Vector spaces over fields are pseudofinite, and this remains true for vector spaces over division rings that are finite-dimensional over their center. We also construct a division ring such that the nontrivial vector spaces over it are not pseudofinite, using Richard Thompson's group F. The idea behind the construction comes from a first-order axiomatization of the class of division rings all whose nontrivial vector spaces are pseudofinite.

Let T be a complete o-minimal extension of the theory of real closed fields. We characterize the convex hulls of elementary substructures of models of T and show that the residue field of such a convex hull has a natural expansion to a model of T. We give a quantifier elimination relative to T for the theory of pairs (R, V) where $\mathscr{R} \models T$ and V ≠ R is the convex hull of an elementary substructure of R. We deduce (...) that the theory of such pairs is complete and weakly o-minimal. We also give a quantifier elimination relative to T for the theory of pairs (R, N) with R a model of T and N a proper elementary substructure that is Dedekind complete in R. We deduce that the theory of such "tame" pairs is complete. (shrink)

I solve here some problems left open in “T-convexity and Tame Extensions” [9]. Familiarity with [9] is assumed, and I will freely use its notations. In particular,Twill denote a completeo-minimal theory extending RCF, the theory of real closed fields. Let (,V) ⊨Tconvex, let=V/m(V)be the residue field, with residue class mapx↦:V↦, and let υ:→ Γ be the associated valuation. “Definable” will mean “definable with parameters”.The main goal of this article is to determine the structure induced by(,V)on its residue fieldand on its (...) value group Γ. In [9] we expanded the ordered fieldto a model ofTas follows. Take a tame elementary substructure′ ofsuch thatR′ ⊆VandR′maps bijectively ontounder the residue class map, and make this bijection into an isomorphism′ ≌ofT-models. (We showed such′ exists, and that this gives an expansion ofto aT-model that is independent of the choice of′.). (shrink)

We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of “logarithmic-exponential series” , which is equipped with a well behaved exponentiation. We show that the LE-series with derivative 0 are exactly the real constants, and we invert operators to show that each LE-series has a formal integral. We give evidence for the conjecture that the field of LE-series is a universal domain for ordered differential algebra in Hardy fields. We define (...) composition of LE-series and establish its basic properties, including the existence of compositional inverses. Various interesting subfields of the field of LE-series are also considered. (shrink)

Related Works: Original Paper: Lou Van Den Dries. $T$-Convexity and Tame Extensions II. J. Symbolic Logic, Volume 62, Issue 1 , 14--34. Project Euclid: euclid.jsl/1183745182.

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)

For any group satisfying a suitable chain condition, we construct a finitely additive measure on it that is invariant under certain actions.

The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from the remainder function rem, meaning that in computing its time complexity function cε, we assume that the values rem are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch (...) more is known about cε, but this simple-to-prove upper bound suggests the proper formulation of the Euclidean's optimality among its peers—algorithms from rem:Conjecture. If an algorithm α computes gcd from rem with time complexity cα, then there is a rational number r > 0 such that for infinitely many pairs a > b > 1, cα > r log2a. (shrink)

The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.

Vector spaces over fields are pseudofinite, and this remains true for vector spaces over division rings that are finite-dimensional over their center. We also construct a division ring such that the nontrivial vector spaces over it are not pseudofinite, using Richard Thompson's group F. The idea behind the construction comes from a first-order axiomatization of the class of division rings all whose nontrivial vector spaces are pseudofinite.

Du gehst zu Frauen? Vergiss die Peitsche nicht!" Kaum ein Zitat aus Friedrich Nietzsches Gesamtwerk durfte bekannter sein - und lange Zeit fur viele die Grundlage, den grossen Philosophen als Frauenhasser zu deklarieren. Nietzsches Schwester Elisabeth Forster-Nietzsche nutzt dieses Werk, um mit dem Vorurteil aufzuraumen. Sie berichtet von Nietzsches Verhaltnis zu Frauen seit der Kindheit. Freundschafts- und Liebesbeziehungen sind ebenso Thema wie auch weibliche Einflusse auf Nietzsches Personlichkeit und schliesslich auch sein Werk. Forster-Nietzsche erzahlt von Frauen wie Cosima Wagner, Lou (...) Andreas-Salome, Malwida von Meysenbug und vielen anderen. In Erinnerungen, Texten und Briefen entwirft sie so ein besonders personliches Bild des Genies, wie ihn nur wenige erleben durften und vermittelt eine weitere entscheidende Dimension zum Verstandnis seines Werks. Elisabeth Forster-Nietzsche (1846-1935) war bereits von Kindesbeinen an eine grosse Bewunderin ihres alteren Bruders, mit dem sie schon fruh ein besonders inniges Verhaltnis verband. Nach Nietzsches Tode alleinige Nachlassverwalterin, begann Forster-Nietzsche, das Bild ihres Bruders in deutsch-nationale und antisemitische Interessen einzupassen und nahm dazu u. a. auch Anderungen an seinen Texten vor, wofur sie spater scharf kritisiert wu. (shrink)

