Aristotle is oftentimes viewed through a strictly philosophical lens as heir to Plato and has having introduced logical rigor where an emphasis on the theory of Forms formerly prevailed. It must be appreciated that Aristotle was the son of a physician, and that his inculcation of the thought of other Greek philosophers addressing health and the natural elements led to an extremely broad set of biologically- and medically-related writings. As this article proposes, Aristotle deepened the fourfold theory of (...) the elements with anatomic and physiologic observations. In books like History of Animals, Parts of Animals, and the lost Anatomai, he actively dissected organisms and recorded his findings. The corpus of medically-related literature Aristotle developed had a direct influence on subsequent Greek thinkers, including Galen, and on Medieval Islamic and modern Western practitioners such as William Harvey. Aristotle's ideas continue to influence modern medical thinkers in Europe and America through both his interpretation by European philosophers gaining the attention of medical humanists, and his writings' enduring impact on medical researchers balancing scientific with more personalistic approaches to medicine. (shrink)

Researchers currently working on relational reasoning typically argue that mental model theory (MMT) is a better account than the inference rule approach (IRA). They predict and observe that determinate (or one-model) problems are easier than indeterminate (or two-model) problems, whereas according to them, IRA should lead to the opposite prediction. However, the predictions attributed to IRA are based on a mistaken argument. The IRA is generally presented in such a way that inference rules only deal with determinate relations (...) and not with indeterminate ones. However, (a) there is no reason to presuppose that a rule-based procedure could not deal with indeterminate relations, and (b) applying a rule-based procedure to indeterminate relations should result in greater difficulty. Hence, none of the recent articles devoted to relational reasoning currently presents a conclusive case for discarding IRA by using the well-known determinate vs indeterminate problems comparison. (shrink)

For Jari-Erik Nurmi, the practice of model-making in psychology is a complex process operating on different levels simultaneously. At first sight, his account seems to reflect Suppes' (1962) notion of a hierarchy of models: from low-level data models to high-level theoretical models, where at each level the model represents "structure" at a different degree of abstraction, and the levels are connected through structural isomorphism.1In this commentary, I want to complement and perhaps somewhat redirect Nurmi's analysis of his (...) own modeling efforts—away from the idea of an interconnected hierarchy of isomorphic structures, towards more autonomous roles of the models at different levels, each with its own .. (shrink)

To describe leadership as ethical is largely a perceptional phenomenon informed by beliefs about what is normatively appropriate. Yet there is a remarkable scarcity in the leadership literature regarding how to define what is "normatively appropriate." To shed light on this issue, we draw upon Relational Models Theory (Fiske, 1992, Psychol Rev, 99:689-723), which differentiates between four types of relationships: communal sharing, authority ranking, equality matching, and market pricing. We describe how each of these relationship models (...) dictates a distinct set of normatively appropriate behaviors. We argue that perceptions of unethical leadership behavior result from one of three situations: (a) a mismatch between leader's and follower's relational models, (b) a different understanding about the behavioral expression, or preos, of the same relational model, or (c) a violation of a previously agreed upon relational model. Further, we argue that the type of relational model mismatch impacts the perceived severity of a transgression. Finally, we discuss the implications of our model with regard to understanding, managing, and regulating ethical leadership failures. (shrink)

One of the most debated questions in psychology and cognitive science is the nature and the functioning of the mental processes involved in deductive reasoning. However, all existing theories refer to a specific deductive domain, like syllogistic, propositional or relational reasoning.Our goal is to unify the main types of deductive reasoning into a single set of basic procedures. In particular, we bring together the microtheories developed from a mental models perspective in a single theory, for which we (...) provide a formal foundation. We validate the theory through a computational model (UNICORE) which allows fine‐grained predictions of subjects' performance in different reasoning domains.The performance of the model is tested against the performance of experimental subjects—as reported in the relevant literature—in the three areas of syllogistic, relational and propositional reasoning. The computational model proves to be a satisfactory artificial subject, reproducing both correct and erroneous performance of the human subjects. Moreover, we introduce a developmental trend in the program, in order to simulate the performance of subjects of different ages, ranging from children (3–6) to adolescents (8–12) to adults (>21). The simulation model performs similarly to the subjects of different ages.Our conclusion is that the validity of the mental model approach is confirmed for the deductive reasoning domain, and that it is possible to devise a unique mechanism able to deal with the specific subareas. The proposed computational model (UNICORE) represents such a unifying structure. (shrink)

