Eduardo Barrio | National Scientific and Technical Research Council (original) (raw)
Papers by Eduardo Barrio
![Research paper thumbnail of RESEÑAS La lógica de la verdad [121-123] La lógica de la verdad](https://attachments.academia-assets.com/94603696/thumbnails/1.jpg)
](
Fil: Barrio, Eduardo Alejandro. Universidad de Buenos Aires. Facultad de Filosofia y Letras. Inst... more Fil: Barrio, Eduardo Alejandro. Universidad de Buenos Aires. Facultad de Filosofia y Letras. Instituto de Filosofia "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina
Crítica (México D. F. En línea), 2014
El objetivo de este artículo es investigar diversos resultados limitativos acerca del concepto de... more 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.
Journal of Philosophical Logic, 2014
Adding a transparent truth predicate to a language completely governed by classical logic is not ... more 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.
Ideas y Valores, 2008
En un célebre artículo de 1936 Alfred Tarski presenta sus ideas sobre la noción de consecuencia l... more En un célebre artículo de 1936 Alfred Tarski presenta sus ideas sobre la noción de consecuencia lógica, discute distintas dificultades conectadas con ella, y señala que una definición formal aceptable de este concepto debe traer luz sobre la noción intuitiva de consecuencia. Con ...
Journal of Philosophical Logic, 2021
It is widely accepted that classical logic is trivialized in the presence of a transparent truth-... more 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. (Journal of Philosophical Logic, 1–28, 2019) and Pailos (The Review of Symbolic Logic, Forthcoming) recovers classical logic, either in the sense that every classical (meta)inferential validity is valid at some point in the hierarchy (as is stressed in Barrio et al. (Journal of Philosophical Logic, 1–28, 2019)), 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 (The Review of Symbolic Logic, Forthcoming)—, and this suggests that, contrary to standard opinions, transparent truth is after all consistent with classical logic. However, Scambler (Journal of Philosophical Logic, 49, 351–370, 2020) 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.
Análisis Filosófico, 2021
The main idea that we want to defend in this paper is that the question of what a logic is should... more 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 (e.g. its logical truths and valid inferences), but not be the same logic.
Journal of Philosophical Logic, 2019
Logic Journal of the IGPL, 2017
Fil: Barrio, Eduardo Alejandro. Instituto de Investigaciones Filosoficas - Sadaf; Argentina. Cons... more Fil: Barrio, Eduardo Alejandro. Instituto de Investigaciones Filosoficas - Sadaf; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina
The Review of Symbolic Logic, 2018
In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoni... more 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 ...
An Essay on Circularity, 2014
Análisis Filosófico, 2021
The main idea that we want to defend in this paper is that the question of what a logic is should... more 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 (e.g. its logical truths and valid inferences), but not be the same logic.
In this article, we will present a number of technical results concerning Classical Logic, ST and... more 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 partic- ular, 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 conse- quence 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 con- sequences 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.
Principia, 2018
In a forthcoming paper, Rodrigues & Carnielli (2016) present two logics motivated by the idea of ... more In a forthcoming paper, Rodrigues & Carnielli (2016) present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE (the Basic Logic of Evidence) and the second-that is a conservative extension of BLE-is named LETJ (the Logic of Evidence and Truth). Roughly, BLE and LETJ are two non-classical (paraconsistent and paracomplete) logics in which the Laws of Explosion (EXP) and Excluded Middle (PEM) are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic of Formal Inconsistency (an LFI). 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. §0 Introduction In this paper, I am interested in analyzing the relationship between pure logics and their interpretations. For example, it could be stimulating to discuss if there are some intrinsic characteristic in pure modal logic S5 (presented by axioms or by Kripke-models) and the well-known David Lewis' interpretation using actual possible worlds and accessibility relations. Is there a single canonical interpretation for S5? Are there any central features S5 sufficient to determine a single canonical interpretation? Questions like those raised for all kinds of logics. In particular, non-classical logics have been motivated considering specific Interpretations that serve as reasons for challenging classical logic. In the context of paraconsistent logics, logicians have provided different ways of interpreting how we should reason in the presence of contradictions. In this way, in a recently work, Rodrigues & Carnielli present 2 two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE (the Basic Logic of Evidence) and the second-that is a conservative extension of BLE-is named LETJ (the Logic of Evidence and Truth). Roughly, BLE and LETJ are two non-classical (paraconsistent and paracomplete) logics in which the Laws of Explosion (EXP) and Excluded Middle (PEM) are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic of Formal Inconsistency (an LFI). This means that there is an operator that, roughly speaking, identifies a formula as having classical behavior. In particular, there are instances of EXP that can be captured inside LETJ using a circle operator. Both formal theories are presented by a natural deduction system (a set of introduction and elimination rules for the conjunction, disjunction and the material conditional), But, they focus on the negation and introduce special rules for refutability. The main idea is 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. As I said before, the underlying motivation provided for BLE and LETJ is that rules should preserve evidence for an assertion rather than its truth. Rodrigues & Carnielli's paper has an interesting and challenging idea. BLE and LETJ are incompatible with dialetheia. It seems to show that these paraconsistent logics cannot be interpreted using truth-conditions that allow true Acknowledgments: I wish to express my gratitude to
in Jacek Malinowski and Walter Carnielli "Between Consistency and Inconsistency," Trends in Logic: Studia Logica series. , 2018
Paraconsistent logics are logical systems that reject the classical conception, usually dubbed Ex... more Paraconsistent logics are logical systems that reject the classical conception, 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 an 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.
