Eduardo Alejandro Barrio

Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively.

In this note we shall argue that Milne’s new effort does not refute Truthmaker Maximalism. According to Truthmaker Maximalism, every truth has a truthmaker. Milne has attempted to refute it using the following self-referential sentence M: This sentence has no truthmaker. Essential to his refutation is that M is like the Gödel sentence and unlike the Liar, and one way in which Milne supports this assimilation is through the claim that his proof is essentially object-level and not semantic. In Section 2, we shall argue that Milne is still begging the question against Truthmaker Maximalism. In Section 3, we shall argue that even assimilating M to the Liar does not force the truthmaker maximalist to maintain the ‘dull option’ that M does not express a proposition. There are other options open and, though they imply revising the logic in Milne’s reasoning, this is not one of the possible revisions he considers. In Section 4, we shall suggest that Milne’s proof requires an implicit appeal to semantic principles and notions. In Section 5, we shall point out that there are two important dissimilarities between M and the Gödel sentence. Section 6 is a brief summary and conclusion

In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic is to be identified with an infinite sequence of consequence relations holding between increasingly complex relata: formulae, inferences, metainferences, and so on. As a result, the present proposal allows not only to differentiate Classical Logic from ST, but also from other systems sharing with it their valid metainferences. Finally, we show how these results have interesting consequences for some topics in the philosophical logic literature, among them for the debate around Logical Pluralism. The reason being that the discussion concerning this topic is usually carried out employing a rivalry criterion for logics that will need to be modified in light of the present investigation, according to which two logics can be non-identical even if they share the same valid inferences.

In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut involving semantic notions. In this article we intend to meet the challenge of answering how to regain all the safe instances of Cut, in the language of the theory, making essential use of a unary recovery operator. To fulfill this goal, we will work within the so-called Goodship Project, which suggests that in order to have nontrivial naïve theories it is sufficient to formulate the corresponding self-referential sentences with suitable biconditionals. Nevertheless, a secondary aim of this article is to propose a novel way to carry this project out, showing that the biconditionals in question can be totally classical. In the context of this article, these biconditionals will be essentially used in expressing the self-referential sentences and, thus, as a collateral result of our work we will prove that none of the recoveries expected of the target theory can be nontrivially achieved if self-reference is expressed through identities.

In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences—and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical systems, and propose an alternative of our own. After that, we consider a number of objections to our account and evaluate a substantially different approach to the same problem.

When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in a clear sense, non-identical to it. We argue that this phenomenon can be generalized, given the existence of logics which coincide with Classical Logic regarding a number of metainferential levels—although they are, again, clearly different systems. We claim this highlights the need to arrive at a more refined version of the Collapse Argument, which we discuss at the end of the paper.

A theory of truth is usually demanded to be consistent, but -consistency is less frequently requested. Recently, Yatabe has argued in favour of -inconsistent first-order theories of truth, minimising their odd consequences. In view of this fact, in this paper, we present five arguments against -inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known -inconsistent theories of truth: the classical theory of symmetric truth FS and the non-classical theory of naïve truth based on ᴌukasiewicz infinitely valued logic: PAᴌT.

In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has argued that such formalization shows that Yablo’s Paradox involves implicit circularity. In the same direction, Beall (2001) has introduced epistemic factors in this discussion. Even more, Priest has also argued that the introduction of infinitary reasoning would be of little help. Finally, one could reject definitions of circularity in term of fixed-point adopting non-well-founded set theory. Then, one could hold that the Yablo paradox and the Liar paradox share the same non-well-founded structure. So, if the latter is circular, the first is too. In all such cases, I survey Cook’s approach (2006, forthcoming) on those arguments for the charge of circularity. In the end, I present my position and summarize the discussion involved in this volume. En este artículo, describo y examino los principales resultados vinculados a la formalización de la paradoja de Yablo en la aritmética. Aunque es natural suponer que hay una representación correcta de la paradoja en la aritmética de primer orden, hay algunos resultados técnicos que hacen surgir dudas acerca de esta posibilidad. Más aún, presento algunos argumentos que han cuestionado que la construcción de Yablo no sea circular. Así, Priest (1997) ha argumentado que la formalización de la paradoja de Yablo en la aritmética de primer orden muestra que la misma involucra implícitamente circularidad. En la misma dirección, Beall (2001) ha introducido factores epistémicos en esta discusión. Más aún, Priest ha también argumentado que la introducción de razonamiento infinitario como complemento de la formalización en la aritmética sería de poca ayuda. Finalmente, se podría rechazar todo intento de dar definiciones de circularidad en términos de puntos fijos adoptando teoría de conjuntos infundados. Entonces, se podría sostener que la paradoja de Yablo y la del mentiroso comparten la misma estructura infundada. Por eso, si la última es circular, también lo es la primera. En todos los casos, presento el enfoque de Roy Cook (2006, en prensa) sobre estos argumentos que atribuyen circularidad a la construcción de Yablo. En el final, presento mi posición y un breve resumen de la discusión involucrada en este volumen

