Although taste and smell seem hard to imagine, some people nevertheless report vivid imagery in these sensory modalities. We investigate whether experts are better able to imagine smells and tastes because they have learned the ability, or whether they are better imaginers in the first place, and so become experts. To test this, we first compared a group of wine experts to yoked novices using a battery of questionnaires. We show for the first time that experts report greater vividness of (...) wine imagery, with no difference in vividness across sensory modalities. In contrast, novices had more vivid color imagery than taste or odor imagery for wines. Experts and novices did not differ on other vividness of imagery measures, suggesting a domain‐specific effect of expertise. Critically, in a second study, we followed a group of students commencing a wine course and a group of matched control participants. Students and controls did not differ before the course, but after the wine course students reported more vivid wine imagery. We provide evidence that expertise improves imagery, exemplifying the extent of plasticity of cognition underlying the chemical senses. (shrink)

The valence–space metaphor research area investigates the metaphorical mapping of valenced concepts onto space. Research findings from this area indicate that positive, neutral, and negative concepts are associated with upward, midward, and downward locations, respectively, in the vertical plane. The same research area has also indicated that such concepts seem to have no preferential location on the horizontal plane. The approach–avoidance effect consists in decreasing the distance between positive stimuli and the body and increasing the distance between negative stimuli and (...) the body. Thus, the valence–space metaphor accounts for the mapping of valenced concepts onto the vertical and horizontal planes, and the approach–avoidance effect accounts for the mapping of valenced concepts onto the “depth” plane. By using a cube conceived for the study of allocation of valenced concepts onto 3D space, we show in three studies that positive concepts are placed in upward locations and near the participants’ body, negative concepts are placed in downward locations and far from the participants’ body, and neutral concepts are placed in between these concepts in both planes. (shrink)

Arguing against the dominant developmental theories (e.g., Piaget, 1945; Vygotsky, 1978) stating that pretend play is limited to early childhood, we illustrate that pretend play is an adaptive human activity of adulthood as well as childhood. We advance this argument on three levels. First, we offer an analysis of why the discipline of developmental psychology in the Western world considered play only as an activity of childhood by neglecting to explore whether or how pretend play exists during adulthood. Second, we (...) discuss the similarities between adult improvisational theater and children’s pretend play in illustrating our thesis that pretend continues to exist during adulthood. In this discussion, we focus on similarities in the definitions, psychological origins, social functions, and developmental consequences of pretend play and adult improvisation. Finally, we end the article with educational implications of conceptualizing pretend play as a life-span activity and offer directions for future research. (shrink)

Relativist and constructivist conceptions of knowledge have become orthodoxy in vast stretches of the academic world in recent times. This book critically examines such views and argues that they are fundamentally flawed. The book focuses on three different ways of reading the claim that knowledge is socially constructed, one about facts and two about justification. All three are rejected. The intuitive, common sense view is that there is a way things are that is independent of human opinion, and that we (...) are capable of arriving at belief about how things are that is objectively reasonable, and is binding on anyone capable of appreciating the relevant evidence, regardless of their social or cultural perspective. Difficult as these notions may be, it is a mistake to think that recent philosophy has uncovered powerful reasons for rejecting them. (shrink)

This essay distinguishes between metaphysical and epistemological conceptions of analyticity. The former is the idea of a sentence that is ‘true purely in virtue of its meaning’ while the latter is the idea of a sentence that ‘can be justifiably believed merely on the basis of understanding its meaning’. It further argues that, while Quine may have been right to reject the metaphysical notion, the epistemological notion can be defended from his critique and put to work explaining a priori justification. (...) Along the way, a number of further distinctions relevant to the theory of analyticity and the theory of apriority are made and their significance is explained. (shrink)

A stellar line-up of leading philosophers from around the world offer new treatments of a topic which has long been central to philosophical debate, and in ...

This chapter aims to provide materials with which to substantiate the claim that, under the appropriate circumstances, the notion of analyticity can help explain how one might have a priori knowledge even in the strong sense. It argues that Implicit Definition, properly understood, is completely independent of any form of irrealism about logic. The chapter defends the thesis of Implicit Definition against Quine's criticisms, and examines the sort of account of the apriority of logic that this doctrine is able to (...) provide. The chapter shows that, against the background of a rejection of indeterminacy, its insolubility cannot be conceded. It also argues that neither a non‐factualism about Frege‐analyticity, nor an error thesis about it, can plausibly fall short of an outright rejection of meaning itself. The chapter shows how the doctrine that appears to offer the most promising account of how we grasp the meanings of the logical constants. (shrink)