In ‘Utility of Religion’, Mill argues that a wholly naturalistic religion of humanity would promote individual and social welfare better than supernatural religions like Christianity; in ‘Theism’, however, Mill defends the salutary effects of hope in an afterlife. While commentators have acknowledged this discrepancy, they have not examined the utilitarian value of what Mill terms ‘illusions’. In this essay, I explain Mill's case against the utility of supernatural religious belief and then argue that Mill cannot dismiss the utility of hope (...) in an ultimate justice since it need not pervert the intellect or morality. There are thus utilitarian grounds to support some supernatural illusions, which undermines Mill's defence of an exclusively naturalistic religion. I conclude with the suggestion that while the utility of religious belief leads Mill toward William James's view, they disagree about whether supernatural religious sentiment has any unique, intrinsic force. (shrink)

This book provides a look at philosophical practice from the viewpoint of the practitioner or prospective practitioner. It answers the questions: What is philosophical practice? What are its aims and methods? How does philosophical counseling differ from psychological counseling and other forms of psychotherapy. How are philosophical practitioners educated and trained? How do philosophical practitioners relate to other professions? What are the politics of philosophical practice? How does one become a practitioner? What is APPA Certification? What are the prospects for (...) philosophical practice in the USA and elsewhere? Handbook of Philosophical Practice provides an account of philosophy's current renaissance as a discipline of applied practice while critiquing the historical, social, and cultural forces which have contributed to its earlier descent into obscurity. (shrink)

On the face of it, normative conflicts are commonplace. Yet standard deontic logic declares them to be logically impossible. That prompts the question, What are the proper principles of normative reasoning if such conflicts are possible? This paper examines several alternatives that have been proposed for a logic of 'ought' that can accommodate normative conflicts, and finds all of them unsatisfactory as measured against three criteria of adequacy. It then introduces a new logic that does meet all three criteria, and (...) so allows for the possibility of genuine normative conflicts. (shrink)

This article takes Heidegger's design distinctions for human being [Dasein] including affectivity, understanding, and speech, and, using these distinctions, generates a Heideggerian definition of empathy [Einfuehlung]. This article distinguishes empathic receptivity, empathic understanding, empathic interpretation, and empathic speech (or responsiveness). It also looks at characteristic breakdowns.

This multiplex semantics incorporates multiple relations of deontic accessibility or multiple preference rankings on alternative worlds to represent distinct normative standards. This provides a convenient framework for deontic logic that allows conflicts of obligation, due either to conflicts between normative standards or to incoherence within a single standard. With the multiplex structures, two general senses of "ought" may be distinguished, an indefinite sense under which something is obligatory when it is enjoined by some normative standard and a core sense for (...) when something is enjoined by all normative standards. Multiple normative standards may themselves be given a preferential order; this leads to a concept of ranked obligation. This paper presents the foundations of this multiplex semantics and the propositional deontic logics they define. (shrink)

This volume presents a definitive introduction to twenty core areas of philosophical logic including classical logic, modal logic, alternative logics and close examinations of key logical concepts.

