As is well known, the variable-sharing property (vsp) is, according to Anderson and Belnap, a necessary property of any relevant logic. In this paper, we shall consider two versions of the vsp, what we label the "weak vsp" (wvsp) and the "strong vsp" (svsp). In addition, the "no loose pieces property," a property related to the wvsp and the svsp, will be defined. Each one of these properties shall generally be characterized by means of a class of logical matrices. (...) In this way, any logic verified by an actual matrix in one of these classes has the property the class generally represents. Particular matrices (and so, logics) in each class are provided. (shrink)

Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables (...) ‘x’ and ‘y’ are synonymous, since sentences differing by the total, proper substitution of ‘x’ for ‘y’ always agree in meaning. We offer a precise interpretation of the challenge posed by (i) and (ii). We then develop some neglected passages of Tarski to show that his semantics for variables has the resources to resolve the antinomy without abandoning standard compositional semantics. (shrink)

Parity games are combinatorial representations of closed Boolean μ-terms. By adding to them draw positions, they have been organized by Arnold and Santocanale [3] and [27] into a μ-calculus whose standard interpretation is over the class of all complete lattices. As done by Berwanger et al. [8] and [9] for the propositional modal μ-calculus, it is possible to classify parity games into levels of a hierarchy according to the number of fixed-point variables. We ask whether this hierarchy collapses w.r.t. the (...) standard interpretation. We answer this question negatively by providing, for each n≥1, a parity game Gn with these properties: it unravels to a μ-term built up with n fixed-point variables, it is not semantically equivalent to any game with strictly less than n−2 fixed-point variables. (shrink)

This paper argues that research on the business case for corporate social responsibility (CSR) must account for the path dependent nature of firm-stakeholderrelations, and develops the construct of stakeholder influence capacity (SIC) to fill this void. SIC helps to explain why the effects of CSR on corporate financial performance (CFP) vary across firms and across time, therein providing a missing link in the study of the business case. This paper distinguishes CSR from related and confounded corporate resource allocations and from (...) corporate social performance (CSP), then incorporates SIC into a model that explains how acts of CSR are transformed into CFP through stakeholder relationships. This paper also develops a set of propositions to aid future research on the contingencies that produce variable financial returns to investments in CSR. (shrink)

The essays in this book explore the different ways the body has been experienced and interpreted in history, from the medieval to the modern period. Challenging the negative perceptions that the term {u2019}disability{u2019} suggests, the essays together present a mosaic of literary representations of bodies and accounts of real lives lived in their particularity and peculiarity. The book does not attempt to be exhaustive, but rather it celebrates the fact that it is not. By presenting a group of individual cases (...) from different periods in history, the collection demonstrates that any overarching way of describing bodies, or unifying description of the experience of the myriad ways of being in a body, is reductive and unhelpful. The variability of each body in its context is our subject. (shrink)

Some 55 years after the publication of Russell's seminal ‘On Denoting’, Quine adopted the theory of definite descriptions presented therein to formulate his perspicuous lingua franca for the sciences. This paper illustrates how, in so doing, Quine's lingua franca inherited an old antinomy at the core of Russell's theory of definite descriptions, specifically, the lack of congruency between notation and metaphysical commitments when the variable assumes the role of fundamental singular reference. In this context, the paper contends that the (...) phrase ‘to be is purely and simply to be the value of the variable’ is far from the straightforward solution Quine initially envisioned for his lingua franca. Additionally, it argues that it is unlikely that an attempt to account for a determinate object theory, such as those propounded by Russell and Quine, can prove successful when grounded in a referential theory of quantificational logic where the variable, seen as a simple range of values, holds fundamental singular referent-position. The paper concludes by suggesting that Meinong's object theory could resolve the problem of the variable, albeit at the cost of potentially undesirable ontological and logical commitments. Alternatively, Kit Fine's recent work on other antinomies in the variable may provide a promising approach to exploring how to salvage the variable as a formal foundation for ontology. (shrink)

Some 55 years after the publication of Russell's seminal ‘On Denoting’, Quine adopted the theory of definite descriptions presented therein to formulate his perspicuous lingua franca for the sciences. This paper illustrates how, in so doing, Quine's lingua franca inherited an old antinomy at the core of Russell's theory of definite descriptions, specifically, the lack of congruency between notation and metaphysical commitments when the variable assumes the role of fundamental singular reference. In this context, the paper contends that the (...) phrase ‘to be is purely and simply to be the value of the variable’ is far from the straightforward solution Quine initially envisioned for his lingua franca. Additionally, it argues that it is unlikely that an attempt to account for a determinate object theory, such as those propounded by Russell and Quine, can prove successful when grounded in a referential theory of quantificational logic where the variable, seen as a simple range of values, holds fundamental singular referent‐position. The paper concludes by suggesting that Meinong's object theory could resolve the problem of the variable, albeit at the cost of potentially undesirable ontological and logical commitments. Alternatively, Kit Fine's recent work on other antinomies in the variable may provide a promising approach to exploring how to salvage the variable as a formal foundation for ontology. (shrink)