This chapter aims to provide materials with which to substantiate the claim that, under the appropriate circumstances, the notion of analyticity can help explain how one might have a priori knowledge even in the strong sense. It argues that Implicit Definition, properly understood, is completely independent of any form of irrealism about logic. The chapter defends the thesis of Implicit Definition against Quine's criticisms, and examines the sort of account of the apriority of logic that this doctrine is able to (...) provide. The chapter shows that, against the background of a rejection of indeterminacy, its insolubility cannot be conceded. It also argues that neither a non‐factualism about Frege‐analyticity, nor an error thesis about it, can plausibly fall short of an outright rejection of meaning itself. The chapter shows how the doctrine that appears to offer the most promising account of how we grasp the meanings of the logical constants. (shrink)

Disasters overwhelm resources and threaten the safety and functioning of communities. Mental health and community needs after catastrophic disasters can be substantial, however the effects of traumatic events are not exclusively bad with many people showing individual resilience and some reporting growth. Sustaining the social fabric of the community and facilitating recovery following disaster depends on leadership=s knowledge of a community=s resilience and vulnerabilities as well as an understanding of the distress, disorder, and health risk behavioral responses. A coordinated systems (...) approach across medical care, public health, and emergency response system is necessary to meet the mental health care needs of a disaster region. (shrink)

Here we work in an arbitrary o-minimal expansion of a divisible ordered abelian group. We say that a definable ring is definably semiprime if squares of nontrivial two-sided ideals definable in the expansion are nontrivial. We prove a definable version of Wedderburn–Artin theorem and give a characterization of definably semiprime rings.

In his biography of Emil Artin, Richard Brauer describes the years from 1931–1941 as a time when “Artin spoke through his students and through the members of his mathematical circle” rather than through written publications. This paper explores these seemingly quiet years when Artin immigrated to America and disseminated ideas about algebraic number theory during this time in his collaboration with George Whaples, a young American mathematician who had just completed his Ph.D. at the University of Wisconsin. (...) The main result of their work is the use of the product formula for valuations to come up with an axiomatic characterization of both algebraic number fields and algebraic function fields with a finite field of constants. These two families of fields are exactly the fields for which class field theory is known to hold. We situate their mathematical work in the broader context of algebraic number theory and their lives within the broader historical context. (shrink)

RésuméNous introduisons la notion de structure algébrique dynamique, inspirée de l'évaluation dynamique et de la théorie des modèles. Nous montrons comment cette notion constructive permet une relecture de la théorie d'Artin-Schreier, avec la modification capitale que le résultat final est alors établi de manière constructive. Nous pensons que ce que nous avons réalisé ici sur un cas d'école peut être généralisé à des parties significatives de l'algèbre classique, et est donc une contribution à la réalisation du programme de Hilbert (...) pour l'algèbre classique.We introduce the notion of “Dynamic Algebraic Structure” inspired by Dynamic Evaluation and Model Theory. We show that this constructive notion allows a rereading of the Artin-Schreier-Robinson solution for the 17th Hilbert Problem. So, once we know how to reread the proofs, this kind of abstract theory contains an algorithm which computes the concrete result . Our method gives a constructive semantic for certain parts of abstract classical mathematics.The idea is the following: replace the classical algebraic structures “constructed” by Choice and Principle of Third Excluded Middle , by DAS and dynamic evaluations of these DAS. Then TEM is replaced by construction of branching in the trees of dynamic evaluation of the DAS. If Choice is used in the form of Godel completeness theorem, it is not really necessary to use it for obtaining concrete results: in DAS, Choice is simply replaced by … nothing!. This is because the classical proof is by contradiction: “if there were not a sum of squares then some formal theory would admit a pathological model”. The constructive reasoning is more direct: since the pathological theory proves 0 = 1 we know how to construct the sum of squares … and classical models have disappeared in the proof. They are replaced by dynamic evaluations of DAS. We think that we have given, for an academic example, a new method, realizing a kind of Hilbert Program for significant parts of classical algebra. (shrink)

My review of Boghossian's book, Fear of Knowledge, is generally sympathetic toward his rejection of epistemic relativism and turns toward an examination of "constructivist" themes in light of an anti-nominalist perspective. In general terms, this is a fine little book, tightly argued, and well worth considerable attention--especially from the friends of relativism and those supporting versions of constructivism. (Constructivism + radical nominalism = relativism.).