In this paper, we present a non-trivial and expressively complete paraconsistent naïve theory of truth, as a step in the route towards semantic closure. We achieve this goal by expressing self-reference with a weak procedure, that uses equivalences between expressions of the language, as opposed to a strong procedure, that uses identities. Finally, we make some remarks regarding the sense in which the theory of truth discussed has a property closely related to functional completeness, and we present a sound and complete three-sided sequent calculus for this expressively rich theory.

Rejecting the Cut rule has been proposed as a strategy to avoid both the usual semantic paradoxes and the so-called v-Curry paradox. In this paper we consider if a Cut-free theory is capable of accurately representing its own notion of validity. We claim that the standard rules governing the validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a serious problem: an internalized version of Cut can be proved for a Curry-like sentence. We also evaluate a number of possible ways of escaping this difficulty.

El contenido de la presente discusión de Análisis Filosófico surge a partir de diversas actividades organizadas por mí en SADAF y en la UBA. En primer lugar, Roy Cook dictó en SADAF el seminario de investigación intensivo On Yablo's Paradox durante la última semana de julio de 2011. En el seminario, el profesor Cook presentó el manuscrito aún sin finalizar de su libro The Yablo Paradox: An Essay on Circularity, Oxford, Oxford UP, (en prensa). Extensas y apasionantes discusiones ocurrieron durante esos encuentros sobre circularidad y construcciones infinitarias. Fue en ese tiempo, donde me surgió la idea de editar una discusión sobre las ideas que Cook defiende en ese trabajo. El proyecto era una extensión natural del trabajo que veníamos realizando con mi grupo de investigación en temas vinculados al concepto de verdad, autorreferencia y paradojas. Luego, durante el segundo cuatrimestre de 2011, dicté el seminario La paradoja de Yablo, en el instituto de filosofía de la UBA. Algunos de los borradores de los artículos que aparecen en el presente volumen tienen su origen en este curso. Finalmente, invité por segunda vez al profesor Cook al Symposium on Yablo's Paradox realizado en SADAF en julio de 2012. En esta oportunidad, se presentaron las versiones finales de los artículos de Lavinia Picollo, Paula Teijeiro, Federico Pailos, Diego Tajer, Lucas Rosenblatt e Ignacio Ojea que se incluyen a continuación. El encuentro incluyó las inteligentes réplicas del profesor Cook y profundas discusiones sobre los mencionados temas lógicosemánticos. Quiero agradecer a todos los integrantes del Gaf[log] que participaron activamente en las mencionadas actividades, ya sea en la publicación posterior o en los coloquios y seminarios que le dieron origen. Agradezco al Comité editorial de Análisis Filosófico, en especial a Alberto Moretti, quienes apoyaron desde sus comienzos este proyecto. Finalmente, y de manera especial, quiero expresar mi gratitud al profesor Roy Cook, quien no sólo apoyó e inspiró el proyecto desde sus comienzos, sino que además compartió generosamente sus ideas y las discutió con estimulante pasión.

In this paper, I attempt to throw some light on modal realism. Since it is David Lewis who has put forward the best arguments for thar position, I focus on his work. In the first, I point out that his approach does not provide an adequate account for the intuitive lack of symmetry between the actual and the possible. To begin with, I try to show that the strategy of appealing to both the spatio-temporal network and causality is not at all satisfactory. Secondly, I criticize the argument for modal realism that is based on theoretical benefits. Then, I defend the view that Lewis' indexical analysis of the concept of actuality does not satisfy his own criterion of acceptability: an analysis of actuality should account for the intuitions about our actual word. I claim thet Lewis' objections to other positions can be raised against his own position. Finally, I conclude that, even though Lewis is right in claiming that actualist conceptions do not explain why the possible is not part of the actual, the realist conception fail to account for the special ontological status that we intuitively grant to our own world.