This study puts forward a rounder conceptual model for interpreting short and long-term effects of choice behavior. Kahneman’s (2011) distinction between cognitive processing System 1 and System 2 reflect the more rigorous distinction between Brief and Immediate and Extended and Elaborated Relational Responding. Specifically, we provide theoretical accounts and applied examples of how nudging, or the manipulation of environmental contingencies, works on the creation and modification of relational frames. The subset denominated educational nudges, or boosts, are particularly useful (...) towards their maintenance. We define and illustrate the fundamental mediating role of verbal behavior towards formulating rules, which inform and guide choice behavior over time. Furthermore, we suggest adopting the Implicit Relations Association Procedure to inform how coherent and immediate responding to new relational frames may be, whenever choices need be made. We provide empirical accounts of consumer behavior, stereotypy and prejudices, eating behavior, and overcoming cognitive biases. The conclusions depict a promising way forward towards an improved model for interpreting and overcoming human errors thanks to changes in the contingencies of choice behavior. (shrink)

This book gives a comprehensive overview of central themes of finite model theory – expressive power, descriptive complexity, and zero-one laws – together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, second-order, fixed-point, (...) and infinitary logics to gain insight into phenomena in complexity theory and combinatorics. The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissé pebble game, as a powerful way to analyze the expressive power of such logics, and illustrates how deep notions from model theory and combinatorics, such as o-minimality and treewidth, arise naturally in the application of finite model theory to database theory and AI. Students of logic and computer science will find here the tools necessary to embark on research into finite model theory, and all readers will experience the excitement of a vibrant area of the application of logic to computer science. (shrink)

We give foundational results for the model theory of AfinK, the ring of finite adeles over a number field, construed as a restricted product of local fields. In contrast to Weispfenning we work in the language of ring theory, and various sortings interpretable therein. In particular we give a systematic treatment of the product valuation and the valuation monoid. Deeper results are given for the adelic version of Krasner's hyperfields, relating them to the Basarab–Kuhlmann formalism.

The question “Are ‘biorobots' good models of biological behaviour?” can be seen as a specific instance of a more general question about the relation between computer programs and models, between models and theories, and between theories and reality. This commentary develops a personal view of these relations, from an antirealism perspective. Programs, models, theories and reality are separate and distinct entities which may converge in particular cases but should never be confused.

