The critics of paraconsistency and of many-valuedness and the geometry of oppositions

In 1995 Slater argued both against Priest’s paraconsistent system LP (1979) and against paraconsistency in general, invoking the fundamental opposition relations ruling the classical logical square. Around 2002 Béziau constructed a double defence of paraconsistency (logical and philosophical), relying, in its philosophical part, on Sesmat’s (1951) and Blanche’s (1953) “logical hexagon”, a geometrical, conservative extension of the logical square, and proposing a new (tridimensional) “solid of opposition”, meant to shed new light on the point raised by Slater. By using n-opposition theory (NOT) we analyse Beziau’s anti-Slater move and show both its right intuitions and its technical limits. Moreover, we suggest that Slater’s criticism is much akin to a well-known one by Suszko (1975) against the conceivability of many-valued logics. This last criticism has been addressed by Malinowski (1990) and Shramko and Wansing (2005), who developed a family of tenable logical counter-examples to it: trans-Suszkian systems are radically many-valued. This family of new logics has some strange logical features, essentially: each system has more than one consequence operator. We show that a new, deeper part of the aforementioned geometry of logical oppositions (NOT), the “logical poly-simplexes of dimension m”, generates new logical-geometrical structures, essentially many-valued, which could be a very natural (and intuitive) geometrical counterpart to the “strange”, new, non-Suszkian logics of Malinowski, Shramko and Wansing. By a similar move, the geometry of opposition therefore sheds light both on the foundations of paraconsistent logics and on those of many-valued logics

Negación y lógicas paraconsistentes

En este traba¡o expondremos el argumento en contra de la posibilidad de la existencia de verdaderas lógicas paraconsistentes y la respuesta de F Paoli [Paoli, 2003] a este argumento. Además, presentaremos un nuevo argumento -inspirado, como el de Paoli, en una sugerencia de Susan Haack- en contra de la tesis de la imposibilidad de la existencia de verdaderas lógicas paraconsistentes

Disagreement about logic

Under embargo until: 2021-02-08What do we disagree about when we disagree about logic? On the face of it, classical and nonclassical logicians disagree about the laws of logic and the nature of logical properties. Yet, sometimes the parties are accused of talking past each other. The worry is that if the parties to the dispute do not mean the same thing with ‘if’, ‘or’, and ‘not’, they fail to have genuine disagreement about the laws in question. After the work of Quine, this objection against genuine disagreement about logic has been called the meaning-variance thesis. We argue that the meaning-variance thesis can be endorsed without blocking genuine disagreement. In fact, even the type of revisionism and nonapriorism championed by Quine turns out to be compatible with meaning-variance.acceptedVersio

En defensa del argumento finitista

En este artículo, analizo las principales respuestas que se han dado al argumento finitista de Etchemendy (1990), y muestro que ninguna de ellas es exitosa. Primero, describo y critico las propuestas que intentan resolverlo apelando a consideraciones modales. Estas soluciones fallan porque presuponen un finitismo demasiado débil, donde se acepta la existencia de infinitos conjuntos o de mundos posibles con infinitos objetos. Pero hay versiones más fuertes del finitismo que reintroducen el problema. Luego considero las soluciones que apelan a categorías semánticas. Una de ellas categoriza incorrectamente este problema como un desacuerdo sobre el significado de los cuantificadores. La otra solución falla porque, si fuera tomada en serio, tendría efectos muy nocivos para la lógica en general. Finalmente argumento que la mejor solución es morder la bala y aceptar que la lógica no debería ser fuertemente independiente de algunos asuntos que tradicionalmente fueron considerados como "extralógicos".In this paper, I analyze the main replies that have been given to Etchemendy’s (1990) finitist argument, and I show that none of them is successful. First, I describe and criticize the proposals that try to solve the problem by appealing to modal considerations. These solutions fail because they presuppose a very weak finitism, where the existence of infinitely many sets, or possible words with infinitely many objects, is accepted. But there are stronger versions of finitism that reintroduce the problem. Then I consider the solutions which appeal to semantical categories. One of them incorrectly categorizes the problem as a disagreement in the meaning of the quantifiers. The other fails because, if taken seriously, it would have harmful effects on logic in general. Finally I argue that the best solution is to bite the bullet and accept that logic shouldn’t be strongly independent from some issues which were traditionally considered as ‘extra-logical’.Fil: Tajer, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentin

