Em linguística gerativa, distinguem-se várias propriedades formais dos sistemas representacionais: a infinidade discreta, a finitude discreta e a infinidade do contínuo. Não é frequente filósofos aplicarem essas distinções ao estudo da forma lógica. O fato de essas distinções serem raramente aplicadas resultou em os filósofos pressuporem, geralmente sem discutir, que todas as formas lógicas apresentam una infinidade discreta, como o faz a linguagem natural. Este artigo defende a existência de outros tipos de forma lógica, além daquela que (...) apresenta infinidade discreta. Na representação mental é possível encontrar formar apresentando infinidade contínua e finitude discreta, além da infinidade discreta. Além disso, tais representações mantêm relações lógicas entre si, parcialmente em virtude dessas formas. Isso equivale à alegação de que o estudo da lógica natural precisa ir além da faculdade de linguagem, abrangendo formas lógicas pertinentes a representações mentais que não se assemelham a sentenças. Isso incluiria formas lógicas pictóricas. O ponto final é que, no estudo da lógica natural, é preciso considerar as formas lógicas representadas a sistemas mentais que antecedem a evolução da linguagem. (shrink)

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2015, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

En este artículo —conmemorativo de los cien años del Tractatus— me centraré en la primera gran obra de Wittgenstein y, en lo que sería su objetivo central que, como él mismo lo reconoce en la introducción, no es otro que el de “Trazar unos límites al pensamiento, o mejor, no al pensamiento, sino a la expresión de los pensamientos”, destacando en el lenguaje la proposición, pues es en esta donde aquel se expresa sensiblemente. Para el temprano Wittgenstein, los límites del (...) pensamiento solo se pueden trazar en el lenguaje y no por fuera de él, pues “lo que está al otro lado del límite no tiene sentido”. (shrink)

Esta investigación trata sobre la Lógica poética formulada por Giambattista Vico en la Ciencia nueva. Se trata de una teoría de la génesis, desarrollo y constitución del λóγος humano, no en cuanto intelecto, sino en cuanto expresión lingüística. Trata pues del origen del lenguaje. Esta investigación se desarrolla en dos partes (sincrónica y diacrónica) de la que aquí presento la primera. En ulteriores investigaciones acometeré la segunda. El trabajo se inicia con un estudio de las fuentes vichianas y su (...) reformulación por parte de nuestro pensador. Seguidamente se analiza el requisito para la formación de cualquier lenguaje natural (es decir, no formal), que para Vico reside en lo que llama una Metafísica poética. El núcleo del trabajo estriba en la comprensión de lo que Vico denomina primera operación de la mente humana. Desde esta teoría del conocimiento cabe acceder al estudio sincrónico de los factores que posibilitan el lenguaje humano. Los divido en tres tipos: biopsicológicos, socio-culturales e internos al mismo lenguaje. (shrink)

Nuestro objetivo es mostrar que una caracterización adecuada de las locuciones modales del lenguaje natural depende fundamentalmente de una correcta descripción de sus propiedades lógicas. Mostramos cómo los análisis escalares en pragmática fracasan porque siguen la lógica modal estándar al tratarlos como operadores preposicionales. Esto produce contradicciones, ya que, en sentido estricto, el estatus lógico de la locución modal es el mismo que el de la proposición simple. Estas expresiones invocan la presencia del hablante y la evidencia que (...) respalda a su afirmación, y tienen por lo tanto un carácter eminentemente deíctico/pragmático.It is our aim in this article to show that an adequate characterization of the interpretation of modally qualified utterances in natural language depends crucially on a correct description of their logical properties. We show that pragmatic analyses in terms of scales fail because they rely on the standard treatment of these expressions in modal logic as operators, and this makes the wrong predictions since, in a strict sense, the logical status of the modally- qualified utterance is the same as that of the bare proposition. We argue that these expressions directly invoke the presence of the speaker and act as indexes to sets of assumptions s/he is relying on as evidence for his/her assertion. (shrink)

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2012, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

