In this paper we study the algebraic structure ofω-stable bilinear maps, arbitrary rings, and nilpotent groups. We will also provide rather complete structure theorems for the above structures in the finite Morley rank case.

The U.S. stock market is one of the largest and most complex marketplaces in the global financial system. Over the past several decades, this market has evolved at multiple structural and temporal scales. New exchanges became active, and others stopped trading, regulations have been introduced and adapted, and technological innovations have pushed the pace of trading activity to blistering speeds. These developments have supported the growth of a rich machine-trading ecology that leads to qualitative differences in trading behavior at (...) human and machine time scales. We conduct a longitudinal analysis of comprehensive market data to quantify nonstationary dynamics throughout this system. We quantify the relationship between fluctuations in the number of active trading venues and realized opportunity costs experienced by market participants. We find that information asymmetries, in the form of quote dislocations, predict market-wide volatility indicators. Lastly, we uncover multiple micro-to-macro level pathways, including those exhibiting evidence of self-organized criticality. (shrink)

According to the algebraic approach to spacetime, a thoroughgoing dynamicism, physical fields exist without an underlying manifold. This view is usually implemented by postulating an algebraic structure (e.g., commutative ring) of scalar-valued functions, which can be interpreted as representing a scalar field, and deriving other structures from it. In this work, we point out that this leads to the unjustified primacy of an undetermined scalar field. Instead, we propose to consider algebraic structures in which all (and only) physical fields (...) are primitive. We explain how the theory of natural operations in differential geometry—the modern formalism behind classifying diffeomorphism-invariant constructions—can be used to obtain concrete implementations of this idea for any given collection of fields. For concrete examples, we illustrate how our approach applies to a number of particular physical fields, including electrodynamics coupled to a Weyl spinor. (shrink)

Van den Dries, L. and J. Holly, Quantifier elimination for modules with scalar variables, Annals of Pure and Applied Logic 57 161–179. We consider modules as two-sorted structures with scalar variables ranging over the ring. We show that each formula in which all scalar variables are free is equivalent to a formula of a very simple form, uniformly and effectively for all torsion-free modules over gcd domains . For the case of Presburger arithmetic with scalar variables the result takes (...) a still simpler form, and we derive in this way the polynomial-time decidability of the sets defined by such formulas. (shrink)

Generalizing Cooper’s method of quantifier elimination for Presburger arithmetic, we give a new proof that all parametric Presburger families \ [as defined by Woods ] are definable by formulas with polynomially bounded quantifiers in an expanded language with predicates for divisibility by f for every polynomial \. In fact, this quantifier bounding method works more generally in expansions of Presburger arithmetic by multiplication by scalars \: \alpha \in R, t \in X\}\) where R is any ring of functions (...) from X into \. (shrink)

We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions.We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution.We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a (...) connection between our theory with non-standard analysis and thus answer, although indirectly, a question raised by Colombeau. This article provides a bridge between Colombeau theory of generalized functions and non-standard analysis. (shrink)

The majority of the Sufi orders, which have their own special ezkar, evrâd, etiquette, and erkan and have survived until today, particularly VI/XII. They were formed over centuries and spread to many parts of the world by dividing into different branches in the historical process. Sufi personalities who belonged to these sufi orders established structures such as dervish lodges and dervish lodges in the regions they reached with great efforts, and they were instrumental in the conversion of many people to (...) Islam. Attributed to its founder, Abdulqadir Geylani, Qadiriyya is one of the most famous of these sufi orders. From the Middle East, especially from Iraq, to Afkaya; It spread over a wide area from Anatolia to the Balkans and China in the east and carried out convent activities with more than fifty branches. The Reshidiyya Sufi Order, which is attributed to Ahmed Reshidi and whose center is in Mosul, is a sect that operates in a wide region from Turkey to India and still has followers in these regions. It can be said that the Reshidiyya Sufi Order, which has its principles and manners, is one of the largest branches of the Qadiriyya. This Sufi order also has relations with the Rifaiyya, Bedewiyya, Desûqiyya, and Suhrawardiyya Sufi Order. Because Ahmed ar-Reshidi, the founder of the sect, is a Sufi figure who received the caliphate from all these sects. Although it is a Sufi order that has spread to this extent in Islamic lands and continues its dervish activities until today, the name of the Reshidiyya sect is not encountered even in the encyclopedic studies conducted in our country on the branches of the Qadiriyya Sufi Order. However, a scholar such as Mollâ Khalil Siirdî, who was mentioned as the "ser ring" in the ijazah ceremonies held in classical madrasahs that continued to be active in Anatolia until today, is one of the caliphs of this order. This humble study has been prepared by making use of the sources obtained through Ahmed ar-Reshidi's last-generation grandchildren after reaching them. With this study, we have been trained in recent times like Ahmed ar-Reshidi, Hz. We will try to introduce a great Sufi figure, who came from the progeny of the Prophet, who devoted his whole life to the task of guidance and who was referred to as the "pole", as well as the principles and manners of the Sufi order he was the founder of. (shrink)