In lieu of an abstract, here is a brief excerpt of the content:Four Philosophical Models of the Relation Between Theory and PracticeEstelle R. JorgensenSince music education straddles theory and practice, my purpose is to sketch the strengths and weaknesses of four philosophical models of the relationship between theory and practice. I demonstrate that none of them suffices when taken alone; each has something to offer and its own detractions. And I conclude with four suggested ways (...) in which the analysis can be helpful to music teachers and those interested in their work.Clarifying what is meant by theory and practice raises a nest of conceptual problems. Concerning theory, it may be tempting to equate the terms "theory" and "philosophy." Among their shared properties, these terms deal with conceptual and abstract entities that, from the Enlightenment at least, have been held to be distinct from the phenomenal world. They also clarify ideas and distinguish one concept from another. Among their different purposes, the object of philosophy is the asking of questions in a search for wisdom or truth whereas theory is formulated for explanatory purposes, especially within the frame of scientific propositions that can be refuted through empirical observations. The tests of philosophy are, therefore, those of symbolic logic evidenced in principles such as [End Page 21] internal consistency, correspondence with evidence (deductive, inductive, or analogical), and coherence within a unity or whole. Although logical criteria may also be important in formulating and testing theory,1 it is tested and refuted primarily through means of qualitative descriptions and quantitative assessments of observable phenomena.Regarding practice, one is also confronted with an ambiguous construct that may be interpreted descriptively (what is done in the phenomenal world or taken to be the general state of affairs) or normatively (what is desirable or ideal). There is also the distinction between the practice of a seasoned performer and practice in the sense of striving towards the mastery of a competent and expert practice. In this regard, Vernon Howard distinguishes between "practice" (or the skills exemplified by proficient or expert performers) and "practise (or acquiring the level of mastery of proficient or expert performance)."2 For him, the ambiguous and paradoxical nature of artistic practice highlights the complexity of degrees of attaining mastery of skills or exemplary practice and the diverse array of skills ranging from habit to critical thinking involved in the practice of any art. Although each practice is distinguished by its own belief systems, rituals, expectations, and commonsense, boundaries between differing practices are sometimes "soft" or fuzzy, as one seeps into another.3 Consequently, it is often difficult to distinguish one from another at the margins where one practice becomes another.DichotomyThe notion of theory and practice as independent or a dichotomous relationship between the phenomenal world on the one hand and the mind and spirit on the other has its roots in the ancient world. For Plato, the world of "appearances," referring to the phenomenal world understood by imagination (eikasia) and belief (pistis), should be distinguished from the higher, abstract "intelligible world" grasped through thinking (dianoia), knowledge (episteme), and intelligence (noesis).4 René Descartes' later bifurcation of the inner and outer worlds and inversion of Platonic values and understandings resulted in the ascendancy of careful and deliberate observation of the phenomenal world over philosophical reflection.5 His ideas helped to set the stage for the Enlightenment and the Industrial, Scientific, and Information Revolutions. Empiricism, science, and technology gradually displaced philosophy as primary ways of knowing the phenomenal world and understanding the nature of mind, human cognition, feeling, and being. Making hard-boundaried distinctions between within and without one's self, the phenomenal world and the world of spiritual things, and theory and practice were important insights. These distinctions provided for limits on the sorts of ways in which truth could be known. Reasoned deliberation [End Page 22] and imaginative thought have particular usefulness in the world of theory while sensory perception and careful observation are especially useful in the phenomenal world of practice. So while the scholar might speculate about phenomena, observational tools are also useful in coming to know and understand them. Reason and observation each have particular strengths, and it ought not be assumed that philosophy or scientific observation... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Four Philosophical Models of the Relation Between Theory and PracticeEstelle R. JorgensenSince music education straddles theory and practice, my purpose is to sketch the strengths and weaknesses of four philosophical models of the relationship between theory and practice. I demonstrate that none of them suffices when taken alone; each has something to offer and its own detractions. And I conclude with four suggested ways (...) in which the analysis can be helpful to music teachers and those interested in their work.Clarifying what is meant by theory and practice raises a nest of conceptual problems. Concerning theory, it may be tempting to equate the terms "theory" and "philosophy." Among their shared properties, these terms deal with conceptual and abstract entities that, from the Enlightenment at least, have been held to be distinct from the phenomenal world. They also clarify ideas and distinguish one concept from another. Among their different purposes, the object of philosophy is the asking of questions in a search for wisdom or truth whereas theory is formulated for explanatory purposes, especially within the frame of scientific propositions that can be refuted through empirical observations. The tests of philosophy are, therefore, those of symbolic logic evidenced in principles such as [End Page 21] internal consistency, correspondence with evidence (deductive, inductive, or analogical), and coherence within a unity or whole. Although logical criteria may also be important in formulating and testing theory,1 it is tested and refuted primarily through means of qualitative descriptions and quantitative assessments of observable phenomena.Regarding practice, one is also confronted with an ambiguous construct that may be interpreted descriptively (what is done in the phenomenal world or taken to be the general state of affairs) or normatively (what is desirable or ideal). There is also the distinction between the practice of a seasoned performer and practice in the sense of striving towards the mastery of a competent and expert practice. In this regard, Vernon Howard distinguishes between "practice" (or the skills exemplified by proficient or expert performers) and "practise (or acquiring the level of mastery of proficient or expert performance)."2 For him, the ambiguous and paradoxical nature of artistic practice highlights the complexity of degrees of attaining mastery of skills or exemplary practice and the diverse array of skills ranging from habit to critical thinking involved in the practice of any art. Although each practice is distinguished by its own belief systems, rituals, expectations, and commonsense, boundaries between differing practices are sometimes "soft" or fuzzy, as one seeps into another.3 Consequently, it is often difficult to distinguish one from another at the margins where one practice becomes another.DichotomyThe notion of theory and practice as independent or a dichotomous relationship between the phenomenal world on the one hand and the mind and spirit on the other has its roots in the ancient world. For Plato, the world of "appearances," referring to the phenomenal world understood by imagination (eikasia) and belief (pistis), should be distinguished from the higher, abstract "intelligible world" grasped through thinking (dianoia), knowledge (episteme), and intelligence (noesis).4 René Descartes' later bifurcation of the inner and outer worlds and inversion of Platonic values and understandings resulted in the ascendancy of careful and deliberate observation of the phenomenal world over philosophical reflection.5 His ideas helped to set the stage for the Enlightenment and the Industrial, Scientific, and Information Revolutions. Empiricism, science, and technology gradually displaced philosophy as primary ways of knowing the phenomenal world and understanding the nature of mind, human cognition, feeling, and being. Making hard-boundaried distinctions between within and without one's self, the phenomenal world and the world of spiritual things, and theory and practice were important insights. These distinctions provided for limits on the sorts of ways in which truth could be known. Reasoned deliberation [End Page 22] and imaginative thought have particular usefulness in the world of theory while sensory perception and careful observation are especially useful in the phenomenal world of practice. So while the scholar might speculate about phenomena, observational tools are also useful in coming to know and understand them. Reason and observation each have particular strengths, and it ought not be assumed that philosophy or scientific observation... (shrink)

We initiate the study of model theory in the absence of the Axiom of Choice, using the Axiom of Determinateness as a powerful substitute. We first show that, in this context, L ω 1 ω is no more powerful than first-order logic. The emphasis then turns to upward Lowenhein-Skolem theorems; ℵ 1 is the Hanf number of first-order logic, of L ω 1 ω , and of a strong fragment of L ω 1 ω . The main technical innovation (...) is the development of iterated ultrapowers using infinite supports; this requires an application of infinite-exponent partition relations. All our theorems can be proven from hypotheses weaker than AD. (shrink)

We explore some topics in the model theory of sheaves of modules. First we describe the formal language that we use. Then we present some examples of sheaves obtained from quivers. These, and other examples, will serve as illustrations and as counterexamples. Then we investigate the notion of strong minimality from model theory to see what it means in this context. We also look briefly at the relation between global, local and pointwise versions of properties related to acyclicity.

Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector spaces over algebraically closed fields (...) is the model-completion of the theory of vector spaces. (shrink)

We study the relations between abelian groups B and C that every universal (resp. universal-existential) sentence true in B is also true in C, and give algebraic criteria for these relations to hold. As a consequence we characterize the inductive complete theories of abelian groups and prove that they are exactly the model-complete theories.

We can look at this model theoretically as follows. By the linearly ordered predicate calculus, we simply mean ordinary predicate calculus with equality and a special binary relation symbol <. It is required that in all interpretations, < be a linear ordering on the domain. Thus we have the usual completeness theorem provided we add the axioms that assert that < is a linear ordering.

Abstract‘Skolem arithmetic’ is the complete theory T of the multiplicative monoid. We give a full characterization of the ‐definable stably embedded sets of T, showing in particular that, up to the relation of having the same definable closure, there is only one non‐trivial one: the set of squarefree elements. We then prove that T has weak elimination of imaginaries but not elimination of finite imaginaries.

The article comments on the supposed need for a paradigm for the theory of contract, primarily by way of engaging with the most prominent source of late of calls for a paradigm shift in contract theory, the relational theory of contract. The article distinguishes between an empirical, a doctrinal-prescriptive and a theoretical–analytical line of argument as offered by relational theory. With regard to the first line of argument, the article argues that the thought that (...) contract law already is ‘relationally constituted’ is informed by a misunderstanding of the available alternatives to relational theory. With regard to the second line of argument, the article argues that the incorporation of relational norms into the law, although occasionally desirable, is not the only way nor always the best way to sustain the relational contract, and explores the proposition that, at times, the law best supports valuable social practices by refraining from absorbing their constitutive norms. Finally, by way of drawing an analogy with a putative relational theory of promise, the article offers an objection to the thesis that the key to a sound theoretical grasp of the nature of contract and its social role lies in the adoption of the relational paradigm. (shrink)

This paper outlines a theory and computer implementation of causal meanings and reasoning. The meanings depend on possibilities, and there are four weak causal relations: A causes B, A prevents B, A allows B, and A allows not‐B, and two stronger relations of cause and prevention. Thus, A causes B corresponds to three possibilities: A and B, not‐A and B, and not‐A and not‐B, with the temporal constraint that B does not precede A; and the stronger relation conveys only (...) the first and last of these possibilities. Individuals represent these relations in mental models of what is true in the various possibilities. The theory predicts a number of phenomena, and, contrary to many accounts, it implies that the meaning of causation is not probabilistic, differs from the meaning of enabling conditions, and does not depend on causal powers or mechanisms. The theory also implies that causal deductions do not depend on schemas or rules. (shrink)

A structure is a triple A = (A, {Ri: i ∈ I}, {ej: j ∈ J}), where A, the domain or universe of A, is a nonempty set, {Ri: i ∈ I} is an indexed family of relations on A and {ej: j ∈ J}) is an indexed set of elements —the designated elements of A. For each i ∈ I there is then a natural number λ(i) —the degree of Ri —such that Ri is a λ(i)-place relation on A, (...) i.e., Ri ⊆ Aλ(i). This λ may be regarded as a function from I to the set ω of natural numbers; the pair (λ, J) is called the type of A. Structures of the same type are said to be similar. Note that since an n-place operation f: An → A can be regarded as an (n+1)-place relation on A, algebraic structures containing operations such as groups, rings, vector spaces, etc. may be construed as structures in the above sense. (shrink)

According to appraisal theory, emotions result from an individual's meaning analysis of the implications of his/her circumstances for personal well-being, and individual differences in emotion arise when individuals appraise similar situations differently. Relational models of appraisal attempt to describe the situational and dispositional antecedents of appraisals, and should allow one to predict such individual differences. In this article, we review three examples of our efforts toward developing relational appraisal models. In two, we start with a (...) particular appraisal component, motivational relevance and problem-focused coping potential (Smith & Lazarus, 1990), respectively, and describe and test the relational model proposed for that component. In the third, as a precursor to developing a true relational model, we examine another appraisal component, emotion-focused coping potential, from a more dispositional perspective. We conclude by considering both the potential value of relational appraisal models, and future directions in the development of these models. (shrink)