More Reflections on Consequence

This special issue collects together nine new essays on logical consequence :the relation obtaining between the premises and the conclusion of a logically valid argument. The present paper is a partial, and opinionated,introduction to the contemporary debate on the topic. We focus on two influential accounts of consequence, the model-theoretic and the proof-theoretic, and on the seeming platitude that valid arguments necessarilypreserve truth. We briefly discuss the main objections these accounts face, as well as Hartry Field’s contention that such objections show consequenceto be a primitive, indefinable notion, and that we must reject the claim that valid arguments necessarily preserve truth. We suggest that the accountsin question have the resources to meet the objections standardly thought to herald their demise and make two main claims: (i) that consequence, as opposed to logical consequence, is the epistemologically significant relation philosophers should be mainly interested in; and (ii) that consequence is a paradoxical notion if truth is

In Difesa del Principio di Non Contraddizione

Questo lavoro ha come obiettivo fondamentale l\u2019elaborazione di una difesa del principio di non contraddizione (PNC), a fronte dell\u2019attacco portato dal dialeteismo, la dottrina che rivendica l\u2019esistenza di contraddizioni vere. Il primo capitolo assesta gli oggetti di discussione principali, occupandosi di stabilire che cos\u2019\ue8 (PNC) e che cos\u2019\ue8 una contraddizione. Distinguo cinque versioni fondamentali di (PNC) e della contraddizione, e sottolineo l\u2019importanza, in tutte le versioni, della condizione dell\u2019identit\ue0 dei rispetti. Nel secondo capitolo presento quello che \ue8 stato tradizionalmente considerato l\u2019argomento pi\uf9 forte contro le contraddizioni, il principio ex contradictione quodlibet (ECQ). Poi introduco la logica paraconsistente e il dialeteismo e delineo la loro relazione. Passo quindi al vaglio diversi sistemi di logica paraconsistente, e mostro che diversi tentativi di costruire contraddizioni, per quanto eterogenei, sono strutturalmente accomunati da una violazione dell\u2019identit\ue0 dei rispetti che segna nello stesso modo il loro fallimento. Nel terzo capitolo esamino la logica paraconsistente approntata da Graham Priest, argomentando che \ue8 superiore a tutte le logiche paraconsistenti discusse nel capitolo 2. Presento due argomentazioni contro la logica paraconsistente sviluppate da David Lewis e Hartley Slater, e le repliche fornite da Bryson Brown, Francesco Paoli e Greg Restall. Quindi miro a rafforzare la linea di difesa della paraconsistenza tracciata da Restall. Il mio contributo conduce al dilemma generale per il difensore di (ECQ). Il quarto capitolo \ue8 preliminare alla difesa vera e propria di (PNC) che concerto nel quinto capitolo. Qui affronto il problema se sia possibile difendere (PNC). Mostro in che modo la natura stessa della critica, quale \ue8 solitamente concepita, dia adito all\u2019accusa dell\u2019impossibilit\ue0 di criticare il dialeteismo, e ripercorro la strategia con cui Priest si impegna a disinnescarla. Mi concentro poi su alcune osservazioni sviluppate da Dutilh Novaes, che rinfocolano il dubbio sulla possibilit\ue0 di criticare il dialeteismo sollevando il dubbio che il dibattito fra il dialeteista e il difensore di (PNC) sia un dibattito verbale, e fugo questo dubbio. Nel quinto capitolo lancio i miei due attacchi contro il dialeteismo. Il primo attacco dimostra che siamo razionalmente giustificati a rigettare una qualsiasi contraddizione in una qualsiasi circostanza, e questo giustifica il rigetto del dialeteismo. Il secondo attacco inizia col concedere che ci siano enunciati della forma "alfa",\uac"alfa" che sono entrambi veri, e dimostra che se due enunciati della forma "alfa",\uac"alfa" sono entrambi veri allora non possono essere contraddittori, per poi concludere che non ci possono essere contraddizioni che siano vere

La diferencia entre lógicas y el cambio de significado de las conectivas: un enfoque categorista

Corrección de errores en Theoria 72 : 369 (2011)En este artículo tratamos de hacer plausible la hipótesis de que las conectivas de diferentes lógicas no necesariamente difieren en significado. Utilizando el tratamiento categorista de las conectivas, argumentaremos contra la tesis quineana de que la diferencia de lógicas implica diferencia de significado entre sus conectivas, y ubicamos el cambio de tema en la diferencia de objetos más bien que en una tal diferencia de significado. Finalmente, intentamos mostrar que ese tratamiento categorista es una forma de minimalismo semántico, de acuerdo con el cual no todos los elementos semánticos usuales son relevantes para determinar el significado de las conectivas