Linear arithmetics are extensions of Presburger arithmetic () by one or more unary functions, each intended as multiplication by a fixed element (scalar), and containing the full induction schemes for their respective languages. In this paper, we construct a model of the 2‐linear arithmetic (linear arithmetic with two scalars) in which an infinitely long initial segment of “Peano multiplication” on is ‐definable. This shows, in particular, that is not model complete in contrast to theories and that are known to (...) satisfy quantifier elimination up to disjunctions of primitive positive formulas. As an application, we show that, as a discretely ordered module over the discretely ordered ring generated by the two scalars, does not have the NIP, answering negatively a question of Chernikov and Hils. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 21.1 (2001) 155-157 [Access article in PDF] Book Review Buddhist Peacework: Creating Cultures of Peace Buddhist Peacework: Creating Cultures of Peace. Edited by David W. Chappell. Somerville, Massachusetts: Wisdom Publications, 1999. 253 pp. This earnest book demonstrates the continuing vitality of Buddhism in many parts of the world. The contributing authors are the leading figures of contemporary engaged Buddhism, and they write from firsthand experience. The Dalai (...) Lama outlines methods for promoting harmony among different religious traditions. Thich Nhat Hanh shows how the principle of nonviolence was tested in the rescue ofVietnamese boat people during the 1970s. A.T. Ariyaratne presents the work of the influential Sarvodaya movement in Sri Lanka. Shih Cheng-yen, sometimes called "the Mother Theresa of Asia," describes the relief work ofTzu Chi, the largest charitable organization in Taiwan. Dhammachari Lokamitra documents the impact of an adopted Buddhism among former "untouchables" in India. Robert Aitken surveys engaged Buddhist activity in North America, including hospice work, prison reform, and sustainable farming. Many of the writers have personally suffered the deprivations of war and oppression; in some cases they continue their work amid threats of violence or arrest.An aim ofBuddhist Peacework is to offer a Buddhist response to a declaration that emerged from a 1994 meeting of world religious leaders organized by UNESCO. This document, "Declaration of the Role of Religion in the Promotion of a Culture of Peace," is included as an appendix. Two of the book's contributors, the Dalai Lama and the senior Cambodian monk Maha Ghosananda, participated in the UNESCO meeting. Indeed, some of the declaration's language has an engaged Buddhist ring: "We must be at peace with ourselves; we strive to achieve inner peace through personal reflection and spiritual growth, and to cultivate a spirituality which manifests itself in action."One of Buddhism's distinctive teachings on the subject of peace is the practice of "internal disarmament," the term used by the Dalai Lama in his essay. Unless individuals are able to tame the forces of greed, anger, and delusion in their own minds, the prospects for peace between communities and between nations are slim. For an engaged Buddhist, there must be alignment between "inner" and "outer" disarmament. One cannot work for peace--or any other worthy social goal--in an agitated, antagonistic way. In this collection, peacework is something one does as spiritual practice.Shakyamuni Buddha approached the existential problem of suffering by analyzing the causes of suffering. In a similar spirit, engaged Buddhists have embarked on a Buddhistic analysis of the causes of war and peace. Contributor José Ignacio Cabezón writes: "Peace cannot arise simply by wishing it into existence, but only by the cultivation of its causes.Viewing peace in this way has the salutary effect of shifting the emphasis of peacework from result to causes." Somewhere in that mix of causes we [End Page 155] eventually encounter ourselves. If the world is truly interdependent, we share responsibility for violence and atrocities occurring "elsewhere."Thich Nhat Hanh, in his essay, declares: "If we look deeply, we will observe that the roots of war are in the unmindful ways we have been living. We have not sown enough seeds of peace and understanding in ourselves and others, therefore we are co-responsible: 'Because I have been like this, they are like that.'" The notion of sowing "seeds of peace" is reinforced in the image on the book's cover: two hands tenderly plant a seedling in receptive soil.But internal disarmament is not enough. As editor David Chappell asserts, "Today there is a new urgency for that [inner] peacework to be manifest socially, ecologically, and materially."Witness the plight of several Buddhist (and formerly Buddhist) nations in Asia. "Recently, Buddhist countries have become notorious arenas of genocide and brutality," writes Karma Lekshe Tsomo. Citing Burma, Cambodia, China, Sri Lanka, and Tibet, Tsomo asks, "What went wrong?" Peacework also has new meanings in an age of ecocrisis. For Stephanie Kaza, "a first step in keeping peace with nature calls for contact with ecological suffering." Kaza highlights four ways to... (shrink)

