Validity, dialetheism and self-reference

It has been argued recently (Beall in Spandrels of truth, Oxford University Press, Oxford, 2009; Beall and Murzi J Philos 110:143–165, 2013) that dialetheist theories are unable to express the concept of naive validity. In this paper, we will show that (Formula presented.) can be non-trivially expanded with a naive validity predicate. The resulting theory, (Formula presented.) reaches this goal by adopting a weak self-referential procedure. We show that (Formula presented.) is sound and complete with respect to the three-sided sequent calculus (Formula presented.). Moreover, (Formula presented.) can be safely expanded with a transparent truth predicate. We will also present an alternative theory (Formula presented.), which includes a non-deterministic validity predicate.Fil: Pailos, Federico Matias. Instituto de Investigaciones Filosóficas - Sadaf; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

A fully classical truth theory characterized by substructural means

We will present a three-valued consequence relation for metainferences, called CM, defined through ST and TS, two well known substructural consequence relations for inferences. While ST recovers every classically valid inference, it invalidates some classically valid metainferences. While CM works as ST at the inferential level, it also recovers every classically valid metainference. Moreover, CM can be safely expanded with a transparent truth predicate. Nevertheless, CM cannot recapture every classically valid meta-metainference. We will afterwards develop a hierarchy of consequence relations CMn for metainferences of level n (for 1 ≤ n < ω). Each CMn recovers every metainference of level n or less, and can be nontrivially expanded with a transparent truth predicate, but cannot recapture every classically valid metainferences of higher levels. Finally, we will present a logic CMω, based on the hierarchy of logics CMn, that is fully classical, in the sense that every classically valid metainference of any level is valid in it. Moreover, CM can be nontrivially expanded with a transparent truth predicate.Fil: 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; Argentina. Universidad de Buenos Aires; Argentin

Disjoint logics

We will present all the mixed and impure disjoint three-valued logics based on the Strong Kleene schema. Some, but not all of them, are (inferentially) empty logics, while one of them is trivial. We will compare them regarding their relative strength. We will also provide a recipe for building philosophical interpretations for each of these logics, and show why the kind of permeability that characterises them is not such a bad feature. Finally, we will present a three-side sequent system for most of these logics.Fil: 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

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

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

A paraconsistent route to semantic closure

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

Hoe to justify propositions when facing skeptical challenges

Los desafíos escépticos cuestionan la justificación de las proposiciones que aceptamos. Pero es posible justificar en términos probabilísticos cada una de las proposiciones empíricas aceptadas. Para eso, su probabilidad condicional al resto de las proposiciones aceptadas, deberá ser mayor que su probabilidad absoluta. Esta justificación es circular, pero virtuosa. Sin embargo, carece de eficacia dialéctica frente al escéptico.Skeptical challenges question that the propositions one accepts are justified. But it is possible to justify each one of them in probabilistic terms. In order to do that,their probability, conditional to the rest of the accepted propositions, must be high-er than their absolute probability. This justification is circular, but virtuous.Nevertheless, it has no dialectical efficiency against the skeptic.Fil: Pailos, Federico Matias. Consejo Nacional de Investigaciones Científicas y Técnicas. Universidad de Buenos Aires; Argentin

The behavior of truth and justification and their relationship to the assertive practice

Crispin Wright afirma que tanto la norma que insta a afirmar lo verdadero como la que exhorta a afirmar lo justificado son distintivas de la práctica asertórica. A pesar de que ellas no son diferentes en la práctica, son distintas. Pero Richard Rorty argumenta que las razones ofrecidas obligarían a Wright a aceptar demasiadas reglas como propias de dicha práctica. Wright admitiría que las normas pueden ser ilimitadas, pero no que son ilimitadas las normas correctas. Para defender esta posición, basta con distinguir, como hace, las normas descriptivas de las prescriptivas. A pesar de ello, la posición de Rorty es admisible, pues no parece haber ventajas visibles en distinguir ambas normas. Si no se exponen (y Wright no lo hace) estas ventajas, la teoría resultante será más débil que una que no lo pretenda (como la que Rorty defiende).Crispin Wright argues that both the standard that urges to assert the truth, and the one that told to assert what is justified, are distinctive of the assertoric practice. Despite that there’s no difference in practice between them, they are different. But Richard Rorty argues that the reasons given, would force Wright to accept too many rules as distinctive of the practice. Wright admits that those kinds of standards can be unlimited, but that the correct standards are not. To defend this position, it’s enough to distinguish descriptive rules from the prescriptive ones. However, Rorty’s position is admissible, because there seems to be no advantages in distinguishing between those two standards. If these advantages are not presented (and Wright does not), the resulting theory will be weaker than one that doesn’t pretend to do it (as Rorty claims).Fil: Pailos, Federico Matias. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

A family of metainferential logics

We will present 12 different mixed metainferential consequence relations. Each one of them is specified using two different inferential Tarskian or non-Tarskian consequence relations: K3, LP, ST or TS+. We will show that it is possible to obtain a Tarskian logic with non-Tarskian inferential logics, but also a non-Tarskian logic with Tarskian inferential logics. Moreover, we will show how some of these metainferential logics work better than the corresponding inferential rivals. Finally, we will show how these logics prove that it is not enough to work with inferences as pairs of sets of formulas to obtain a contractive logic.Fil: 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

Validity in a dialetheist framework

In this paper, we develop two theories of validity in a dialetheist framework, both based on Meadows (2014). The first one, LPV∗, has LP's consequence relation but the validity predicate of Meadows' fixed point construction. The second theory, DT (the one we favour), is defined in terms of its validity predicate. Therefore, in DT, the validity predicate and the consequence relation coincide. Moreover, this theory, unlike Meadows' VAL, is reflexive.Fil: Pailos, Federico Matias. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; ArgentinaFil: Tajer, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentin