En este artículo presentamos una posible vía para interpretar las nociones de posibilidad y necesidad desarrolladas en el seno de la lógica megárico-estoica como operadores modales aléticos. Se introducirá la semántica megárico-estoica como trasfondo metafísico de las definiciones de necesidad y posibilidad y se ofrecerán argumentos para abandonar las interpretaciones predominantes que incluyen variables temporales ad hoc. Tras proponer la lectura de las definiciones diodóricas desde una semántica modal relacional se señalará una serie de temas que merecen ser (...) revisitados desde esta óptica. (shrink)

In this paper we intend to offer a first approach to the incorporation of certain formal tools in the elucidation of some issues discussed in epistemological contexts. The aim is not to offer an exhaustive resolution of these problems but merely to point out the usefulness of modal semantics when applied to different fields. Here we will show how a series of skeptical arguments eventually involve a modal (counterfactual) structure, which we will try to generalise into a useful (...) scheme. -/- . (shrink)

El presente trabajo pretende explicitar que los operadores modales, como construcciones lógicas, insertos en las interpretaciones modales (MI) de la mecánica cuántica son usados de manera informal sin una semántica modal adecuada. Primero se estudiarán en detalle los motivos por los que ninguna lógica cuántica puede ofrecer una base apropiada para formalizar estos operadores en contextos mecánico-cuánticos. A continuación, se presentará el enfoque de las historias cuánticas como una nueva lógica cuántica (NQL) intrínsecamente booleana como posible herramienta (...) para formalizar operadores modales en el contexto de las MI. Tras comentar brevemente las principales MI, se propondrá abordar un estudio de las modalidades presentes en ellas desde esta NQL prestando siempre especial atención al problema de la medida como hilo conductor. Finalmente, se pretende señalar cuáles han de ser los primeros pasos necesarios para ofrecer una exposición lógicamente consistente de las modalidades en contextos cuánticos relevantes con NQL como herramienta, así como señalar las ventajas que esta perspectiva podría llegar a ofrecer. (shrink)

This paper examines two alleged limitations in the use of formal languages: on the one hand, the trade-offs between expressive and inferential power, and on the other, the phenomenon of system imprisonment. After reconceptualizing the issue, we consider the role played by modality in the understanding of certain aspects of mathematical structures and argue for its centrality.

Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their (...) primitive operations arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of _weak implicative semilattices_, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus. (shrink)

Discuto la tesi di Micheletti secondo la quale ogni spiegazione fattuale presuppone premesse di ordine superiore rispetto alla spiegazione (M.Micheletti, “Radical Divine Alterity and the God-World Relationship”). Nella prima sezione del testo introdurrò la tesi, muovendo dalla analisi di alcuni esempi di spiegazione, ed elencherò le ragioni che (apparentemente) richiedono la postulazione di higher-degree propositions per rendere conto di factual propositions. Nella seconda sezione regimenterò logicamente la tesi di Micheletti. Nella terza sezione discuterò la validità della logica della spiegazione così (...) introdotta, con un’attenzione particolare alla analisi semantica della nozione di spiegazione, allo statuto modale delle ragioni che costituiscono una spiegazione, e all’approccio grammaticale alle higher order propositions. Nella quarta e ultima sezione avanzerò brevissime considerazioni conclusive. (shrink)

Luiz Henrique Lopes dos Santos, em seu texto sobre "Leibniz e a questão dos futuros contingentes”, argumenta em favor de seu diagnóstico segundo o qual, no fundo, a principal diferença entre as doutrinas de Espinosa e Leibniz reside no fato de que o primeiro, diferentemente do segundo, não sabia lógica. Este texto procura objetar à sua posição, respondendo às críticas do autor à posição de Espinosa quanto à liberdade divina. Procurarei mostrar que, sob o aspecto preciso da articulação aí (...) estabelecida entre a distinção vontade/entendimento e a questão dos possíveis jamais realizados, ela não poderia estar disponível para a metafísica de Espinosa, não por ele ter ignorado um princípio básico da lógica modal, como alega o autor, mas porque ele compreende diferentemente o estatuto ontológico da unidade das coisas individuais e, portanto, dos agentes humanos. (shrink)

A solid foundation of modal logic requires a clear conception of the notion of modality. Modern modal logic treats modality as a propositional operator. I shall present an alternative according to which modality applies primarily to illocutionary force, that is, to the force, or mood, of a speech act. By a first step of internalization, modality applied at this level is pushed to the level of speech-act content. By a second step of internalization, we reach a propositional operator (...) validating the modal logic S4. After a brief discussion of problematic modality and possibility, the article concludes with an extension of the account that identifies modality with illocutionary force. Throughout, close attention is paid to the intended interpretation of the formalism. All of the rules stipulated will be justified on the basis of this interpretation. (shrink)

This book is an introduction to first-order modal logic. It starts with classical propositional logic and ends with first-order modal logic. The text introduces the basic theory of sets, graphs and a chapter on argumentation from contemporary pragmatics.