The three books before us are consolingly conservative. They observe the pieties; they display an unusually acute sense of history; they try to find out what Plato said instead of being angry with him for neglecting to read J. S. Mill and Wittgenstein; and they say faithfully and sympathetically what can be said for him even when he tries them hard. This is true criticism: and it stands out sharply against the spleen of the "detractors," as Professor Levinson has happily (...) called them. (shrink)

Multiple Originals: New Approaches to Hebrew Bible Textual Criticism. By Gary D. Martin. SBL Text-Critical Studies, vol. 7. Atlanta: Society of Biblical Literature, 2010. Pp. xiv + 341. $42.95.

According to Belegradek, a first order structure is weakly small if there are countably many $1$-types over any of its finite subset. We show the following results. A field extension of finite degree of an infinite weakly small field has no Artin-Schreier extension. A weakly small field of characteristic $2$ is finite or algebraically closed. A weakly small division ring of positive characteristic is locally finite dimensional over its centre. A weakly small division ring of characteristic $2$ is a (...) field. (shrink)

The Artin‐Schreier theorem says that every formally real field has orders. Friedman, Simpson and Smith showed in [6] that the Artin‐Schreier theorem is equivalent to over. We first prove that the generalization of the Artin‐Schreier theorem to noncommutative rings is equivalent to over. In the theory of orderings on rings, following an idea of Serre, we often show the existence of orders on formally real rings by extending pre‐orders to orders, where Zorn's lemma is used. We then (...) prove that “pre‐orders on rings not necessarily commutative extend to orders” is equivalent to. (shrink)

In this paper we present and study a categorical formulation of the W-types of Martin-Löf. These are essentially free term algebras where the operations may have finite or infinite arity. It is shown that W-types are preserved under the construction of sheaves and Artin gluing. In the proofs we avoid using impredicative or nonconstructive principles.

Schur’s Lemma says that the endomorphism ring of a simple left R-module is a division ring. It plays a fundamental role to prove classical ring structure theorems like the Jacobson Density Theorem and the Wedderburn–Artin Theorem. We first define the endomorphism ring of simple left R-modules by their Π10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{0}_{1}$$\end{document} subsets and show that Schur’s Lemma is provable in RCA0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm RCA_{0}$$\end{document}. A (...) ring R is left primitive if there is a faithful simple left R-module and left semisimple if the left regular module RR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{R}R$$\end{document} is semisimple. The Jacobson Density Theorem and the Wedderburn-Artin Theorem characterize left primitive ring and left semisimple ring, respectively. We then study such theorems from the standpoint of reverse mathematics. (shrink)

Jan Krajíček posed the following problem: Is there is a generalization result in the theory of real closed fields of the form: If A is provable in length k for all n ϵ ω , then A is provable? It is argued that the answer to this question depends on the particular formulation of the “theory of real closed fields.” Four distinct formulations are investigated with respect to their generalization behavior. It is shown that there is a positive answer to (...) Krajíček's question for 1. the axiom system RCF of Artin-Schreier with Gentzen's LK as underlying logical calculus, 2. RCF with the variant LK B of LK allowing introduction of several quantifiers of the same type in one step, 3. LK B and the first-order schemata corresponding to Dedekind cuts and the supremum principle. A negative answer is given for 4. any system containing the schema of extensionality. (shrink)

Profinite groups are Galois groups. The effective study of infinite Galois groups was initiated by Metakides and Nerode [8] and further developed by LaRoche [5]. In this paper we study profinite groups without considering Galois extensions of fields. The Artin method of representing a finite group as a Galois group has been generalized by Waterhouse [14] to profinite groups. Thus, there is no loss of relevance in our approach.The fundamental notions of a co-r.e. profinite group, recursively profinite group, and (...) the degree of a co-r.e. profinite group are defined in §1. In this section we prove that every co-r.e. profinite group can be effectively represented as an inverse limit of finite groups. The degree invariant is shown to behave very well with respect to open subgroups and quotients. The work done in this section is basic to the rest of the paper.The commutator subgroup, the Frattini subgroup, thep-Sylow subgroups, and the center of a profinite group are essential in the study of profinite groups. It is only natural to ask if these subgroups are effective. The following question exemplifies our approach to this problem: Is the center a co-r.e. profinite group? Theorem 2 provides a general method for answering this type of question negatively. Examples 3,4 and 5 are all applications of this theorem. (shrink)

