Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic (...) to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated. (shrink)

The debate on love's reasons ignores unrequited love, which—I argue—can be as genuine and as valuable as reciprocated love. I start by showing that the relationship view of love cannot account for either the reasons or the value of unrequited love. I then present the simple property view, an alternative to the relationship view that is beset with its own problems. In order to solve these problems, I present a more sophisticated version of the property view that integrates ideas from (...) different property theorists in the love literature. However, even this more sophisticated property view falls short in accounting for unrequited love's reasons. In response, I develop a new version of the property view that I call the experiential view. On this view, we love a person not only in virtue of properties shaped by and experienced in a reciprocal loving relationship, but also in virtue of perspectival properties, whose value can be properly assessed also outside of a reciprocal loving relationship. The experiential view is the only view that can account not only for reciprocated love's reasons, but also for unrequited love's reasons. (shrink)

In this paper I present a novel taxonomy of envy, according to which there are four kinds of envy: emulative, inert, aggressive and spiteful envy. An inquiry into the varieties of envy is valuable not only to understand it as a psychological phenomenon, but also to shed light on the nature of its alleged viciousness. The first section introduces the intuition that there is more than one kind of envy, together with the anecdotal and linguistic evidence that supports it. The (...) second section proposes and explains in detail a definition of envy tout court. The third section presents a recurring distinction between behavioral tendencies of envy, which has been explained in two distinct ways, one mostly proposed by psychologists, the other discernible in the philosophical tradition. The fourth section argues that these models of explanation track two variables, whose interplay is responsible for the existence of the four envies. The fifth section illustrates four paradigmatic cases, and provides a detailed analysis of the phenomenology, motivational structure, and typical behavioral outputs of each. The paper ends with a brief discussion of the implications of the taxonomy for moral education. (shrink)

A general method for generating contraction- and cut-free sequent calculi for a large family of normal modal logics is presented. The method covers all modal logics characterized by Kripke frames determined by universal or geometric properties and it can be extended to treat also Gödel-Löb provability logic. The calculi provide direct decision methods through terminating proof search. Syntactic proofs of modal undefinability results are obtained in the form of conservativity theorems.

I argue for the view that envy and jealousy are distinct emotions, whose crucial difference is that envy involves a perception of lack while jealousy involves a perception of loss. I start by noting the common practice of using ‘envy’ and ‘jealousy’ almost interchangeably, and I contrast it with the empirical evidence that shows that envy and jealousy are distinct, albeit similar and often co-occurring, emotions. I then argue in favor of a specific way of understanding their distinction: the view (...) that envy is a response to a perceived lack of a valuable object, while jealousy is a response to a perceived loss of a valuable object. I compare such a view with the most compelling alternative theories, and show that it accounts better for paradigmatic cases. I conclude by showing how the lack vs. loss model can handle complications: ambiguous cases, that is, when it is epistemically unclear whether one experiences lack or loss; hybrid cases, that is, when one seems to experience both lack and loss; and borderline cases, that is, when it is metaphysically unclear whether one experiences lack or loss. (shrink)

The creative process has the potential to increase wellbeing and foster human flourishing (Dolan and Metcalfe, 2012 ; Forgeard and Eichner, 2014 ; O’Brien and Murray, 2015 ; Conner et al., 2018 ; Kaufman, 2018 ), yet has received little attention in the humanistic management literature. In this paper, we present three experiments showing that idea originators experience greater relationship conflict with counterparts who have committed perceived “idea theft”, i.e., proposed identical or related ideas. We test a model that identifies (...) a mechanism—self-threat—that mediates the relationship between idea theft and relationship conflict and identifies an intervention to ameliorate that self-threat via self-affirmation. Study 1 demonstrates the idea originator’s attribution of malign attributions to, and negative moral emotions toward, the counterpart. Study 2 demonstrates that idea originators ostracize both those who propose identical ideas and those who propose merely related ideas. In Study 3, evidence for self-threat as the mechanism underlying the negative relational consequences is provided via both a direct test of mediation as well as via moderation by self-affirmation. Our research contributes to the nascent idea theft literature and suggests a way to reduce its negative consequences. (shrink)

In this paper, I advance a counterexample to the collective agency thesis.

