This paper presents an enrichment of the Gabbay–Woods schema of Peirce’s 1903 logical form of abduction with illocutionary acts, drawing from logic for pragmatics and its resources to model justified assertions. It analyses the enriched schema and puts it into the perspective of Peirce’s logic and philosophy.

Following the speech act theory, we take hypotheses and assertions as linguistic acts with different illocutionary forces. We assume that a hypothesis is justified if there is at least a scintilla of evidence for the truth of its propositional content, while an assertion is justified when there is conclusive evidence that its propositional content is true. Here we extend the logical treatment for assertions given by Dalla Pozza and Garola by outlining a pragmatic logic for assertions and hypotheses. On the (...) basis of this extension we analyse the standard logical opposition relations for assertions and hypotheses. We formulate a pragmatic square of oppositions for assertions and a hexagon of oppositions for hypotheses. Finally, we give a mixed hexagon of oppositions to point out the opposition relations for assertions and hypotheses. (shrink)

We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the (...) S4 modal translation, we give a de nition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is de ned and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, de ned as a hypothesis that in some situation the truth of p is epistemically necessary. (shrink)

A lot of attention has recently been devoted to the notion of Trustworthy AI (TAI). However, the very applicability of the notions of trust and trustworthiness to AI systems has been called into question. A purely epistemic account of trust can hardly ground the distinction between trustworthy and merely reliable AI, while it has been argued that insisting on the importance of the trustee’s motivations and goodwill makes the notion of TAI a categorical error. After providing an overview of the (...) debate, we contend that the prevailing views on trust and AI fail to account for the ethically relevant and value-laden aspects of the design and use of AI systems, and we propose an understanding of the notion of TAI that explicitly aims at capturing these aspects. The problems involved in applying trust and trustworthiness to AI systems are overcome by keeping apart trust in AI systems and interpersonal trust. These notions share a conceptual core but should be treated as distinct ones. (shrink)

The potential development of self-driving cars (also known as autonomous vehicles or AVs – particularly Level 5 AVs) has called the attention of different interested parties. Yet, there are still only a few relevant international regulations on them, no emergency patterns accepted by communities and Original Equipment Manufacturers (OEMs), and no publicly accepted solutions to some of their pending ethical problems. Thus, this paper aims to provide some possible answers to these moral and practical dilemmas. In particular, we focus on (...) what AVs should do in no-win scenarios and on who should be held responsible for these types of decisions. A naturalistic perspective on ethics informs our proposal, which, we argue, could represent a pragmatic and realistic solution to the regulation of AVs. We discuss the proposals already set out in the current literature regarding both policy-making strategies and theoretical accounts. In fact, we consider and reject descriptive approaches to the problem as well as the option of using either a strict deontological view or a solely utilitarian one to set AVs’ ethical choices. Instead, to provide concrete answers to AVs’ ethical problems, we examine three hierarchical levels of decision-making processes: country-wide regulations, OEM policies, and buyers’ moral attitudes. By appropriately distributing ethical decisions and considering their practical implications, we maintain that our proposal based on ethical naturalism recognizes the importance of all stakeholders and allows the most able of them to take actions (the OEMs and buyers) to reflect on the moral leeway and weight of their options. (shrink)

Following the speech act theory, we take hypotheses and assertions as linguistic acts with different illocutionary forces. We assume that a hypothesis is justified if there is at least a scintilla of evidence for the truth of its propositional content, while an assertion is justified when there is conclusive evidence that its propositional content is true. Here we extend the logical treatment for assertions given by Dalla Pozza and Garola (1995, Erkenntnis, 43, 81–109) by outlining a pragmatic logic for assertions (...) and hypotheses. On the basis of this extension we analyse the standard logical opposition relations for assertions and hypotheses. We formulate a pragmatic square of oppositions for assertions and a hexagon of oppositions for hypotheses. Finally, we give a mixed hexagon of oppositions to point out the opposition relations for assertions and hypotheses. (shrink)