The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω-inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, I show that in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω- inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth.

Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate together with classical logic. Nevertheless, there are some interesting issues concerning the set of metainferences validated by this logic. In this paper, we show that this logic, once it is adequately understood, is weaker than classical logic. Moreover, the logic is in a way similar to the paraconsistent logic LP

Many authors have considered that the notions of paraconsistency and dialetheism are intrinsically connected, in many cases, to the extent of confusing both phenomena. However, paraconsistency is a formal feature of some logics that consists in invalidating the rule of explosion, whereas dialetheism is a semantical/ontological position consisting in accepting true contradictions. In this paper, we argue against this connection and show that it is perfectly possible to adopt a paraconsistent logic and reject dialetheism, and, moreover, that there are examples of non-paraconsistent logics that can be interpreted in a dialetheic way.

It is widely accepted that a theory of truth for arithmetic should be consistent, but -consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting -inconsistent theories of truth are considered: the revision theory of nearly stable truth T # and the classical theory of symmetric truth FS. Briefly, we present some conceptual problems with ω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.

En este artículo, me propongo exponer algunas dificultades relacionadas con la posibilidad de que la Teoría de Modelos pueda constituirse en una Teoría General de la Interpretación. Específicamente la idea que sostengo es que lo que nos muestra la Paradoja de Orayen es que las interpretaciones no pueden ser ni conjuntos ni objetos. Por eso, una elucidación del concepto intuitivo de interpretación, que apele a este tipo de entidades, está condenada al fracaso. De manera secundaria, muestro que no hay algún supuesto conjuntista que sea imprescindible para que surja la mencionada paradoja: sólo se necesita que las interpretaciones sean objetos. Voy a argumentar que si las interpretaciones son objetos, tal como lo supone la posibilidad de cuantificar sobre las mismas para poder dar una caracterización satisfactoria de consecuencia lógica, la au-toaplicación (como un caso de aplicación de los recursos semánticos de la teoría de modelos para encontrar una interpretación con máxima generalidad) es imposible. Finalmente, discuto cada una de las dos soluciones que el propio Orayen imaginó frente a su paradoja, y muestro que cada una posee diferentes dificultades.In this paper, I intend to present some problems to construe the Model Theory as a Theory of Interpretation. Specifically, I am going to defend that, according to the Paradox of Orayen, interpretations can not be neither set nor object. Thus, an explication of the intuitive concept of interpretation that appeals to these types of entities will be condemned to failure. Secondary, I will show that there is not any like-set assumption indispensable to get rise to that paradox: only all is needed is the assumption that interpretations are objects. I am going to argue that if interpretations are objects, as it is assumed by the possibility of quantifying over interpretations in order to offer an satisfactory characterization of logical consequence, self-application (as a case of application of semantics resources of the Model Theory for finding a interpretation with absolute generality) is not possible. Eventually, I will discuss both of the solutions provided by Orayen to his paradox and I will support that both have different difficulties

Belnap and Gupta have recently maintained that truth is a circular concept: its extension cannot be established without being previously hypothesized. This has led Yaqub to claim that the circular character in question cannot be made compatible with the thesis that semantic properties tlre supervenient ones. Belnap and Gupta have explicitly denied sitch a claim any plausibility. In this paper, I offir some new arguments in support of Yaqub 's position. Such arguments are based on an analysis of some aspects of Belnap and Gupta's theory that, as for as I know, had not been considered before.

Anti-exceptionalism about logic states that logical theories have no special epistemological status. Such theories are continuous with scientific theories. Contemporary anti-exceptionalists include the semantic paradoxes as a part of the elements to accept a logical theory. Exploring the Buenos Aires Plan, the recent development of the metainferential hierarchy of ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-logics shows that there are multiple options to deal with such paradoxes. There is a whole ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-based hierarchy, of which LP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {LP}}$$\end{document} and ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document} themselves are only the first steps. This means that the logics in this hierarchy are also options to analyze the inferential patterns allowed in a language that contains its own truth predicate. This paper explores these responses analyzing some reasons to go beyond the first steps. We show that LP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {LP}}$$\end{document}, ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document} and the logics of the ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-hierarchy offer different diagnoses for the same evidence: the inferences and metainferences the agents endorse in the presence of the truth-predicate. But even if the data are not enough to adopt one of these logics, there are other elements to evaluate the revision of classical logic. Which is the best explanation for the logical principles to deal with semantic paradoxes? How close should we be to classical logic? And mainly, how could a logic obey the validities it contains? From an anti-exceptionalist perspective, we argue that ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-metainferential logics in general—and STTω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {STT}}_{\omega }$$\end{document} in particular—are the best available options to explain the inferential principles involved with the notion of truth.