This book marks the inauguration of the Historia Logicae book series, which seeks to publish high-quality monographs, dissertations, textbooks, proceedings, and anthologies on the history of logic in either German or English. Serving as the inaugural volume in this series, the book explores the contemporary interpretation of logic across many centuries and cultures. The first section of the volume comprises a compilation of papers dedicated to ancient and medieval logic, examining prominent thinkers such as Plato, Aristotle, Seneca, Porphyry, Proclus, Boethius, (...) Buridan, and Kilwardby. The second section shifts focus towards early-modern and contemporary logics, including the works of Caramuel, Kant, Drobisch, Husserl, and Jaskowski. Topics of discussion encompass the relationship between mathematics and logic, natural deduction, intuitionism, graph theory, categorical judgments, theories of truth, modal logic, opposition relations, logic diagrams, definitions of formal logic, many-sorted logic, model theory, and paraconsistent logic. (shrink)

Este trabajo presenta en su primera parte un resumen de la teoría de la argumentación de Chaim Perelman y Lucie Olbrechts-Tyteca. En él se destacan los elementos esenciales de esa teoría: su punto de partida como crítica a la concepción clásica de la racionalidad en Occidente, pensada desde Descartes como idéntica a la razón demostrativa; el origen aristotélico de la argumentación en la retórica o arte de la persuasión; el concepto de "auditorio universal" como destinatario de los argumentos; la noción (...) de "razonable" y su relación con el concepto de lo "racional". En la segunda parte se somete a crítica la posición de los autores frente a la relación entre lo racional y lo razonable. Se defiende la tesis de que lo racional es condición necesaria de lo razonable (cosa que no aceptan Perelman y Olbrechts), y para hacerlo, se apela a las ideas de Piaget sobre la existencia de una "lógica natural"; se usa el concepto de cálculo de la deducción natural como una clase de formalismo lógico aplicado a la argumentación; se utilizan las ideas de Apostel y de Grice sobre la implicación conversacional, y se aplica el formalismo construido por von Wright para el análisis lógico de la acción, con el fin de clasificar los tipos elementales de acción argumentativa. (shrink)

RESUMO No Livro I, parte IV, do "Tratado da natureza humana", Hume desenvolve aquilo que vamos chamar de lógica da ficção. Não se trata de um simples erro da imaginação enquanto fantasia, mas de uma propensão a criar ideias, entidades e objetos a partir das percepções presentes na mente. O que resulta daí é um sentido rico e novo de ficção que permite a Hume desenvolver uma história natural da filosofia, descrevendo a gênese inevitável de conceitos metafísicos. Partindo (...) de uma inspiração kantiana, iremos abordar esse tema ressaltando as semelhanças e diferenças entre as ficções naturais e a ilusão transcendental. ABSTRACT In Book I, part IV, of the "Treatise of Human Nature", Hume develops what we will call logic of fiction. It is not the case of a mere error of imagination as fancy, but a tendency to feign ideas, entities and objects from the perceptions in the mind. The result is a rich and new sense of fiction that allows Hume to establish a natural history of Philosophy, describing the unavoidable genesis of metaphysical concepts. From a Kantian point of view, we will approach this subject by highlighting the similarities as well as the differences between the natural fictions and the transcendental illusion. (shrink)

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2013, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2019, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

This volume of the Logica Yearbook series brings together articles based on selected abstracts accepted for presentation at the annual international symposium Logica 2020, Hejnice, the Czech Republic, which was cancelled due to the Covid-19 pandemic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2010, Hejnice, the Czech Republic. the articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

