Inconsistency, paraconsistency and ω-inconsistency

In this paper I'll explore the relation between ω-inconsistency and plain inconsistency, in the context of theories that intend to capture semantic concepts. In particular, I'll focus on two very well known inconsistent but non-trivial theories of truth: LP and STTT. Both have the interesting feature of being able to handle semantic and arithmetic concepts, maintaining the standard model. However, it can be easily shown that both theories are ω-inconsistent. Although usually a theory of truth is generally expected to be ω-consistent, all conceptual concerns don't apply to inconsistent theories. Finally, I'll explore if it's possible to have an inconsistent, but ω-consistent theory of truth, restricting my analysis to substructural theories.Fil: Da Re, Bruno. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto de Investigaciones Filosóficas - Sadaf; Argentin

Theories of truth based on four-valued infectious logics

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems

Immune Logics

This article is concerned with an exploration of a family of systems—called immune logics—that arise from certain dualizations of the well-known family of infectious logics. The distinctive feature of the semantic of infectious logics is the presence of a certain “infectious” semantic value, by which two different though equivalent things are meant. On the one hand, it is meant that these values are zero elements for all the operations in the underlying algebraic structure. On the other hand, it is meant that these values behave in a value-in-value-out fashion for all the operations in the underlying algebraic structure. Thus, in a rather informal manner, we will refer to immune logics as those systems whose underlying semantics count with a certain “immune” semantic value behaving in a way that is somewhat dual to that of the infectious values. In a more formal manner, carrying out this dualization will prove to be not as straightforward as one could imagine, since the two characterizations of infectiousness discussed above lead to two different outcomes when one tries to conduct them. We explore these alternatives and provide technical results regarding them, and the various logical systems defined using such semantics

Immune Logics

This article is concerned with an exploration of a family of systems—called immune logics—that arise from certain dualizations of the well-known family of infectious logics. The distinctive feature of the semantic of infectious logics is the presence of a certain “infectious” semantic value, by which two different though equivalent things are meant. On the one hand, it is meant that these values are zero elements for all the operations in the underlying algebraic structure. On the other hand, it is meant that these values behave in a value-in-value-out fashion for all the operations in the underlying algebraic structure. Thus, in a rather informal manner, we will refer to immune logics as those systems whose underlying semantics count with a certain “immune” semantic value behaving in a way that is somewhat dual to that of the infectious values. In a more formal manner, carrying out this dualization will prove to be not as straightforward as one could imagine, since the two characterizations of infectiousness discussed above lead to two different outcomes when one tries to conduct them. We explore these alternatives and provide technical results regarding them, and the various logical systems defined using such semantics

Sorites, curry and suitable models

In this paper we present two new approaches for dealing with semantic paradoxes and soritical predicates based on fuzzy logic. We show that both of them have conceptual advantages over the more traditional Łukasiewicz approach, and that the second one even avoids standard proofs of w-inconsistency.Fil: Da Re, Bruno. 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: Teijeiro, Paula. 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

Two-valued Weak Kleene logics

In the literature, Weak Kleene logics are usually taken as three-valued logics. However, Suszko has challenged the main idea of many-valued logic claiming thatevery logic can be presented in a two-valued fashion. In this paper, we providetwo-valued semantics for the Weak Kleene logics and for a number of four-valuedsubsystems of them. We do the same for the so-called Logics of Nonsense, which are extensions of theWeak Kleene logics with unary operators that allow looking at them as Logics of Formal Inconsistency (LFIs) and Logics of Formal Underterminedness (LFUs). Our aim with this work, rather than arguing for Suszko´s thesis, is to show that two-valued presentations of these peculiar logics enlighten the non-standard behavior of their logical connectives. More specically, the two-valued presentations of paraconsistent logics illustrate and clarify the disjunctive flavor of the conjunction, and dually, the two-valued presentations of paracomplete subsystems ofWeak Kleene logics reveal the conjunctive flavor of the disjunction.Fil: Da Re, Bruno. 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: Szmuc, Damián Enrique. 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