En este trabajo, me propongo discutir la plausibilidad de la tesis de que es posible captar las características modales del concepto intuitivo de consecuencia a través de un concepto de consecuencia definido generalizando sobre interpretaciones. Desde mi perspectiva, las argumentaciones que han ofrecido aquellos que, como Ray, quieren salvar el salto de lo general a lo modal, mostrando que hay suficientes interpretaciones como para representar las características modales de la noción preteórica de consecuencia, poseen un mismo tipo de limitación. La misma es producto de la imposibilidad de contar con una interpretación de los cuantificadores suficientemente general como para abarcar sin restricción contextual alguna, la totalidad de las interpretaciones. Al mismo tiempo, sostengo que estos problemas están emparentados con los límites expresivos propios de la estrategia que intenta ofrecer una teoría matemática precisa del concepto de interpretación por medio de algún tipo de cuantificación sobre estructuras (sean estas conjuntistas o no). Por eso, tales límites expresivos no tienen que ver especialmente con los rasgos modales propiamente dichos del concepto de consecuencia, sino con la cuantificación irrestricta que el análisis requeriría para ser adecuado.

It is widely accepted that classical logic is trivialized in the presence of a transparent truth-predicate. In this paper, we will explain why this point of view must be given up. The hierarchy of metainferential logics defined in Barrio et al. and Pailos recovers classical logic, either in the sense that every classical inferential validity is valid at some point in the hierarchy ), or because a logic of a transfinite level defined in terms of the hierarchy shares its validities with classical logic. Each of these logics is consistent with transparent truth—as is shown in Pailos —, and this suggests that, contrary to standard opinions, transparent truth is after all consistent with classical logic. However, Scambler presents a major challenge to this approach. He argues that this hierarchy cannot be identified with classical logic in any way, because it recovers no classical antivalidities. We embrace Scambler’s challenge and develop a new logic based on these hierarchies. This logic recovers both every classical validity and every classical antivalidity. Moreover, we will follow the same strategy and show that contingencies need also be taken into account, and that none of the logics so far presented is enough to capture classical contingencies. Then, we will develop a multi-standard approach to elaborate a new logic that captures not only every classical validity, but also every classical antivalidity and contingency. As a€truth-predicate can be added to this logic, this result can be interpreted as showing that, despite the claims that are extremely widely accepted, classical logic does not trivialize in the context of transparent truth.

In different papers, Carnielli, W. & Rodrigues, A., Carnielli, W. Coniglio, M. & Rodrigues, A. and Rodrigues & Carnielli, present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE and the second—that is a conservative extension of BLE—is named LETJ. Roughly, BLE and LETJ are two non-classical logics in which the Laws of Explosion and Excluded Middle are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic of Formal Inconsistency. This means that there is an operator that, roughly speaking, identifies a formula as having classical behavior. Both systems are motivated by the idea that there are different conditions for accepting or rejecting a sentence of our natural language. So, there are some special introduction and elimination rules in the theory that are capturing different conditions of use. Rodrigues & Carnielli’s paper has an interesting and challenging idea. According to them, BLE and LETJ are incompatible with dialetheia. It seems to show that these paraconsistent logics cannot be interpreted using truth-conditions that allow true contradictions. In short, BLE and LETJ talk about conflicting evidence avoiding to talk about gluts. I am going to argue against this point of view. Basically, I will firstly offer a new interpretation of BLE and LETJ that is compatible with dialetheia. The background of my position is to reject the one canonical interpretation thesis: the idea according to which a logical system has one standard interpretation. Then, I will secondly show that there is no logical basis to fix that Rodrigues & Carnielli’s interpretation is the canonical way to establish the content of logical notions of BLE and LETJ. Furthermore, the system LETJ captures inside classical logic. Then, I am also going to use this technical result to offer some further doubts about the one canonical interpretation thesis.

