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131Meta-Classical Non-Classical LogicsReview of Symbolic Logic. forthcoming.Recently, it has been proposed to understand a logic as containing not only a validity canon for inferences but also a validity canon for metainferences of any finite level. Then, it has been shown that it is possible to construct infinite hierarchies of "increasingly classical" logics—that is, logics that are classical at the level of inferences and of increasingly higher metainferences—all of which admit a transparent truth predicate. In this paper, we extend this line of investigation by taki…Read more
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20The logics of a universal languageAsian Journal of Philosophy 3 (1): 1-22. 2024.Semantic paradoxes pose a real threat to logics that attempt to be capable of expressing their own semantic concepts. Particularly, Curry paradoxes seem to show that many solutions must change our intuitive concepts of truth or validity or impose limits on certain inferences that are intuitively valid. In this way, the logic of a universal language would have serious problems. In this paper, we explore a different solution that tries to avoid both limitations as much as possible. Thus, we argue …Read more
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22Reglas lógicas y cambio de práctica inferencialAnálisis Filosófico 42 (2): 205-211. 2022.¿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 i…Read more
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20El problema de la adopción de reglas lógicasAnálisis Filosófico 42 (1): 33-42. 2022.¿Seguimos reglas de inferencia al razonar? Por más intuitiva que resulte la respuesta positiva a esta pregunta, hay una serie de dificultades para vincular reglas lógicas y prácticas inferenciales. El Problema de la Adopción de Reglas de Inferencia constituye un desafío para todo aquel que proponga que podemos seguir nuevos patrones inferenciales a partir del reconocimiento de reglas. En esta sección temática se exploran diversos asuntos conectados a si podemos seguir un nuevo patrón inferencial…Read more
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738Substructural logics, pluralism and collapseSynthese 198 (Suppl 20): 4991-5007. 2018.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 cl…Read more
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18Volume II: New advances in Logics of Formal InconsistencyLogic Journal of the IGPL 28 (5): 845-850. 2020.
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969Truthmaker Maximalism defended againAnalysis 75 (1): 3-8. 2015.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 Sec…Read more
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18A SaulAnálisis Filosófico 42 (2): 203. 2022.Esta sección temática constituye la segunda discusión sobre el desafío de la adopción de reglas lógicas publicado en Análisis Filosófico. Al igual que la primera, esta colección de artículos puede verse como el resultado de la colaboración internacional que durante más de dos décadas hemos mantenido entre el Saul Kripke Center (SKC) y el IIF-SADAF-CONICET. Y más precisamente, entre Saul, Romina y el grupo de lógica de Buenos Aires (BA-Logic). Visitas, seminarios, workshops, proyectos internacio…Read more
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24Editorial Introduction: Substructural Logics and MetainferencesJournal of Philosophical Logic 51 (6): 1215-1231. 2022.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…Read more
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37Why a Logic is not only its Set of Valid InferencesAnálisis Filosófico 41 (2): 261-272. 2021.The main idea that we want to defend in this paper is that the question of what a logic is should be addressed differently when structural properties enter the game. In particular, we want to support the idea according to which it is not enough to identify the set of valid inferences to characterize a logic. In other words, we will argue that two logical theories could identify the same set of validities, but not be the same logic.
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59Anti-exceptionalism, truth and the BA-planSynthese 199 (5-6): 12561-12586. 2021.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{amsb…Read more
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54Validities, antivalidities and contingencies: A multi-standard approachJournal of Philosophical Logic 51 (1): 75-98. 2021.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 …Read more
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17Volume I: Recovery operators in logics of formal inconsistencyLogic Journal of the IGPL 28 (5): 615-623. 2020.There are a considerable number of logics that do not seem to share the same inferential principles. Intuitionistic logics do not include the law of the exclude.
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12Introducing consistency in a dialogical framework for paraconsistent logicLogic Journal of the IGPL 28 (5): 953-972. 2020.The logics of formal inconsistency are logics tolerant to some amount of contradiction, but in which some versions of explosion still hold. The main result of this paper is a reconstruction of two such logics in the dialogical framework. By doing so, we achieve two things. On the one hand, we provide a formal approach to argumentative situations where some contradictions may occur while keeping the idea that there may still be situations in which some propositions are ‘safe’ in the sense of immu…Read more
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750(Meta)inferential levels of entailment beyond the Tarskian paradigmSynthese 198 (S22): 5265-5289. 2019.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…Read more
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806A Hierarchy of Classical and Paraconsistent LogicsJournal of Philosophical Logic 49 (1): 93-120. 2020.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 cla…Read more
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1321What is a Paraconsistent Logic?In Walter Carnielli & Jacek Malinowski (eds.), Contradictions, from Consistency to Inconsistency, Springer. 2018.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…Read more
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33Models & Proofs: LFIs Without a Canonical InterpretationsPrincipia: An International Journal of Epistemology 22 (1): 87-112. 2018.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 Form…Read more
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3Expresabilidad, validez y recursos lógicosCritica 46 (138): 3-36. 2014.El objetivo de este artículo es investigar diversos resultados limitativos acerca del concepto de validez. En particular, argumento que ninguna teoría lógica de orden superior con semántica estándar puede tener recursos expresivos suficientes como para capturar su propio concepto de validez. Además, muestro que la lógica de la verdad transparente que Hartry Field desarrolló recientemente conduce a resultados limitativos similares.
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758A recovery operator for nontransitive approachesReview of Symbolic Logic 13 (1): 80-104. 2020.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 …Read more
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83Paraconsistency and its Philosophical InterpretationsAustralasian Journal of Logic 15 (2): 151-170. 2018.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 logi…Read more
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521Truth without standard models: some conceptual problems reloadedJournal of Applied Non-Classical Logics 28 (1): 122-139. 2017.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 the…Read more
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435A paraconsistent route to semantic closureLogic Journal of the IGPL 25 (4): 387-407. 2017.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 pre…Read more
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13Modelos, autoaplicación y máxima generalidad (Models, self-application and absolute generality)Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 22 (2): 133-152. 2007.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…Read more
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40Theories of Truth without Standard Models and Yablo’s SequencesStudia Logica 96 (3): 375-391. 2010.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 wit…Read more
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27Reglas, expresión y objetividadManuscrito 25 (1): 115-136. 2002.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 …Read more
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20Collapse, Plurals and SetsPrincipia: An International Journal of Epistemology 18 (3): 419. 2014.This paper raises the question under what circumstances a plurality forms a set. My main point is that not always all things form sets. A provocative way of presenting my position is that, as a result of my approach, there are more pluralities than sets. Another way of presenting the same thesis claims that there are ways of talking about objects that do not always collapse into sets. My argument is related to expressive powers of formal languages. Assuming classical logic, I show that if all pl…Read more