We introduce a relational semantics based on poset products, and provide sufficient conditions guaranteeing its soundness and completeness for various substructural logics. We also demonstrate that our relational semantics unifies and generalizes two semantics already appearing in the literature: Aguzzoli, Bianchi, and Marra’s temporal flow semantics for Hájek’s basic logic, and Lewis-Smith, Oliva, and Robinson’s semantics for intuitionistic Łukasiewicz logic. As a consequence of our general theory, we recover the soundness and completeness results of these prior studies (...) in a uniform fashion, and extend them to infinitely-many other substructural logics. (shrink)

Structural realists contend that the properties and relations in the world are more fundamental than the individuals. However, the standard model theory used to analyse the structure of logical theories can make it difficult to see how such an idea could be coherent or workable: for in that theory, properties and relations are constructed as sets of individuals. In this paper, I look at three ways in which structuralists might hope for an alternative: by appealing to predicate-functor logic, (...) Tractarian geometry, or cylindric algebras. I argue that the first two are problematic, but that the third is promising. (shrink)

This monograph is the first really systematic study of the model theory of many-valued logic. The authors develop model theory for systems of logic whose truth-values lie in a compact topological space; the results are analogous to those for two-valued logic—they yield the two valued logics as special cases—but often the methods of proof are more complicated and tend to reveal some of the deep structure of these logics. There is presupposed a fair knowledge of naive set (...) class='Hi'>theory and point-set topology, but no knowledge of classical logic is required although it will be of help in seeing the motivation behind various results. The first three chapters are concerned with preliminaries on topology, model theory, and continuous logic. The next chapter examines the relation of elementary equivalence among models, including the downward Skolem-Löwenheim theorem; the fifth chapter contains the generalizations of such classical results as the compactness and upward S-L theorems. The authors specialize their work in the sixth chapter to consider certain particular kinds of models: saturated models, universal models. The last chapter considers classes of models closed under various algebraic operations. There is a bibliography, historical notes, and indices of exercises, symbols, and definitions. This book is the prolegomenon to any future study of many-valued logic.—P. J. M. (shrink)

Mancosu, P., Generalizing classical and effective model theory in theories of operations and classes, Annas of Pure and Applied Logic 52 249-308 . In this paper I propose a family of theories of operations and classes with the aim of developing abstract versions of model-theoretic results. The systems are closely related to those introduced and already used by Feferman for developing his program of ‘explicit mathematics’. The theories in question are two-sorted, with one kind of variable for individuals and (...) the other for classes. The individual variables range over a domain closed under pairing and containing, among other things, natural numbers and operations.All the theories used assume a common group of axioms that insure that the individuals in the domain satisfy the conditions for a partial combinatory algebra with pairing. We also assume a class of natural numbers and a class induction axiom on . Finally there are various class existence axioms. I work mainly with three theories, FMT0, FMT and FMTΩ, which differ from each other both in their class existence axioms as well as in some further applicative axioms.These theories have various interpretations in which every object is explicitly presented by some means of definition as well as classical, or ‘standard’, set-theoretical interpretation. The systems are formulated in a flexible general language which can be used to prove abstract theorems of mathematics , thereby generalizing recursive, hyperarithmetic and admissible versions of classical mathematics.The aim of my work is to give an abstract development of portions of model theory in the afore-mentioned theories, in a way to look as much as possible like classical mathematics. Thus, FMT0 generalizes portions of countable and recursive model theory; FMT further generalizes portions of countable and hyperarithmetical model theory and finally FMTΩ provides a generalization of the classical L-completeness theorem and of an admissible version of L-completeness due to Bruce and Keisler. This continues the development of the program mentioned above, originating with Feferman. (shrink)

We prove that compactness is equivalent to the amalgamation property, provided the occurrence number of the logic is smaller than the first uncountable measurable cardinal. We also relate compactness to the existence of certain regular ultrafilters related to the logic and develop a general theory of compactness and its consequences. We also prove some combinatorial results of independent interest.

In the aftermath of various corporate scandals, management research and practice have taken great interest in ethical leadership. Ethical leadership is referred to as “normatively appropriate conduct” (Brown et al. in Organ Behav Hum Decis Process 97(2):117–134, 2005), but the prescriptive norms that actually underlie this understanding constitute an open question. We address this research gap by turning to relational models theory (Fiske in Structures of social life: the four elementary forms of human relations, Free Press, New (...) York, 1991), which contextualizes four distinct moralities in four distinct interactional norms (i.e., the relational models). We expect that the norms inherent in each model dictate the type of leader relationship that followers deem ethical. Specifically, we hypothesize that, for each norm, followers will perceive leaders as less ethical the more discrepant, i.e., the more incongruent, followers’ ideal relational norm is with the perceived norm that they attribute to their actual leader–follower interaction. We tested the respective incongruence hypothesis in a cross-sectional survey of 101 Dutch employees. Polynomial regression and surface response analyses provide support for the hypothesized incongruence effects in each of the four relational models, suggesting that normatively appropriate conduct should not be limited to caring (i.e., community-oriented) behaviors. Indeed, all four relational models can predict ethical leadership perceptions. We discuss the implications in the context of ethical leadership research and managerial practice. (shrink)