The beliefs involved in the placebo effect are often assumed to be self-fulfilling, that is, the truth of these beliefs would merely require the patient to hold them. Such a view is commonly shared in epistemology. Many epistemologists focused, in fact, on the self-fulfilling nature of these beliefs, which have been investigated because they raise some important counterexamples to Nozick’s “tracking theory of knowledge.” We challenge the self-fulfilling nature of placebo-based beliefs in multi-agent contexts, analyzing their deep epistemological nature and (...) the role of higher-order beliefs involved in the placebo effect. (shrink)

The pragmatic logic of assertions shows a connection between ignorance and decidability. In it, we can express pragmatic factual ignorance and first-order ignorance as well as some of their variants. We also show how some pragmatic versions of second-order ignorance and of Rumsfeld-ignorance may be formulated. A specific variant of second-order ignorance is particularly relevant. This indicates a strong pragmatic version of ignorance of ignorance, irreducible to any previous form of ignorance, which defines limits to what can justifiably be asserted (...) about higher-order ignorance. Finally, we relate the justified assertion of second-order ignorance with scientific assertions. (shrink)

This paper explores the intertwining of uncertainty and values. We consider an important but underexplored field of fundamental uncertainty and values in decision-making. Some proposed methodologies to deal with fundamental uncertainty have included potential surprise theory, scenario planning and hypothetical retrospection. We focus on the principle of uncertainty transduction in hypothetical retrospection as an illustrative case of how values interact with fundamental uncertainty. We show that while uncertainty transduction appears intuitive in decision contexts it nevertheless fails in important ranges of (...) strategic game-theoretic cases. The methodological reasons behind the failure are then examined. (shrink)

The paper proposes two logical analyses of (the norms of) justification. In a first, realist-minded case, truth is logically independent from justification and leads to a pragmatic logic LP including two epistemic and pragmatic operators, namely, assertion and hypothesis. In a second, antirealist-minded case, truth is not logically independent from justification and results in two logical systems of information and justification: AR4 and AR4¢, respectively, provided with a question-answer semantics. The latter proposes many more epistemic agents, each corresponding to a (...) wide variety of epistemic norms. After comparing the different norms of justification involved in these logical systems, two hexagons expressing Aristotelian relations of opposition will be gathered in order to clarify how (a fragment of) pragmatic formulas can be interpreted in a fuzzy-based question-answer semantics. (shrink)

Peirce and Frege both distinguished between the propositional content of an assertion and the assertion of a propositional content, but with different notational means. We present a modification of Peirce’s graphical method of logic that can be used to reason about assertions in a manner similar to Peirce’s original method. We propose a new system of Assertive Graphs, which unlike the tradition that follows Frege involves no ad hoc sign of assertion. We show that axioms of intuitionistic logic can be (...) derived from AGs, and argue that AGs analyse and represent assertions and illocutionary content in a way which is motivated both by its logical properties and its historical connection with the ideas that led to the development of the graphical method. (shrink)

This book offers a philosophically-based, yet clinically-oriented perspective on current medical reasoning aiming at 1) identifying important forms of uncertainty permeating current clinical reasoning and practice 2) promoting the application of an abductive methodology in the health context in order to deal with those clinical uncertainties 3) bridging the gap between biomedical knowledge, clinical practice, and research and values in both clinical and philosophical literature. With a clear philosophical emphasis, the book investigates themes lying at the border between several disciplines, (...) such as medicine, nursing, logic, epistemology, and philosophy of science; but also ethics, epidemiology, and statistics. At the same time, it critically discusses and compares several professional approaches to clinical practice such as the one of medical doctors, nurses and other clinical practitioners, showing the need for developing a unified framework of reasoning, which merges methods and resources from many different clinical but also non-clinical disciplines. In particular, this book shows how to leverage nursing knowledge and practice, which has been considerably neglected so far, to further shape the interdisciplinary nature of clinical reasoning. Furthermore, a thorough philosophical investigation on the values involved in health care is provided, based on both the clinical and philosophical literature. The book concludes by proposing an integrative approach to health and disease going beyond the so-called “classical biomedical model of care”. (shrink)