Este livro marca o início da Série Investigação Filosófica. Uma série de livros de traduções de textos de plataformas internacionalmente reconhecidas, que possa servir tanto como material didático para os professores das diferentes subáreas e níveis da Filosofia quanto como material de estudo para o desenvolvimento pesquisas relevantes na área. Nós, professores, sabemos o quão difícil é encontrar bons materiais em português para indicarmos. E há uma certa deficiência na graduação brasileira de filosofia, principalmente em localizações menos favorecidas, com relação (...) ao conhecimento de outras línguas, como o inglês e o francês. Tentamos, então, suprir essa deficiência, ao introduzirmos traduções de textos importantes ao público de língua portuguesa, sem nenhuma finalidade comercial e meramente pela glória da filosofia. O presente volume é constituído de três traduções de verbetes importantes sobre lógica, da Enciclopédia de Filosofia da Stanford: (1) A Lógica de Aristóteles, (2) Lógica Clássica, (3) Lógica Modal. (shrink)

In this paper, we examine two conceptions of the application of logic and assess their comparative merits. The first is a platonist monist conception that characterizes the logical consequence relation as an abstract relation among propositions. We argue that this proposal, which insists on logic’s topic neutrality, accommodates very well the objectivity of logic. From this perspective, there are no constraints on particular topics. As a result, we have the universality that allows us to go through a wide scope of (...) contexts where logic is applied. In contrast, a non-platonist pluralist conception is examined, and it characterizes the variety of logical consequence relations as concrete, context-dependent in particular cases, and topic-dependent. As will become clear, this conception is particularly well suited to make room for the applications of logic. We conclude that, in order to solve the ontological debate about logic, we need to go beyond its applications. (shrink)

Complete deductive systems are constructed for the non-valid (refutable) formulae and sequents of some propositional modal logics. Thus, complete syntactic characterizations in the sense of Lukasiewicz are established for these logics and, in particular, purely syntactic decision procedures for them are obtained. The paper also contains some historical remarks and a general discussion on refutation systems.

In this paper, I claim that two ways of defining validity for modal languages (“real-world” and “general” validity), corresponding to distinction between a correct and an incorrect way of defining modal valid- ity, correspond instead to two substantive ways of conceiving modal truth. At the same time, I claim that the major logical manifestation of the real- world/general validity distinction in modal propositional languages with the actuality operator should not be taken seriously, but simply as a (...) by-product of the way in which the semantics of such an operator is usually given. (shrink)

In this fragment of Opuscula Logica it is displayed an arithmetical treatment of the aristotelic syllogisms upon the previous interpretations of Christine Ladd-Franklin and Jean Piaget. For the first time, the whole deductive corpus for each syllogism is presented in the two innovative modalities first proposed by Hugo Padilla Chacón. A. The Projection method (all the possible expressions that can be deduced through the conditional from a logical expression) and B. The Retrojection method (all the possible valid antecedents or premises (...) conjunction for an expression proposed as a conclusion). The results are numerically expressed, with their equivalents in the propositional language of bivalent logic. (shrink)

Some philosophers advance the claim that the phenomena of logical omniscience and of the indiscernibility of metaphysical statements, which arise in (certain) interpretations of normal modal logic, provide strong reasons in favour of impossible world approaches. These two specific lines of argument will be presented and discussed in this paper. Contrary to the recent much-held view that the characteristics of these two phenomena provide us with strong reasons to adopt impossible world approaches, the view defended here is that no (...) such ‘knock-down arguments’ do emanate on those grounds. This is not to rule out that there cannot be any other good reasons for assuming impossible world semantics. However, the discussion of a further argument for impossible worlds will suggest that different attempts to argue for them likely present intertwined problems. (shrink)

A certain type of inference rules in modal logics, generalizing Gabbay's Irreflexivity rule, is introduced and some general completeness results about modal logics axiomatized with such rules are proved.

The paper sketches an argument against modal monism, more specifically against the reduction of physical possibility to metaphysical possibility. The argument is based on the non-categoricity of quantum logic.

