Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof as they transition to advanced mathematics. Using several strategies, students will develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow.

This book investigates the phenomenological ways that dance choreographing and dance performance exemplify both Truth and meaning-making within Native American epistemology, from an analytic philosophical perspective. Given that within Native American communities dance is regarded both as an integral cultural conduit and “a doorway to a powerful wisdom,” Shay Welch argues that dance and dancing can both create and communicate knowledge. She explains that dance—as a form of oral, narrative storytelling—has the power to communicate knowledge of beliefs and histories, (...) and that dance is a form of embodied narrative storytelling. Welch provides analytic clarity on how this happens, what conditions are required for it to succeed, and how dance can satisfy the relational and ethical facets of Native epistemology. (shrink)

This essay will examine some rather serious trouble confronting claims that mathematicalia might be social constructs. Because of the clarity with which he makes the case and the philosophical rigor he applies to his analysis, our exemplar of a social constructivist in this sense is Julian Cole, especially the work in his 2009 and 2013 papers on the topic. In a 2010 paper, Jill Dieterle criticized the view in Cole’s 2009 paper for being unable to account for the atemporality of (...) mathematical existents. Cole’s 2013 paper addresses this objection, providing a modification of his 2009 paper allowing for atemporal mathematicalia. An unusual consequence of Cole’s account is that at least some existential claims about mathematicalia used to be false but now have always been true. By examining the semantics of such claims, we demonstrate that social constructivism is in fact, despite Cole’s attempts to rectify matters, incompatible with atemporal mathematicalia. In the course of examining these semantic details, however, an alternative hybrid view of fictionalism and social constructivism emerges. Those tempted by social constructivism, while perhaps disappointed by the negative results of the paper, may be encouraged by how much of their view can be recovered in this alternative account. (shrink)

In 1988, Kit Fine published a semantic theory for quantified relevant logics. He referred to this theory as stratified semantics. While it has received some attention in the literature, 1–20, 1992; Mares & Goldblatt, Journal of Symbolic Logic 71, 163–187, 2006), stratified semantics has overall received much less attention than it deserves. There are two plausible reasons for this. First, the only two dedicated treatments of stratified semantics available are, 27–59, 1988; Mares, Studia Logica 51, 1–20, 1992), both of which (...) are quite dense and technically challenging. Second, there are a number of prima facie reasons to be worried about stratified semantics. The purpose of this paper is to revitalize research on stratified semantics. I will do so by giving a ‘user friendly’ presentation of the semantics, and by giving reasons to think that the prima facie reasons to be worried about it are too simplistic. (shrink)

Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these (...) two properties. I also show how to use this fact to demonstrate that these logics seem to be constructive in previously unknown ways. (shrink)

Formal symptoms of relevance usually concern the propositional variables shared between the antecedent and the consequent of provable conditionals. Among the most famous results about such symptoms are Belnap’s early results showing that for sublogics of the strong relevant logic R, provable conditionals share a signed variable between antecedent and consequent. For logics weaker than R stronger variable sharing results are available. In 1984, Ross Brady gave one well-known example of such a result. As a corollary to the main result (...) of the paper, we give a very simple proof of a related but strictly stronger result. (shrink)

In this paper, I explore a number of issues related to a life lived with borderline personality disorder (BPD). Primarily, I am interested in discussing how one unwillingly changes their personal identity by forced medicating—demanded by others implicitly and explicitly. My motivation is something deep and invasive in me. I want to know, I have always wanted to know, why others want me to not be Me so badly. I have thought about this question for years, and though others may (...) simply chalk it up to just one of the standard paranoid or narcissistic traits of borderline personality disorder, there is something more to this question that many of us agonize over most of our lives. There is a deeply normative component to this question that extends beyond the mere fear of abandonment; it is tied to a desire by others to erase—literally—who we are for their own comfort. In this sense, then, I invite you to travel along a path of what it can mean to be a BPDer, from a narrative, phenomenological, and cognitive lived, embodied perspective. My purpose is to show that the treatments for us that others desire cannot avoid (and usually do not want to avoid) the unraveling of who we really are. Whether we want to or not, we give up our self to keep other people with us. And for many, this is too much to ask, and can be one, though not the only, reason suicide and self‐harm seem to be necessary recourses. One in 10 people with BPD commit suicide. So this is a serious matter, indeed. (shrink)

Linnebo and Pettigrew present some objections to category theory as an autonomous foundation. They do a commendable job making clear several distinct senses of ‘autonomous’ as it occurs in the phrase ‘autonomous foundation’. Unfortunately, their paper seems to treat the ‘categorist’ perspective rather unfairly. Several infelicities of this sort were addressed by McLarty. In this note I address yet another apparent infelicity.