This study addresses the question of normative analysis of the value‐based aspects of nursing. In our perspective, values in science may be distinguished into (i) epistemic when related to the goals of truth and objectivity and (ii) non‐epistemic when related to social, cultural or political aspects. Furthermore, values can be called constitutive when necessary for a scientific enterprise, or contextual when contingently associated with science. Analysis of the roles of the various forms of values and models of knowledge translation provides (...) the ground to understand the specific role of values in nursing. A conceptual framework has been built to classify some of the classical perspectives on nursing knowledge and to examine the relationships between values and different forms of knowledge in nursing. It follows that adopting a normative perspective in the analysis of nursing knowledge provides key elements to identify its proper dimension. (shrink)

This article presents and defends an integrated view of the placebo effect, termed “affective-meaning-making” model, which draws from theoretical reflection, clinical outcomes, and neurophysiological findings. We consider the theoretical limitations of those proposals associated with the “meaning view” on the placebo effect which leave the general aspects of meaning unspecified, fail to analyze fully the role of emotions and affect, and establish no clear connection between the theoretical, physiological, and psychological aspects of the effect. We point out that a promising (...) way to overcome these limitations is given by grounding the placebo effect on Peirce’s theory of meaning, in which the role of the meaning constitution and change is placed in logical and objective structures. We also show the connection between our theoretical proposal and the appraisal theory and integrate it with emotion regulation. (shrink)

Diagnostic frameworks are essential to many scientific and technological activities and clinical practice. This study examines the main fundamental aspects of such frameworks. The three components required for all diagnoses are identified and examined, i.e. their normative dimension, temporal nature and structure, and teleological perspective.The normative dimension of a diagnosis is based on (1) epistemic values when associated with Hempel's inductive risk concerning the balance between false‐positive and false‐negative outcomes, leading to probabilistic judgements; and (2) non‐epistemic values when related to (...) ideas such as well‐being, normality, illness, etc, as idealized norms or ideal points of reference.It should be noted that medical diagnoses match the three necessary components, while some essential diagnostic frameworks – the taxonomies of Gordon and NANDA – in nursing lack some components. The main lack is normative as the most popular frameworks in nursing diagnosis seem to be descriptions of observed reality rather than normative and value‐based judgements in which both epistemic and non‐epistemic values may coexist. (shrink)

The goal of this paper is to review and critically discuss the philosophical aspects of probabilistic seismic hazard analysis (PSHA). Given that estimates of seismic hazard are typically riddled with uncertainty, diferent epistemic values (related to the pursuit of scientifc knowledge) compete in the selection of seismic hazard models, in a context infuenced by non-epistemic values (related to practical goals and aims) as well. We frst distinguish between the diferent types of uncertainty in PSHA. We claim that epistemic and nonepistemic (...) considerations are closely related in the selection of the appropriate estimate of seismic hazard by the experts. Finally, we argue that the division of scientifc responsibility among the experts can lead to responsibility gaps. This raises a problem for the ownership of the results (“no one’s model” problem) similar to the “problem of many hands” in the ethics of technology. We conclude with a plea for a close collaboration between philosophy and engineering. (shrink)

The present paper is devoted to present two pragmatic logics and their corresponding intended interpretations according to which an illocutionary act of hypothesis-making is justified by a scintilla of evidence. The paper first introduces a general pragmatic frame for assertions, expanded to hypotheses, ${\mathsf{AH}}$ and a hypothetical pragmatic logic for evidence ${\mathsf{HLP}}$. Both ${\mathsf{AH}}$ and ${\mathsf{HLP}}$ are extensions of the Logic for Pragmatics, $\mathcal{L}^P$. We compare ${\mathsf{AH}}$ and $\mathsf{HLP}$. Then, we underline the expressive and inferential richness of both systems in (...) dealing with hypothetical judgements, especially when based on different, sometimes conflicting, evidence. (shrink)

. Decision-making under uncertainty is sometimes investigated as a homogeneous problem, independently of the type of decision-maker and the level and nature of the decision itself. However, when the decision-maker is a public authority, there immediately arise problems additional to those that concern any other decision-maker. This is not always clearly recognised in orthodox discussions on decisions under conditions of uncertainty. This article investigates the methodological, strategic and procedural challenges of taking public decisions in such conditions. It focuses mainly on (...) decisions involving urban contexts, such as planning decisions regarding land use and building transformations, by trying to develop some pioneering research studies in this field. (shrink)

