A recovery operator for nontransitive approaches

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

Indexicalidad Y Realismo Modal

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

Consecuencia lógica: modelos conjuntistas y aspectos modales

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

Absoluta Generalidad y Validez lógica

The aim of this paper is to investigate various limiting results about the concept of validity. In particular, I argue that assuming the absolute generality thesis, the higher-order logic with standard semantics and plural logic cannot be sufficiently expressive to capture its own concept of validity. Moreover, I show that several modifications of classical logic leads to the same results limiting.Fil: Barrio, Eduardo Alejandro. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

A recovery operator for non-transitive approaches

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.Fil: Barrio, Eduardo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto de Investigaciones Filosóficas - Sadaf; ArgentinaFil: Pailos, Federico Matias. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto de Investigaciones Filosóficas - Sadaf; ArgentinaFil: Szmuc, Damián Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto de Investigaciones Filosóficas - Sadaf; Argentin

Truthmaker Maximalism defended again

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 conclusio

Notes on w-inconsistent Theories of Truth in Second-Order Languages

It is widely accepted that a theory of truth for arithmetic should be consistent, but ω-consistency is less frequently required. This paper argues that ω-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 ω-inconsistent truth theories for arithmetic is unsatisfiability. In order to bring out this point, well known ω-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.Fil: Barrio, Eduardo Alejandro. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Picollo, Lavinia María. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Por qué una lógica no es solo un conjunto de inferencias válidas

La idea principal que queremos defender en este artículo es que la pregunta acerca de qué es una lógica debería ser abordada de una manera especial cuando entran en juego las propiedades estructurales de la relación de consecuencia. En particular, queremos argumentar que no es suficiente identificar el conjunto de inferencias válidas para caracterizar una lógica. En otras palabras, argumentaremos que dos teorías lógicas pueden identificar el mismo conjunto de inferencias y fórmulas válidas, pero no ser la misma lógica.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.Fil: Barrio, Eduardo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Filosóficas. - Sociedad Argentina de Análisis Filosófico. Instituto de Investigaciones Filosóficas; ArgentinaFil: Pailos, Federico Matias. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Filosóficas. - Sociedad Argentina de Análisis Filosófico. Instituto de Investigaciones Filosóficas; Argentin

The Yablo Paradox and Circularity

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

Models & Proofs: LFIs Without a Canonical Interpretations

In different papers, Carnielli, W. & Rodrigues, A. (2012), Carnielli, W. Coniglio, M. & Rodrigues, A. (2017) and 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