BackgroundSleep, physical activity, and diet have been associated with mental health and well-being individually in young adults. However, which of these “big three” health behaviors most strongly predicts mental health and well-being, and their higher-order relationships in predictive models, is less known. This study investigated the differential and higher-order associations between sleep, physical activity, and dietary factors as predictors of mental health and well-being in young adults.MethodIn a cross-sectional survey design, 1,111 young adults ages 18–25 from New Zealand and the (...) United States answered an online survey measuring typical sleep quantity and quality; physical activity; and consumption of raw and processed fruit and vegetables, fast food, sweets, and soda, along with extensive covariates and the outcome measures of depressive symptoms [measured by the Center for Epidemiological Depression Scale ] and well-being.ResultsControlling for covariates, sleep quality was the strongest predictor of depressive symptoms and well-being, followed by sleep quantity and physical activity. Only one dietary factor—raw fruit and vegetable consumption—predicted greater well-being but not depressive symptoms when controlling for covariates. There were some higher-order interactions among health behaviors in predicting the outcomes, but these did not survive cross-validation.ConclusionSleep quality is an important predictor of mental health and well-being in young adults, whereas physical activity and diet are secondary but still significant factors. Although strictly correlational, these patterns suggest that future interventions could prioritize sleep quality to maximize mental health and well-being in young adults. (shrink)

In this paper, we provide a semantics for a range of positive substructural logics, including both logics with and logics without modal connectives. The semantics is novel insofar as it is meant to explicitly capture the computational flavor of these logics, and to do so in a way that builds in both nondeterministic and nonconcurrent computational processes.

I construct an analysis of social trust that attends distinctively to cooperation in social relations that has the capability to (begin to) counter the default social distrust obtained due to oppressive conditions via a form of collective reasoning. For social trust to overcome oppression it must be a normatively transparent form of trust. Transparent trust can counter the effects of oppression on social interaction and foster social cooperation by correcting unequal positions of social vulnerability and improving disparities in credibility resultant (...) of oppression since collective reasoning in norm legitimization permits all individuals to participate in the process of self and other defining and the development of the concomitant norms that guide these processes. (shrink)

The articles in this volume offer a fresh perspective on the important role of the concept of law (lex) in the moral and political philosophy of the 'School of Salamanca'.

The Against Apion of Josephus is not only a defense of Judaism and Jewish history, but also an essay in historiography and historical criticism, as an outline of the work reveals. Josephus explains how history should and should not be written, and attempts to prove that certain versions of the past are truer than others. The Against Apion may attack the reliability and integrity of Greek historiography as being divisive and instable, but it is from the Greeks that Josephus learned (...) the idea and techniques of historical criticism. He develops his argument by appeal to the superiority of Jewish history, canon, and community, but all these pro-Jewish and anti-Greek arguments have Greek origins. The Greek argument from consensus shaped the historical and theological argumentation of the Against Apion, and Greek precedents provided the basis for the ahistorical or antihistorical view of Judaism that Josephus proposes. Josephus' polemic proves weakest in his argument from canon, and in his contrasting Jewish stability with Greek restiveness. (shrink)

If${\cal C}$is a category whose objects are themselves categories, and${\cal C}$has a rich enough structure, it is known that we can recover the internal structure of thecategoriesin${\cal C}$entirely in terms of thearrowsin${\cal C}$. In this sense, the internal structure of the categories in a rich enough category of categories is visible in the structure of the category of categories itself.In this paper, we demonstrate that this result follows as a matter of logic – given one starts from the right definitions. (...) This is demonstrated by first producing an abstraction principle whose abstracts are functors, and then actually recovering the internal structure of the individual categories that intuitively stand at the sources and targets of these functors by examining the way these functors interact. The technique used in this construction will be useful elsewhere, and involves providing an abstract corresponding not to everyobjectof some given family, but to all the relevantmappingsof some family of objects.This construction should settle, in particular, questions about whether categories of categories qualify asautonomousmathematical objects – categories of categories are perfectly acceptable autonomous objects and thus, in particular, suitable for foundational purposes. (shrink)