Filosofia limbajului are legătură cu studiul modului în care limbajul nostru se implică și interacționează cu gândirea noastră. Studierea logicii și relația dintre logică și vorbirea obișnuită poate ajuta o persoană să își structureze mai bine propriile argumente și să critice argumentele celorlalți. Înțelesul este modul în care pot fi considerate în mod corespunzător cuvinte, simboluri, idei și convingeri, definiția sa depinzând de teoria abordată, precum teoria corespondenței, teoria coerenței, teoria constructivistă, teoria consensului sau teoria pragmatică. Există mai multe explicații (...) distince despre ceea ce înseamnă un „sens” lingvistic, în funcție de diverse teorii (ideologice, adevăr-condiționale, de utilizare a limbajului, constructiviste, de referință, verificaționiste, pragmatice, etc.) Investigațiile privind modul în care limbajul interacționează cu lumea sunt numite teorii de referință. Sensul unei propoziții este gândul pe care îl exprimă. Un astfel de gând este abstract, universal și obiectiv. Sensurile determină referința și sunt, de asemenea, modurile de prezentare a obiectelor la care se referă expresiile. Referințele sunt obiectele din lume despre care vorbesc cuvintele. Filosofia limbajului explorează relația dintre limbă și realitate, în special filosofia problemelor de studiu lingvistic care nu pot fi abordate de alte domenii. Logica filozofică se ocupă de descrieri formale ale limbajului obișnuit, nespecializat („natural”). -/- CUPRINS: -/- 1. Filosofia limbajului - 1.1 Istorie - - Filosofia antică - - Filosofia medievală - - Filosofia modernă - - Filosofia contemporană - 1.2 Subiecte și sub-domenii majore - - Compoziție și părți - - Natura sensului - - Referinţă - - Mintea și limba - - - Înnăscut și învățat - - - Limba și gândul - - Interacțiunea socială și limba - 1.3 Limbajul și filozofia continentală - 1.4 Probleme în filosofia limbajului - - Imprecizia - - Problema universalului și a compoziției - - Natura limbajului - - Abordări formale versus informale - - Traducere și interpretare - 1.5 Nominalism - - Istorie - - - Filozofia greacă veche - - - Filozofia medievală - - - Filosofia modernă și contemporană - - Problema universalelor - - Tipuri - - - Filosofie analitică și matematică - - Critica originilor istorice ale termenului 2. Înțeles - 2.1 Adevăr și înțeles - - Teorii majore ale înțelesului - - - Teoria corespondenței - - - Teoria coerenței - - - Teoria constructivistă - - - Teoria consensului - - - Teoria pragmatică - - Teorii și comentarii asociate - - - Logica și limbajul - - - Gottlob Frege - - - Bertrand Russell - - - Alte teorii ale adevărului - - - Saul Kripke - - - Criticile teoriilor de adevăr ale înțelesului - 2.2 Bertrand Russell, Despre denotare - - "Fraza care denotă" - - - Concepția lui Russell despre o frază care denotă - - - Referința la ceva care nu există - - - Epistemologie - - Teoria descrierilor - - - Descrierea matematică - - - Ilustrare - - - Meinong - - Rezolvarea problemei existențialelor negative - - - Declarații despre concepte în care obiectul nu există - - - Ambiguitate - - - Nume fictive - - Critici - 2.3 Sens și referință - - Precursori - - - Antistene - - - John Stuart Mill - 2.3.1 Sens - - Sens și descriere - - Traducerea Bedeutung - - Natura sensului - 2.3.2 Referinţă - 2.4 Nume proprii - - Problema - 2.4.1 Teorii - - Teoria lui Mill - - Teoria bazată pe sensul numelor - - Teoria descriptivă - - Teoria cauzală a numelor - - Teorii de referință directă - - Filosofia continentală - 2.5 Gottlob Frege, Despre sens și referință - 2.6 Teorii cauzale ale referinței - - Motivaţie - - Variații - 2.6.1 Teoria cauzală a referinței a lui Saul Kripke - 2.6.2 Teoria cauzală a referinței a lui Gareth Evans - 2.6.3 Teoria cauzală a referinței a lui Michael Devitt - 2.6.4 Blockchain și arborele cauzal al referinței - 2.6.5 Perspective - 2.7 Saul Kripke, Numire și necesitate - 2.7.1 Prelegerea I - 2.7.2 Prelegerea II - 2.7.3 Prelegerea III - 2.7.4 Concluzii - 2.8 Kit Fine, Relaționismul semantic - - A. Antinomia variabilei - - B. Abordarea tarskiană - - C. Respingerea rolului semantic - - D. Abordarea instanțială - - E. Abordarea algebrică - - F. Abordarea relațională - - G. Semantica relațională pentru logica de primul ordin 3. Logica - Concepte - - Forma logică - - Semantică - - Inferență - - Sisteme logice - - Logică și raționalitate - - Concepte rivale - Tipuri - - Logica silogistică - - Logica propozițională - - Logica predicatelor - - Logica modală - - Raționament informal și dialectică - - Logica matematică - - Logica filozofică - - Logica computațională - - Logica non-clasică - Controverse - - "Este logica empirică?" - - Implicare: Strictă sau materială - - Tolerarea imposibilului - - Respingerea adevărului logic - 3.1 Filosofia logicii - - Adevăr - - - Purtătorii de adevăr - - - Adevăruri analitice, adevăr logic, valabilitate, consecință logică și implicare - 3.2 Logica propozițională - - Explicaţie - - Istorie - - Terminologie - - Noțiuni de bază - - - Închiderea sub operații - - - Argument - 3.3 Logica predicatelor - - Introducere - - Sintaxa - - - Alfabetul - - - - Simboluri logice - - - - Simboluri non-logice - - - Regulile formării - - - - Termeni - - - - Formule - - - - Convenții notaționale - - - Variabile libere și legate - - Semantica - - - Structuri de prim ordin - - - Evaluarea valorilor de adevăr - - - Valabilitate, satisfabilitate și consecință logică - - - Algebrizare - - - Teorii, modele și clase elementare de prim ordin - - - Domenii goale - 3.4 Logica modală - - Dezvoltarea logicii modale - - Semantica - - - Teoria modelului - - - Sisteme axiomatice - - - Teoria dovezilor structurale - - - Metode de decizie - - Tipuri de logici modale - - - Logica aletică - - - Logica epistemică - - - Logica temporală - - - Logica deontică - - - Logica doxastică - - - Alte logici modale - - Ontologia posibilității - - Controverse - 3.5 Declarații - - Declarația ca o entitate abstractă - 3.6 Dileme - - Utilizarea dilemei în logică - 3.7 Argumente - - Formal și informal - - Tipuri standard - - - Argumente deductive - - - Argumente inductive - 3.8 Actualism - - Exemplu - - Puncte de vedere filosofice - - Analiza indexicală a actualității - 3.9 Lumi posibile - - Posibilitate, necesitate și contingență - - Semantica formală a logicii modale - - De la logica modală la instrumentul filosofic - - Teoria lumii posibile în studiile literare - 3.9.1 Lumi reale, ne-reale dar posibile, și imposibile - - Lumi posibile logic - - Constituienții lumilor posibile - 3.10 Saul Kripke - - Wittgenstein - - Adevăr - 3.10.1 Logica modală - - Modele canonice - - Modele Carlson - 3.10.2 Logica intuiționistă - - Logica intuiționistă de ordinul întâi - 3.10.3 Nume și Necesitate - - "Un puzzle despre credință" Referințe Despre autor - Nicolae Sfetcu - - De același autor - - Contact Editura - MultiMedia Publishing . 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Las máquinas aceleradas de Turing (ATMs) son dispositivos capaces de ejecutar súper-tareas. Sin embargo, el simple ejercicio de definirlas ha generado varias paradojas. En el presente artículo se definirán las nociones de súper-tarea y ATM de manera exhaustiva y se aclarará qué debe entenderse en un contexto lógico-formal cuando se pregunta por la existencia de un objeto. A partir de la distinción entre posibilidades lógicas y físicas se disolverán las paradojas y se concluirá que las ATMs son posibles y existen (...) como objetos abstractos. (shrink)