Fil: Barrio, Eduardo Alejandro. Universidad de Buenos Aires. Facultad de Filosofia y Letras. Inst... more Fil: Barrio, Eduardo Alejandro. Universidad de Buenos Aires. Facultad de Filosofia y Letras. Instituto de Filosofia "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina
Crítica (México D. F. En línea), 2014
El objetivo de este artículo es investigar diversos resultados limitativos acerca del concepto de... more 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.
Journal of Philosophical Logic, 2014
Adding a transparent truth predicate to a language completely governed by classical logic is not ... more 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.
Ideas y Valores, 2008
En un célebre artículo de 1936 Alfred Tarski presenta sus ideas sobre la noción de consecuencia l... more En un célebre artículo de 1936 Alfred Tarski presenta sus ideas sobre la noción de consecuencia lógica, discute distintas dificultades conectadas con ella, y señala que una definición formal aceptable de este concepto debe traer luz sobre la noción intuitiva de consecuencia. Con ...
Journal of Philosophical Logic, 2021
It is widely accepted that classical logic is trivialized in the presence of a transparent truth-... more 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. (Journal of Philosophical Logic, 1–28, 2019) and Pailos (The Review of Symbolic Logic, Forthcoming) recovers classical logic, either in the sense that every classical (meta)inferential validity is valid at some point in the hierarchy (as is stressed in Barrio et al. (Journal of Philosophical Logic, 1–28, 2019)), 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 (The Review of Symbolic Logic, Forthcoming)—, and this suggests that, contrary to standard opinions, transparent truth is after all consistent with classical logic. However, Scambler (Journal of Philosophical Logic, 49, 351–370, 2020) 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.
Análisis Filosófico, 2021
The main idea that we want to defend in this paper is that the question of what a logic is should... more 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 (e.g. its logical truths and valid inferences), but not be the same logic.
Journal of Philosophical Logic, 2019
Logic Journal of the IGPL, 2017
Fil: Barrio, Eduardo Alejandro. Instituto de Investigaciones Filosoficas - Sadaf; Argentina. Cons... more Fil: Barrio, Eduardo Alejandro. Instituto de Investigaciones Filosoficas - Sadaf; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina
The Review of Symbolic Logic, 2018
In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoni... more 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 ...
An Essay on Circularity, 2014
Análisis Filosófico, 2021
The main idea that we want to defend in this paper is that the question of what a logic is should... more 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 (e.g. its logical truths and valid inferences), but not be the same logic.
In this article, we will present a number of technical results concerning Classical Logic, ST and... more 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 partic- ular, 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 conse- quence 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 con- sequences 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.
