On y montre qu'un corps stable de caractéristique positive est de dimension finie sur son centre, puis on généralise la chose aux corps simples.

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.

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)

We observe simple links between equivalence relations, groups, fields and groupoids (and between preorders, semi-groups, rings and categories), which are type-definable in an arbitrary structure, and apply these observations to the particular context of small and simple structures. Recall that a structure is small if it has countably many n-types with no parameters for each natural number n. We show that a θ-type-definable group in a small structure is the conjunction of definable groups, and extend the result to semi-groups, fields, (...) rings, categories, groupoids and preorders which are θ-type-definable in a small structure. For an A-type-definable group G A (where the set A may be infinite) in a small and simple structure, we deduce that (1) if G A is included in some definable set X such that boundedly many translates of G A cover X, then G A is the conjunction of definable groups. (2) for any finite tuple ḡ in G A , there is a definable group containing ḡ. (shrink)

A group is small if it has only countably many complete n-types over the empty set for each natural number n. More generally, a group G is weakly small if it has only countably many complete 1-types over every finite subset of G. We show here that in a weakly small group, subgroups which are definable with parameters lying in a finitely generated algebraic closure satisfy the descending chain conditions for their traces in any finitely generated algebraic closure. An infinite (...) weakly small group has an infinite abelian subgroup, which may not be definable. A small nilpotent group is the central product of a definable divisible group with a definable one of bounded exponent. In a group with simple theory, any set of pairwise commuting elements is contained in a definable finite-by-abelian subgroup. First corollary: a weakly small group with simple theory has an infinite definable finite-by-abelian subgroup. Secondly, in a group with simple theory, a solvable group A of derived length n is contained in an A-definable almost solvable group of class at most 2n — 1. (shrink)

Wedderburn showed in 1905 that finite fields are commutative. As for infinite fields, we know that superstable (Cherlin, Shelah) and supersimple (Pillay, Scanlon, Wagner) ones are commutative. In their proof, Cherlin and Shelah use the fact that a superstable field is algebraically closed. Wagner showed that a small field is algebraically closed , and asked whether a small field should be commutative. We shall answer this question positively in non-zero characteristic.

It is shown that a stable division ring with positive characteristic has finite dimension over its centre. This is then extended to simple division rings.

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

The Minimalist Program for linguistic theory is Noam Chomsky's boldest and most radical version of his naturalistic approach to language. Cedric Boeckz examines its foundations, explains its underlying philosophy, exemplifies its methods, and considers the significance of its empirical results. He explores the roots and antecedents of the Program and shows how its methodologies parallel those of sciences such as physics and biology. He disentangles and clarifies current debates and issues around the nature of minimalist research in linguistics and shows (...) how the aims and ambitions of the Minimalist Program lie at the centre of the enterprise to understand how the human language faculty operates in the mind and is manifested in the world's languages.Professor Boeckx writes for advanced and graduate students of linguistics and for all those, in fields such as cognitive science and evolutionary biology, who want to know more about current developments in theoretical linguistics. (shrink)

Cedric Boeckx focuses on two core components of grammar: phrase structure and locality.

Figurative drawing is a skill that takes time to learn, and it evolves during different childhood phases that begin with scribbling and end with representational drawing. Between these phases, it is difficult to assess when and how children demonstrate intentions and representativeness in their drawings. The marks produced are increasingly goal-oriented and efficient as the child’s skills progress from scribbles to figurative drawings. Pre-figurative activities provide an opportunity to focus on drawing processes. We applied fourteen metrics to two different datasets (...) (_N_ = 65 and _N_ = 344) to better understand the intentional and representational processes behind drawing, and combined these metrics using principal component analysis (PCA) in different biologically significant dimensions. Three dimensions were identified: efficiency based on spatial metrics, diversity with color metrics, and temporal sequentiality. The metrics at play in each dimension are similar for both datasets, and PCA explains 77% of the variance in both datasets. Gender had no effect, but age influenced all three dimensions differently. These analyses for instance differentiate scribbles by children from those drawn by adults. The three dimensions highlighted by this study provide a better understanding of the emergence of intentions and representativeness in drawings. We discussed the perspectives of such findings in comparative psychology and evolutionary anthropology. (shrink)