The purpose of this study is to propose new similarity measures namely rough variational coefficient similarity measure under the rough neutrosophic environment. The weighted rough variational coefficient similarity measure has been also defined. The weighted rough variational coefficient similarity measures between the rough ideal alternative and each alternative are xxxxx calculated to find the best alternative. The ranking order of all the alternatives can be determined by using the numerical values of similarity measures. Finally, an illustrative example has been provided (...) to show the effectiveness and validity of the proposed approach. Comparisons of decision results of existing rough similarity measures have been provided. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

La logica modale è nata per studiare i ragionamenti su ciò che è possibile e ciò che è necessario. Negli ultimi decenni, a partire dal lavoro di logici e filosofi quali Rudolf Carnap, Saul Kripke e David Lewis, la sua applicazione è stata progressivamente estesa ad altri ambiti, quali il ragionamento sul tempo, sulla conoscenza e sui sistemi di norme. Queste ricerche hanno condotto a un complesso e intrigante dialogo con alcune fondamentali branche della filosofia: la metafisica, l’epistemologia, la filosofia (...) del linguaggio. Lo scopo del volume è offrire una panoramica di questo dialogo al contempo accessibile e rigorosa, pensata sia per gli studenti di un corso universitario, sia per il lettore non specialista. Se da un lato tutte le necessarie nozioni tecniche sono rese accessibili ai non addetti ai lavori, dall'altro si restituisce un'immagine fedele delle sfide concettuali che la ricerca in questi settori è oggi chiamata ad affrontare. (shrink)

Nosso objetivo neste trabalho é apresentar uma proposta de solução a paradoxos relacionados à lógica deôntica presentes na literatura, reunidos sob o que é chamado de dilemas deônticos - situações nas quais duas obrigações conflitantes estão presentes num mesmo sistema normativo. Situações deste tipo, quando formalizadas (em SDL - standard deontic logic - ou em outras lógicas relacionadas), levam a uma inconsistência. Nossa proposta baseia-se em relações de preferência que geram uma ferramenta de escolha dentre as duas soluções normativas (...) conflitantes, o que evita a inconsistência e permite o pleno cumprimento do sistema. Justificativas filosóficas são fornecidas as ferramentas lógicas, bem como as suas implicações. (shrink)

En este artículo se presentan dos demostraciones del teorema de interpolación: Una para la lógica proposicional y otra para la lógica de primer orden. Ambas se realizan en el contexto de la teoría de modelos. El teorema de interpolación afirma que si A y B son fórmulas, donde A no es una contradicción, B no es válida, y B es una consecuencia lógica de A, entonces existe una fórmula C que esta escrita en el lenguaje común al (...) de A y de B, tal que C es una consecuencia lógica de A y B es una consecuencia lógica de C. El teorema de interpolación fue demostrado por primera vez para la lógica de primer orden por William Craig en 1957, y desde entonces se ha investigado la posibilidad de generalizarlo o aplicarlo. Dicho teorema tiene generalizaciones o aplicaciones en teoría de la demostración, teoría de modelos abstracta, ciencias de la computación, lógica modal, lógica intuicionista, etc. Se presentan ejemplos de aplicaciones o generalizaciones de la propiedad de interpolación relacionados con lógicas infinitarias, cuantificadores generalizados, segundo orden, no clásicas, abstractas, etc. También se ofrecen referencias de problemas abiertos sobre interpolación en el contexto de la teoría de modelos abstracta. (shrink)