El objeto principal de este trabajo consiste en discutir una propuesta de C. Alchourrón y A. Martino para hacer frente al problema de la fundamentación de la lógica deóntica, planteado por el dilema de Jørgensen. La propuesta criticada se basa en la idea de que no existe obstáculo alguno en compatibilizar la idea de que las normas carecen de valor de verdad con la idea de que poseen una lógica, una vez que se renuncia al "prejuicio filosófico" de (...) que es indispensable caracterizar semánticamente las relaciones y propiedades lógicas y se explica la lógica a partir de la noción abstracta de consecuencia, desligándola de las nociones de verdad y falsedad. Sostienen que el significado de los operadores deónticos, al igual que el de los términos lógicos en la deducción natural, puede quedar totalmente expresado una vez que se explicita su uso mediante reglas de introducción y eliminación. Para ilustrar su propuesta, pretenden ofrecer una fundamentación puramente sintáctica de la lógica deóntica standard. Mis críticas se centran en tres puntos: a) no utilizan auténticas reglas de introducción para los operadores deónticos; b) no derivan la lógica deóntica standard como pretenden haber hecho, y c) no se establecen criterios para relacionar las fórmulas del cálculo con el lenguaje normativo ordinario, con lo que no existen razones para considerar que se trata de una lógica deóntica. Defiendo la idea de que, a los fines de fundamentar semánticamente la lógica deóntica, sólo es necesario que existan interpretaciones admisibles que atribuyan valores de verdad a las normas, y que este requisito es cumplido por la semántica usual de la lógica deóntica standard, con lo que el dilema de Jørgensen resulta ser un seudoproblema. In this paper I discuss a proposal from C. Alchourrón and A. Martino with which they try to face the problem posed to the foundation of deontic logic by Jørgensen' s dilemma. Their proposal is based on the idea that there is no problem at all in compatibilizing the fact that norms lack truth values with their possession of a logic, once it is denied that it is absolutely necessary to offer a semantic characterization of logical properties and relations, and the abstract notion of consequence is taken as primitive. They claim that the meaning of deontic operators, like that of logical terms in natural deduction, is completely expressed through their use, which is explained by means of rules of introduction and elimination. As an illustration, they present a calculus with which they intend to offer a foundation for standard deontic logic. I make three objections: a) They don' t use real rules of introduction for deontic operators; b) They don' t have derived standard deontic logic as they claim; c) There are no criteria for relating the formulas with ordinary normative discourse; so there are no reasons for considering their calculus as a deontic logic. I claim that, in order to give a semantical foundation to deontic logic it is only necessary that there are admissible interpretations that assign truth values to norms, and that this requisite is satisfied by the usual semantic of standard deontic logic. I conclude that Jørgensen' s dilemma is a pseudoproblem. (shrink)

Logic is usually presented as a tool of rational inquiry; however, many logicians in fact treat logic so that it does not serve us, but rather governs us – as rational beings we are subordinated to the logical laws we aspire to disclose. We denote the view that logic primarily serves us as logica serviens, while denoting the thesis that it primarily governs our reasoning as logica dominans. We argue that treating logic as logica dominans is misguided, for it leads (...) to the idea of a “genuine” logic within a “genuine” language. Instead of this, we offer a naturalistic picture, according to which the only languages that exist are the natural languages and the artificial languages logicians have built. There is, we argue, no language beyond these, especially none that would be a wholesome vehicle of reasoning like the natural languages and yet be transparently rigorous like the artificial ones. Logic is a matter of using the artificial languages as idealized models of the natural ones, whereby we pinpoint the laws of logic by means of zooming in on a reflective equilibrium. (shrink)

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2018, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

This volume of the Logica Yearbook series brings together articles based on selected abstracts accepted for presentation at the annual international symposium Logica 2021, in Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2017, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