Categorial logic, as its name suggests, applies the techniques and machinery of category theory to topics traditionally classified as part of logic. We claim that these tools deserve attention from a greater range of philosophers than just the mathematical logicians. We support this claim with an example. In this paper we show how one particular tool from categorial logic---hyperdoctrines---suggests interesting metaphysics. Hyperdoctrines can provide semantics for quantified languages, but this account of quantification suggests a metaphysical picture quite different from the (...) one suggested by standard model-theoretic semantics. (shrink)

There is a natural story about what logic is that sees it as tied up with two operations: a ‘throw things into a bag’ operation and a ‘closure’ operation. In a pair of recent papers, Jc Beall has fleshed out the account of logic this leaves us with in more detail. Using Beall’s exposition as a guide, this paper points out some problems with taking the second operation to be closure in the usual sense. After pointing out these problems, I (...) then turn to fixing them in a restricted case and modulo a few simplifying assumptions. In a followup paper, the simplifications and restrictions will be removed. (shrink)

The task of this paper is to ground the notion of cyberethics of co-operation. The evolution of modern society has resulted in a shift from industrial society towards informational capitalism. This transformation is a multidimensional shift that affects all aspects of society. Hence also the ethical system of society is penetrated by the emergence of the knowledge society and ethical guidelines for the information age are needed. Ethical issues and conflicts in the knowledge society are connected to topics of ecological (...) and social sustainability. For information ethics and cyberethics, the sustainable design of society, social, and socio-technological systems is important. In this context the notions of sustainability and co-operation are discussed. Based on these categories, the approach of cyberethics of co-operation can be theoretically grounded. (shrink)

Aus den Debatten der Philosophie des Geistes und der Phänomenologie kaum wegzudenken, hat sich die begriffliche Erforschung des „Selbst“ hier eine Bedeutung erkämpft, deren Spuren in den psychopathologischen Klassifikationssystemen kaum wiederzufinden sind. Erst in jüngster Zeit werden Versuche unternommen, die durch diesen Begriff und seine philosophische Erforschung eröffnete Dimension des Verstehens auf psychiatrische Störungsbilder wie etwa der Schizophrenie anzuwenden, deren Erleben sich einem deskriptiven Zugang immer wieder entzieht. Welche Arten des Selbsterlebens, welche „Selbste“ lassen sich aber konzeptuell und phänomenal unterscheiden? (...) Wie ist es um die psychologischen Korrelata dieser Beschreibungen bestellt und welche Erkenntnisse hinsichtlich der Stabilität dieser Strukturen halten gerade jene Psychopathologien bereit, die teilweise oder gänzlich Selbsterfahrungen beeinträchtigen? Neben grundsätzlichen philosophischen Auseinandersetzungen mit der Thematik von Selbst und Selbststörungen vereint der Sammelband auch psychiatrische Forschungen, die interdisziplinäre Anschlüsse ermöglichen. So bieten gerade Störungen des Selbsterlebens der Philosophie die Möglichkeit, als Prüfsteine für ihre interpretativen Begriffe des Selbst zu fungieren. Mit Beiträgen von Thomas Fuchs, Mads Gram Henriksen/Joseph Parnas, Alice Holzhey-Kunz, Wouter Kusters, Stefano Micali, Philipp Schmidt, Alexander Schnell, László Tengelyi und Zeno Van Duppen. (shrink)

Relevance logics are a misunderstood lot. Despite being the subject of intense study for nearly a century, they remain maligned as too complicated, too abstruse, or too silly to be worth learning much about. This Element aims to dispel these misunderstandings. By focusing on the weak relevant logic B, the discussion provides an entry point into a rich and diverse family of logics. Also, it contains the first-ever textbook treatment of quantification in relevance logics, as well as an overview of (...) the cutting edge on variable sharing results and a guide to further topics in the field. (shrink)

Abstraction principles provide implicit definitions of mathematical objects. In this paper, an abstraction principle defining categories is proposed. It is unsatisfiable and inconsistent in the expected ways. Two restricted versions of the principle which are consistent are presented.