This study addresses the question of normative analysis of the value‐based aspects of nursing. In our perspective, values in science may be distinguished into (i) epistemic when related to the goals of truth and objectivity and (ii) non‐epistemic when related to social, cultural or political aspects. Furthermore, values can be called constitutive when necessary for a scientific enterprise, or contextual when contingently associated with science. Analysis of the roles of the various forms of values and models of knowledge translation provides (...) the ground to understand the specific role of values in nursing. A conceptual framework has been built to classify some of the classical perspectives on nursing knowledge and to examine the relationships between values and different forms of knowledge in nursing. It follows that adopting a normative perspective in the analysis of nursing knowledge provides key elements to identify its proper dimension. (shrink)

The Knowability Paradox is a logical argument showing that if all truths are knowable in principle, then all truths are, in fact, known. Many strategies have been suggested in order to avoid the paradoxical conclusion. A family of solutions –ncalled logical revision – has been proposed to solve the paradox, revising the logic underneath, with an intuitionistic revision included. In this paper, we focus on so-called revisionary solutions to the paradox – solutions that put the blame on the underlying logic. (...) Specifically, we analyse a possibile translation of the paradox into a modified intuitionistic fragment of a logic for pragmatics inspired by Dalla Pozza and Garola in 1995. Our aim is to understand if KILP is a candidate for the logical revision of the paradox and to compare it with the standard intuitionistic solution to the paradox. (shrink)

Clinical equipoise has been proposed as an ethical principle relating uncertainty and moral leeway in clinical research. Although CE has traditionally been indicated as a necessary condition for a morally justified introduction of a new RCT, questions related to the interpretation of this principle remain woefully open. Recent proposals to rehabilitate CE have divided the bioethical community on its ethical merits. This paper presents a new argument that brings out the epistemological difficulties we encounter in justifying CE as a principle (...) to connect uncertainty and moral leeway in clinical ethics. The argument proposes, first, that the methodology of hypothetical retrospection is applicable to the RCT design and that it can accommodate uncertainty. As currently understood, however, HR should give up its reliance on the assumption of uncertainty transduction, because the latter assumes the principle of indifference, which does not accommodate uncertainty in the right way. The same principle is then seen to distort also the received interpretations of CE. (shrink)

Scientific evidence and scientific values under risk and uncertainty are strictly connected from the point of view of Peirce’s pragmaticism. In addition, economy and statistics play a key role in both choosing and testing hypotheses. Hence we may show also the connection between the methodology of the economy of research and statistical frequentism, both originating from pragmaticism. The connection is drawn by the regulative principles of synechism, tychism and uberty. These principles are values that have both epistemic and non-epistemic dimension. (...) They concern both the decisions to test a hypothesis as well as inductive risk. The validity of this result stems from the values cost–benefit analysis imposes on scientific inquiry. Values associated with the economy of research are important not only in the pre-test phases of generating hypotheses but also when hypotheses are effectively tested. Peirce took these economic considerations to leave room for an interpretation of probability which is not only a frequentist and propensity-theoretic but also a conceptualist one referring to degrees of belief. We show that this leeway nonetheless agrees with the theory of the economy of scientific methods. (shrink)

Nursing knowledge stems from a dynamic interplay between population‐based scientific knowledge (the general) and specific clinical cases (the particular). We compared the ‘cascade model of knowledge translation’, also known as ‘classical biomedical model’ in clinical practice (in which knowledge gained at population level may be applied directly to a specific clinical context), with an emergentist model of knowledge translation. The structure and dynamics of nursing knowledge are outlined, adopting the distinction between epistemic and non‐epistemic values. Then, a (moderately) emergentist approach (...) to nursing knowledge is proposed, based on the assumption of a two‐way flow from the general to the particular and vice versa. The case of the ‘placebo effect’ is analysed as an example of emergentist knowledge. The placebo effect is usually considered difficult to be explained within the classical biomedical model, and we underscore its importance in shaping nursing knowledge. In fact, nurses are primarily responsible for administering placebo in the clinical setting and have an essential role in promoting the placebo effect and reducing the nocebo effect. The beliefs responsible for the placebo effect are as follows: (1) interactive, because they depend on the relationship between patients and health care professionals; (2) situated, because they occur in a given clinical context related to certain rituals; and (3) grounded on higher order beliefs concerning what an individual thinks about the beliefs of others. It is essential to know the clinical context and to understand other people's beliefs to make sense of the placebo effect. The placebo effect only works when the (higher order) beliefs of doctors, nurses and patients interact in a given setting. Finally, we argue for a close relationship between placebo effect and nursing knowledge. (shrink)