Most syntacticians, no matter their theoretical persuasion, agree that features are the most important units of analysis. Within Chomskyan generative grammar, the importance of features has grown steadily and within minimalism, it can be said that everything depends on features. They are obstacles in any interdisciplinary investigation concerning the nature of language and it is hard to imagine a syntactic description that does not explore them. For the first time, this book turns grammar upside down and proposes a new model (...) of syntax that is better suited for interdisciplinary interactions, and shows how syntax can proceed free of lexical influence. The empirical domain examined is vast, and all the fundamental units and properties of syntax are rethought. Opening up new avenues of investigation, this book will be invaluable to researchers and students in syntactic theory, and linguistics more broadly. (shrink)

Après deux millénaires de culpabilité chrétienne, on pourrait penser que la liberté de mœurs s'est imposée, or aucune liberté ne va sans angoisse. Afin de dissoudre cette angoisse de la sexualité, d'en éclairer les zones d'ombre, d'en annuler les déterminismes, la société contemporaine s'est lancée dans une folle entreprise : l'encadrer, comme tout échange, par les formes contractuelles des normes juridiques. Mais le contrat peut-il s'appliquer à la sexualité?? A-t-il les moyens de clarifier la relation humaine la plus intime qui (...) soit, de résoudre toutes les tensions liées au contact avec l'altérité?? Cédric Lagandré reprend le débat du statut culturel de la sexualité en Occident pour défendre, sur le socle du consentement mutuel, sa nature nécessairement infra-juridique. On ne peut accéder innocemment à la sexualité, non au sens où le désir sexuel serait moralement coupable, mais au sens où il implique un vertige, une angoisse et une mise à nu. La forme juridique, loin de civiliser la sexualité, l'enferme donc dans un cadre défini par la prostitution, et ne la repousse pas moins que la pornographie dans le registre trivial du besoin. L'effort contemporain pour passer l'intégralité du réel au crible des catégories juridiques ne peut donc qu'échouer devant l'ordre du symbolique: l'obscurité du désir rend la sexualité insaisissable à toute volonté de l'encadrer par la règle. (shrink)

Formal learning theory constitutes an attempt to describe and explain the phenomenon of learning, in particular of language acquisition. The considerations in this domain are also applicable in philosophy of science, where it can be interpreted as a description of the process of scientific inquiry. The theory focuses on various properties of the process of hypothesis change over time. Treating conjectures as informational states, we link the process of conjecture-change to epistemic update. We reconstruct and analyze the temporal aspect of (...) learning in the context of dynamic and temporal logics of epistemic change. We first introduce the basic formal notions of learning theory and basic epistemic logic. We provide a translation of the components of learning scenarios into the domain of epistemic logic. Then, we propose a characterization of finite identifiability in an epistemic temporal language. In the end we discuss consequences and possible extensions of our work. (shrink)

An intellectual biography of Don Isaac ben Judah Abravanel, a 15th century Portuguese rabbi, scholar, Bible commentator, philosopher, and statesman.

In 2013, Bennett proposed a mereological theory in which the parthood relation is defined on the basis of two primitive relations: a is a part of b iff a fills a slot owned by b. However, this theory has issues counting how many parts an entity has. We explore the various counting problems and propose a new theory to solve them. Keeping the core idea of Bennett’s slots, this theory introduces mereological relations between slots. This theory enables us to solve (...) all known counting problems and to go beyond the limits of Bennett’s theory by theorising expected features of mereological theories: supplementation principles and mereological sum and fusion. The theory is illustrated on ontological issues on the nature of structural universals and informational entities. (shrink)

Self-sufficient ideographies are rare because they are stifled by the issue of standardization. Similar issues arise with abstract art or drawings created by young children or great apes. We propose that mathematical indices and artificial intelligence can help us decode ideography, and if not to understand its meaning, at least to know that meaning exists.

