterion of sanity that depends on a normative theory of right and wrong, Wilson is able to ensure that individuals like JoJo are not judged to be insane and hence not morally responsible for their actions. Wilson is right to stress the importance of our not applying notions such as “mental illness” or “insanity” too widely, especially in such a way as to allow blameworthy persons to escape blame and punishment.But are Wilson’s own criteria of sanity free from dependence on a normative theory, or a normative standard, of right and wrong? First, let us note that Wilson states Edwards’s seventh condition of practical rationality as follows: “holding values that are or would be adopted under the conditions of (negative) freedom.” Edwards’s own formulation of this condition is the following: “having values which have been (or would be) adopted under conditions of freedom, enlightenment and impartiality” (1982, 315). Wilson explains “freedom” as the absence of coercion. It is uncertain what “enlightenment” means in this context. Impartiality would seem to include being impartial between oneself and others and between one’s own tribe, nation or race and that of others. Although this requirement is perhaps too general to be regarded as a sufficient standard [End Page 303] of right and wrong, it is at least part of such normative theories as utilitarianism and Kant’s moral theory, while it is inconsistent with ethical egoism, i.e., the view that an action is right or wrong depending on whether it serves or frustrates the agent’s overall best interests. One could dispute Wilson’s claim, therefore, that Edwards’s seventh item is not a “loaded” axiological criterion.Second, Wilson maintains that we can avoid assuming a loaded axiological criterion for sanity by adopting the position of value pluralism. Wolf’s axiological criterion for sanity is that the agent should be capable of knowing the difference between right and wrong. Wilson holds that this criterion, as presented, invokes a normative theory of right and wrong. The criterion would not do so if it were applied in accordance with value pluralism, which, Wilson says, “rejects the notion that there is one monolithic theory of right and wrong without denying that an actor may behave virtuously or viciously.” Wilson appears to assume that an “unloaded” version of Wolf’s axiological criterion would be more or less equivalent to Edwards’s seventh condition of practical rationality.Value pluralism maintains that there are incompatible forms of life that display distinct virtues. “Whichever form of life one is pursuing there are virtues which elude one because they are available only to people pursuing alternative and... (shrink)

In this thesis, we study transfer principles in the context of certain Henselian valued fields, namely Henselian valued fields of equicharacteristic $0$, algebraically closed valued fields, algebraically maximal Kaplansky valued fields, and unramified mixed characteristic Henselian valued fields with perfect residue field. First, we compute the burden of such a valued field in terms of the burden of its value group and its residue field. The burden is a cardinal (...) related to the model theoretic complexity and a notion of dimension associated to $\text {NTP}_2$ theories. We show, for instance, that the Hahn field $\mathbb {F}_p^{\text {alg}})$ is inp-minimal, and that the ring of Witt vectors $W$ over $\mathbb {F}_p^{\text {alg}}$ is not strong. This result extends previous work by Chernikov and Simon and realizes an important step toward the classification of Henselian valued fields of finite burden. Second, we show a transfer principle for the property that all types realized in a given elementary extension are definable. It can be written as follows: a valued field as above is stably embedded in an elementary extension if and only if its value group is stably embedded in the corresponding extension of value groups, its residue field is stably embedded in the corresponding extension of residue fields, and the extension of valued fields satisfies a certain algebraic condition. We show, for instance, that all types over the power series field $\mathbb {R})$ are definable. Similarly, all types over the quotient field of $W$ are definable. This extends previous work of Cubides and Delon and of Cubides and Ye.These distinct results use a common approach, which has been developed recently. It consists of establishing first a reduction to an intermediate structure called the leading term structure, or $\operatorname {\mathrm {RV}}$ -sort, and then of reducing to the value group and residue field. This leads us to develop similar reduction principles in the context of pure short exact sequences of abelian groups.prepared by Pierre Touchard.E-mail: [email protected]: https://miami.uni-muenster.de/Record/a612cf73-0a2f-42c4-b1e4-7d28934138a9. (shrink)

I offer a line of argument that aims at the conclusion that the notion of radically different and incommensurable systems of value is incoherent, which would mean that the presumption of some significant common ground of valuation is rationally required in value inquiry.