One of the practical ethical areas that Thaddeus Metz applied his Relational Moral Theory (RMT) to is business ethics. In this important area of applied ethics, Metz examines the question of how business owners, and related agents ought to deal with others, especially workers and consumers. He argues that the relational account of obligations recommends a stakeholder model of business and provides a plausible alternative (if not better to) familiar kinds of utilitarianism and Kantianism. In this article, (...) I discuss and engage with this claim by raising a number of issues for RMT. For although I believe that Metz’s moral account could, in general and under certain description, be positioned as a viable competitor to utilitarianism and Kantianism, it is not clear that in certain theoretical aspects of the stakeholder account of business, it fares better than, for example, utilitarianism. Furthermore, I argue, on the one hand, that RMT should be understood as a _heterochthonous account_ of African ethics and, on the other hand, that an _autochthonous account_ of African ethics captures better or comes closer to the moral sensibilities of indigenous Africans. An _autochthonous account_ of African ethics has a different take on the issue of the stakeholder model of business and does conceptualize the business relationship in terms of needs and welfare whereby a “distant” individual may be owed more duties than a “local” individual. (shrink)

The Martin-Steel coarse inner model theory is employed in obtaining new results in descriptive set theory. $\underset{\sim}{\Pi}$ determinacy implies that for every thin Σ 1 2 equivalence relation there is a Δ 1 3 real, N, over which every equivalence class is generic--and hence there is a good Δ 1 2 (N ♯ ) wellordering of the equivalence classes. Analogous results are obtained for Π 1 2 and Δ 1 2 quasilinear orderings and $\underset{\sim}{\Pi}^1_2$ determinacy is shown to (...) imply that every Π 1 2 prewellorder has rank less than $\underset{\sim}{\delta}^1_2$. (shrink)

This thesis is concerned with the expansions of algebraic structures and their fit in Shelah’s classification landscape.The first part deals with the expansion of a theory by a random predicate for a substructure model of a reduct of the theory. Let T be a theory in a language $\mathcal {L}$. Let $T_0$ be a reduct of T. Let $\mathcal {L}_S = \mathcal {L}\cup \{S\}$, for S a new unary predicate symbol, and $T_S$ be the $\mathcal {L}_S$ - (...) class='Hi'>theory that axiomatises the following structures: $$ consist of a model $\mathscr {M}$ of T and S is a predicate for a model $\mathscr {M}_0$ of $T_0$ which is a substructure of $\mathscr {M}$. We present a setting for the existence of a model-companion $TS$ of $T_S$. As a consequence, we obtain the existence of the model-companion of the following theories, for $p>0$ a prime number: • $\mathrm {ACF}_p$, $\mathrm {SCF}_{e,p}$, $\mathrm {Psf}_p$, $\mathrm {ACFA}_p$, $\mathrm {ACVF}_{p,p}$ in appropriate languages expanded by arbitrarily many predicates for additive subgroups;• $\mathrm {ACF}_p$, $\mathrm {ACF}_0$ in the language of rings expanded by a single predicate for a multiplicative subgroup;• $\mathrm {PAC}_p$ -fields, in an appropriate language expanded by arbitrarily many predicates for additive subgroups.From an independence relation in T, we define independence relations in $TS$ and identify which properties of are transferred to those new independence relations in $TS$, and under which conditions. This allows us to exhibit hypotheses under which the expansion from T to $TS$ preserves $\mathrm {NSOP}_{1}$, simplicity, or stability. In particular, under some technical hypothesis on T, we may draw the following picture : Configuration $T_0\subseteq T$ Generic expansion $TS$ $T_0 = T$ Preserves stability $T_0\subseteq T$ Preserves $\mathrm {NSOP}_{1}$ $T_0 = \emptyset $ Preserves simplicityIn particular, this construction produces new examples of $\mathrm {NSOP}_{1}$ not simple theories, and we study in depth a particular example: the expansion of an algebraically closed field of positive characteristic by a generic additive subgroup. We give a full description of imaginaries, forking, and Kim-forking in this example.The second part studies expansions of the group of integers by p-adic valuations. We prove quantifier elimination in a natural language and compute the dp-rank of these expansions: it equals the number of independent p-adic valuations considered. Thus, the expansion of the integers by one p-adic valuation is a new dp-minimal expansion of the group of integers. Finally, we prove that the latter expansion does not admit intermediate structures: any definable set in the expansion is either definable in the group structure or is able to “reconstruct” the valuation using only the group operation.prepared by Christian d’Elbée.E-mail: [email protected]: https://choum.net/~chris/page_perso. (shrink)

In this paper, we study bounded versions of some model-theoretic notions and results. We apply these results to the context of models of bounded arithmetic theories as well as some related complexity questions. As an example, we show that if the theory \(\rm S_2 ^1(PV)\) has bounded model companion then \(\rm NP=coNP\). We also study bounded versions of some other related notions such as Stone topology.