This paper studies two dual notions in module theory—namely, radicals and socles—from the standpoint of reverse mathematics. We first consider radicals of Z-modules, where the radical of a Z-module M is defined as the intersection of pM={px:x∈M} with p taken from all primes. It shows that ACA0 is equivalent to the existence of radicals of Z-modules over RCA0. We then study socles of modules over commutative rings with identity. The socle of an R-module M is the largest semisimple submodule (...) of M. We show that the existence of socles of modules over a commutative ring with identity is equivalent to ACA0 over RCA0. Vector spaces are semisimple modules over fields. In general, semisimple modules possess nice properties of vector spaces. Lastly, we study characterizations of semisimple modules over commutative rings using techniques of reverse mathematics. (shrink)

Traditionally, discussions of moral participation – and in particular moral agency – have focused on fully formed human actors. There has been some interest in the development of morality in humans, as well as interest in cultural differences when it comes to moral practices, commitments, and actions. However, until relatively recently, there has been little focus on the possibility that nonhuman animals have any role to play in morality, save being the objects of moral concern. Moreover, when nonhuman cases are (...) considered as evidence of moral agency or subjecthood, there has been an anthropocentric tendency to focus on those behaviors that inform our attributions of moral agency to humans. For example, some argue that the ability to evaluate the principles upon which a moral norm is grounded is required for full moral agency. Certainly, if a moral agent must understand what makes an action right or wrong, then most nonhuman animals would not qualify (and perhaps some humans too). However, if we are to understand the evolution of moral psychology and moral practice, we need to turn our attention to the foundations of full moral agency. We must first pay attention to the more broadly normative practices of other animals. Here, we begin that project by considering evidence that great apes and cetaceans participate in normative practices. (shrink)

Let Uq be the quantum group associated to sl2 with char≠2 and qk not a root of unity. The article is devoted to the model-theoretic study of the quantum plane kq[x,y], considered as an -structure, where is the language of representations of Uq. It is proved that the lattice of definable k-subspaces of kq[x,y] is complemented. This is deduced from the same result for the Uq-module M, which is defined to be the direct sum of all finite dimensional representations of (...) Uq. It follows that the ring of definable scalars for the quantum plane is a von Neumann regular epimorphic ring extension of the quantum group Uq. (shrink)

