In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight.

The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something that has (...) until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRW world, for example the number of collapses in a system during a chosen time interval. (shrink)

A brief review of the historicalrelation between logic and ontologyand of the opposition between the viewsof logic as language and logic as calculusis given. We argue that predication is morefundamental than membership and that differenttheories of predication are based on differenttheories of universals, the three most importantbeing nominalism, conceptualism, and realism.These theories can be formulated as formalontologies, each with its own logic, andcompared with one another in terms of theirrespective explanatory powers. After a briefsurvey of such a comparison, we argue (...) that anextended form of conceptual realism provides themost coherent formal ontology and, as such, canbe used to defend the view of logic as language. (shrink)

Russell's involuted path in the development of his theory of logical types from 1903 to 1910-13 is examined and explained in terms of the development in his early philosophy of the notion of a logical subject vis-a-vis the problem of the one and many; i.e., the problem for russell, first, of a class-as-one as a logical subject as opposed to a class as many, and, secondly, of a propositional function as a single and separate logical subject as opposed to existing (...) only in the many propositions that are its values. (shrink)

Some internal and philosophical remarks are made regarding a system of a second order logic of existence axiomatized by the author. Attributes are distinguished in the system according as their possession entails existence or not, The former being called e-Attributes. Some discussion of the special principles assumed for e-Attributes is given as well as of the two notions of identity resulting from such a distinction among attributes. Non-Existing objects are of course indiscernible in terms of e-Attributes. In addition, However, Existing (...) objects indiscernible in terms of e-Attributes are indiscernible in terms of all attributes. (shrink)

A minimal second order modal logic of natural kinds is formulated. Concepts are distinguished from properties and relations in the conceptual-logistic background of the logic through a distinction between free and bound predicate variables. Not all concepts (as indicated by free predicate variables) need have a property or relation corresponding to them (as values of bound predicate variables). Issues pertaining to identity and existence as impredicative concepts are examined and an analysis of mass terms as nominalized predicates for kinds of (...) stuff is proposed. The minimal logic is extendible through a summum genus, an infima species or a partition principle for natural kinds. (shrink)

En este artículo, presentamos un sistema de lógica modal que permite representar relaciones entre conjuntos o clases de individuos definidos por una propiedad específica. Introducimos dos operadores modales, [a] y, que se utilizan respectivamente para expresar "para todo A" y "existe un A". Tanto la sintaxis como la semántica del sistema tienen dos niveles que evitan el anidamiento del operador modal. La semántica se basa en una variante de la semántica de Kripke, en donde los operadores modales se indexan sobre (...) fórmulas de lógica proposicional (“pre-fórmulas” en el trabajo). Además, presentamos un conjunto de axiomas y reglas que rigen el sistema, y demostramos que el sistema es correcto y completo con relación a los modelos de Kripke. En la sección final del artículo, discutimos posibles trabajos futuros. Consideramos la posibilidad de combinar nuestro operador modal con otras modalidades, como necesidad o conocimiento. Además, como ejemplo de la utilidad de nuestro operador modal, analizamos brevemente la fórmula de Barcan adaptada de manera conveniente dentro del marco de nuestro sistema. En resumen, proponemos la combinación de nuestro operador modal con otros como una forma más simple y compacta, aunque con un menor poder expresivo, para abordar la lógica modal cuantificada. (shrink)

While operators for logical necessity and possibility represent "internal" conditions of propositions (or of their corresponding states of affairs), These conditions will be "formal", As is required by logical atomism, And not "material" in content if from the (pseudo) semantical point of view the modal operators range over "all the possible worlds" of a logical space rather than over arbitrary non-Empty sets of worlds (as is usually done in modal logic). Some of the implications of this requirement are noted and (...) though several variants of realist logical atomism are distinguished and discussed, The theory of logical form developed is nominalist. Many of nominalism's difficulties and inadequacies become transparent in the context of logical atomism and are so noted. (shrink)

A semantic analysis of mass nouns is given in terms of a logic of classes as many. In previous work it was shown that plural reference and predication for count nouns can be interpreted within this logic of classes as many in terms of the subclasses of the classes that are the extensions of those count nouns. A brief review of that account of plurals is given here and it is then shown how the same kind of interpretation can also (...) be given for mass nouns. (shrink)

Bohmian mechanics is a theory about point particles moving along trajectories. It has the property that in a world governed by Bohmian mechanics, observers see the same statistics for experimental results as predicted by quantum mechanics. Bohmian mechanics thus provides an explanation of quantum mechanics. Moreover, the Bohmian trajectories are defined in a non-conspiratorial way by a few simple laws.