A presente dissertação tem como objetivo uma apresentação da proposta de Charles Kielkopf, de tradução da lógica deôntica standard em uma lógica normal alética e de seusresultados quanto à construção de um sistema de lógica deôntica que capture conceitos eprincípios kantianos como necessidade causal e as formulações do Imperativo Categórico acerca do Reino da Natureza e do Reino dos Fins. Uma vez que este processo resulta em uma interpretação de aspectos da filosofia kantiana, optou-se inicialmente por uma (...) apresentação em linhas gerais destas concepções e, tendo em vista as dificuldades referentes a aplicabilidade de um processo de tradução entre princípios deônticos e ônticos,fez-se necessária também uma exposição acerca do problema das barreiras inferenciais, bem como de sua conseqüência mais imediata, a saber, o Dilema de Jörgensen. Num segundo momento, também foi feita uma caracterização dos sistemas modais normais, tanto deônticos quanto aléticos, bem como da noção de tradução entre lógicas e dos modelos de Dawson. O capítulo final consiste justamente num exame crítico da proposta de Kielkopf, o qual faz uso dos modelos de Dawson para desenvolver uma lógica deôntica a partir do sistema lógico K1. Tais modelos de Dawson permitem a definição de uma lógica deôntica em termos de modalidades aléticas iteradas, com o que este modelo constitui-se em uma maneira de evitar os problemas referentes às barreiras inferenciais. O desenvolvimento de uma alternativa para a atribuição de um status lógico a concepções deônticas não constitui,contudo, o aspecto inovador desta proposta, tal aspecto encontra-se justamente na utilização por Kielkopf, de seu modelo formal como uma ferramenta para a investigação de concepções filosóficas, no caso, as concepções kantianas já citadas. -/- The current dissertation has as its main objective an exposition and critical analysis of Charles Kielkopf's translation of the Standard Deontic Logic (SDL) into a normal alethic logic, and the resulting construction of a system of deontic logic that captures Kantian fundamental concepts and principles such as the concept of causal necessity and the formulations of the Categorical Imperative concerning Kingdom of Nature and Kingdom of Ends. Since this process results in an interpretation of aspects of the Kantian philosophy, it has been chosen,initially, a presentation in general lines of these concepts and, considering the difficulties regarding the applicability of a translation process between deontic and ontic principles, it was done necessary also an exhibition concerning the problem of the inferential barriers, as well as of his more immediate consequence, i. e., Jörgensen's Dilemma. In a secon dmoment, it was also made a characterization of normal modal systems, deontic ones andalethic ones, as well as of the notions of translation between logics and of Dawson modelling. The final chapter consists of a critical examination of Kielkopf's proposal, which uses Dawson modelling to develop a deontic logic based on the alethic system K1. Such Dawson modelling allows the definition of a deontic modalities in terms of iterated alethic modalities,therefore this model constitutes a way of avoiding the problems regarding inferential barriers. The development of an alternative for attribution of logical status to deontic concepts doesn't constitute, however, in an innovative aspect of this proposal, such aspect can be founded inthe use made by Kielkopf of his formal model as a tool for the investigation of philosophical concepts, such as the Kantian concepts already mentioned. (shrink)

In this paper we present an overview, with historical and critical remarks, of two articles by S. Jaśkowski ([20, 21] 1948 and [22, 23] 1949), which contain the oldest known formulation of a paraconsistent logic. Jaśkowski has built the logic – he termed discussive (D2) – by defining two new connectives and by introducing a modal translation map from D2 systems into Lewis’ modal logic S5. Discussive systems, for their formal details and their original philosophical justification, have attracted (...) discrete attention among experts. Indeed, in what follows, after having introduced Jaśkowski methodology of building D2 and his main philosophical motivations for providing such a system, we will explore some of the main contributions to the development of D2. (shrink)

We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities.En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways, game identities into modal formulae.The completeness proof is based on reduction of game terms to a (...) certain ‘minimal canonical form’, by using only the axiomatic identities, and on showing that the equivalence of two minimal canonical terms can be established from these identities. (shrink)

In this paper, I shall consider the challenge that Quine posed in 1947 to the advocates of quantified modal logic to provide an explanation, or interpretation, of modal notions that is intuitively clear, allows “quantifying in”, and does not presuppose, mysterious, intensional entities. The modal concepts that Quine and his contemporaries, e.g. Carnap and Ruth Barcan Marcus, were primarily concerned with in the 1940’s were the notions of (broadly) logical, or analytical, necessity and possibility, rather than the (...) metaphysical modalities that have since become popular, largely due to the influence of Kripke. In the 1950’s modal logicians responded to Quine’s challenge by providing quantified modal logic with model-theoretic semantics of various types. In doing so they also, explicitly or implicitly addressed Quine’s interpretation problem. Here I shall consider the approaches developed by Carnap in the late 1940’s, and by Kanger, Hintikka, Montague, and Kripke in the 1950’s, and discuss to what extent these approaches were successful in meeting Quine’s doubts about the intelligibility of quantified modal logic. (shrink)

We show that we in ways related to the classical Square of Opposition may define a Cube of Opposition for some useful statements, and we as a by-product isolate a distinct directive of being inviolable which deserves attention; a second central purpose is to show that we may extend our construction to isolate hypercubes of opposition of any finite cardinality when given enough independent modalities. The cube of opposition for obligations was first introduced publically in a lecture for the Square (...) of Opposition Conference in the Vatican in May 2014. -/- A COLORFUL ERRATUM: The article Cubes and Hypercubes of Opposition, with Ethical Ruminations on Inviolability, suffered a couple of mishaps when it was published in Logica Universalis, ISSN 1661-8297, 10(2-3), p. 373–376. The worst of them was that the colorful cube was printed in shades of grey, instead of decorating the sides with two transparent sides, and then a red, a yellow, a blue and a green side. The text of the article is not quite understandable because of this mishap, so I avail a colorfully updated version of the original article here. -/- . (shrink)