When Wittgenstein said psychology contains conceptual confusions and experimental results, one item he had in mind was the psycho-physiological theory of kinaesthesis, which offers an account of how we know limb movement and position. The aim of this essay is to develop and evaluate the objections to that theory which have been produced by Wittgenstein, Melden and Anscombe. That project involves specifying clearly what is involved in the theory, resolving various disagreements between the critics, showing the pattern of the objections, (...) and lastly evaluating the success of the case against the theory. That case amounts to the thesis that the kinaesthetic sensations we do have simply are not adequate to the evidential burden placed on them by the theory. Unless one thinks that they must constitute such evidence no one would have thought that they do so. (shrink)

When Wittgenstein said psychology contains conceptual confusions and experimental results, one item he had in mind was the psycho-physiological theory of kinaesthesis, which offers an account of how we know limb movement and position. The aim of this essay is to develop and evaluate the objections to that theory which have been produced by Wittgenstein, Melden and Anscombe. That project involves specifying clearly what is involved in the theory, resolving various disagreements between the critics, showing the pattern of the objections, (...) and lastly evaluating the success of the case against the theory. That case amounts to the thesis that the kinaesthetic sensations we do have simply are not adequate to the evidential burden placed on them by the theory. Unless one thinks that they must constitute such evidence (the piece of conceptual confusion) no one would have thought that they do so. (shrink)

When Wittgenstein said psychology contains conceptual confusions and experimental results, one item he had in mind was the psycho-physiological theory of kinaesthesis, which offers an account of how we know limb movement and position. The aim of this essay is to develop and evaluate the objections to that theory which have been produced by Wittgenstein, Melden and Anscombe. That project involves specifying clearly what is involved in the theory, resolving various disagreements between the critics, showing the pattern of the objections, (...) and lastly evaluating the success of the case against the theory. That case amounts to the thesis that the kinaesthetic sensations we do have simply are not adequate to the evidential burden placed on them by the theory. Unless one thinks that they must constitute such evidence (the piece of conceptual confusion) no one would have thought that they do so. (shrink)

The paper develops a uniform compositional analysis of the various readings of the scalar particle still and its German counterpart noch. Noch/still is a presuppositional scalar particle that gives rise to implicatures. Interpretive possibilities arise through different choices for the scale that the particle associates with, different attachment sites in the syntax, and interaction with focus. These interpretive parameters allow for a wide range of possible sentence interpretations, which overlap, but do not coincide for still and noch. The contrastive perspective (...) allows us to examine the role of scales in the grammar. The implicatures triggered by the scalar item open an interesting perspective for the generation of implicatures in general. (shrink)

본 연구의 목적은 인간의 본성에 대한 철학적 탐구의 역사와 인간의 도덕성의 기원에 대한 객관적 검토를 통하여 도덕교육의 필요성과 의의를 확인하는 데 있다. 이러한 작업을 위하여 본 연구에서는 먼저 플라톤과 소피스트의 논쟁을 중심으로 인간의 도덕성의 기원문제에 대한 객관적 검토를 시행할 것이다. 그리고 홉스의 계약론에 대한 분석을 통하여 인간이 비록 이기적 존재이지만 합리적 선택의 능력을 가진 이성적 존재라는 측면에 주목하면서 합리적 합의로부터 도출되는 도덕성을 설명하는 데 필요한 장치와 가정을 검토할 것이다. 그리고 마지막으로 사회가 점점 상호 협력하는 환경, 즉 보다 정의로운 사회 환경이 (...) 조성될수록 개인은 더욱 더 협력하고 정의롭게 행위 한다는 경험적 사실을 바탕으로 개인의 도덕교육의 필요성과 의의를 강조할 것이다. (shrink)

Is a rational morality a necessary evil—a mean between what an individual would judge best—bettering his situation at whatever cost to others, and worst—having one's situation worsened at other's pleasure? It would seem that Glaucon's fable of the ring of Gyges may be applied to our account of morality. And indeed, matters may be worse—a contractarian morality such as we have developed may seem to be a tool for the clever and strong to use in domination, using the language (...) of cooperation to conceal the reality of exploitation. If we understand ourselves on the model of economic man, treating all basic motivation as exemplifying asociality and all human relationships as contractual, we may find these conclusions hard to escape. Even though we could understand the rational arguments in support of morality, our feelings would be engaged only by our own concerns, and we would lack any affective capacity for morality. (shrink)

Study on Budhist Pramāṇa-vāda (doctrine of proof: an epistemological study of the nature of knowledge) and Hetu-vidya (science of causes: a system of logic).