It is common in attempts to extend the theory of evolution to culture to generalize from the causal basis of biological evolution, so that evolutionary theory becomes the theory of copying processes. Generalizing from the formal dynamics of evolution allows greater leeway in what kinds of things cultural entities can be, if they are to evolve. By understanding the phenomenon of cultural transmission in terms of coordinated phenotypic variability, we can have a theory of cultural evolution which allows us to (...) avoid the various difficulties with the elaboration of informational entities such as the cultural replicator, or meme. Such an account is a boon to the project of evolutionary epistemology since it confirms the presumption in favor of the general adaptiveness of culture, illuminating rather than obscuring the inherent intimacy of our relationship to (e.g.) our ideas. (shrink)

Children are those whose lives are most affected by political conflict. Efforts to establish global peace, equality, justice, and security should, therefore, consider best approaches for aiding and...

There is a solution to the antinomy of the variable that does not call for semantic relationism. I argue that if we carefully distinguish between variable types and variable tokens or occurrences, and if we take the number of variable types involved properly into account, then coordination among variable tokens or occurrences is reducible to an intrinsic semantic feature of those tokens or occurrences. The fact that two tokens or occurrences of the same variable (...) type contained in the same sentence or context assume the same value at a time derives from an intrinsic semantic feature of a token or occurrence, namely from being a token or occurrence of a type whose tokens or occurrences must assume the same value at a time if contained in the same sentence or context. (shrink)

Moral capacity is an important feature of what it means to be human. In this volume, the contributors have taken on the daunting task of trying to distinguish between legal and moral capacity. This distinction is difficult at times for clinicians, philosophers and legal scholars alike. Part of the challenge of defining moral capacity lies in the difficulty of adequately categorizing it. For this reason, the editors have chosen to divide the book into three parts. The first looks at the (...) concepts involved in the discussion of moral capacity; the second considers the role of moral capacity in the lives of professionals; and the final part reflects on case studies of moral capacity or incapacity illustrating the challenge that moral capacity presents - its definition lying between two seemingly incommensurable models, those of the threshold and continuum. This volume takes a multidisciplinary approach to the subject, and ties the disciplines of medicine, philosophy and law into the health context. It will be of interest to medical health professionals as well as researchers working in the areas of philosophy and law. (shrink)

This paper argues that research on the business case for corporate social responsibility (CSR) must account for the path dependent nature of firm-stakeholderrelations, and develops the construct of stakeholder influence capacity (SIC) to fill this void. SIC helps to explain why the effects of CSR on corporate financial performance (CFP) vary across firms and across time, therein providing a missing link in the study of the business case. This paper distinguishes CSR from related and confounded corporate resource allocations and from (...) corporate social performance (CSP), then incorporates SIC into a model that explains how acts of CSR are transformed into CFP through stakeholder relationships. This paper also develops a set of propositions to aid future research on the contingencies that produce variable financial returns to investments in CSR. (shrink)

In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′serving the same purpose that RMLs, to wit: any logic verified by an RML′has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R.

The logic TM is the result of adding the mingle axiom, M to Ticket Entailment logic, T. In the present study, it is proved that TM has the variable-sharing property . Ternary relational semantics for TM is provided. Finally, an interesting extension of TM with the vsp is briefly discussed.

Sex differences in behavior are most interesting when they are the result of inherent differences in the operational rules motivating behavior and not merely a reflection of differing life history experiences. American men and women exhibit a few differences in testamentary patterns of property allocation that appear to be due to inherently different rules of allocation. Even when analyses control for resources and surviving kin configurations, women distribute their property among a greater number of individual beneficiaries than do men. The (...) most striking differences in property allocation between men and women occur within the nuclear family and reflect differences in reproductive life span and the resulting reproductive conflicts between spouses that can endure beyond death. (shrink)

As it is well known, Relevance Logic R plus the axiom mingle (R-Mingle) does not have the variable-sharing property (vsp). The aim of this paper is to improve this result by defining a weak logic with the axiom mingle and not included in minimal logic BM lacking the vsp.

Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper shows an acute form of non-conservativeness, namely that the Boolean-free fragment of the Boolean extension of a relevant logic need not always satisfy the variable-sharing property. In fact, it is shown that such an extension can in fact yield classical logic. For a vast range of relevant logic, however, it is shown that the variable-sharing property, restricted to the Boolean-free fragment, still holds for the (...) Boolean extended logic. (shrink)

Bodies of Information initiates the Routledge Advances in the History of Bioethics series by encompassing interdisciplinary Bioethical discussions on a wide range of descriptions of bodies in relation to their contexts from varying perspectives: including literary analysis, sociology, criminology, anthropology, osteology and cultural studies, to read a variety of types of artefacts, from the Romano-British period to Hip Hop. Van Renslaer Potter coined the phrase Global Bioethics to define human relationships with their contexts. This and subsequent volumes return to Potter's (...) founding vision from historical perspectives, and asks, how did we get here from then? (shrink)

A restriction of R-Mingle with the variable-sharing property and the Ackermann properties is defined. From an intuitive semantical point of view, this restriction is an alternative to Anderson and Belnap’s logic of entailment E.

The paper reviews the leading attempts in the literature—contextualist, relativist, and interest-relative invariantist—to provide a satisfactory semantic theory of the ways in which the correctness conditions of ascriptions of knowledge seem to vary in tandem with variation in pragmatic factors—interests, stakes, and sentences—afflicting the parties concerned. It is argued that none of these attempts provides a satisfactory account of all the variability phenomena save at the cost of mis-predicting other aspects of what we count as acceptable uses of “knows” and (...) its cognates. The paper concludes with the suggestion that the correct reaction to this finding is not a reversion to the traditional kind of invariantism about knowledge, but rather a move to a kind of deflationism about “knows” broadly comparable to the familiar deflationist account of “true”. (shrink)

We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is (...) defined in terms of a \-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints. (shrink)

The literature’s interest has been focused on the study of well-being or depression. However, there has been little research that investigates the relationship between well-being and hopelessness (HPL) and the underlying contextual and dispositional variables. Therefore, the aim of the present study was to examine the relationship between some contextual (need-supportive interpersonal behavior and need-thwarting interpersonal behavior) and dispositional variables (dispositional optimism, positive/negative affectivity, explanatory style), academic achievement, general well-being, and school HPL in adolescent students. The results showed that general (...) well-being was positively predicted by need-supportive interpersonal behavior, dispositional optimism, positive affectivity, and adaptive explanatory style (attribution to commitment in the school context), while it was negatively predicted by negative affectivity. Meanwhile, school HPL was positively predicted by need-thwarting interpersonal behavior, negative affectivity, dysfunctional explanatory style (attribution to luck in the school context), while it was negatively predicted by attribution to commitment in the school context and academic achievement. These results provide useful data for the implementation of well-being promotion and school HPL prevention. The implications are discussed as follows. (shrink)

The question addressed in this paper is how the degree of justification of a belief is determined. A conclusion may be supported by several different arguments, the arguments typically being defeasible, and there may also be arguments of varying strengths for defeaters for some of the supporting arguments. What is sought is a way of computing the “on sum” degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all (...) relevant reasons. (shrink)

Variability is prevalent in early language acquisition, but, whether it supports or hinders learning is unclear; while target variability has been shown to facilitate word learning, variability in competitor items has been shown to make the task harder. Here, we tested whether background variability could boost learning in a referent selection task. Two groups of 2-year-old children saw arrays of one novel and two known objects on a screen, and they heard a novel or known label. Stimuli were identical across (...) conditions, with the exception that in the constant color condition objects appeared on a uniform white background, and in the variable color condition backgrounds were different, uniform colors. At test, only children in the variable condition showed evidence of retaining label-object associations. These data support findings from the adult memory literature, which suggest that variability supports learning by decontextualizing representations. We argue that these data are consistent with dynamic systems accounts of learning in which low-level entropy adds sufficient noise to the developmental system to precipitate a change in behavior. (shrink)

The present studies tested the hypothesis that strong assumptions about within-category homogeneity impede children’s recognition of the inductive value of diverse samples of evidence. In Study 1a, children (7-year-olds) and adults were randomly assigned to receive a prime emphasizing within-category variability, a prime emphasizing within-category similarities, or to not receive a prime. Only following the variability prime, children demonstrated a reliable preference for evaluating diverse over nondiverse samples to determine whether there is support for a category-wide generalization. Adults demonstrated a (...) robust preference for diverse samples in all conditions. These effects extended beyond the specific categories included in the prime, as well as to multiple types of test questions. Study 1b demonstrated that priming variability leads children to select diverse samples only when doing so is informative for induction. Implications for conceptual development are discussed. (shrink)