SUMMARY Major theories of philosophical psychology and philosophy of mind are examined on the basis of the fundamental questions of ontology, metaphysics, epistemology, semantics and logic. The result is the choice between language of eliminative reductionism and dualism, neither of which answers properly the relation between mind and body. In the search for a non–dualistic and non–reductive language, Wittgenstein’s notion of language–games as the representative links between language and the world is considered together with Peirce’s semeiosis of cognition. The result (...) is a redefined notion of cognition as the goal–oriented ability to instantiate strategies from the rules of the language–games. Cognition is considered within the four-dimensional languagegames: rules/strategies, primitive/complete language-games, family-resemblances/forms of life, and non-temporal continuum as the language-games’ modality. Cognition is seen as a continuum process of non–individualized elements that unites perception, volition, emotion, will and thought against the commonly accepted understandings of cognition in exclusive terms of perception and thinking. The alternative to the mind/body problem is the continuity of cognition where rules and strategies, syntax and semantics, are considered inseparable within language–games. This continuity of cognition is explained in terms of virtual (univocal) identity, replacing the old philosophical paradigm of the mind/body problem. -/- SOMMARIO Le teorie maggiori della psicologia filosofica e filosofia della mente sono esaminate a partire dalle questioni fondamentali di ontologia, metafisica, epistemologia, semantica e logica. Il risultato è la scelta tra un linguaggio riduzionista eliminativo e un dualismo che però non confronta in modo adeguato la relazione tra mente e corpo. Nella ricerca per un linguaggio non-dualistico e non-riduttivo, viene considerata la nozione del gioco linguistico di Wittgenstein come un legame rappresentativo tra il linguaggio e il mondo insieme con la semiosi cognitiva di Peirce. Il risultato è la nozione ridefinita della cognizione come abilità goal-orientata di creare le strategie dalle regole dei giochi linguistici. La cognizione è considerata entro le quattro dimensioni dei giochi linguistici: regole/strategie, giochi linguistici primitivi/completi, somiglianze di famiglia/forme di vita, e la continuità atemporale come la modalità dei giochi linguistici. La cognizione diventa un processo continuo degli elementi non-individualizzati che tende ad unificare la percezione, volizione, emozione, la volontà e il pensiero contro un concetto generalmente accettato di vedere la cognizione nei termini esclusivamente di percezione e di pensiero. L’alternativa al problema della mente/corpo è la continuità della cognizione, dove le regole e le strategie, la sintassi e la semantica, sono considerate inseparabili nei giochi linguistici. Questa continuità della cognizione è spiegata nei termini dell’identità virtuale (univoca) sostituendo un paradigma filosofico previo del problema della mente/corpo. (shrink)

Este no es un libro perfecto, pero es único, y si usted hojean las primeras 400 o así páginas, el último 300 (de unos 700) son un buen intento de aplicar lo que se sabe sobre el comportamiento a los cambios sociales en la violencia y las costumbres con el tiempo. El tema básico es: ¿Cómo controla y limita el cambio social nuestra genética? Sorprendentemente, no puede describir la naturaleza de la selección de parientes (aptitud inclusiva) que explica gran parte (...) de la vida social humana y animal. Él también (como casi todo el mundo) carece de un marco claro para describir la estructura lógica de la racionalidad (LSR-el término preferido de John Searle) que prefiero llamar la psicología descriptiva del pensamiento de orden superior (DPHOT). Debería haber dicho algo sobre las muchas otras formas de abusar y explotar a la gente y el planeta, ya que ahora son mucho más severos que hacer otras formas de violencia Casi Irrelevante. Ampliar el concepto de violencia para incluir el largo-consecuencias a término de la replicación de los genes de alguien, y tener una comprensión de la naturaleza de cómo funciona la evolución (es decir, la selección de parientes) proporcionará una perspectiva muy diferente sobre la historia, los acontecimientos actuales y cómo es probable que las cosas vayan en los próximos cientos de años. Uno podría comenzar señalando que la disminución de la violencia física sobre la historia se ha igualado (y hecho posible) por la violación despiadada en constante aumento del planeta (es decir, por la destrucción de las personas de su propio descendiente’s futuro). Pinker (como la mayoría de las personas la mayoría del tiempo) a menudo se distrae por las superficialidades de la cultura cuando es la biología lo que importa. Vea mis reseñas recientes de ' la conquista social de la tierra ' de Wilson y de los ' SuperCooperators ' de Nowak y Highfield aquí y en la red para obtener un breve resumen de la vacuidad de ' true Altruismo' (selección de grupo), y el funcionamiento de la selección de parientes y la inutilidad y la superficialidad de describir el comportamiento en términos culturales. Esta es la naturaleza clásica/tema de la crianza y la naturaleza triunfa-infinitamente. Lo que realmente importa es la violencia que se ha hecho a la tierra por el incesante aumento de la población y la destrucción de los recursos (debido a la medicina y la tecnología y la supresión de conflictos por la policía y los militares). Acerca de 200.000 más personas al día (otra las Vegas cada 10 días, otro los Angeles cada mes), el 6 Toneladas o así de la tierra que va al mar/persona/año – alrededor del 1% del total del mundo desapareciendo anualmente, etc. significan que a menos que ocurra algún milagro, la Biosfera y la civilización colapsarán en gran medida Durante próximos dos siglos, y habrá hambre, miseria y violencia de todo tipo en una escala asombrosa. Los modales, las opiniones y las tendencias de las personas para cometer actos violentos no son pertinentes a menos que puedan hacer algo para evitar esta catástrofe, y no veo cómo va a suceder. No hay espacio para los argumentos, y ningún punto o bien (sí soy un fatalista), así que voy a hacer algunos comentarios como si fueran hechos. No Imagine que tengo una participación personal en la promoción de un grupo a expensas de otros. Tengo 78, no tienen descendientes ni parientes cercanos y no se identifican con ningún grupo político, nacional o religioso y consideran que los que pertenezco por defecto son tan repulsivos como todos los demás. Los padres son los peores enemigos de la vida en la tierra y, tomando la visión amplia de las cosas, las mujeres son tan violentas como los hombres cuando uno considera el hecho de que la violencia de las mujeres (como la mayoría de los que hacen los hombres) se hace en gran medida en cámara lenta, a una distancia en el tiempo y el espacio y en su mayoría realizado por sus descendientes y por los hombres. Cada vez más, las mujeres tienen hijos sin importar si tienen una pareja y el efecto de detener a una mujer de la cría es en promedio mucho mayor que detener a un hombre, ya que son el cuello de botella reproductivo. Uno puede tomar la opinión de que las personas y sus crías merecen abundantemente cualquier miseria que se le presente y (con raras excepciones) los ricos y famosos son los peores delincuentes. Meryl Streep o Bill Gates o J. K Rowling y cada uno de sus hijos puede destruir 50 toneladas de tierra vegetal cada año por generaciones en el futuro, mientras que un granjero indio y su puede destruir 1 tonelada. Si alguien lo niega está bien, y a sus descendientes le digo "Bienvenido al infierno en la tierra" (WTHOE). El énfasis hoy en día siempre está en los derechos humanos, pero está claro que si la civilización tiene una oportunidad, las responsabilidades humanas deben reemplazar a los derechos humanos. Nadie obtiene derechos sin ser un ciudadano responsable y lo primero que esto significa es minimal destrucción ambiental. La responsabilidad más básica no son los niños a menos que su sociedad le pida que los produzca. Una sociedad o un mundo que permite a las personas reproducirse al azar siempre será explotada por los genes egoístas hasta que colapse (o llegue a un punto donde la vida es tan horrorosa que no vale la pena vivir). Si la sociedad continúa manteniendo los derechos humanos como principal, para sus descendientes uno puede decir con confianza "WTHOE". El mismo tipo de comentarios se aplican a su libro más reciente 'Englightenment Now' (Iluminacion Ahora), es decir, mejorar nuestra situación ahora garantiza el infierno en la tierra para nuestros descendientes. Aquellos que deseen un marco completo hasta la fecha para el comportamiento humano de la moderna Dos Sistemas Punto de Vista puede consultar mi libro 'La estructura lógica de la filosofía, la psicología, la mente y lenguaje En Ludwig Wittgenstein y John Searle ' 2Nd Ed (2019). Los interesados en más de mis escritos pueden ver 'Monos parlantes--filosofía, psicología, ciencia, religión y política en un planeta condenado--artículos y reseñas 2006-2017' 3a Ed (2019) y otras. (shrink)