Not only our conscious expectations, wishes and intentions are directed towards the future, but also pre- or unconscious tendencies, hunches and anticipations. Using a term coined by Ernst Bloch, they can be summarized as the not-yet-conscious. This not-yet-consciousness usually unfolds spontaneously and without a plan; it is not expected or striven for, but rather emerges in consciousness in such a way that the subject is surprised by itself, so to speak. This gives rise to phenomena such as the conspicuous, the (...) accidental, the new and the improvised, which are particularly important for understanding creative and therapeutic processes. The aim of this article is to develop a general phenomenological framework for understanding not-yet-conscious dynamics and their unfolding in different contexts. To this end, the structure of the not-yet-conscious is examined in the light of protention, in which the phenomenon is fundamentally located. (shrink)

While universalistic assumptions have been undermined by experiences of cultural difference, the notion of culture has been universalized. But it seems that the notion of culture, the way it has prevailed in public discourse as well as in social and cultural studies, has to be seen as the main stumbling block to intercultural dialogue. The article argues for an interactional concept of culture, or interpretation, as also of research and representation. Emphasis has to be put on modes of linkage between (...) social action and discourses and on social reflexivity. While attempting to avoid the logic of identity, epistemologically, identity has to be understood as a social project. Thus universalism, which `as such' is underdetermined and shows only contextually, has to be seen not as something achieved and secured, but as an objective. Universalism has to prove itself within difference, it cannot be imposed by one side. (shrink)

We prove that there are groups in the constructible universe whose automorphism towers are highly malleable by forcing. This is a consequence of the fact that, under a suitable diamond hypothesis, there are sufficiently many highly rigid non-isomorphic Souslin trees whose isomorphism relation can be precisely controlled by forcing.

Excerpt“We have invented happiness,” said the last men, and they blinked. Friedrich Nietzsche, Thus Spoke Zarathustra1Introduction One of the key issues in the Marxist sociopolitical theory of the critique of capitalism regards the idea of “domination” or “control.” Webster's Dictionary defines domination as: (1) supremacy or preeminence over another; (2) exercise of mastery or ruling power; (3) exercise of preponderant, governing, or controlling influence.2 From a sociopolitical perspective, domination can be addressed using two different approaches. The first, a traditional approach, (...) views domination as external to the individual or the group…. (shrink)

A collection of photographs depicts life on Chicago's west side between 1949 and mid-1960s.

Includes bibliographical references and index (p. [181]-187) and index.

The distinction of „understanding“ and „explaining“, formulated by Karl Jaspers in his „General Psychopathology“, has had a lasting effect on psychiatry. As a result, phenomenological, hermeneutic, or psychodynamic approaches have often been accorded only descriptive or epiphenomenal status, while the actual causes of mental illness have been sought in neurobiologically or genetically based explanations. In contrast, this paper defends the explanatory role of understanding and phenomenological approaches. To this end, two levels of explanation are distinguished and shown to be equally (...) justified in principle, namely, motivational explanation at the macro-level and physical explanation at the micro-level. The actual causal role of motivational, i.e., understandable connections is then demonstrated by means of a conception of circular causality, which includes downward causality. Finally, the explanatory role of phenomenological analyses is also shown in psychotic disorders that refuse motivational understanding, using the example of schizophrenic delusion. (shrink)

In this paper we introduce a novel way of building arithmetics whose background logic is R. The purpose of doing this is to point in the direction of a novel family of systems that could be candidates for being the infamous R#1/2 that Meyer suggested we look for.

This paper presents a new semantics for the weak relevant logic DW that makes the role of the infamous Routley star more explicable. Central to this rewriting is combining aspects of both the American and Australian plan for understanding negations in relevance logics.