Metainferential Paraconsistency

In this article, our aim is to take a step towards a full understanding of the notion of paraconsistency in the context of metainferential logics. Following the work initiated by Barrio et al (2018), we will consider a metainferential logic to be paraconsistent whenever the metainferentialversion of Explosion (or meta-Explosion) is invalid. However, our contribution consists in modifying the definition of meta-Explosion by extending the standard framework and introducing a negation for inferences and metainferences. From this new perspective, Tarskian paraconsistent logics such asLP will not result to be metainferentially paraconsistent, in contrast to, for instance, non-transitive logics like ST. Finally, we will end up by defining a logic which is metainferentially paraconsistent in every level, and discussing whether this logic is uniform through translations.Fil: Da Re, Bruno. 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: Rubin, Mariela. 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: Teijeiro, Paula. 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 Substructural Solution to Paradoxes and the Problem of the Dependence

En los últimos años se han desarrollado diversas soluciones subestructurales a las paradojas semánticas. En particular, se han postulado teorías no transitivas, no contractivas, no reflexivas y, recientemente, no monotónicas. Sin embargo, cuando dichas soluciones son presentadas mediante cálculos de secuentes surge el problema de la dependencia . En pocas palabras, este problema consiste en que no es posible separar las reglas estructurales de la formulación de las otras reglas del cálculo. En este artículo, presentaré este problema y mostraré que, de hecho, es posible construir un cálculo que no contiene ninguna regla estructural de manera explícita y que, sin embargo, resulta trivial al agregarle un predicado veritativo transparente con ciertos axiomas. Luego, delimitaré los alcances de dicho problema, concluyendo que la metodología correcta para seleccionar una solución subestructural a las paradojas semánticas debe basarse en argumentos filosóficos y, tal vez, en un estudio empírico sobre el fenómeno de la paradojicidad y no en la comparación de derivaciones en cálculos particulares.In past years, several substructural solutions to semantical paradoxes have been developed. In particular, nontransitive, noncontractive, nonmonotonic and nonreflexive theories have been proposed. However, when such solutions are presented using sequent-calculi it emerges what I call the problem of the dependence. In a nutshell, this problem consists in that it’s not easy (or sometimes even possible) to distinguish between the structural rules and the other rules of the calculus. In this article, I will present in detail this problem and I show that even worst there is a calculus such that it doesn’t contain any structural rule but cannot nontrivially handle semantical vocabulary. Finally, I will delimit this problem and I will conclude that the correct methodology for preferring one specific substructural theory should be based on philosophical arguments (or in some case, on empirical bases), but not in the comparison between derivations in particular calculi.Fil: Da Re, Bruno. 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

Paraconsistencia Total

Dentro del conjunto de las lógicas no clásicas, las lógicas paraconsistentes han suscitado de manera particular el interés de diversos filósofos. Además de las definiciones tradicionales, en los últimos años, se han propuesto nuevas maneras de caracterizar a la paraconsistencia. Lo que tienen en común todas estas definiciones es que alguna forma de la regla o de la metarregla de explosión debe ser rechazada. En este artículo, presentaré dichas definiciones y evaluaré el rol que juegan la negación y la transitividad en ellas. Finalmente, propondré una nueva caracterización de la paraconsistencia, la que llamaré paraconsistencia total y mostraré que la regla de monotonía juega un rol crucial en todas las presentaciones de dicho concepto.In the context of non-classical logics, many philosophers have been particularly interested in the paraconsistent logics. In addition to traditional definitions, in recent years, new ways of characterizing the notion of paraconsistency have been proposed. In all of these definitions the rule or the meta-rule of explosion is abandoned. In this article, I present those definitions and evaluate the role that the negation and the transitivity play in each of them. Finally, I propose a new definition of paraconsistency which I call total paraconsistency and show that the rule of weakening plays a crucial role in all of the characterizations of such a concept.Fil: Da Re, Bruno. 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

Paraconsistency and its Philosophical Interpretations

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