I argue that fitting envy plays a special role in safeguarding our happiness and flourishing. After presenting my theory of envy and its fittingness conditions, I contrast Kant’s view that envy is always unfitting with D’Arms and Jacobson’s defense of fitting envy as an evolutionarily-shaped response to a deep and wide human concern, that is, relative positioning. However, D’Arms and Jacobson don’t go far enough. First, I expand on their analysis of positional goodness, distinguishing between an epistemic claim, according to (...) which we use implicit or explicit comparison to know what position we occupy in a continuum of goodness, and thus to form judgments of goodness, and a metaphysical one, according to which much human goodness depends on implicit or explicit rankings and positionality. Second, I argue that fitting envy is not only intrinsically valuable qua fitting response to authentic goodness, but can be epistemically, morally and prudentially valuable. (shrink)

In this paper, I examine the manner in which analyses of the action of single agents have been pressed into service for constructing accounts of collective action. Specifically, I argue that the best analogy to collective action is a class of individual action that Carl Ginet has called 'aggregate action.' Furthermore, once we use aggregate action as a model of collective action, then we see that existing accounts of collective action have failed to accommodate an important class of (what I (...) shall call) 'unintentional collective actions.'. (shrink)

Writers on collective action are in broad agreement that in order for a group of agents to form a collective intention, the members of that group must have beliefs about the beliefs of the other members. But in spite of the fact that this so-called "interactive knowledge" is central to virtually every account of collective intention, writers on this subject have not offered a detailed account of the nature of interactive knowledge. In this paper, we argue that such an account (...) is necessary for any adequate analysis of collective intention. Furthermore, we argue that an application of Robert Aumann's theory of interactive knowledge may be used to address several puzzling features of collective intention. CiteULike Connotea Del.icio.us What's this? (shrink)

The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.

In this paper, an attempt is made to solve various problems posed to current theories of verisimilitude: the problem of linguistic variance; the problem of which are the best scientific methods for getting the most verisimilar theories; and the question of the ontological commitment in scientific theories. As a result of my solution to these problems, and with the help of other considerations of epistemological character, I conclude that the notion of 'Tarskian truth' is dispensable in a rational interpretation of (...) the scientific enterprise. As a logical result, however, falsificationism will be vindicated. (shrink)

Proofs and countermodels are the two sides of completeness proofs, but, in general, failure to find one does not automatically give the other. The limitation is encountered also for decidable non-classical logics in traditional completeness proofs based on Henkin’s method of maximal consistent sets of formulas. A method is presented that makes it possible to establish completeness in a direct way: For any given sequent either a proof in the given logical system or a countermodel in the corresponding frame class (...) is found. The method is a synthesis of a generation of calculi with internalized relational semantics, a Tait–Schütte–Takeuti style completeness proof, and procedures to finitize the countermodel construction. Finitizations for intuitionistic propositional logic are obtained through the search for a minimal derivation, through pruning of infinite branches in search trees by means of a suitable syntactic counterpart of semantic filtration, or through a proof-theoretic embedding into an appropriate provability logic. A number of examples illustrates the method, its subtleties, challenges, and present scope. (shrink)

Large portions of mathematics such as algebra and geometry can be formalized using first-order axiomatizations. In many cases it is even possible to use a very well-behaved class of first-order axioms, namely, what are called coherent or geometric implications. Such class of axioms can be translated to inference rules that can be added to a sequent calculus while preserving its structural properties. In this work, this fundamental result is extended to their infinitary generalizations as extensions of sequent calculi for both (...) classical and intuitionistic infinitary logic. As an application, a simple proof of the infinitary Barr’s theorem without the axioms of choice is shown. (shrink)

A way is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive theories. All results are proved for systems in which also the rules of weakening and contraction can be eliminated. Applications include a system of predicate logic (...) with equality in which also cuts on the equality axioms are eliminated. (shrink)

In this paper, we offer an analysis of ‘group intentions.’ On our proposal, group intentions should be understood as a state of equilibrium among the beliefs of the members of a group. Although the discussion in this paper is non-technical, the equilibrium concept is drawn from the formal theory of interactive epistemology due to Robert Aumann. The goal of this paper is to provide an analysis of group intentions that is informed by important work in economics and formal epistemology.