In 2010, the Eurozone became the epicentre of the world crisis. The vulnerability of Europe appears to be linked to the specific institutional arrangement which organises monetary, financial and budgetary policies within the Eurozone. This article tries to understand the evolution of theeuduring a short but decisive historical sequence in a theoretical framework that puts elements of Gramsci’s reflections on the theme of crisis, and especially his notion of ‘Caesarism’, at its centre. It addresses the current debate concerning the relationships (...) between democratic politics and neoliberalism, while focusing on how the radicalisation of the crisis put at stake the co-construction of capitalism and representative democracy in the Western world sincewwii. (shrink)

This article revisits an historic exchange between two black ex-communists, Harold Cruse and Harry Haywood, a debate that prefigured many of the central contradictions of the black-power era. Their exchange followed Cruse’s influential 1962 essay forStudies on the Left, ‘Revolutionary Nationalism and the Afro-American’, which declared that the American Negro was a ‘subject of domestic colonialism’. Written against the prevailing liberal integrationist commitments of the civil-rights movement, his essay called for black economic and political independence, and inspired many of the (...) younger activists who would give birth to the black-power movement. In a series of essays for the Bay Area black radical journalSoulbook, Haywood criticised Cruse’s mishandling of class politics among blacks, and his retreat from anti-capitalism. This forgotten episode is important on its own terms, for what it says about the character and limitations of left-political thinking during the sixties, and equally for understanding and contesting those commonsensical notions of African-American public life in our times which too often remain rooted in the vanished social context and political realities of the twentieth-century racial ghetto. (shrink)

If $G$ is a group with a supersimple theory having a finite $SU$-rank, then the subgroup of $G$ generated by all of its normal nilpotent subgroups is definable and nilpotent. This answers a question asked by Elwes, Jaligot, Macpherson and Ryten. If $H$ is any group with a supersimple theory, then the subgroup of $H$ generated by all of its normal soluble subgroups is definable and soluble.

The role intellectual virtues play in scientific inquiry has raised significant discussions in the recent literature. A number of authors have recently explored the link between virtue epistemology and philosophy of science with the aim to show whether epistemic virtues can contribute to the resolution of the problem of theory choice. This paper analyses how intellectual virtues can be beneficial for successful resolution of theory choice. We explore the role of virtues as well as vices in scientific inquiry and their (...) beneficial effects in the context of theory choice. We argue that vices can play a role in widening the set of potential candidate theories and support our claim with historical examples and normative arguments from formal social epistemology. We argue that even though virtues appear to be neither necessary nor sufficient for scientific success, they have a positive effect because they accelerate successful convergence amongst scientists in theory choice situations. (shrink)

Non-classical views about important issues in logic and its philosophy are a distinctive trait of Shahid Rahman's work. This volume has been designed, on the occasion of his 50th birthday, as a gathering place for unconventional approaches, original ideas and attempts to question well-established standards. Some of the world top philosophers and logicians contributed to a brilliant collection of papers, some of which doubtlessly leave their mark on the work to come in logic and in philosophy of formal sciences. Contributors (...) are: Philippe Balbiani, Diderik Batens, Johan van Benthem, Giacomo Bonanno, Walter A. Carnielli, Newton C. A. Da Costa, Michel Crubellier, Francisco A. Doria, Dov M. Gabbay, Olivier Gasquet, Gerhard Heinzmann, Andreas Herzig, Jaakko Hintikka, Justine Jacot, Reinhard Kahle, Erik C. W. Krabbe, Decio Krause, Franck Lihoreau, Kuno Lorenz, Ilkka Niiniluoto, Graham Priest, Stephen Read, Manuel Rebuschi, Greg Restall, Gabriel Sandu, Gerhard Schurz, Francois Schwarzentruber, Yaroslav Shramko, Goran Sundholm, John Symons, Christian Thiel, Nicolas Troquard, Tero Tulenheimo, Jean Paul Van Bendegem, Daniel Vanderveken, Yde Venema, Heinrich Wansing, Jan Wolenski and John Woods. (shrink)

In his 1962 essay ‘Revolutionary Nationalism and the Afro-American,’ Harold Cruse quipped, ‘American Marxists cannot “see” the Negro at all, unless he is storming the barricades, either in the pres...