Not only our conscious expectations, wishes and intentions are directed towards the future, but also pre- or unconscious tendencies, hunches and anticipations. Using a term of Ernst Bloch, they can be summarized as the not-yet-conscious. This not-yet-conscious mostly unfolds spontaneously and without plan; it is not directly anticipated or aimed at, but rather comes to awareness in such a way that the subject is, as it were, surprised by itself. Thus it gives rise to phenomena such as the striking, the (...) coincidental, the new, and the improvised, which are particularly important for understanding creative and therapeutic processes. The paper aims at providing a general phenomenological framework for the understanding of not-yet-conscious dynamics and their unfolding in different contexts. To this end, the structure of the not-yet-conscious is examined in light of protention, in which the phenomenon is fundamentally to be located. I propose to describe the general structure of protention as a future-directed horizon of graded probabilities, i.e., as a “protentional cone”. This cone is fed by current experiences and bodily tendencies and is focused to varying degrees by attention. This results in either more focused or rather defocused states of anticipation, the latter giving space to the not-yet-conscious as a meaning “in statu nascendi”. On this basis, selected manifestations of the not-yet-conscious are analyzed, including extemporaneous speech, artistic improvisation and creativity, bodily meaning implicates, decision-making, and meaningful coincidence. (shrink)

I present a version of Kit Fine's stratified semantics for the logic RWQ and define a natural family of related structures called RW hyperdoctrines. After proving that RWQ is sound with respect to RW hyperdoctrines, we show how to construct, for each stratified model, a hyperdoctrine that verifies precisely the same sentences. Completeness of RWQ for hyperdoctrinal semantics then follows from completeness for stratified semantics, which is proved in an appendix. By examining the base category of RW hyperdoctrines, we find (...) reason to be worried about the ontology of stratified models. (shrink)

Despite its complex experiential structure, the phenomenon of grief following bereavement has not been a major topic of phenomenological research. The paper investigates its basic structures, elaborating as its core characteristic a conflict between a presentifying and a ‘de-presentifying’ intention: In grief, the subject experiences a fundamental ambiguity between presence and absence of the deceased, between the present and the past, indeed between two worlds he lives in. This phenomenological structure will be analyzed under several aspects: regarding bodily experience, as (...) disruption of a shared intercorporeality; as a loss of the shared world and shared habitualities, leaving the bereaved person with ubiquitous indications of absence and with a contraction of their own self; regarding temporality, as a separation of two strands of time, namely a still ongoing past and an alienated present which become more and more desynchronized; finally, as an “as-if presence” of the deceased which the bereaved continue to feel and sometimes to perceive, leading to a cognitive-affective conflict between two experienced realities. The transforming process of grief is then analyzed as a gradual adjustment to the loss, finally enabling a re-integration of the conflicting realities. This is achieved through an incorporation and identification with the deceased on the one hand, and through various forms of representation on the other hand, in particular by recollection and symbolization. (shrink)

This book focuses on feminist analyses of women’s oppression-perpetuating choices in order to ascertain how such biases in theorizing can undermine liberation.