O objetivo desse artigo é apresentar com base no pensamento do filósofo alemão Gottlob Frege, a concepção de conhecimento, partindo especialmente dos artigos “Sobre o sentido e a referência” e “As fontes de conhecimento em Matemática e em Ciências Naturais Matemáticas”. Para Frege só poderíamos afirmar que conhecemos alguma coisa, se o pensamento expressado por esta coisa for reconhecido como verdadeiro. Desta forma, antes de apresentarmos a concepção do autor relacionada à forma de reconhecer a verdade expressada por um pensamento, (...) temos que compreender o que Frege entende por verdade. Abordaremos primeiramente aquilo que Frege chama de “fontes do conhecimento”, que seriam as possibilidades de verificação de verdade de um enunciado, e em sequência, a concepção da linguagem, visando apontar de que modo “verdade” e “linguagem” se relacionam. Em seguida, buscaremos orientar nosso trabalho em torno das fontes de conhecimento como formas de reconhecer a verdade, apresentando suas contribuições e suas dificuldades.: The following article aims to present based in the thought of the german philosophy Gottlob Frege, the conception of knowledge, especially starting from the articles “On Sense and Reference” and “The sources of knowledge in Mathematics and Mathematical Natural Sciences”. For Frege we could only affirm we know something, if the expressed thought by this thing is recognized as truth. Thus, before we present the author’s conception related to how to recognize the truth expressed by a thought, we have to understand what Frege understand by truth. First we will discuss what Frege calls "sources of knowledge", which would be the possibilities of truth’s verification of a statement, and in sequence, the language’s conception aiming to identify how "truth" and "language" are related. Then we seek to guide our work around the sources of knowledge as ways to recognize the truth, presenting their contributions and their difficulties. Keywords: Experience. Logic. Geometry. Truth. Knowledge. (shrink)

In this paper we discuss the way logical consequence depends on what sets there are. We try to find out what set-theoretical assumptions have to be made to determine a logic, i.e., to give a definite answer to whether any given argument is correct. Consideration of second order logic -which is left highly indetermined by the usual set-theoretical axioms- prompts us to suggest a slightly different but natural nation of logical consequence, which reduces second order logic indeterminacy without interfering (...) with first order logic. (shrink)

This paper is a comparative analysis of the Logica Campsale Anglici, valde utilis et realis contra Ocham , from an anonymous author known as pseudo Richard of Campsall, and Ockham’s Summa logicae , in answer to which the former was written. We summarize both authors’s fundamental positions on five key issues: 1) the synonymy between abstract and concrete terms, 2) the reference of primary and secondary intentions, 3) the nature of the relations of predication between terms in propositions, 4) the (...) status of the “passions of the soul” and 5) the prime signification of spoken words. Our aim is to sketch the polemic between Nominalism and Realism in the second decade of the XIVth century. (shrink)

In this paper we discuss the way logical consequence depends on what sets there are. We try to find out what set-theoretical assumptions have to be made to determine a logic, i.e., to give a definite answer to whether any given argument is correct. Consideration of second order logic -which is left highly indetermined by the usual set-theoretical axioms- prompts us to suggest a slightly different but natural nation of logical consequence, which reduces second order logic indeterminacy without interfering (...) with first order logic. (shrink)

The article offers an analysis of Kant’ s “Third Antinomy of Pure Reason” (in which he examines the possibility of reconciling Transcendental freedom with natural Determinism), in order to show the lack of grounds of the interpretation that claims that the critical resolution of the antinomy implies a shift with respect to the cosmological terms in which the conflict was initially stated. Through a detailed analysis of the sources, we will suggest that the conflict analyzed in the Third Antinomy (...) is not exclusively cosmological, but rather that it also –and to the same degree– constitutes a practical conflict, and, secondly, that the critical solution is not developed in exclusively practical terms, but that it also involves certain aspects directly linked to the cosmological question initially formulated. (shrink)

The paper wishes to investigate the way Giles of Rome thought about logic: as a discipline, as a method, through an examination of the powers of logic, but also as a teaching subject. It tries to illuminate his views on logical education, and how he may have acted in favour of the latter as an Augustinian leader. It first offers a general presentation of the logical productions, from the 1270s to 1291. It then addresses the topic of logical education from (...) two viewpoints: by a look taken at Giles’ views on logic in the De regimine principum, and by a quick survey of the history of the teaching of logic in the studia of the Augustinian order from the mid-1280s on. The last section is dedicated to the philosophy and anthropology of logic. It tries to enlighten the originality of Giles’ s position, as a new departure taken from traditional theories regarding the absolute necessity of logic as a science, as an art, and as the underlying logic of all sciences, itself included. Rather than essentially necessary for any kind of philosophical endeavour, logic is presented a need for men, due to the fallible nature of his potential intellect. Rather than a science, it is described as a method for science which doesn’t use its more powerful instrument, i.e. the theory of scientific syllogism, since it proceeds in a non-demonstrative manner in the theory of demonstration. Logic and metaphysics are compared as respectively under and above special sciences. The last paragraph deals with the problem of the powers of logic in the context of metaphysical knowledge. (shrink)