In this paper, I will argue that there is a version of possibilism—inspired by the modal analogue of Kit Fine’s fragmentalism—that can be combined with a weakening of actualism. The reasons for analysing this view, which I call Modal Fragmentalism, are twofold. Firstly, it can enrich our understanding of the actualism/possibilism divide, by showing that, at least in principle, the adoption of possibilia does not correspond to an outright rejection of the actualist intuitions. Secondly, and more specifically, it (...) can enrich our understanding of concretism, by proving that, at least in principle, the idea that objects have properties in an absolute manner is compatible with transworld identity. (shrink)

The paper begins with a clarification of the notions of intuition (and, in particular, modal intuition), modal error, conceivability, metaphysical possibility, and epistemic possibility. It is argued that two-dimensionalism is the wrong framework for modal epistemology and that a certain nonreductionist approach to the theory of concepts and propositions is required instead. Finally, there is an examination of moderate rationalism’s impact on modal arguments in the philosophy of mind -- for example, Yablo’s disembodiment argument and Chalmers’s (...) zombie argument. A less vulnerable style of modal argument is defended, which nevertheless wins the same anti-materialist conclusions sought by these other arguments. (shrink)

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are (...) explored. (shrink)

This paper motivates and develops a novel semantic framework for deontic modals. The framework is designed to shed light on two things: the relationship between deontic modals and substantive theories of practical rationality and the interaction of deontic modals with conditionals, epistemic modals and probability operators. I argue that, in order to model inferential connections between deontic modals and probability operators, we need more structure than is provided by classical intensional theories. In particular, we need probabilistic structure that interacts directly (...) with the compositional semantics of deontic modals. However, I reject theories that provide this probabilistic structure by claiming that the semantics of deontic modals is linked to the Bayesian notion of expectation. I offer a probabilistic premise semantics that explains all the data that create trouble for the rival theories. (shrink)

Provisional draft, pre-production copy of my book “The Modal Future” (forthcoming with Cambridge University Press).

According to the simple modal account of essence, an object has a property essentially just in case it has it in every world in which it exists. As many have observed, the simple modal account is implausible for a number of reasons. This has led to various proposals for strengthening the account, for example, by adding a restriction to the intrinsic or sparse properties. I argue, however, that these amendments to the simple modal account themselves fail. Drawing (...) on lessons from these failures, I propose a new version of a modal account, inspired by Ruth Barcan Marcus's defense of the coherence of quantified modal logic, according to which an object has a property essentially just in case (i) it has it in every world in which it exists, (ii) the property is discriminating (or non-trivial), and (iii) the property is qualitative. The resulting account of essence does not face any of the standard objections other accounts face, and I defend it from other potential objections. (shrink)

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the (...) following results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal logic. (...) Those assumptions arguably include some necessitist principles. -/- Too often, philosophers have discussed ‘metaphysical’ modality — possibility, contingency, necessity — in isolation. Yet metaphysical modality is just a special case of a broad range of modalities, which we may call ‘objective’ by contrast with epistemic and doxastic modalities, and indeed deontic and teleological ones (compare the distinction between objective probabilities and epistemic or subjective probabilities). Thus metaphysical possibility, physical possibility and immediate practical possibility are all types of objective possibility. We should study the metaphysics and epistemology of metaphysical modality as part of a broader study of the metaphysics and epistemology of the objective modalities, on pain of radical misunderstanding. Since objective modalities are in general open to, and receive, natural scientific investigation, we should not treat the metaphysics and epistemology of metaphysical modality in isolation from the metaphysics and epistemology of the natural sciences. -/- In what follows, Section 1 gives a preliminary sketch of metaphysical modality and its place in the general category of objective modality. Section 2 reviews some familiar forms of scepticism about metaphysical modality in that light. Later sections explore a few of the many ways in which natural science deals with questions of objective modality, including questions of quantified modal logic. (shrink)

Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality.