Recently there has been a lively revival of interest in implicatures, particularly scalar implicatures. Building on the resulting literature, our main goal in the present paper is to establish an empirical generalization, namely that SIs can occur systematically and freely in arbitrarily embedded positions. We are not so much concerned with the question whether drawing implicatures is a costly option (in terms of semantic processing, or of some other markedness measure). Nor are we specifically concerned with how implicatures come about (...) (even though, to get going, we will have to make some specific assumptions on this matter). The focus of our discussion is testing the claim of the pervasive embeddability of SIs in just about any context, a claim that remains so far controversial. While our main goal is the establishment of an empirical generalization, if we succeed, a predominant view on the division of labor between semantics and pragmatics will have to be revised. A secondary goal of this paper is to hint at evidence that a revision is needed on independent grounds. But let us first present, in a rather impressionistic way, the reasons why a revision would be required if our main generalization on embedded SIs turns out to be correct. In the tradition stemming from Grice (1989), implicatures are considered a wholly pragmatic phenomenon and SIs are often used as paramount examples. Within such a tradition, 㳊 semantics is taken to deal with the compositional construction of sentence meaning (a term which we are using for now in a loose, non technical way), while pragmatics deals with how sentence meaning is actually put to use (i.e. enriched and possibly modified through reasoning about speakers’ intentions, contextually relevant information, etc.). Simply put, on this view pragmatics takes place at the level of complete utterances and pragmatic enrichments are a root phenomenon (something that happens globally to sentences) rather than a compositional one.. (shrink)

This paper explores how the virtuous aesthetic cosmopolitan—one actively engaged in cultivating an authoritative appreciation for culturally unfamiliar works or traditions of art, in a manner informed by moral cosmopolitan principles—engages with the ‘exotic’ artwork in a manner that is both morally responsible and aesthetically discerning. After providing an overview of philosophical cosmopolitanism and the aesthetic cosmopolitan’s project, I consider in depth a particular example: the music of Mauritanian singer Noura Mint Seymali as encountered by an unaccustomed listener. I explore (...) potential problematic responses to the work, including both chauvinistic and exoticizing responses. I then consider possible strategies for alternative responses, informed by the aesthetic and hermeneutic theories of Hume, Gadamer, and Charles Taylor. Having revealed deficiencies with these alternatives, I go on to argue that the cosmopolitan’s best strategy is a mode of appreciation that is ‘conversational’ in nature, an open-ended approach modeled on an exchange between the appreciator and an other-cultural interlocutor. In proposing such a model, I draw on the work of Kwame Appiah and Maria Lugones, as well as Anthony Laden’s recent work on conversational norms. (shrink)

The worldwide integration of capital markets continues to make progress and has resulted in both issuers and investors being active in various markets on both sides of the Atlantic. In times of financial crisis, this brings one question to the centre of attention which has not been discussed exhaustively before: in the situation of securities liability to investors in an international context, which is the applicable law to the liability claim? The harmonization of private international law rules in Europe gives (...) rise to new reflections on the problem of international issuer liability. In the United States, on the other hand, the Supreme Court has just ruled for the first time on matters relating to the international application of the US securities regulation, thereby overruling the settled case law of decades. This paper understands the role of issuer liability in a broader context as a ‘corporate governance’ device, and from this starting point, develops a new approach to the legal problem of cross-border securities liability. (shrink)

Community acts of material signification are an important form of sculpture that occur through an exchange of human and non-human agents. First these acts of sculpture are discussed in relation to extended mind, the morphogenic model of making, material engagement theory and entanglement to frame how humans shape the world as collaborators with non-humans by extending mind through material. I then discuss various acts of community material accumulation that I consider sculpture, skateboarding and clay forming as evidence of extended mind, (...) comparison of the morphogenic to the hylomorphic model of making, occurrences of materials affecting other materials absent of human intervention and my recent participatory installation Stone Fruit. These topics are used to present a lens for understanding the production of sculpture as a collaboration with opposed to dictation on systems of materials, places and people. This lens, in turn, presents community sites of material accumulation to be an important form of sculpture production. (shrink)

We prove the triviality of the Grothendieck ring of a Z-valued field K under slight conditions on the logical language and on K. We construct a definable bijection from the plane K 2 to itself minus a point. When we specialized to local fields with finite residue field, we construct a definable bijection from the valuation ring to itself minus a point.