The paper wishes to investigate the way Giles of Rome thought about logic: as a discipline, as a method, through an examination of the powers of logic, but also as a teaching subject. It tries to illuminate his views on logical education, and how he may have acted in favour of the latter as an Augustinian leader. It first offers a general presentation of the logical productions, from the 1270s to 1291. It then addresses the topic of logical education from (...) two viewpoints: by a look taken at Giles’ views on logic in the De regimine principum, and by a quick survey of the history of the teaching of logic in the studia of the Augustinian order from the mid-1280s on. The last section is dedicated to the philosophy and anthropology of logic. It tries to enlighten the originality of Giles’ s position, as a new departure taken from traditional theories regarding the absolute necessity of logic as a science, as an art, and as the underlying logic of all sciences, itself included. Rather than essentially necessary for any kind of philosophical endeavour, logic is presented a need for men, due to the fallible nature of his potential intellect. Rather than a science, it is described as a method for science which doesn’t use its more powerful instrument, i.e. the theory of scientific syllogism, since it proceeds in a non-demonstrative manner in the theory of demonstration. Logic and metaphysics are compared as respectively under and above special sciences. The last paragraph deals with the problem of the powers of logic in the context of metaphysical knowledge. (shrink)

El artículo ofrece una caracterización de las constantes lógicas, [CL], analizando el significado de las expresiones que son sus contrapartidas en el lenguaje natural. [CL] recoge los rasgos sintácticos, semánticos y pragmáticos individualmente necesarios y conjuntamente suficientes para que una expresión sea una constante lógica. Se obtendrá la siguiente conclusión: que la lista de las expresiones que habitualmente se consideran constantes lógicas no comparten rasgos relevantes desde el punto de vista del significado que justifiquen su tratamiento como un (...) grupo homogéneo. Sólo algunos usos del condicional, de la negación y de ciertos cuantificadores son constantes lógicas genuinas. (shrink)

Introducción a la lógica moderna es un libro de texto dedicado al estudio de la lógica simbólica elemental. No presupone familiaridad alguna con la lógica, las matemáticas o la filosofía, y se ha hecho un esfuerzo deliberado por adaptarlo a los intereses de estudiantes provenientes de las más diversas disciplinas. Al mismo tiempo, los conceptos centrales son expuestos de una manera precisa y rigurosa, sin ocultar los detalles y problemas técnicos y filosóficos que hacen de la (...) class='Hi'>lógica un área de estudio interesante en sí misma. El libro está dividido en tres partes. La primera se ocupa de la lógica proposicional, la segunda de la lógica de primer orden y la tercera de la lógica modal proposicional. Los tres temas se estudian semánticamente utilizando árboles de verdad, y sintácticamente a través de sistemas de deducción natural. Al final de cada sección hay numerosos ejercicios de práctica, la mitad de los cuales son resueltos en el apéndice. El texto está diseñado para un curso de un año de duración y permite gran flexibilidad en el diseño del mismo. (shrink)

ResumoApresentam-se alguns conceitos fundamentais e posições representativas referentes a três debates correntesna filosofia da lógica, a saber aquele acerca da natureza da relação de consequência, o que versasobre o problema do pluralismo lógico (e sua alternativa fundamental, o monismo) e o que gira em tornoda chamada proposta anti-excepcionalista, que nega o caráter excepcional da lógica e a põe numa relaçãode continuidade essencial com as demais ciências, de modo a evidenciar pontos de conexão entre as trêsdiscussões mencionadas. Levanta-se, por (...) fim, a questão da plausibilidade da posição, presentementeminoritária, de um anti-excepcionalismo pluralista, vinculando-a, por sua vez, à aceitação de algumavariedade de pluralismo científico.Palavras-chave: consequência lógica; pluralismo lógico; anti-excepcionalismo lógico.AbstractSome fundamental concepts are presented, along with the theses relative to three current debates in thephilosophy of logic, namely the one concerning the nature of the relation of logical consequence, the oneover the problem of logical pluralism (and its fundemental alternative, monism), and the one around theso-called anti-exceptionalist proposal, which denies logic’s exceptional character and puts it in a relationof essential continuity with the remaining sciences, so as to highlight the points of connection betweenthe three aforementioned discussions. The question is raised, finally, of the plausibility of the position,presently of small currency, of a pluralist anti-exceptionalism, which is associated, in its turn, to the acceptanceof some variety of scientific pluralism. (shrink)