As is well known, it was only in 1926 that a comprehensive mathematical theory of braids was published—that of Emil Artin. That said, braids had been researched mathematically before Artin’s treatment: Alexandre Theophile Vandermonde, Carl Friedrich Gauß and Peter Guthrie Tait had all attempted to introduce notations for braids. Nevertheless, it was only Artin’s approach that proved to be successful. Though the historical reasons for the success of Artin’s approach are known, a question arises as to (...) whether other approaches to deal with braids existed, approaches that were developed after Artin’s article and were essentially different from his approach. The answer, as will be shown, is positive: Modesto Dedò developed in 1950 another notation for braids, though one, which was afterward forgotten or ignored. This raises a more general question: what was the role of Artin’s notation, or, respectively, Dedò’s, that enabled either the acceptance or the neglect of their theories? More philosophically, can notation be an epistemic technique, prompting new discoveries, or rather, can it also operate an as obstacle? The paper will analyze the method introduced by Dedò to notate braids, and also its history and implications. It aims to show that Dedò, in contrast to Artin, focused on factorizations of braids and the algebraic relations between the operations done on these factorizations. Dedò’s research was done against the background of Oscar Chisini’s research of algebraic curves on the one hand and of Artin’s successful notation of braids on the other hand. Taking this into account, the paper will in addition look into the epistemic role of notation, comparing Dedò’s work with Artin’s, as both presented different notations of braids and their deformations. (shrink)

We show that, for each finite group G, there exists an axiomatization of the class of abelian-by-G groups with a single sentence. In the proof, we use the definability of the subgroups M n in an abelian-by-finite group M, and the Auslander-Reiten sequences for modules over an Artin algebra.

The editorial note recommending the book by Vladimir Kantor Russkaya Klasika Ili Bytiye Rassiyi communicates that the author (philosopher, novelist and historian) believes that only this culture is fully valuable whose most representative artists’ work turns into classics, thus gaining the status of high culture. It indicates the extent to which the great names of Russian literature write with an awareness that in order to make it into the classics canon of European literature, too, one needs to reckon with the (...) previous work of Dante, Goethe, Schiller, Cervantes, Shakespeare, Hegel, Marx, Feuerbach, Nietzsche, and a number of other prominent representatives of the culture of the West. This is not to say that Pushkin, Goncharov, Tolstoy, Gogol or Dostoyevsky were imitators. By reproducing patterns or themes developed by the literature of the West, they set those in realities fundamentally different from the social realities of the West, often in a polemic vein. Kantor stresses that the great artistic ambitions or the Russian classics are accompanied by great social duties because they lived and created their artin a country that had been lagging behind for centuries. It did catch up at times, but it was successful only as of Czar Peter I, not without periodic regressive collapses, though. The sense of social obligations, characteristic of Russian writers, intellectuals, or intelligentsia, and to be more precise, the implementation of these obligations, enabled Kantor to prove that the progress of literature—the great classics in particular—was linked in Russia with civilizational progress, and that in terms of the weight of these links, Russia was very different in civilizational progress from Europe, which lay ahead civilization-wise. (shrink)

The editorial note recommending the book by Vladimir Kantor Russkaya Klasika Ili Bytiye Rassiyi communicates that the author (philosopher, novelist and historian) believes that only this culture is fully valuable whose most representative artists’ work turns into classics, thus gaining the status of high culture. It indicates the extent to which the great names of Russian literature write with an awareness that in order to make it into the classics canon of European literature, too, one needs to reckon with the (...) previous work of Dante, Goethe, Schiller, Cervantes, Shakespeare, Hegel, Marx, Feuerbach, Nietzsche, and a number of other prominent representatives of the culture of the West. This is not to say that Pushkin, Goncharov, Tolstoy, Gogol or Dostoyevsky were imitators. By reproducing patterns or themes developed by the literature of the West, they set those in realities fundamentally different from the social realities of the West, often in a polemic vein. Kantor stresses that the great artistic ambitions or the Russian classics are accompanied by great social duties because they lived and created their artin a country that had been lagging behind for centuries. It did catch up at times, but it was successful only as of Czar Peter I, not without periodic regressive collapses, though. The sense of social obligations, characteristic of Russian writers, intellectuals, or intelligentsia, and to be more precise, the implementation of these obligations, enabled Kantor to prove that the progress of literature—the great classics in particular—was linked in Russia with civilizational progress, and that in terms of the weight of these links, Russia was very different in civilizational progress from Europe, which lay ahead civilization-wise. (shrink)

This paper studies the structure of semisimple rings using techniques of reverse mathematics, where a ring is left semisimple if the left regular module is a finite direct sum of simple submodules. The structure theorem of left semisimple rings, also called Wedderburn-Artin Theorem, is a famous theorem in noncommutative algebra, says that a ring is left semisimple if and only if it is isomorphic to a finite direct product of matrix rings over division rings. We provide a proof for (...) the theorem in $$\mathrm RCA_{0}$$, showing the structure theorem for computable semisimple rings. The decomposition of semisimple rings as finite direct products of matrix rings over division rings is unique. Based on an effective proof of the Jordan-Hölder Theorem for modules with composition series, we also provide an effective proof for the uniqueness of the matrix decomposition of semisimple rings in $$\mathrm RCA_{0}$$. (shrink)