In this dissertation I offer a theory of intrinsic value based on contextualist principles drawn from the value theories of John Dewey and Alfred North Whitehead. The point of departure for the argument is the contextualist view that the qualitative patters representing in experience objects of states of affairs to which we attribute values provide necessary, but not sufficient, conditions to elicit particular valuations, and ground the evaluative judgments we make. The sufficient conditions for valuation include a broader context (...) of memories, beliefs, and peripheral qualia that combine in an integral experiential whole whose value is not reducible to that of its parts. It is first argued that value is, as G.E. Moore suggested, a simple, indefinable property. This property is emergent from experiential qualitative patterns in the sense that value is conditioned by the patterns, but is not itself a condition of them. An analysis of experiential qualitative pattern is then offered, which indicates how some parts of these patterns are focused on in evaluative judgment as crucial for the reproduction of particular values through practical action, whereas the influence of other parts is largely ignored, thus forming a relatively constant experiential context. Finally, a theory of evaluative judgment is offered based on contextualist principles. It is suggested that a contextualist theory can answer the challenge of value relativism by showing how evaluative judgment is 'position relative' rather than 'author relative'. That is, two subjects many come to different evaluative judgments on account of their differing positions or situations, while both may agree that the other's judgment is sound given his or her situation. (shrink)

Using methods of geometric stability , we determine the structure of Abelian groups definable in ACFA, the model companion of fields with an automorphism. We also give general bounds on sets definable in ACFA. We show that these tools can be used to study torsion points on Abelian varieties; among other results, we deduce a fairly general case of a conjecture of Tate and Voloch on p-adic distances of torsion points from subvarieties.

In a previous article, I have attempted to summarize the evidence of Aristotle about the relations of Socrates and Plato in the development of the theory of Ideas. It may be of interest now to carry the enquiry further, and to see whether writers later than Aristotle have anything of importance to say about the whole question of the general intellectual relationship between the two men. In particular we must enquire whether or how far they regard or say anything (...) to lead us to regard the Dialogues of Plato as a record of Plato's own thought or as a biographical account of the thought of Socrates or—a third possibility—as both at the same time. And, in addition to this, we shall have to attempt some estimate of the value, if any, which we can put upon such statements—an estimate which would depend in its turn on our answer to the question how far they had access to original sources of information no longer extant. (shrink)

In a previous article, I have attempted to summarize the evidence of Aristotle about the relations of Socrates and Plato in the development of the theory of Ideas. It may be of interest now to carry the enquiry further, and to see whether writers later than Aristotle have anything of importance to say about the whole question of the general intellectual relationship between the two men. In particular we must enquire whether or how far they regard or say anything (...) to lead us to regard the Dialogues of Plato as a record of Plato's own thought or as a biographical account of the thought of Socrates or—a third possibility—as both at the same time. And, in addition to this, we shall have to attempt some estimate of the value, if any, which we can put upon such statements—an estimate which would depend in its turn on our answer to the question how far they had access to original sources of information no longer extant. (shrink)

Using the analytic framework of normative logic presented in Fisher, Lovell, and Valero-Silva, provided here are five original business ethics mini-cases that may be used to teach and practice case analysis. We have taken the six questions that are used in the analytic framework of normative logic to solve ethical problems and have adapted them to seven steps that can be applied to conflict resolution of mini-cases in class. Then the adapted normative logic model has seven steps: Describe the (...) “fundamental needs of humankind” as they relate to the case, e.g. caring, supporting, reciprocity, fairness, trust; Explain the established norms, values, and laws that can be seen to apply in this case; State in brief the facts of the situation; Examine the network of circumstances that preceded the situation ; Generate at least three alternative positions and actions open to the actor in the case; Speculate on the hypothesized consequences of the different positions or actions the actor in the case may take; and Choose among the alternative positions the actor in the case might take and give your informed and judged reason for making that choice. A suggested answer is provided for one case, which could be reproduced as a class handout for students to examine after having done their own analysis and having discussed the case as a class. (shrink)

A relational-self theory claims that one’s self is constituted by one’s relationships. The type of ethics that is said to arise from this concept of self is often called an ethics of care, whereby the focus of ethical deliberation is on preserving and nurturing those relationships. Some environmental philosophers advocating a relational-self theory tend to assume that the particular relationships that constitute the self will prioritize the natural world. I question this assumption by introducing the problem of artifact (...) relationships. It is unclear whether a relational-self theory recognizes relationships with the artificial world as beingmeaningful in any moral sense, and whether such relationships, if they can exist, should be accorded equal value to relationships with the natural world. The problem of artifact relationships becomes particularly apparent when the relational-self theory is linked to place-based ethics. If our ethics are to develop from our relations to place, and our place is largely an artificial world, is there not a danger that our ethical deliberations will tend to neglect the natural world? I adapt Holmes Rolston’s concept of “storied residence” to show how the inclusion of the artificial world will lead to different questions regarding one’s resident environment, and perhaps a different emphasis on what is valued. My aim in raising these questions is to challenge the optimism that writers such as Karen Warren and Jim Cheney have shown in supporting relational-self theories and place-based ethics. I conclude that the challenge to develop a relational-self/place-based ethic does not appear to have been met within Western environmental philosophy, which has perpetuated a silence on the matter of our embedment in the artificial world. (shrink)