In the current American iconoclash, certain monuments are subject to vandalism and municipal removal from their pedestals. Phrases such as “the erasure of history” and “damnatio memoriae” point to concerns that iconoclasm is an attempt to censor history or even remove certain individuals from public memory altogether. Because these phrases beckon the past, this wave of iconoclasm calls for a close examination of previous image-breaking to establish motives. Drawing first from art history, we analyze Byzantine iconoclasm and anxieties over the (...) nature of icons’ power, before contextualizing these findings within image destruction from the Paleolithic to the present day. Each comparison is suggestive of an enduring aesthetic principle: that what appears inanimate is not always inert. Next, drawing from cultural anthropology, we argue that principles of sympathetic magic are at the heart of contemporary iconoclasms, but not in the way media outlets often suggest. Instead, the fear of history’s erasure betrays a deeply rooted equivalence between the representation and the represented. In perceiving their fates as shared, sympathetic magic is seen to persist in the way humans create, interpret, and desecrate images. We conclude with the speculative realist proposition that iconoclasm can produce new, original artworks, which carries implications for the autonomy of art and its distribution between artist and artwork. (shrink)

We examined how children’s strategy choices in solving complex subtraction problems are related to grade and to variations in problem complexity. In two studies, third- and fifth-grade children (N≈160 each study) solved multi-digit subtraction problems (e.g., 34 - 18) and described their solution strategies. In the first experiment, strategy selection was investigated by means of a free-choice paradigm, whereas in the second study a discrete-choice approach was implemented. In both experiments, analyses of strategy repertoire indicated that third-grade children were more (...) likely to report less-efficient strategies (i.e., counting) and relied more on the right-to-left solution algorithm compared to fifth-grade children who more often used efficient memory-based retrieval and conceptually-based left-to-right (i.e., decomposition) strategies. Nevertheless, all strategies were reported or selected by both older and younger children and strategy use varied with problem complexity and presentation format for both age groups. These results supported the overlapping waves model of strategy development and provide detailed information about patterns of strategy choice on complex subtraction problems. (shrink)

In this chapter, I argue that a certain kind of envy is not only morally permissible, but also, sometimes, more fitting and productive than admiration. Envy and admiration are part of our emotional palette, our toolbox of evolutionary adaptations, and they play complementary roles. I start by introducing my original taxonomy of envy, which allows me to present emulative envy, a species of envy sometimes confused with admiration. After reviewing how the two emotions differ from a psychological perspective, I focus (...) in particular on the distinct and complementary roles they play in the ethical and political domains. (shrink)

Stakeholder management devices (SMDs) are the mechanisms through which organizations respond to stakeholder concerns. Given that SMDs serve as organizational control systems for employees and managers, this research investigates the internal rather than the external effects of a firm's SMDs. Unlike most previous research, I examined the effects of these formal structures, processes, and procedures in the aggregate, rather than focusing attention on a single type of device. The study investigates the effects of a firm's stakeholder management devices, in the (...) aggregate, on three factors that influence individual behavior in organizations: expectations, attitudes, and perceived organizational climates. Respondents were managers in 112 for-profit businesses located throughout the United States. Results suggest that a firm's stakeholder management devices affect the perceived moral climates in the firm, and affect managers' expectations about the consequences of good corporate social performance, but do not affect organization members' attitudes about corporate social responsibility. (shrink)

Just as we may ask whether, and under what conditions, a collection of objects composes a single object, we may ask whether, and under what conditions, a collection of actions composes a single action. In the material objects literature, this question is known as the "special composition question," and I take it that there is a similar question to be asked of collections of actions. I will call that question the "special composition question in action," and argue that the correct (...) answer to this question depends on a particular kind of consequence produced by the individual constituent actions. (shrink)