An enlargement of a previous work by the author, this work is intended as a reference source for study in the theory of models of logical systems, and as a textbook; the latter aim is reached by including numerous problems, many of them of a high level of difficulty, at the end of each chapter. The sections deal with, respectively, the lower predicate calculus, the structure of algebraic theories, concepts from model theory, completeness of various systems, definability (...) of concepts, generalizations of algebraic concepts, the metamathematical theories of ideals and varieties, and various selected topics including non-standard analysis. Unfortunately, there are numerous misprints which mar an otherwise excellent presentation. Much of the material presented is new, or is presented in new form. Robinson's approach is mildly idiosyncratic and often at variance with more conventional presentations, and this may make for difficulty in relating it to these presentations. Nevertheless, for the reader with a working knowledge of algebra and no small perseverance, this book will be rewarding.—P. J. M. (shrink)

This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.

Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences—which is closely related to the latter’s foundational contribution to model theory. In this note we show in a model-theoretic framework how Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also connects Arrow’s (...) seminal result to key developments and concepts in the history of model theory, notably ultraproducts and preservation results. (shrink)

Our present models and theories of African history and prehistory are profoundly influenced by the physical anthropologists’ perceptions of human reality in present-day Africa. Professor P. V. Tobias has suggested that the present-day people of Africa, excluding the recent arrivals from Europe and Asia, descended from a common proto-Negriform stock which gave birth first to the so-called “Khoisan” (I am using here the terminology of my source, not the historically justified Khoe and San, meaning the Hottentots and the Bushmen) (...) and later to the Negro genetic type. Of greater importance to archaeologists, who deal mainly with the so-called pre-history, is the fact that, genetically speaking, the difference between the “Khoisan” and the Negroids is smaller than the difference between these two African racial types and all other non-African types. This realisation tends to have one consequence: the pre-historic and even historic developments are generally perceived as explainable from within Africa, without any need for external clues or explanations. Archaeological finds are thus taken for evidence of a basically internal evolution and the finds of foreign glass beads, though very frequent and spread all over Africa, are seen as belonging to the same category as Persian, Chinese, or Arab ceramics and are explained as indication of a coastal trade. (shrink)

Simple Reduction and Beyond Traditional and New Wave models of reduction in science have not lacked for ambition. Philosophers have presented single models to account for the full range of interesting intertheoretic relations, for scientific progress, and for the unity of science (Nagel, 1961; Oppenheim and Putnam, 1958). Early critics attacked the logical empiricists' proposals about the character of intertheoretic connections (Feyerabend, 1962; Kuhn, 1970). New Wave reductionists have similarly argued that various intertheoretic relations fall at different points (...) on a continuum of goodness-of-intertheoretic-mapping. Still, whatever their differences with the logical empiricists, New Wave reductionists have retained traditional aspirations for a single, comprehensive model of reduction that will make sense of the wide range of intertheoretic relations, of progressive scientific change, and of how the various sciences hang together (Hooker, 1981; Churchland and Churchland, 1990; Bickle, 1998). Both logical empiricists and their New Wave successors proffer such unified, multi-purpose models. Regardless of the field, multi-purpose tools typically sacrifice precision for versatility. Recent analyses of mechanistic explanation have helped to reveal that these models of scientific reduction are no exceptions to this rule, and the cost of sacrificing precision is one that the mechanists are unwilling to pay. Traditional and New Wave reductionists manifest allegiances (1) to the (virtually exclusive) analysis of theories and intertheoretic relations and (2) to conceptions of explanatory levels in science rooted in considerations pertaining to the size of and the mereological relations between the sciences' objects of study. (Discussions of both explanatory levels and mereological relations follow in subsequent sections.) By contrast, advocates of mechanistic analysis offer detailed accounts of particular systems' functioning that survey their components, their operations, and the larger systems to which they contribute (Bechtel and Richardson, 1993; Glennan, 1996; Machamer, Darden and Craver, 2000; Craver, 2001; Bechtel, 2006).. (shrink)

The Kubovy-Epstein proposal for the formalization of the relation between kinematic geometry and perception of motion has formal problems in itself. Motion phenomena are inadequately captured by the relational structures and the notion of isomorphism taken over from measurement theory. [Kubovy & Epstein].