Does the materiality of a three-dimensional model have an effect on how this model operates in an exploratory way, how it prompts discovery of new mathematical results? Material mathematical models were produced and used during the second half of the nineteenth century, visualizing mathematical objects, such as curves and surfaces—and these were produced from a variety of materials: paper, cardboard, plaster, strings, wood. However, the question, whether their materiality influenced the status of these models—considered as exploratory, technical, or representational—was hardly (...) touched upon. This article aims to approach this question by investigating two case studies: Beltrami’s paper models vs. Dyck’s plaster ones of the hyperbolic plane; and Chisini’s string models of braids vs. Artin’s and Moishezon’s algebraization of these braids. These two case studies indicate that materiality might have a decisive role in how the model was taken into account mathematically: either as an exploratory or rather as a technical or pedagogical object. (shrink)

Rasprava tematizira osnovne značajke ontologijskog prilaza umjetnosti u djelu Ivana Fochta, jednog od naših najvećih estetičara i ontologa umjetnosti. Problematskog je karaktera i obuhvaća četiri bitne teme njegova mišljenja: Istina i biće umjetnosti uvodi u središnju Fochtovu ˝pred-postavljenost˝, njegov ontologijski prosedê, pitanjem: Što je to biće umjetnosti?; Moderna umjetnost kao ontološki problem raspravlja problematiziranje ontoloških pitanja moderne umjetnosti i njezin promijenjeni status u bitku suvremenog svijeta: umjetnost više nije ˝Schein˝ nego ˝Sein˝ i spoznaje smisao bitka tako što ga pravi; Bit (...) književnosti ispituje ontološke pretpostavke književnog djela kao predmet specijalne ontologije umjetnosti : njezine ontološke ˝planove˝, mjesto među drugim umjetničkim vrstama i u modernoj umjetnosti; Bit glazbe suočava se s ˝tajnom glazbe˝: pitanje Što je glazba? jedno je od najtežih pitanja koja su se postavljala filozofiji umjetnosti; u glazbi, misli Focht, krije se odgovor na pitanje o tajni umjetnosti.The article places its interest on basic characteristics of ontological approach to artin the work of Ivan Focht, one of the greatest aestheticians and ontologists of art. Itconsists of four essential themes in his thought. The Truth and Being of art introducesus into central Focht’s »vor-stellung«, into his ontological procédé,with a question: ‘What is the being of art?’. Modern art as ontological problem discussesthe themes of ontological issues of modern art and its changed status in the Being of contemporary world; the artwork is no more Schein but Sein and it knows the meaning of Being by making it. TheEssence of Literature challenges ontological presuppositions of literary work , as an issue of special ontology of artwork – its ontological »landscapes«, its place amongother artistic forms and in modern art. The part Essence of Music confronts itselfwith »secret of music«; the question ‘What is Music?’ is one of the most complicatedquestions which were asked by philosophy of art. In the music, says Focht, is the hiddenanswer to the question on the secret of art itself. (shrink)

We investigate some common points between stable structures and weakly small structures and define a structureMto befineif the Cantor-Bendixson rank of the topological space${S_\varphi }\left} \right)$is an ordinal for every finite subsetAofMand every formula$\varphi \left$wherexis of arity 1. By definition, a theory isfineif all its models are so. Stable theories and small theories are fine, and weakly minimal structures are fine. For any finite subsetAof a fine groupG, the traces on the algebraic closure$acl\left$ofAof definable subgroups ofGover$acl\left$which are boolean combinations of (...) instances of an arbitrary fixed formula can decrease only finitely many times. An infinite field with a fine theory has no additive nor multiplicative proper definable subgroups of finite index, nor Artin-Schreier extensions. (shrink)

The desire for authenticity now occupies a central position in contemporary culture. Whether in our search for selfhood, leisure experience, or in our material purchases, we search for the real, the genuine. These terms are not, however, descriptive, but must be situated and defined by audiences. In this analysis, I examine the development of the market for self-taught art, an artistic domain in which the authentic is a central defining feature, conferring value on objects and creators. Self-taught art is a (...) form of identity artin which the characteristics of the artists and their life stories are as important as the formal features of the created objects. The article examines the justifications for this emphasis and the battles over the construction of biography. My examination of self-taught art is grounded in five years of ethnographic observation, interviews, and analyses of texts. (shrink)