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 9.3 (2002) 261-264 [Access article in PDF] Mind, Meaning, and the Brain Thomas Fuchs, MD, PhD Keywords: Mind, brain, meaning, translation, depression. A Systemic View of the Mind Progress in brain research over the past two decades demonstrates the power of the neurobiological paradigm. However, this progress is connected with a restricted field of vision typical of any scientific paradigm. The psychiatrist should be (...) aware of this restriction, because, unlike the brain scientist, he deals with patients, not with brains. The restricted view may be described by the terms of (1) reductionism, (2) reification, and (3) isolation.Reductionism: Neurobiology tends to regard subjectivity as a mere by-product of the brain's activity as a symbol-manipulating machine or an information processor. Consciousness becomes an epiphenomon of the neuronal machinery that, operating behind our back, creates the illusion of a continuous self and of an autonomous will (Churchland 1995; Roth 1996).Reification: Mental or subjective states seem to be localizable in the brain; thoughts or feelings, it appears, may be observed in the colored illumination of cortical and subcortical structures. This results in the belief that brain images could also show the cause of a mental illness, or even the illness itself, which then manifests, for instance, in a reduced metabolic activity in certain areas of the cortex.Isolation: As a further consequence, this view isolates the individual patient and considers his illness separated from the interconnections with his environment. However, on these interconnections his personal experiences and dispositions are founded, and it is the actual interpersonal situation that has triggered his present illness.Walter Glannon's paper successfully counters these tendencies toward a neurobiological reductionism with an extended view of the mind: "... the mind is not located in any one place but is distributed among the brain, the body, and the environment." Of course, who observes someone's brain will never see his thoughts, his pain, or his anxiety. For consciousness is not a localizable object or state at all but a process of relating to something: a perceiving of, remembering of, wishing for, aiming at, and so on. Thus on the phenomenological level, there is nothing like a "mental event" that could be isolated from the world and from the stream of conscious experiences. The mind exists only embedded in the world and in the temporal process of life.The same applies to the biological level: Consciousness is based on the continuous interaction of the brain with the organism, and of the organism as a whole with the environment. The role of the brain for mental phenomena is thus comparable to the role of the heart in the circulatory system or of the lung in the respiratory system. Of course, the lung is the central organ of breathing, but respiration may not be restricted to the [End Page 261] lung, nor to the organism as a whole. It means constant exchange with the environment, and there is no sense in asking whether the air taken in still belongs to the surroundings or already to the organism. The same systemic unity is found in the circle of perception and action mediated by the brain: When I am writing a letter, there is no place in the unity of action where my "self" ends and the "world" begins, no border that separates inner and outer worlds.There is another argument to be raised against the reification of the mind if we consider the aspect of a historical biology. From birth on, our mind as well as the correlated brain structures are essentially formed by social and cultural influences. The brain is not inserted into the world as a prefabricated apparatus but through its plastic development in and from the world. Thus it adapts epigenetically to its specific natural and social environment like a key to a lock. This complementarity makes it impossible to restrict one's view to the anatomic organ and requires an interdisciplinary approach to brain-environment investigation, as for example, under the heading of a "social cognitive neuroscience" (Ochsner and Lieberman 2001).As Glannon goes on to argue, to overcome... (shrink)

In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We take cues from Franz Berto’s recent work on topic to show an alignment between families of variable sharing properties and responses to the topic transparency of relevant implication and negation. We then introduce and defend novel variable sharing properties stronger than strong depth relevance—which we call cn-relevance and lossless cn-relevance—showing that the properties are satisfied by the weak (...) relevant logics and , respectively. We argue that such properties address a sort of semantic lossiness of strong depth relevance. (shrink)

For the purpose of advancing the feminist commitment to inclusion and nonliberal articulations of pluralism, in this essay I conceptualize the Native account of individual autonomy that itself evolves from a commitment to pluralism. I demonstrate that Native individual autonomy is concurrently strong and feminist in nature—what I call “radical-cum-relational.” That is, Native autonomy is more radical than the traditional liberal conception and is simultaneously grounded in relationality, which is the basis of much of feminist ethics. I demonstrate that the (...) Native conception of autonomy is radical and promotes the highest degree of individual self-determination and independence qua individuality and particularity. Yet this radical self-determination depends on intense social interdependency. The grounding metaphysics and epistemology of the Native framework are conceived entirely in terms of ethical relationships between and responsibilities to other individuals, animals, and the Earth. That is, no part of the Native paradigm can be understood outside of the ethical connections persons have by virtue of their primary position as community members. It is by situating radical autonomy against a background of ethical social interdependence, together with thebackground condition of gender equality of Native practices, that the radical construal of Native individual freedom is feminist. To shore up and illustrate the connection between Native autonomy and feminism, I argue that an identification between the Native social practice of gifting and feminist reciprocity can be made, specifically Iris Marion Young’s notion of asymmetrical reciprocity. Finally, I argue that this connection avoids the problem of incommensurability and so is theoretically possible, responsible, and fits the criterion of respectfulness also at the foundation of the Native framework. Broadly speaking, the problem of incommensurability is concerned with theorists’ inability to recognize foundational incompatibilities between paradigms and their forced attempts to mergethem, often at the price of ignoring inconsistencies, inaccuracies, and contradictions that result from impossible translations and conversions. Historically and to the present day, Western philosophy has been egregiously guilty of distorting Native theories and practices. In this essay I argue that since translation takes place at the level of praxis rather than at the level of language, my argument circumvents problems that arise from failed attempts to map cultural concepts onto others that do not share similar foundations. (shrink)