A relational-self theory claims that one’s self is constituted by one’s relationships. The type of ethics that is said to arise from this concept of self is often called an ethics of care, whereby the focus of ethical deliberation is on preserving and nurturing those relationships. Some environmental philosophers advocating a relational-self theory tend to assume that the particular relationships that constitute the self will prioritize the natural world. I question this assumption by introducing the problem of artifact (...) relationships. It is unclear whether a relational-self theory recognizes relationships with the artificial world as beingmeaningful in any moral sense, and whether such relationships, if they can exist, should be accorded equal value to relationships with the natural world. The problem of artifact relationships becomes particularly apparent when the relational-self theory is linked to place-based ethics. If our ethics are to develop from our relations to place, and our place is largely an artificial world, is there not a danger that our ethical deliberations will tend to neglect the natural world? I adapt Holmes Rolston’s concept of “storied residence” to show how the inclusion of the artificial world will lead to different questions regarding one’s resident environment, and perhaps a different emphasis on what is valued. My aim in raising these questions is to challenge the optimism that writers such as Karen Warren and Jim Cheney have shown in supporting relational-self theories and place-based ethics. I conclude that the challenge to develop a relational-self/place-based ethic does not appear to have been met within Western environmental philosophy, which has perpetuated a silence on the matter of our embedment in the artificial world. (shrink)

A relational-self theory claims that one’s self is constituted by one’s relationships. The type of ethics that is said to arise from this concept of self is often called an ethics of care, whereby the focus of ethical deliberation is on preserving and nurturing those relationships. Some environmental philosophers advocating a relational-self theory tend to assume that the particular relationships that constitute the self will prioritize the natural world. I question this assumption by introducing the problem of artifact (...) relationships. It is unclear whether a relational-self theory recognizes relationships with the artificial world as beingmeaningful in any moral sense, and whether such relationships, if they can exist, should be accorded equal value to relationships with the natural world. The problem of artifact relationships becomes particularly apparent when the relational-self theory is linked to place-based ethics. If our ethics are to develop from our relations to place, and our place is largely an artificial world, is there not a danger that our ethical deliberations will tend to neglect the natural world? I adapt Holmes Rolston’s concept of “storied residence” to show how the inclusion of the artificial world will lead to different questions regarding one’s resident environment, and perhaps a different emphasis on what is valued. My aim in raising these questions is to challenge the optimism that writers such as Karen Warren and Jim Cheney have shown in supporting relational-self theories and place-based ethics. I conclude that the challenge to develop a relational-self/place-based ethic does not appear to have been met within Western environmental philosophy, which has perpetuated a silence on the matter of our embedment in the artificial world. (shrink)

Arguments by Sorkin (Impossible measurements on quantum fields. In: Directions in general relativity: proceedings of the 1993 International Symposium, Maryland, vol 2, pp 293–305, 1993) and Borsten et al. (Phys Rev D 104(2), 2021. https://doi.org/10.1103/PhysRevD.104.025012 ) establish that a natural extension of quantum measurement theory from non-relativistic quantum mechanics to relativistic quantum theory leads to the unacceptable consequence that expectation values in one region depend on which unitary operation is performed in a spacelike separated region. Sorkin [ (...) 1 ] labels such scenarios ‘impossible measurements’. We explicitly present these arguments as a no-go result with the logical form of a reductio argument and investigate the consequences for measurement in quantum field theory (QFT). Sorkin-type impossible measurement scenarios clearly illustrate the moral that Microcausality is not by itself sufficient to rule out superluminal signalling in relativistic quantum theories that use Lüders’ rule. We review three different approaches to formulating an account of measurement for QFT and analyze their responses to the ‘impossible measurements’ problem. Two of the approaches are: a measurement theory based on detector models proposed in Polo-Gómez et al. (Phys Rev D, 2022. https://doi.org/10.1103/physrevd.105.065003 ) and a measurement framework for algebraic QFT proposed in Fewster and Verch (Commun Math Phys 378(2):851–889, 2020). Of particular interest for foundations of QFT is that they share common features that may hold general morals about how to represent measurement in QFT. These morals are about the role that dynamics plays in eliminating ‘impossible measurements’, the abandonment of the operational interpretation of local algebras \({\mathcal {A}}(O)\) as representing possible operations carried out in region _O_, and the interpretation of state update rules. Finally, we examine the form that the ‘impossible measurements’ problem takes in histories-based approaches and we discuss the remaining challenges. (shrink)