The logic of assertive graphs is a modification of Peirce’s logic of existential graphs, which is intuitionistic and which takes assertions as its explicit object of study. In this paper we extend AGs into a classical graphical logic of assertions whose internal logic is classical. The characteristic feature is that both AGs and ClAG retain deep-inference rules of transformation. Unlike classical EGs, both AGs and ClAG can do so without explicitly introducing polarities of areas in their language. We then compare (...) advantages of these two graphical approaches to the logic of assertions with a reference to a number of topics in philosophy of logic and to their deep-inferential nature of proofs. (shrink)

The aim of this paper is twofold: First, we present and develop a system of logic for pragmatics including the act of denial. Second, we analyse in our framework the so-called paradox of assertability. We show that it is possible to yield sentences that are not assertable. Moreover, under certain conditions, a symmetric result can be obtained: There is a specular paradox of deniability. However, this paradox is based on the problematic principle of classical denial equivalence.

Volume 32, Issue 1, March 2019, Page 65-67.

In Die Grundgesetze der Arithmetik (I, §48), Frege introduces his rule of the fusion of horizontals, according to which if an occurrence of the horizontal stroke is followed by another occurrence of the same stroke, either in isolation or “contained” in a propositional connective, the two occurrences can be fused with each other. However, the role of this rule, and of the horizontal sign more generally, is controversial; Michael Dummett notoriously claimed, for instance, that the horizontal is “wholly superfluous” in (...) Frege's logical system. In this paper, we challenge Dummett's view by providing a comprehensive analysis of the significance of the horizontal stroke. After some preliminary remarks, we argue that even if Frege's connectives in some sense “contain” the horizontal, yet they are total functions. Then, we take up the question of the sense expressed by the horizontal, and we claim that, unlike other sentential operators, the horizontal is not sense‐compositional. Finally, we consider the semantic and pragmatic aspects of Frege's horizontal in connection to his judgment stroke and the double judgment stroke. Contra Dummett, we argue that the horizontal is a special and indispensable element of Frege's logic. (shrink)

Technological innovation is almost always investigated from an economic perspective; with few exceptions, the specific technological and social nature of innovation is often ignored. We argue that a novel way to characterise and make sense of different types of technological innovation is to start considering uncertainty. This seems plausible since technological development and innovation almost always occur under conditions of uncertainty. We rely on the distinction between, on the one hand, uncertainty that can be quantified (e.g. probabilistic risk) and, on (...) the other, deep forms of uncertainty that may resist the possibility of being quantified (e.g. severe or fundamental uncertainties). On the basis of these different ingredients of uncertainty in technological innovation, we propose a new taxonomy that reveals the technological nature of innovation. Unlike previous taxonomies employed to handle different types of technological innovations, our taxonomy does not consider the economic value of innovation alone; it is much more oriented towards societal preferences and forms of technological uncertainty. Finally, we investigate the coherence of our proposal with the dual nature of technological artefacts, showing that innovation can be grounded on structural and functional factors and not just on economic ones. (shrink)

The pragmatic notion of assertion has an important inferential role in logic. There are also many notational forms to express assertions in logical systems. This paper reviews, compares and analyses languages with signs for assertions, including explicit signs such as Frege’s and Dalla Pozza’s logical systems and implicit signs with no specific sign for assertion, such as Peirce’s algebraic and graphical logics and the recent modification of the latter termed Assertive Graphs. We identify and discuss the main ‘points’ of these (...) notations on the logical representation of assertions, and evaluate their systems from the perspective of the philosophy of logical notations. Pragmatic assertions turn out to be useful in providing intended interpretations of a variety of logical systems. (shrink)

