Normality Operators and Classical Collapse

In this paper, we extend the expressive power of the logics K3, LP and FDE with anormality operator, which is able to express whether a for-mula is assigned a classical truth value or not. We then establish classical recapture theorems for the resulting logics. Finally, we compare the approach via normality operator with the classical collapse approach devisedby Jc Beall

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

Normality operators and Classical Recapture in Extensions of Kleene Logics

In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a classical recapture result based on the two logics. In the second part of the paper, we compare the approach in terms of normality operators with an established approach to classical recapture, namely minimal inconsistency. Finally, we discuss technical issues connecting LPe and Ke3 to the tradition of Logics of Formal Inconsistency and Underterminedness

The Dream of Recapture

As a response to the semantic and logical paradoxes, theorists often reject some principles of classical logic. However, classical logic is entangled with mathematics, and giving up mathematics is too high a price to pay, even for nonclassical theorists. The so-called recapture theorems come to the rescue. When reasoning with concepts such as truth/class membership/property instantiation, if ones is interested in consequences of the theory that only contain mathematical vocabulary, nothing is lost by reasoning in the nonclassical framework. It is shown that this claim is highly misleading, if not simply false. Under natural assumptions, recapture claims are incorrect

Recapture, Transparency, Negation and a Logic for the Catuskoti

The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s (2009) and Graham Priest’s (2010) interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mūla-madhyamaka-kārikā. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices – orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps's (1975) framework of First Degree Entailment. Cotnoir (2015) has argued that the lattices of Priest and Garfield cannot ground the logic of the catuskoti. The concern is simple: on the one hand, FDE brings with it the failure of classical principles such as modus ponens. On the other hand, we frequently encounter Nāgārjuna using classical principles in other arguments in the MMK. There is a problem of validity. If FDE is Nāgārjuna’s logic of choice, he is facing what is commonly called the classical recapture problem: how to make sense of cases where classical principles like modus pones are valid? One cannot just add principles like modus ponens as assumptions, because in the background paraconsistent logic this does not rule out their negations. In this essay, I shall explore and critically evaluate Cotnoir’s proposal. In detail, I shall reveal that his framework suffers collapse of the kotis. Furthermore, I shall argue that the Collapse Argument has been misguided from the outset. The last chapter suggests a formulation of the catuskoti in classical Boolean Algebra, extended by the notion of an external negation as an illocutionary act. I will focus on purely formal considerations, leaving doctrinal matters to the scholarly discourse – as far as this is possible

Recapture, Transparency, Negation and a Logic for the Catuṣkoṭi

The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s (2009) and Graham Priest’s (2010) interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mūla-madhyamaka-kārikā. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices – orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps\u27s (1975) framework of First Degree Entailment. Cotnoir (2015) has argued that the lattices of Priest and Garfield cannot ground the logic of the catuskoti. The concern is simple: on the one hand, FDE brings with it the failure of classical principles such as modus ponens. On the other hand, we frequently encounter Nāgārjuna using classical principles in other arguments in the MMK. There is a problem of validity. If FDE is Nāgārjuna’s logic of choice, he is facing what is commonly called the classical recapture problem: how to make sense of cases where classical principles like modus pones are valid? One cannot just add principles like modus pones as assumptions, because in the background paraconsistent logic this does not rule out their negations. In this essay, I shall explore and critically evaluate Cotnoir’s proposal. In detail, I shall reveal that his framework suffers collapse of the kotis. Taking Cotnoir’s concerns seriously, I shall suggest a formulation of the catuskoti in classical Boolean Algebra, extended by the notion of an external negation as an illocutionary act. I will focus on purely formal considerations, leaving doctrinal matters to the scholarly discourse – as far as this is possible

God of the Gaps : a neglected reply to God’s stone problem

Traditional monotheism has long faced logical puzzles (omniscience, omnipotence, and more). We argue that such puzzles rest on the assumed logical truth of the Law of Excluded Middle, which we suggest there is little theological reason to accept. By way of illustration we focus on God's alleged stone problem, and present a simple but plausible ‘gappy’ framework for addressing this puzzle. We assume familiarity with the proposed (subclassical) logic but an appendix is offered as a brief review.PostprintPeer reviewe

Two-valued Logics for Transparent Truth Theory

It is part of the current wisdom that the Liar and similar semantic paradoxes can be taken care of by the use of certain non-classical multivalued logics. It is also well-known that some of these logics can be characterized by means of two-valued semantics. An immediate consequence of this is that there are two-valued logics that support a transparent truth predicate. In this paper I want to suggest that these logics are not just interesting from a formal point of view but also from a philosophical perspective. In particular, I will argue that the two-valued presentation of these logics has a number of advantages over the more usual presentations.Fil: Rosenblatt, Lucas Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentina. Instituto de Investigaciones Filosóficas - Sadaf; Argentin

Reflective equilibrium on the fringe : The tragic threefold story of a failed methodology for logical theorising

Reflective equilibrium, as a methodology for the ‘formation of log- ics’, fails on the fringe, where intricate details can make or break a logical the- ory. On the fringe, the process of theorification cannot be methodologically governed by anything like reflective equilibrium. When logical theorising gets tricky, there is nothing on the pre-theoretical side on which our theoretical claims can reflect of—at least not in any meaningful way. Indeed, the fringe is exclusively the domain of theoretical negotiations and the methodological power of reflective equilibrium is merely nominal.info:eu-repo/semantics/acceptedVersio

Against Classical Paraconsistent Metatheory

There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it is designed to study