En el presente artículo, se examinan y discuten dos argumentos con consecuencias reduccionistas debidos a Jaegwon Kim y a Theodore Sider respectivamente. De acuerdo con el argumento de Kim, la superveniencia fuerte implicaría la coexistencia necesaria de propiedades (es decir, tal y como normalmente se interpreta, la reducción). De acuerdo con el de Sider, ocurriría lo mismo con la superveniencia global. Uno y otro hacen un uso esencial de sendas nociones de propiedad maximal, las cuales son discutidas aquí a la (...) luz de una interpretación natural e interesante de la teoría de las propiedades implícita en sus argumentos. Bajo esta nueva interpretación, en términos modelo-teóricos (véase apartado 4), obtenemos diversas posibilidades de relaciones formales entre las tesis de superveniencia y la reducción, según la lógica utilizada. Al menos bajo una interpretación interesante, los argumentos de Kim y Sider no son correctos, quedando demos-trado así que dichos argumentos no son válidos en general. We discuss and analyze two reductive arguments due to Jaegwon Kim and Theodore Sider respectively. According to the first one, strong supervenience would imply necessary coextension of properties (i.e., reduction). According to the second, this would be also the case of global supervenience. Kim and Sider make essential use of their respective notions of maximal properties, which we analyze here in the light of a natural and interesting interpretation of the underlying theory of properties. Under this interpretation, in terms of model theory (see § 4), we obtain different possibilities of formal relations between the superveniencie theses and reduction, depending on the logic we use. Under at least one interesting interpretation, the arguments of Kim and Sider are not correct and we become the conclusion that these arguments are not valid in general. (shrink)

En el presente artículo, se examinan y discuten dos argumentos con consecuencias reduccionistas debidos a Jaegwon Kim y a Theodore Sider respectivamente. De acuerdo con el argumento de Kim, la superveniencia fuerte implicaría la coexistencia necesaria de propiedades (es decir, tal y como normalmente se interpreta, la reducción). De acuerdo con el de Sider, ocurriría lo mismo con la superveniencia global. Uno y otro hacen un uso esencial de sendas nociones de propiedad maximal, las cuales son discutidas aquí a la (...) luz de una interpretación natural e interesante de la teoría de las propiedades implícita en sus argumentos. Bajo esta nueva interpretación, en términos modelo-teóricos (véase apartado 4), obtenemos diversas posibilidades de relaciones formales entre las tesis de superveniencia y la reducción, según la lógica utilizada. Al menos bajo una interpretación interesante, los argumentos de Kim y Sider no son correctos, quedando demos-trado así que dichos argumentos no son válidos en general. We discuss and analyze two reductive arguments due to Jaegwon Kim and Theodore Sider respectively. According to the first one, strong supervenience would imply necessary coextension of properties (i.e., reduction). According to the second, this would be also the case of global supervenience. Kim and Sider make essential use of their respective notions of maximal properties, which we analyze here in the light of a natural and interesting interpretation of the underlying theory of properties. Under this interpretation, in terms of model theory (see § 4), we obtain different possibilities of formal relations between the superveniencie theses and reduction, depending on the logic we use. Under at least one interesting interpretation, the arguments of Kim and Sider are not correct and we become the conclusion that these arguments are not valid in general. (shrink)

En el presente artículo, se examinan y discuten dos argumentos con consecuencias reduccionistas debidos a Jaegwon Kim y a Theodore Sider respectivamente. De acuerdo con el argumento de Kim, la superveniencia fuerte implicaría la coexistencia necesaria de propiedades (es decir, tal y como normalmente se interpreta, la reducción). De acuerdo con el de Sider, ocurriría lo mismo con la superveniencia global. Uno y otro hacen un uso esencial de sendas nociones de propiedad maximal, las cuales son discutidas aquí a la (...) luz de una interpretación natural e interesante de la teoría de las propiedades implícita en sus argumentos. Bajo esta nueva interpretación, en términos modelo-teóricos (véase apartado 4), obtenemos diversas posibilidades de relaciones formales entre las tesis de superveniencia y la reducción, según la lógica utilizada. Al menos bajo una interpretación interesante, los argumentos de Kim y Sider no son correctos, quedando demos-trado así que dichos argumentos no son válidos en general. We discuss and analyze two reductive arguments due to Jaegwon Kim and Theodore Sider respectively. According to the first one, strong supervenience would imply necessary coextension of properties (i.e., reduction). According to the second, this would be also the case of global supervenience. Kim and Sider make essential use of their respective notions of maximal properties, which we analyze here in the light of a natural and interesting interpretation of the underlying theory of properties. Under this interpretation, in terms of model theory (see § 4), we obtain different possibilities of formal relations between the superveniencie theses and reduction, depending on the logic we use. Under at least one interesting interpretation, the arguments of Kim and Sider are not correct and we become the conclusion that these arguments are not valid in general. (shrink)