By presenting a case study based on the argumentative analysis of news in the press, this article introduces and discusses strategic manoeuvring with contextual frames. Drawing on the linguistic notion of frame, I introduce the concept of contextual frame to refer to the news context, that is, the background against which a certain event is presented as a piece of news. I argue that newspapers and journalists make use of contextual frames in the apparently neutral genre of news reporting to (...) propose specific interpretations of the facts at issue, which become the basis for explicit comments and editorials. To show how this works, I investigate in detail a case of newspaper coverage of a complex episode using the pragma-dialectical notion of strategic manoeuvring and the Argumentum Model of Topics to analyse argument schemes. I show that, in the use of contextual frames, there is a prominent relation between presentational devices and topical potential; contextual frames provide the implicit material premises which are at the basis of argumentations through which newspapers interpret and comment on the news. (shrink)

Scientific research is reconstructed as a language game along the lines of Robert Brandom's inferentialism. Researchers are assumed to aim at persuading their colleagues of the validity of some claims. The assertions each scientist is allowed or committed to make depend on her previous claims and on the inferential norms of her research community. A classification of the most relevant types of inferential rules governing such a game is offered, and some ways in which this inferentialist approach can be used (...) for assessing scientific knowledge and practices are explored. Some similarities and differences with a game-theoretic analysis are discussed. (shrink)

Grounded theory, a research method born out of the social sciences field, offers a flexible technique that allows simultaneous data collection and processing. Researchers using this method immerse themselves in an area of study, focusing their observations on the data and taking into consideration not only their own interpretations, but also those of the other subjects involved, in order to strengthen their understanding of the social phenomena under examination. This text briefly describes the concept of grounded theory and uses concrete (...) examples to illustrate how data are analysed from the standpoint of the stereotype as an object of study. La teoría fundamentada, nacida al interior de las ciencias sociales, es un método de investigación que posee una técnica flexible y que realiza simultáneamente la recolección y el procesamiento de los datos. En este método, el investigador se encuentra inmerso en el campo de estudio y sus observaciones se abocan al dato, considerando tanto su interpretación como la de los otros sujetos implicados, con la finalidad de fortalecer la comprensión del fenómeno social investigado. En este texto se describe brevemente la teoría fundamentada y cómo se analizan los datos mediante ejemplos concretos, que se presentan a partir del estereotipo como objeto de estudio. (shrink)

An epistemic notion of verisimilitude (as the 'degree in which a theory seems closer to the full truth to a scientific community') is defined in several ways. Application to the structuralist description of theories is carried out by introducing a notion of 'empirical regularity' in structuralist terms. It is argued that these definitions of verisimilitude can be used to give formal reconstructions of scientific methodologies such as falsificationism, conventionalism and normal science.

Ortega trasladó sus ideas pedagógicas a su quehacer como profesor universitario. Muchos de sus discípulos y colaboradores han dejado constancia de ello, como aquí se refiere. Fue para ellos, sobre todo ejemplo, ejemplo de vida, de orientación vital, de sinceridad intelectual en su quehacer filosófico. En este artículo no analizamos la filosofía de Ortega, lo que hemos hecho en otros textos, sino el impacto que causó la «persona» Ortega en sus colaboradores y discípulos. Aunque es algo estudiando, nunca se ha (...) presentado de esta forma sintética que muestra la envergadura del impacto que Ortega produjo en el mundo intelectual de la Edad de Plata de la cultura española. (shrink)

Scientists can choose different claims as interpretations of the results of their research. Scientific rhetoric is understood as the attempt to make those claims most beneficial for the scientists' interests. A rational choice, game-theoretic model is developed to analyze how this choice can be made and to assess it from a normative point of view. The main conclusion is that `social' interests (pursuit of recognition) may conflict with `cognitive' ones when no constraints are put on the choices of the authors (...) of scientific papers, as in an `ideal free speech situation'. Scientific institutions may help to solve this conflict. Lastly, some empirical predictions are offered that can inspire future social research of the refereeing process. (shrink)

A sequent calculus is given in which the management of weakening and contraction is organized as in natural deduction. The latter has no explicit weakening or contraction, but vacuous and multiple discharges in rules that discharge assumptions. A comparison to natural deduction is given through translation of derivations between the two systems. It is proved that if a cut formula is never principal in a derivation leading to the right premiss of cut, it is a subformula of the conclusion. Therefore (...) it is sufficient to eliminate those cuts that correspond to detour and permutation conversions in natural deduction. (shrink)