The importance of epistemic values in science is universally recognized, whereas the role of non-epistemic values is sometimes considered disputable. It has often been argued that non-epistemic values are more relevant in applied sciences, where the goals are often practical and not merely scientific. In this paper, we present a case study concerning earthquake engineering. So far, the philosophical literature has considered various branches of engineering, but very rarely earthquake engineering. We claim that the assessment of seismic hazard models is (...) sensitive to both epistemic and non-epistemic values. In particular, we argue that the selection and evaluation of these models are justified by epistemic values, even if they may be contingently influenced by non-epistemic values. By contrast, the aggregation of different models into an ensemble is justified by non-epistemic values, even if epistemic values may play an instrumental role in the attainment of these non-epistemic values. A careful consideration of the different epistemic and non-epistemic values at play in the choice of seismic hazard models is thus practically important when alternative models are available and there is uncertainty in the scientific community about which model should be used. (shrink)

We consider a “polarized” version of bi-intuitionistic logic [5, 2, 6, 4] as a logic of assertions and hypotheses and show that it supports a “rich proof theory” and an interesting categorical interpretation, unlike the standard approach of C. Rauszer’s Heyting-Brouwer logic [28, 29], whose categorical models are all partial orders by Crolard’s theorem [8]. We show that P.A. Melliès notion of chirality [21, 22] appears as the right mathematical representation of the mirror symmetry between the intuitionistic and co-intuitionistc sides (...) of polarized bi-intuitionism. Philosophically, we extend Dalla Pozza and Garola’s pragmatic interpretation of intuitionism as a logic of assertions [10] to bi-intuitionism as a logic of assertions and hypotheses. We focus on the logical role of illocutionary forces and justification conditions in order to provide “intended interpretations” of logical systems that classify inferential uses in natural language and remain acceptable from an intuitionistic point of view. Although Dalla Pozza and Garola originally provide a constructive interpretation of intuitionism in a classical setting, we claim that some conceptual refinements suffice to make their “pragmatic interpretation” a bona fide representation of intuitionism. We sketch a meaning-asuse interpretation of co-intuitionism that seems to fulfil the requirements of Dummett and Prawitz’s justificationist approach. We extend the Brouwer-Heyting-Kolmogorov interpretation to bi-intuitionism by regarding co-intuitionistic formulas as types of the evidence for them: if conclusive evidence is needed to justify assertions, only a scintilla of evidence suffices to justify hypotheses. (shrink)

The present paper is intended to analyse from a theoretical point of view the relationships between natural language and idiolects in the context of communication by means of the Davidson–Dummett controversy on the nature of language. I will explore from a pragmatic point of view the reliability of an alternative position inspired by the recent literalism/contextualism debate in philosophy of language in order to overcome some limitations of Dummett’s and Davidson’s perspectives on language, idiolects and communication.

This Special Issue titled "Severe Uncertainty in Science, Medicine and Technology" aims to shed new light on the understanding of severe uncertainty and its multifaceted implications. The main idea of the papers of this collection is that, despite possible sophisticated statistical judgments towards future risks in science, medicine, and technology, severe forms of uncertainty still exist.While ignorance is usually assumed to be a total absence of knowledge, uncertainty often refers to the incompleteness of knowledge or information. In its extreme form, (...) this is called "severe uncertainty" but is also known as "fundamental," "radical," "deep," "great," or "genuine" uncertainty. A common characteristic of these... (shrink)

This paper discusses the outstanding problem of replicability of empirical data in the context of recent work on meta-analysis, especially within the field of evidence-based medicine. Specifically, it deals with the methodological issue of how to determine the degrees of heterogeneity between different collected studies. After critically reviewing the standard measures used to quantify meta-analytical heterogeneity, we argue that they should be revised in such a way to take into account the statistical power of the individual studies. We thus propose (...) some new measures of heterogeneity. Subsequently, we apply them to re-assess concrete case-studies from clinical research, thereby showing explicitly how the relevant values of heterogeneity diverge from those obtained with the original measures. (shrink)