The fundamental link between logical and semantic inquiries is emphasized, and by relating some of Frege’s ideas on the concepts of logic and truth with others of Davidson’s on the Tarskian structure of interpretation, an attempt is made to clarify the Fregean point of view about the nature of the logical-semantic reflection.

Any historical and critical appreciation of Hegel's basic thesis of the identity of metaphysics with logic cannot fail to compare it with his charging Kant and Fichte with attaching a merely subjective meaning to logical determinations, as well as Schelling with spinozism and extrinsicalness in conceiving the absolute indifference of subject with object. This paper aims to give an account of Hegel's notion of nature as it arises from the fulfillment of the logical idea (as the Anderssein of the idea (...) in which it is in the form of the alienation (Entaeusserung)) by focussing attention on the logical pathway of the notion of externality (Aeusserlichkeit) in the Doctrine of Being. I argue for an alternative to the received view on the outcome of the Logic of Being, by pointing out two different meanings, overlooked so far, attached to the category of measure vs. the notion of Mode and to Spinoza's substance in 1812 and 1832. (shrink)

El artículo revisa los límites teóricos que unen y separan la lógica de Aristóteles de la lógica aristotélica y la lógica de primer orden. Considera las razones para sostener la actualidad de la lógica de Aristóteles y se pregunta por la unidad de la disciplina, destacando la importancia de la noción de ciencia en la definición de lógica. The article deals with the theoretical limits which unify Aristotle's logic with Aristotelian logic and First Order Logic, (...) and it realizes their differences too. It examines the reasons to maintain the presence and actuality of Aristotle's logic and discovers the importance of the notion of science in defining the nature of logic. (shrink)

El artículo revisa los límites teóricos que unen y separan la lógica de Aristóteles de la lógica aristotélica y la lógica de primer orden. Considera las razones para sostener la actualidad de la lógica de Aristóteles y se pregunta por la unidad de la disciplina, destacando la importancia de la noción de ciencia en la definición de lógica. The article deals with the theoretical limits which unify Aristotle's logic with Aristotelian logic and First Order Logic, (...) and it realizes their differences too. It examines the reasons to maintain the presence and actuality of Aristotle's logic and discovers the importance of the notion of science in defining the nature of logic. (shrink)

Para determinar el papel de la filosofía kantiana en la lógica dialéctica, se proponen ocho aspectos del aporte de Kant a su desarrollo. Kant, al mostrar la dialéctica inmanente de la actividad sintética del pensamiento teórico, marcó el punto de partida de la lógica dialéctica moderna como la filosofía epistémica acorde con la nueva cosmovisión científico-natural que él mismo iniciara. Sin embargo, al no llevar estos aspectos dialécticos hasta sus últimas consecuencias, la filosofía kantiana, quedó en el (...) comienzo mismo del movimiento que, por mediación de otros pensadores, arribaría a la lógica dialéctica marxista. (shrink)

This paper focuses on natural dualities for varieties of bilattice-based algebras. Such varieties have been widely studied as semantic models in situations where information is incomplete or inconsistent. The most popular tool for studying bilattices-based algebras is product representation. The authors recently set up a widely applicable algebraic framework which enabled product representations over a base variety to be derived in a uniform and categorical manner. By combining this methodology with that of natural duality theory, we demonstrate how (...) to build a natural duality for any bilattice-based variety which has a suitable product representation over a dualisable base variety. This procedure allows us systematically to present economical natural dualities for many bilattice-based varieties, for most of which no dual representation has previously been given. Among our results we highlight that for bilattices with a generalised conflation operation. Here both the associated product representation and the duality are new. Finally we outline analogous procedures for pre-bilattice-based algebras. (shrink)