Can we love and envy the same person at the same time? There is an overwhelming, cross-cultural and cross-disciplinary, consensus that love and envy are deeply incompatible. In this paper, I challenge this consensus, and focus in particular on the normative thesis that true love should be void of envy proper. I first propose an indirect argument. Because love and envy thrive in the same psychological conditions, it is not unlikely to feel envy toward the beloved. If we want ideals (...) that do not go against our psychological propensities, then we should not aim for a love that is wholly void of envy. I then propose a direct argument, in defense of two positive ideals. I argue that a certain kind of envy—emulative envy—can be beneficial to the loving relationship; in turn, a certain kind of love—wise love— which accepts the presence of envy, can be beneficial to our lives. Thus, that love and envy are so linked in our psychology is not something that we should merely tolerate, but wholeheartedly embrace. (shrink)

The scientist's decision of accepting a given proposition is assumed to be dependent on two factors: the scientist's 'private' information about the value of that statement and the proportion of colleagues who also accept it. This interdependence is modelled in an economic fashion, and it is shown that it may lead to multiple equilibria. The main conclusions are that the evolution of scientific knowledge can be path, dependent, that scientific revolutions can be due to very small changes in the empirical (...) evidence, and that not all possible equilibria are necessarily efficient, neither in the economic nor in the epistemic sense. These inefficiencies, however, can be eliminated if scientists can form coalitions. (shrink)

I examine the role played by the emotions of envy and resentment in interpersonal online dynamics during the COVID19 pandemic. I start by reviewing what we know about the interplay of social media use, social comparison and well-being, and by applying this knowledge to current circumstances. Then, I introduce some philosophical distinctions that complicate the already complex empirical evidence, differentiating, in particular, between envy and resentment, and between different kinds of envy. I argue that we can use the knowledge of (...) these distinctions to better cope with these painful, but sometimes productive and always informative, emotions. (shrink)

Decolonial/anti-colonial Black, Indigenous and Mestiza feminist movements and scholar-activists foreground how the oft-touted apocalypse that the Covid-19 pandemic heralds is not new, nor does it signify the great rupture into chaos that those from within modernity-coloniality often claim it to be. Rather Covid-19 is preceded by and will be out-lived by the apocalyptic anti-life onto-epistemological logics that are foundational to the production of hetero-patriarchal capitalist- coloniality. However, one would commit the violence of reproduction of the epistemological logics and rationalities constitutive (...) of the current system if the story ended there. We have survived and our survival points to the urgent necessity and responsibility of social theory to listen to the story of the pandemic from a Black/Indigenous genealogy and to begin the sense-making of the Covid-19 pandemic, from prior to this particular virus, outside, against and beyond the politics of knowledge of critical social theory itself. Thus, I invite you to journey to an affirmative re-enfleshment of reason and theory-making in relation to and dialogue with Black, Indigenous, and subaltern Mestiza feminist movements in southwest Colombia and in southeast so-called Australia in the unceded lands of the Awabakal and the Worimi. I explore this through the metaphor, the materiality, the cosmology and the herstory of the mangrove swamps a knowing-being otherwise visible to the dehumanising gave of Whiteness and bring to thought three stories of a politics of knowledge of/as the Black/racialised and feminised body/flesh. To do this is to suggest that the co-creation of pathways which are life affirming and life making beyond and out of the post-Covid 19 conjuncture involves an epistemological-political project which decolonises and feminises the containments of reason and knowing being of coloniality/modernity. (shrink)

A proof-theoretical analysis of elementary theories of order relations is effected through the formulation of order axioms as mathematical rules added to contraction-free sequent calculus. Among the results obtained are proof-theoretical formulations of conservativity theorems corresponding to Szpilrajn’s theorem on the extension of a partial order into a linear one. Decidability of the theories of partial and linear order for quantifier-free sequents is shown by giving terminating methods of proof-search.