We present numerous natural algebraic examples without the so-called Canonical Base Property (CBP). We prove that every commutative unitary ring of finite Morley rank without finite-index proper ideals satisfies the CBP if and only if it is a field, a ring of positive characteristic or a finite direct product of these. In addition, we construct a CM-trivial commutative local ring with a finite residue field without the CBP. Furthermore, we also show that finite-dimensional non-associative algebras over an (...) algebraically closed field of characteristic [Formula: see text] give rise to triangular rings without the CBP. This also applies to Baudisch’s [Formula: see text]-step nilpotent Lie algebras, which yields the existence of a [Formula: see text]-step nilpotent group of finite Morley rank whose theory, in the pure language of groups, is CM-trivial and does not satisfy the CBP. (shrink)

Originally published in 1941. Herodicus was a Greek physician of the fifth century BC, and a native of Selymbria. The first use of therapeutic exercise for the treatment of disease and maintenance of health is credited to him, and he is believed to have been one of the tutors of Hippocates.

Plato’s Socrates holds that we always have reason to be just, since being just is essential for living a happy and successful life. In Book II of Plato’s Republic, Socrates’ main interlocutor, Glaucon, raises a vivid and powerful challenge to this claim. He presents the case of Gyges, a Lydian shepherd who possesses a ring that gives him the power of invisibility. Glaucon’s contention is that Gyges does not have reason to be just in this circumstance, since being just (...) will not promote his happiness. Thus, the argument poses the following challenge: what reason do we have to be just, particularly in circumstances where we can get away with injustice? In this essay, we describe Glaucon’s challenge, highlight its similarity to challenges offered by other skeptical figures in the history of philosophy, namely, Hobbes’ Foole and Hume’s sensible knave, and present three broad lines of response. (shrink)

In Alastair Norcross argues that scalar consequentialism is the most plausible form of consequentialism, but his arguments are flawed: he is simply mistaken when he suggests that there is a problem with deriving absolutes like right and wrong from gradable properties such as goodness; he cannot justify his claim that the choice of a threshold will always be arbitrary; and his argument only shows that the consequentialist doesn't care about permissibility. Furthermore, I argue that, although Norcross was right to claim (...) that a scalar theory can be action-guiding (to an extent), he was mistaken to think that ought If anything can be said in favour of scalar consequentialism, it is only that it is the most honest form of consequentialism, because it doesn't pretend to care about permissibility. (shrink)

Does morality override self-interest? Or does self-interest override morality? These questions become important in situations where there is conflict between the overall verdicts of morality and self-interest, situations where morality on balance requires an action that is contrary to our self-interest, or where considerations of self-interest on balance call for an action that is forbidden by morality. In situations of this kind, we want to know what we ought simpliciter to do. If one of these standpoints over-rides the other, then (...) there is a straightforward answer. We ought simpliciter to act on the verdict of the overriding standpoint. For purposes of this essay, I assume that there are possible cases in which the overall verdicts of morality and self-interest conflict. I will call cases of this kind “conflict cases.” The verdict of morality in a conflict case would be a proposition as to what we ought morally to do, or as to what we have the most moral reason to do; the verdict of self-interest would be a proposition as to what we ought to do in our self-interest, or as to what action is best supported by reasons or considerations of self-interest. These propositions are action-guiding or normative in a familiar sense. The conflict between morality and self-interest in conflict cases is there-fore a normative conflict; it is a conflict between the overall verdicts of different normative standpoints. I take it that the question of whether morality overrides self-interest is the question of whether the verdicts of morality are normatively more important than the verdicts of self-interest. In due course, I will explain the idea of normative importance as well as the ideas of a normative proposition and of a reason. (shrink)

We prove the triviality of the Grothendieck ring of a $\mathbb{Z}$-valued field K under slight conditions on the logical language and on K. We construct a definable bijection from the plane K$^2$ to itself minus a point. When we specialized to local fields with finite residue field, we construct a definable bijection from the valuation ring to itself minus a point.