Robert Brandom has maintained that Wittgenstein is wrong in denying the notion of interpretation any theoretical role in the task of accounting for our linguistic practices. In this paper, I intend to throw some doubts on this thesis. First of all, I argue that Brandom´s objection is unfair: in my opinion, giving up the concept of interpretation does not amount to condemning oneself to silence on rule – governed practices. Secondly, I try to show that Brandom´s appeal to the concept of implicit interpretation is not without problems in as far as it involves the thesis that all the participants in a certain practice may be wrong about the interpretation of its rules. This makes room for a dichotomy between what we do and what we say we do, which should be thoroughly avoided

En este artículo, tengo dos objetivos distintos. En primer lugar, mostrar que no es una buena idea tener una teoría de la verdad que, aunque consistente, sea omega-inconsistente. Para discutir este punto, considero un caso particular: la teoría de Friedman-Sheard FS. Argumento que en los lenguajes de primer orden omega inconsistencia implica que la teoría de la verdad no tiene modelo estándar. Esto es, no hay un modelo cuyo dominio sea el conjunto de los números naturales en el cual esta teoría de la verdad pueda tener una interpretación consistente. En ese sentido, la introducción del predicado veritativo no mantiene la ontología estándar. Además, cuando se considera un lenguaje de orden superior, la situación es aun peor. En teorías de segundo orden con semántica estándar, la misma introducción produce una teoría que no tiene modelo. Por eso, si la omega-inconsistencia es un mal síntoma, la insatisfacibilidad de una teoría es aun peor. En segundo lugar, propongo abandonar el principio de unión de teorías FSn y aceptar una extensibilidad indefinida de teorías FS0, FS1, FS2, FS3,.... De acuerdo a mi punto de vista, la secuencia de teorías tiene las mismas virtudes que FS sin sus desagradables consecuencias. In this paper, I have two different purposes. Firstly, I want to show that it's not a good idea to have a theory of truth that is consistent but omega-inconsistent. In order to bring out this point, it is useful to consider a particular case: FS. I argue that in First-order languages omega-inconsistency implies that a theory of truth has not standard model. Then, there is no model whose domain is the set of natural numbers in which this theory of truth could acquire a consistent interpretation. So, in theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. I add that in Higher-order languages the situation is even worst. In second order theories with standard semantic the same introduction produces a theory that doesn't have a model. So, if an omega-inconsistent theory of truth is bad, an unsatisfiable theory is really bad. Secondly, I propose to give up the union principle of theories FSn and accept an indefinite extensibility of theories FS0, FS1, FS2, FS3,... According to my view, the sequence of theories has the same virtues of FS without its disgusting consequences

According to Etchemendy, in attempting to offer an analysis of the modal features of the intuitive concept of logical consequence, Tarski has committed a modal fallacy. In this paper, I consider the thesis according to it is posible to analyze the modals properties of concept of logical consequence through of a generalization on set-theoretical interpretations. As is known, some philosophers have tried to argue for the transit from the general to the modal by showing that there are enough settheoretic interpretations so as to be able to represent the modal features of the intuitive concept of consequence. As is also known, those people have encountered a lot of difficulties. In the present paper, I will try to show that those problems are related not with the specific possibility of accounting for the modal features by means of a set-theoretic notion of model but with the possibility of coming up with a precise mathematical theory for the concept of interpretation, and, as such, they can be solved by way of appealing to the usual solutions to this problem

The concept of _substructural logic_ was originally introduced in relation to limitations of Gentzen’s structural rules of Contraction, Weakening and Exchange. Recent years have witnessed the development of substructural logics also challenging the Tarskian properties of Reflexivity and Transitivity of logical consequence. In this introduction we explain this recent development and two aspects in which it leads to a reassessment of the bounds of classical logic. On the one hand, standard ways of defining the notion of logical consequence in classical logic naturally induce substructural logics when admitting more than two truth values; on the other hand, these substructural logics give rise to hierarchies of _metainferences_ that can be used to approximate classical logic at different levels.

¿Podemos adoptar una regla de inferencia como si fuera una hipótesis e inferir algo en virtud de esa regla? ¿Podemos revisar nuestras reglas y principios lógicos en virtud de la evidencia disponible? El antiexcepcionalismo lógico desafía la idea de que la lógica es excepcional y la vincula con el resto de las teorías científicas. Sin embargo, el desafío de la adopción planteado por Kripke y Padró imponen límites a esta concepción. En esta sección, se exploran distintos aspectos vinculados a la imposibilidad de adoptar reglas, el antiexcepcionalismo, la revisión y la normatividad de la lógica.