Contraction-free sequent calculi for intuitionistic theories of apartness and order are given and cut-elimination for the calculi proved. Among the consequences of the result is the disjunction property for these theories. Through methods of proof analysis and permutation of rules, we establish conservativity of the theory of apartness over the theory of equality defined as the negation of apartness, for sequents in which all atomic formulas appear negated. The proof extends to conservativity results for the theories of constructive order over (...) the usual theories of order. (shrink)

The concept of solidarity is of central importance to the political sense of collective action. But it is a curious fact that solidarity is virtually unmentioned across the large and growing literature in philosophical collective action theory. Instead, we see discussions of collective action overwhelmingly focus on epistemic conditions and group-level correlates of individual action explanations such as collective intentions, collective beliefs, and so on. The aim of this paper is to elucidate the relationship between solidarity and collective action theory. (...) I will try to answer two questions: (1) What is it about the structure of accounts of collective action that seems to preclude discussions of solidarity and related concepts; and (2) How can solidarity be made to play a useful role in those accounts? (shrink)

The decision whether to have a realist or an anti-realist attitude towards scientific hypotheses is interpreted in this paper as a choice that scientists themselves have to face in their work as scientists, rather than as a ‘philosophical’ problem. Scientists’ choices between realism and instrumentalism are interpreted in this paper with the help of two different conceptual tools: a deflationary semantics grounded in the inferentialist approach to linguistic practices developed by some authors, and an epistemic utility function that tries to (...) represent the cognitive preferences of scientists. The first tool is applied to two different questions traditionally related to the problem of scientific realism: the non-miracle argument, and the continuity of reference. The second one is applied to the problem of unconceived alternatives, and to the distinction between realist and instrumentalist attitudes towards scientific hypotheses. (shrink)

Some peculiarities of the evaluation of theories within scientific research programmes and of the assessing of rival SRPs are described assuming that scientists try to maximise an ‘epistemic utility function’ under economic and institutional constraints. Special attention is given to Lakatos' concepts of ‘empirical progress’ and ‘theoretical progress’. A notion of ‘empirical verisimilitude’ is defended as an appropriate utility function. The neologism ‘methodonomics’ is applied to this kind of studies.

A uniform calculus for linear logic is presented. The calculus has the form of a natural deduction system in sequent calculus style with general introduction and elimination rules. General elimination rules are motivated through an inversion principle, the dual form of which gives the general introduction rules. By restricting all the rules to their single-succedent versions, a uniform calculus for intuitionistic linear logic is obtained. The calculus encompasses both natural deduction and sequent calculus that are obtained as special instances from (...) the uniform calculus. Other instances give all the invertibilities and partial invertibilities for the sequent calculus rules of linear logic. The calculus is normalizing and satisfies the subformula property for normal derivations. (shrink)

The connection between scientific knowledge and our empirical access to realityis not well explained within the structuralist approach to scientific theories. I arguethat this is due to the use of a semantics not rich enough from the philosophical pointof view. My proposal is to employ Sellars–Brandom's inferential semantics to understand how can scientific terms have empirical content, and Hintikka's game-theoretical semantics to analyse how can theories be empirically tested. The main conclusions are that scientific concepts gain their meaning through `basic (...) theories' grounded on `common sense, and that scientific method usually allows the pragmatic verification and falsification of scientific theories. (shrink)

The constitution of a collective judgment is analyzed from a contractarian point of view. The optimal collective judgment is defined as the one that maximizes the sum of the utility each member gets from the collective adoption of that judgment. It is argued that judgment aggregation is a different process from the aggregation of information and public deliberation. This entails that the adoption of a collective judgment should not make any rational member of the group change her individual opinion, and (...) so the collective judgment can not have any kind of epistemic superiority over the individual ones. ‡The author acknowledges Spanish Government's research projects HUM2005–01686/FISO and HUM2005-25447-E, as well as the grant PR2006-0108 which allowed a three months stay at the Helsinki Collegium for Advanced Studies, in which a big part of this paper was written. †To contact the author, please write to: Universidad Nacional de Educación a Distancia, Dpto. de Lógica, Historia y F. de la ciencia, Humanidades, Paseo de Senda del rey 7, 28040 Madrid, Spain; e-mail: [email protected]. (shrink)