Technology acceptance by users has been extensively studied in recent years in various fields such as technologies for learning, e-commerce, and business technologies. This review focuses specifically on Human Resource Information Systems and its acceptance by users. Given their widespread use in organisations, HRIS acceptance has been researched but not synthesised in any way. This article aims to review the effectiveness of the classical TAM and UTAUT models commonly used for new technologies and to identify the variables added to these (...) models to better predict HRIS acceptance by employees. It also highlights the importance of the human-machine-organisation relationship to contribute to the understanding of HRIS acceptance in professional environments. This review confirms the effectiveness of the TAM and UTAUT models and proposes to develop them by variables reffering to technological characteristics, user satisfaction with the system, and organisational variables. The discussion focuses on the retroaction possibilities between the different Human-Machine-Organisation relation levels. (shrink)

Natural languages vary widely in the degree to which they make use of nested compositional structure in their grammars. It has long been noted by linguists that the languages historically spoken in small communities develop much deeper levels of compositional embedding than those spoken by larger groups. Recently, this observation has been confirmed by a robust statistical analysis of the World Atlas of Language Structures. In order to examine this connection mechanistically, we propose an agent‐based model that accounts for key (...) cultural evolutionary features of language transfer and language change. We identify transitivity as a physical parameter of social networks critical for the evolution of compositional structure and the hierarchical patterning of scale‐free distributions as inhibitory. (shrink)

Philosophical counseling is an educational activity in which philosophers engage in dialogue with clients who wish to address questions or manage problems that arise during the course of everyday life. This chapter offers three contrasting perspectives on the question of what philosophical counselors do: first, an institutional scope of practice for philosophical counseling; second, an anecdotal list of common issues for which clients seek philosophical counseling; and third, a heterogeneous set of views by several pioneers of philosophical counseling. From what (...) we have seen thus far, it may already be clear that there exist both parallels and anti‐parallels between philosophical counseling and psychotherapy. First and foremost, anyone who wants to become a philosophical counselor should earn an accredited graduate degree in philosophy in whichever area of specialization captures their interest. (shrink)

The distinction between “empathy” and “sympathy” in the context of ethics is a dynamic and challenging one. The eighteenth century texts of David Hume and Adam Smith used the word "sympathy," but not "empathy," although the conceptual distinction marked by empathy was doing essential work in their writings. After discussing the early uses of these terms, this article is organized historically. Two traditions are distinguished. The first is the Anglo-American tradition, and it extends from Hume and Smith to the twenty-first (...) century work of Michael Slote. Stephen Darwall’s contribution is applied in engaging Hume and Smith. Finally, the interrelation of empathy, sympathy and altruism is explored in the work of John Rawls and Thomas Nagel. The second tradition is the Continental one. It extends from the spirituality of Johann Herder to the phenomenological movement of Edmund Husserl, Martin Heidegger, Max Scheler, and Edith Stein. The intentional analysis of empathy is directly relevant to the constitution of the social community in a broad, normative relationship with the "Other." Available without fee at the Internet Encyclopedia of Philosophy (IEP). (shrink)

This paper presents a neighborhood semantics for logics of entailment. It begins with a minimal system Min that expresses the most fundamental assumptions about the entailment relation, and continues by examining various extensions that reflect further assumptions that might be made about entailment. This leads first to the logic B that is the basic relevant logic, and then to more powerful systems. All of these logics are proved to be sound and strongly complete. With B the neighborhood semantics meets the (...) Routley-Meyer relational semantics for relevant logic; these connections are examined. The minimal and basic entailment logics are shown to have the finite model property, and hence to be decidable. (shrink)

From the author of the international bestseller Plato Not Prozac!, a vital guide to the art of living. Professor Lou Marinoff's first book drew on the wisdom of the great philosophers to solve our everyday problems, launching a movement that restored philosophy to what it once was: useful in all walks of life. Now, in The Big Questions, he takes the concept to the next level, applying centuries of philosophy and great literature to answer central questions of modern existence. Urging (...) us not to accept victimhood as the by-product of modern life, Professor Marinoff uses specific case studies from his counseling practice to show how wisdom from the great thinkers can help us define our own philosophy, and thereby reclaim our sense of well-being. He asks and answers questions that go to the heart of the human condition: How do we know what is right? How can we cope with change? Why can't we all get along? And, most centrally, how can we use the centuries of wisdom that have come before us to help us answer these questions and feel at ease in the world? Accessible, entertaining, and profoundly useful, The Big Questions mixes wisdom from the great thinkers with specific case studies to illuminate how a shift in perspective can truly be life changing. (shrink)

James Watson February 6, 2002 Genes, Girls, and Gamow Lou Massa: Welcome to Science & the Written Word. I'm Lou Massa. Dr. James D. Watson is President of ...