We outline a neo-Meinongian framework labeled as Modal Meinongian Metaphysics (MMM) to account for the ontology and semantics of fictional discourse. Several competing accounts of fictional objects are originated by the fact that our talking of them mirrors incoherent intuitions: mainstream theories of fiction privilege some such intuitions, but are forced to account for others via complicated paraphrases of the relevant sentences. An ideal theory should resort to as few paraphrases as possible. In Sect. 1, we make this explicit (...) via two methodological principles, called the Minimal Revision and the Acceptability Constraint. In Sect. 2, we introduce the standard distinction between internal and external fictional discourse. In Sects. 3–5, we discuss the approaches of (traditional) Meinongianism, Fictionalism, and Realism—and their main troubles. In Sect. 6 we propose our MMM approach. This is based upon (1) a modal semantics including impossible worlds (Subsect. 6.1); (2) a qualified Comprehension Principle for objects (Subsect. 6.2); (3) a notion of existence-entailment for properties (Subsect. 6.3). In Sect. 7 we present a formal semantics for MMM based upon a representation operator. And in Sect. 8 we have a look at how MMM solves the problems of the three aforementioned theories. (shrink)

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically (...) significant” about metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (shrink)

We reply to various arguments by Otavio Bueno and Edward Zalta (‘Object Theory and Modal Meinongianism’) against Modal Meinongianism, including that it presupposes, but cannot maintain, a unique denotation for names of fictional characters, and that it is not generalizable to higher-order objects. We individuate the crucial difference between Modal Meinongianism and Object Theory in the former’s resorting to an apparatus of worlds, possible and impossible, for the representational purposes for which the latter resorts to a distinction (...) between two kinds of predication, exemplification and encoding. We show that encoding has fewer forerunners in the history of philosophy than Bueno and Zalta want, and that there’s a reason why the notion has been found baffling by some. (shrink)

The modal argument against materialism, in its most standard form, relies on a compatibility thesis to the effect that the physical truths are compatible with the absence of consciousness. I propose an alternative modal argument that relies on an incompatibility thesis: The existence of consciousness is incompatible with the proposition that the physical truths provide a complete description of reality. I show that everyone who accepts the premises of the standard modal argument must accept the premises of (...) the revised modal argument, but not vice versa. (shrink)

An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the `width' of the set theoretic universe, such as Cantor's continuum hypothesis. Within a higher-order framework I show that contingency about the (...) width of the set-theoretic universe refutes two orthodoxies concerning the structure of modal reality: the view that the broadest necessity has a logic of S5, and the "Leibniz biconditionals" stating that what is possible, in the broadest sense of possible, is what is true in some possible world. Nonetheless, I suggest that the underlying picture of modal set-theory is coherent and has attractions. (shrink)

We introduce and study a variety of modal logics of parallelism, orthogonality, and affine geometries, for which we establish several completeness, decidability and complexity results and state a number of related open, and apparently difficult problems. We also demonstrate that lack of the finite model property of modal logics for sufficiently rich affine or projective geometries (incl. the real affine and projective planes) is a rather common phenomenon.

This essay defends a novel form of virtue epistemology: Modal Virtue Epistemology. It borrows from traditional virtue epistemology the idea that knowledge is a type of skillful performance. But it goes on to understand skillfulness in purely modal terms — that is, in terms of success across a range of counterfactual scenarios. We argue that this approach offers a promising way of synthesizing virtue epistemology with a modal account of knowledge, according to which knowledge is safe belief. (...) In particular, we argue that the modal elements of the view offer important advantages over traditional virtue epistemology, which assigns a central explanatory role to aptness. At the same time, the virtue epistemological elements of the theory reveal new avenues for overcoming obstacles to traditional modal accounts of knowledge. Finally, we highlight the advantages of Modal Virtue Epistemology over alternative syntheses, such as Pritchard's (2012) hybrid approach. (shrink)

What does 'might' mean? One hypothesis is that 'It might be raining' is essentially an avowal of ignorance like 'For all I know, it's raining'. But it turns out these two constructions embed in different ways, in particular as parts of larger constructions like Wittgenstein's 'It might be raining and it's not' and Moore's 'It's raining and I don't know it', respectively. A variety of approaches have been developed to account for those differences. All approaches agree that both Moore sentences (...) and Wittgenstein sentences are classically consistent. In this paper I argue against this consensus. I adduce a variety of new data which I argue can best be accounted for if we treat Wittgenstein sentences as being classically inconsistent. This creates a puzzle, since there is decisive reason to think that 'Might p' is classically consistent with 'Not p'. How can it also be that 'Might p and not p' and 'Not p and might p' are classically inconsistent? To make sense of this situation, I propose a new theory of epistemic modals and their interaction with embedding operators. This account makes sense of the subtle embedding behavior of epistemic modals, shedding new light on their meaning and, more broadly, the dynamics of information in natural language. -/- . (shrink)