With A Theory of General Ethics Warwick Fox both defines the field of General Ethics and offers the first example of a truly general ethics. Specifically, he develops a single, integrated approach to ethics that encompasses the realms of interhuman ethics, the ethics of the natural environment, and the ethics of the built environment. Thus Fox offers what is in effect the first example of an ethical "Theory of Everything."Fox refers to his own approach to General Ethics as (...) the "theory of responsive cohesion." He argues that the best examples in any domain of interest--from psychology to politics, from conversations to theories--exemplify the quality of responsive cohesion, that is, they hold together by virtue of the mutual responsiveness of the elements that constitute them. Fox argues that the relational quality of responsive cohesion represents the most fundamental value there is. He then develops the theory of responsive cohesion, central features of which include the elaboration of a "theory of contexts" as well as a differentiated model of our obligations in respect of all beings. In doing this, he draws on cutting-edge work in cognitive science in order to develop a powerful distinction between beings who use language and beings that do not.Fox tests his theory against eighteen central problems in General Ethics--including challenges raised by abortion, euthanasia, personal obligations, politics, animal welfare, invasive species, ecological management, architecture, and planning--and shows that it offers sensible and defensible answers to the widest possible range of ethical problems. (shrink)

he model theory of groups of unitriangular matrices over rings is studied. An important tool in these studies is a new notion of a quasiunitriangular group. The models of the theory of all unitriangular groups are algebraically characterized; it turns out that all they are quasiunitriangular groups. It is proved that if R and S are domains or commutative associative rings then two quasiunitriangular groups over R and S are isomorphic only if R and S are isomorphic (...) or antiisomorphic. This algebraic result is new even for ordinary unitriangular groups. The groups elementarily equivalent to a single unitriangular group UTn are studied. If R is a skew field, they are of the form UTn, for some S ≡ R. In general, the situation is not so nice. Examples are constructed demonstrating that such a group need not be a unitriangular group over some ring; moreover, there are rings P and R such that UTn ≡ UTn, but UTn cannot be represented in the form UTn for S ≡ R. We also study the number of models in a power of the theory of a unitriangular group. In particular, we prove that, for any communicative associative ring R and any infinite power λ, I = I). We construct an associative ring such that I = 3 and I) = 2. We also study models of the theory of UTn in the case of categorical R. (shrink)

Fields of characteristic zero with several commuting derivations can be treated as fields equipped with a space of derivations that is closed under the Lie bracket. The existentially closed instances of such structures can then be given a coordinate-free characterization in terms of differential forms. The main tool for doing this is a generalization of the Frobenius Theorem of differential geometry.

The basic idea of the conceptual paper is to discuss the notion of value creation in the business and society field and to present the public value concept as a way of extending the understanding of business’s value creation for society. First, the paper draws on the value balance accountability model by Schwartz and Carroll, in which value creation is identified as a central element in the business and society field. Second, based on this, we critically evaluate the VBA (...) model’s value notion, which appears to be relatively vague and narrow. Third, in order to tackle these gaps, we present Meynhardt’s public value approach, which provides an extended notion of value creation. We further propose a combined public value-balance-accountability-framework. Public value fills the framework’s value dimension with actual content and provides a microfoundation. It helps to overcome the separation fallacy. The combined framework contributes to both theory and practice in the business and society field. (shrink)

The aim of the study is to contribute to a better understanding of some aspects of the structure of biological knowledge and to make clearer to what extent the methods of reasoning may be useful in this field when only qualitative information is available. A fragment of biological knowledge (theory of cell motility) is analysed from the logico-methodological point of view as a coherent system and the possibility of its formal representation is investigated. The analysis is based on distinguishing (...) the main objects and their features (attributes) of which a given piece of knowledge is composed and on the values which these features may display. The features are interconnected by relations (in which various number of arguments appear) and these relations constitute the main (general, higher level) laws of a given fragment of knowledge (theory). Values of attributes are also mutually connected and these relations correspond to the detailed (lower level) laws. A computer system (in which Prolog language was used) enables to perform inference operations of progressive as well as regressive type. The main categories of reasoning procedures are described and illustrated by examples, namely a) search for conclusions which may be confronted with the actual knowledge in order to verify the system as a whole, b) formation of working hypotheses in the process of their empirical verification and explanation of facts and laws. The problem of development and modification of the system is also discussed. (shrink)

In, Marker and Steinhorn characterized models of an o‐minimal theory such that all types over M realized in N are definable. In this article we characterize pairs of algebraically closed valued fields satisfying the same property. In o‐minimal theories, a pair of models for which all 1‐types over M realized in N are definable has already the desired property. Although it is true that if M is an algebraically closed valued field such that all 1‐types over (...) M are definable then all types over M are definable, we build a counterexample for the relative statement, i.e., we show for any that there is a pair of algebraically closed valued fields such that all n‐types over M realized in N are definable but there is an ‐type over M realized in N which is not definable. (shrink)