En el marco del naturalismo moral PeterF. Strawson propone que la moralidades parte de nuestra natural participaciónen relaciones humanas donde los otrosno pueden resultarnos indiferentes. Sinembargo, esta innegable ganancia teóricade Strawson, puede quedar debilitadapor la insuficiente importancia que elanglosajón concede a las comunidadesmorales. Como agudamente lo ha puestode pr e s e nt e Ror t y, l os s e nt i mi e nt osmorales, tal como los concebía Strawson,no t ranscurren f uera o al margen dediversas comunidades (...) morales. Cuestiónque nos ha conducido a afirmar, inspiradosen Rorty, que responsabilizarse por el otrodepende de la posibilidad de constituircomunidades morales más incluyentes.A e l l o de b e s uma r s e , pe ns a mo s , e lplanteamiento de Baeir, de una educaciónsentimental que comienza en el nacimientocon el recibimiento amoroso de nuestrosfamiliares, quienes a través de su afectoprogresi vamente nos van entregandoesa confianza inicial que nos permitirác o n q u i s t a r “ u n a v e r s i ó n mo d e s t a ,atemperada, no fanática de la hermandadcristiana”*las comuniDaDes moralesfrom partiCipative interaCtions to moral Communitiesde alcance universalIn the framework of the moral naturalism Peter F. Strawson proposes that moralityis part of our natural participation inhuman rel ati ons where others cannotturn out indifferent to us. Nevertheless,this undeniable theoretical achievementof Strawson, can result weakened becauseof the insufficient importance that the Anglo-saxon gives to moral communities.Acutely, has said Rorty, moral sentimentsin the way conceived by Strawson do nottakes place outside or to the margin ofdiverse moral communities. This issuehas conducted us to affirm, inspired inRorty, that being responsible for the otherdepends on the possibility of built moreinclusive moral communities. We guessBaeir’s approach related to sentimentaleducation should be added to that, which starts from the birth with the lovely reception of our relatives, who throughtheir dearness progressively are giving usthe initial trust that will permit us conquer“a modest version, attenuated, non fanaticof the Christian brotherhood”of universal reach. (shrink)

The author deals with one aspect of the justification of governmental action and its product (the law). He focuses on the authoritative character of legal rule, analyzing the apparent capacity of governments to produce reasons for action not grounded on substantive moral considerations. The assumption of that capacity seems necessary in order to establish a general moral obligation to obey a government irrespective of the actions required. This question is faced in connection with the thesis that only a particular form (...) of government, democracy, is morally justified insofar as it rests on legal rules issued by a legitimate source. (shrink)

This short preface is meant to explain the purpose of the present volume and point to the diverse approaches and lines of argument pursued by the contributors.

This study utilizing correlation, regression, confirmatory factor analyses, ANOVA, moderation and mediation analysis investigated connections of stereotypes, emotions, and sociocultural variables in a single-sample/single-group design. Prior to data processing, Georgian versions of the Stereotype Content Model questionnaires were validated through CFA. The study looked at Georgian students' attitudes to: representatives of German-speaking countries and representatives of English-speaking countries. Emotions predicted to these groups by social–structural antecedents—vitality and fear of assimilation—and stereotypes were admiration, pride, and sympathy. In addition, envy was predicted (...) for the English-speaking group. The prediction of envy is explained by moderation analysis according to which it is elicited by the interplay of warmth and competence, as well as fear of assimilation and competence. The former interaction mediates the link between social–structural antecedents to emotions. Thus, distant out-groups elicit envy as a result of their perceived vitality, fear of assimilation, warmth, and competence. Social–structural antecedents come forward to elicit emotions of envy independently as well as in interaction with stereotypes when small country representatives evaluate representatives of the influential group of English-speaking people. (shrink)

Pure type systems arise as a generalisation of simply typed lambda calculus. The contemporary development of mathematics has renewed the interest in type theories, as they are not just the object of mere historical research, but have an active role in the development of computational science and core mathematics. It is worth exploring some of them in depth, particularly predicative Martin-Löf’s intuitionistic type theory and impredicative Coquand’s calculus of constructions. The logical and philosophical differences and similarities between them will be (...) studied, showing the relationship between these type theories and other fields of logic. (shrink)

This book explores human possibility at the end of the twentieth century. It takes the form of discussion between an eminent philosopher and a skilled journalist about “the human measure” as it engages false absolutes and their accompanying utopias. The book proposes a “third way” between capitalism and socialism, and it concludes with comments on end-of-century phenomena, including democracy, intellectuals, and terrorism.