The United Kingdom case R v Lee EWCA Crim 1404 resulted in a pharmacist being convicted for an inadvertent dispensing error and paved way for the decriminalisation of such errors by way of a due diligence defence enacted in 2018. In relation to Hong Kong, what is its legal position for dispensing errors, and can it follow the decriminalising steps of UK? The primary objective of this paper is to explore whether and how HK can reach the normative position for (...) a dispensing error legal regime: I posit that the normative position for healthcare professional liability for dispensing errors should prioritise the public interest of minimisation of future dispensing errors over the retribution of past wrongs; I illustrate HK’s current position for the liabilities of HCPs on dispensing errors, focusing analysis on the relatively controversial aspects of HK’s criminal liability, referencing the landmark cases Hin Lin Yee v HKSAR 13 HKCFAR 142 and Kulemesin v HKSAR 16 HKCFAR 195 to assist my analysis of the requisite mental element for relevant statutory offences; through comparison with UK’s development post-R v Lee and application of Rule of Law principles, HK’s current position is critiqued, coming to the conclusion that while there are compelling reasons for the decriminalisation of dispensing errors in HK, the prerequisite for this to happen is an overhaul of regulatory frameworks by significantly increasing levels of accountability. (shrink)

Flagging labor governance in far-flung supply networks has prompted greater scrutiny of instrumental CSR and calls for models that are tethered more closely to accountability, constraint, and oversight. Political CSR is an apt response, but this paper seeks to buttress its deliberative moorings by arguing that the agonist notion of ‘domesticated conflict’ provides a necessary foundation for substantive deliberation. Because deliberation is more viable and effective when coupled with some means of coercion, a concept of CSR solely premised on reciprocal (...) corporate-stakeholder engagement is pre-mature; efforts should first be directed toward the antecedents of reciprocity and how it is to be achieved, and only then does deliberation become a reliably substantive exercise. The resulting account of agonistic CSR is generated through agonistic principles of realism, pro-action, contestation, and countervailence, and illustrated by the Bangladesh Accord. (shrink)

Major depression is associated with a decrease of 1st person visual perspective in autobiographical memory, even after full remission. This study aimed to examine visual perspective in healthy never-depressed subjects presenting with either genetic or psychological vulnerability for depression. Sixty healthy participants performed the Autobiographical Memory Test with an assessment of visual perspective. Genetic vulnerability was defined by the presence of at least one S or LG allele of the polymorphism of the serotonin-transporter-linked promoter region . Psychological vulnerability was defined (...) by high scores of harm avoidance measured by the Temperament and Character Inventory. Life stress exposure, depressive mood, rumination, and familial history of depression were assessed through standardized procedures. Visual perspective for positive memories was independently predicted by both harm avoidance and a gene by environment interaction between the 5-HTTLPR polymorphism and life stress exposure. Visual perspective and vulnerability for depression may share some biological bases. (shrink)

A theory of planned behavior framework was employed to investigate the impact of corporate social responsibility perceptions on the job choice intentions of American, Chinese, and Lebanese college students. Attitudes toward CSR, subjective norm, and perceived behavioral control explained moderate levels of the variance in job choice intention in all three countries. Attitudes toward CSR, which entailed individual evaluations of CSR, were positively related to job choice intentions among Lebanese and American respondents, but not Chinese respondents. Subjective norm, the importance (...) accorded the views of significant others, was most strongly related to job choice intentions among Chinese respondents. Perceived behavioral control, the perceived degree of control over one’s actions and outcomes, had the strongest relationship to job choice intentions among American respondents. The authors concluded that respondents in the three countries did not differ in the extent to which they intend to work for socially responsible firms but tended to derive their intentions in different ways. Implications for tailoring CSR and recruitment efforts across countries are derived based on the findings. (shrink)

Leopold Kronecker constructs in two articles published in 1869 and 1878, a theory which has its roots in Sturm’s work on the determination of the number of real solutions of an equation. The presentation of this theory of characteristics by Émile Picard will give rise to a controversy between the two mathematicians, who claimed the fame for a formula giving the number of solutions of certain systems of several equations. In this article, after an overview of the theory of characteristics, (...) we will show how, through this dispute, it is actually the way these two mathematicians approach mathematics that is at stake. (shrink)