Principia, 2018
In a forthcoming paper, Rodrigues & Carnielli (2016) present two logics motivated by the idea of ... more In a forthcoming paper, Rodrigues & Carnielli (2016) present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE (the Basic Logic of Evidence) and the second-that is a conservative extension of BLE-is named LETJ (the Logic of Evidence and Truth). Roughly, BLE and LETJ are two non-classical (paraconsistent and paracomplete) logics in which the Laws of Explosion (EXP) and Excluded Middle (PEM) are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic of Formal Inconsistency (an LFI). 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. §0 Introduction In this paper, I am interested in analyzing the relationship between pure logics and their interpretations. For example, it could be stimulating to discuss if there are some intrinsic characteristic in pure modal logic S5 (presented by axioms or by Kripke-models) and the well-known David Lewis' interpretation using actual possible worlds and accessibility relations. Is there a single canonical interpretation for S5? Are there any central features S5 sufficient to determine a single canonical interpretation? Questions like those raised for all kinds of logics. In particular, non-classical logics have been motivated considering specific Interpretations that serve as reasons for challenging classical logic. In the context of paraconsistent logics, logicians have provided different ways of interpreting how we should reason in the presence of contradictions. In this way, in a recently work, Rodrigues & Carnielli present 2 two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE (the Basic Logic of Evidence) and the second-that is a conservative extension of BLE-is named LETJ (the Logic of Evidence and Truth). Roughly, BLE and LETJ are two non-classical (paraconsistent and paracomplete) logics in which the Laws of Explosion (EXP) and Excluded Middle (PEM) are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic of Formal Inconsistency (an LFI). This means that there is an operator that, roughly speaking, identifies a formula as having classical behavior. In particular, there are instances of EXP that can be captured inside LETJ using a circle operator. Both formal theories are presented by a natural deduction system (a set of introduction and elimination rules for the conjunction, disjunction and the material conditional), But, they focus on the negation and introduce special rules for refutability. The main idea is 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. As I said before, the underlying motivation provided for BLE and LETJ is that rules should preserve evidence for an assertion rather than its truth. Rodrigues & Carnielli's paper has an interesting and challenging idea. BLE and LETJ are incompatible with dialetheia. It seems to show that these paraconsistent logics cannot be interpreted using truth-conditions that allow true Acknowledgments: I wish to express my gratitude to
in Jacek Malinowski and Walter Carnielli "Between Consistency and Inconsistency," Trends in Logic: Studia Logica series. , 2018
Paraconsistent logics are logical systems that reject the classical conception, usually dubbed Ex... more Paraconsistent logics are logical systems that reject the classical conception, 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 an 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.
College Publications, 2014
En Paradojas, Paradojas y más Paradojas se analiza de modo claro y preciso un problema fundamenta... more En Paradojas, Paradojas y más Paradojas se analiza de modo claro y preciso un problema fundamental: ¿Qué es una paradoja y cuál es su importancia en la filosofía contemporánea? El libro pone al alcance del lector no especializado una selección de las paradojas más conocidas e inquietantes, y realiza un análisis y discusión que permite que el lector pueda tener una comprensión profunda de ellas y de las alternativas que surgen frente a ellas. Las paradojas son un fenómeno multidisciplinario: la verdad, la racionalidad, el conocimiento, la justificación y el infinito son algunos de los conceptos que en diferentes campos del saber han sido afectados por ellas.
by John Corcoran, JY B, Marcelo Esteban Coniglio, Marcelo Coniglio, Eduardo Barrio, Amílcar Sernadas, Dirk Greimann, Radmila Jovanovic, Aldo Figallo Orellano, Ricardo Bianconi, Gustavo Pelaitay, and radmila jovanovic
South America is one of the 7 continents of the earth with many different countries and languages... more South America is one of the 7 continents of the earth with many different countries and languages. The SAJL will promote interaction among logicians based in South America and also between logicians from South America and logicians from other continents.
The aim of the South American Journal of Logic is to promote logic in all its aspects: philosophical, mathematical, computational, historical by publishing high quality peer-reviewed papers.
http://www.sa-logic.org/
Anti-exceptionalism about logic is the approach that logical theories have no special epistemolog... more Anti-exceptionalism about logic is the approach that logical theories have no special epistemological status. Such theories are continuous with scientific theories. Contemporary anti-exceptionalists include data about semantic paradoxes as a part of the logical evidence. Exploring the Buenos Aires Plan, the recent development of the metainferential hierarchy of ST-logics shows that there are multiple options to deal with such paradoxes. There is a whole ST-based hierarchy, of which LP and ST itself are only the first steps. The logics in this hierarchy and ST ω 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, ST and the logics of the ST-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 is not enough to adopt one of these logics, there are other elements to evaluate the revision of classical logic. How close should we be to classical logic? Which logic should be used during the revision? Should a logic be closed under its own rules? How could a logic obey the validities they contain? And mainly, Which is the best explanation of the logical principles to deal with semantic paradoxes? We will argue that, if the answers to these questions are provided by an anti-exceptionalist perspective, ST-metainferential logics in general-and STT ω in particular-are the best available options.
Paraconsistent logics are logical systems that reject the classical conception, usually dubbed Ex... more Paraconsistent logics are logical systems that reject the classical conception, 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 an 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.