In a book in which the severity of the critique betrays some iconoclasm, Statera first examines the three-way discussion of Schlick, Carnap, and Neurath concerning protocols and verification, then describes the systematic goals of the Encyclopedia of Unified Science, and concludes with an exposition and appraisal of Neurath's work in the philosophy of the social sciences. The selection of Neurath for this preliminary study is a happy one. Neurath's efforts to overcome the gap between sciences of nature and sciences of (...) man are central for an understanding of the complementary and conflicting aspects of the main trends in the philosophy of the social sciences in our time. These main trends are: the historical sociologism of Dilthey and Weber, Marxism, Logical Positivism, and Pragmatism. These four schools, while autonomous and even antagonistic in their work, have nevertheless interacted with each other more than is commonly known, or accepted, in certain quarters. In particular, in the case of Neurath, his association of Logical Positivism with Marxism first, and later with pragmatic notions, is an eloquent proof of the impossibility to dissociate these viewpoints altogether.--A. M. (shrink)

The techniques of natural duality theory are applied to certain finitely generated varieties of Heyting algebras to obtain optimal dualities for these varieties, and thereby to address algebraic questions about them. In particular, a complete characterisation is given of the endodualisable finite subdirectly irreducible Heyting algebras. The procedures involved rely heavily on Priestley duality for Heyting algebras.

We present a framework for machine implementation of families of non-classical logics with Kripke-style semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke models. By appropriate combinations we capture both partial and complete fragments of large families of non-classical logics such as modal, relevance, and intuitionistic logics. Our approach is modular and supports uniform proofs of soundness, completeness (...) and proof normalization. We have implemented our work in the Isabelle Logical Framework. (shrink)

According to the standard characterization of logic in Frege’s writings, the word “true” indicates the essence of logic, as the word “good” indicates the essence of ethics and the word “beautiful” the essence of aesthetics. In a posthumous writing from 1915, however, Frege says that it is the assertoric force, and not the word “true”, which indicates the essence of logic properly. Prima facie, this correction is in conflict with Frege’s criticism of the psychologist conception of logic. For according to (...) this criticism, logic is not the science of the laws of “being taken as true”, but the science of the laws of “being true”, while the assertoric force expresses being taken as true. In previous writings, I tried to resolve this conflict by a reconstruction of Frege’s conception of truth that is based on his thesis that truth is expressed in natural language by the “form of the assertoric sentence”. The goal of this paper is to defend this interpretation against the objections recently made by Marco Ruffino. (shrink)

In a book in which the severity of the critique betrays some iconoclasm, Statera first examines the three-way discussion of Schlick, Carnap, and Neurath concerning protocols and verification, then describes the systematic goals of the Encyclopedia of Unified Science, and concludes with an exposition and appraisal of Neurath's work in the philosophy of the social sciences. The selection of Neurath for this preliminary study is a happy one. Neurath's efforts to overcome the gap between sciences of nature and sciences of (...) man are central for an understanding of the complementary and conflicting aspects of the main trends in the philosophy of the social sciences in our time. These main trends are: the historical sociologism of Dilthey and Weber, Marxism, Logical Positivism, and Pragmatism. These four schools, while autonomous and even antagonistic in their work, have nevertheless interacted with each other more than is commonly known, or accepted, in certain quarters. In particular, in the case of Neurath, his association of Logical Positivism with Marxism first, and later with pragmatic notions, is an eloquent proof of the impossibility to dissociate these viewpoints altogether.--A. M. (shrink)

In this paper we present labelled sequent calculi and labelled natural deduction calculi for the counterfactual logics CK + {ID, MP}. As for the sequent calculi we prove, in a semantic manner, that the cut-rule is admissible. As for the natural deduction calculi we prove, in a purely syntactic way, the normalization theorem. Finally, we demonstrate that both calculi are sound and complete with respect to Nute semantics [12] and that the natural deduction calculi can be effectively (...) transformed into the sequent calculi. (shrink)