We show that elliptic curves whose Mordell–Weil groups are finitely generated over some infinite extensions of ${\mathbb {Q}}$ , can be used to show the Diophantine undecidability of the rings of integers and bigger rings contained in some infinite extensions of rational numbers.

This paper examines alvin goldman's contention that a belief is justified only if the process that produces it is reliable. It is argued that none of several possible interpretations of the reliability theory provides an account of justified belief which satisfies the constraints goldman places on his theory.

This article argues that ‘the digital’ and ‘big data’ are metaphors of obfuscation, which are used to screen the real effects of technologies on lived experiences and the planet. Now that technolog...

A conversational implicature is an inference that consists in attributing to a speaker an implicit meaning that goes beyond the explicit linguistic meaning of an utterance. This paper experimentallyinvestigates scalar implicature, a paradigmatic case of implicature in which a speaker's use of a term like Some indicates that the speaker had reasons not to use a more informative one from the samescale, e.g. All; thus, Some implicates Not all. Pragmatic theorists like Grice would predict that a pragmatic interpretation is determined (...) only after its explicit, logical meaning is incorporated (e.g. whereSome means at least one). The present work aims to developmentally unpack this prediction by showing how younger, albeit competent, reasoners initially treat a relatively weak term logically beforebecoming aware of its pragmatic potential. Three experiments are presented. Experiment 1 presents a modal reasoning scenario offering an exhaustive set of conclusions; critical among these isparticipants' evaluation of a statement expressing Might be x when the context indicates that the stronger Must be x is true. The conversationally-infelicitous Might be x can be understood logically(e.g. as compatible with Must) or pragmatically (as exclusive to must). Results from five-, seven-, and nine-year-olds as well as adults revealed that a) seven-year-olds are the youngest to demonstratemodal competence overall and that; b) seven- and nine-year-olds treat the infelicitous Might logically significantly more often than adults do. Experiment 2 showed how training with the modal taskcan suspend the implicatures for adults. Experiment 3 provides converging evidence of the developmental pragmatic effect with the French existential quantifier Certains (Some). Whilelinguistically-sophisticated children (eight- and ten-year-olds olds) typically treat Certains as compatible with Tous (All), adults are equivocal. These results, which are consistent with unanticipatedfindings in classic developmental papers, reveal a consistent ordering in which representations of weak scalar terms tend to be treated logically by young competent participants and morepragmatically by older ones. This work is also relevant to the treatment of scalar implicatures in the reasoning literature. (shrink)

Let l be a commutative field; Bauval [1] showed that the theory of the ring l[X1,...,Xm] is the same as the weak second-order theory of the field l. Now, l[X1,...,Xm] is the ring of the monoid m, so it may be asked what properties of m we can deduce from the theory of l[;m], that is, if l[m] is elementarily equivalent to the ring of monoid k[G], with k, a field and G, a monoid, what do we (...) know not only about the first-order theory of G but also about more properties of G. We prove that in this case G is isomorphic to m.Bauval [1, Theorem V.2.1] proved that if a factorial ring A is elementarily equivalent to l[;X1,...,Xm], then A is isomorphic to F[X1,...,Xm], with F being the field of invertible elements of A.Our result is different from this property because, a priori, the field k is not the field of invertible elements . Furthermore, k[G]; is not always factorial or Neotherian: if G is isomorphic to the cartesian product ∏i<ω, then the number of irreducible elements that divide elements that divide X is infinite, and the ideal generated by the monomials X is not finitely generated.We recall that to be factorial of Neotherian are not elementary properties. (shrink)