Invariance and Logicality in Perspective

Although the invariance criterion of logicality first emerged as a criterion of a purely mathematical interest, it has developed into a criterion of considerable linguistic and philosophical interest. In this paper I compare two different perspectives on this criterion. The first is the perspective of natural language. Here, the invariance criterion is measured by its success in capturing our linguistic intuitions about logicality and explaining our logical behavior in natural-linguistic settings. The second perspective is more theoretical. Here, the invariance criterion is used as a tool for developing a theoretical foundation of logic, focused on a critical examination, explanation, and justification of its veridicality and modal force

Introduction and Commentary on Jennifer Hornsby's "Truth: The Identity Theory"

Jennifer Hornsby’s 1997 paper, ‘Truth: The Identity Theory’, has been highly influential in making the identity theory of truth a viable option in contemporary philosophy. In this introduction and commentary I focus on what distinguishes her theory and its methodology from the correspondence theory and the ‘substantivist’ methodology, and on other issues that have not been widely discussed in earlier commentaries yet are central to the current debate on truth

Where Are You Going, Metaphysics, and How are You Getting There? - Grounding Theory as a Case Study

The viability of metaphysics as a field of knowledge has been challenged time and again. But in spite of the continuing tendency to dismiss metaphysics, there has been considerable progress in this field in the 20th- and 21st- centuries. One of the newest − though, in a sense, also oldest − frontiers of metaphysics is the grounding project. In this paper I raise a methodological challenge to the new grounding project and propose a constructive solution. Both the challenge and its solution apply to metaphysics in general, but grounding theory puts the challenge in an especially sharp focus. The solution consists of a new methodology, holistic grounding or holistic metaphysics. This methodology is modeled after a recent epistemic methodology, foundational holism, that enables us to pursue the foundational project of epistemology without being hampered by the problems associated with foundationalism

Three ways in which logic might be normative

According to tradition, logic is normative for reasoning. Gilbert Harman challenged the view that there is any straightforward connection between logical consequence and norms of reasoning. Authors including John MacFarlane and Hartry Field have sought to rehabilitate the traditional view. I argue that the debate is marred by a failure to distinguish three types of normative assessment, and hence three ways to understand the question of the normativity of logic. Logical principles might be thought to provide the reasoning agent with first-personal directives; they might be thought to serve as third-personal evaluative standards; or they might underwrite our third-personal appraisals of others whereby we attribute praise and blame. I characterize the three normative functions in general terms and show how a failure to appreciate this threefold distinction has led disputants to talk past one another. I further show how the distinction encourages fruitful engagement with and, ultimately, resolution of the question

Characterizing Invariance

I argue that in order to apply the most common type of criteria for logicality, invariance criteria, to natural language, we need to consider both invariance of content—modeled by functions from contexts into extensions—and invariance of character—modeled, à la Kaplan, by functions from contexts of use into contents. Logical expressions should be invariant in both senses. If we do not require this, then old objections due to Timothy McCarthy and William Hanson, suitably modified, demonstrate that content invariant expressions can display intuitive marks of non-logicality. If we do require this, we neatly avoid these objections while also managing to demonstrate desirable connections of logicality to necessity. The resulting view is more adequate as a demarcation of the logical expressions of natural language

Extensionality and logicality

Tarski characterized logical notions as invariant under permutations of the domain. The outcome, according to Tarski, is that our logic, which is commonly said to be a logic of extension rather than intension, is not even a logic of extension - it is a logic of cardinality (or, more accurately, of "isomorphism type"). In this paper, I make this idea precise. We look at a scale inspired by Ruth Barcan Marcus of various levels of meaning: extensions, intensions and hyperintensions. On this scale, the lower the level of meaning, the more coarse-grained and less "intensional" it is. I propose to extend this scale to accommodate a level of meaning appropriate for logic. Thus, below the level of extension, we will have a more coarse-grained level of form. I employ a semantic conception of form, adopted from Sher, where forms are features of things "in the world''. Each expression in the language embodies a form, and by the definition we give, forms will be invariant under permutations and thus Tarskian logical notions. I then define the logical terms of a language as those terms whose extension can be determined by their form. Logicality will be shown to be a lower level analogue of rigidity. Using Barcan Marcus's principles of explicit and implicit extensionality, we are able to characterize purely logical languages as "sub-extensional", namely, as concerned only with form, and we thus obtain a wider perspective on both logicality and extensionality

Extensionality and logicality

Tarski characterized logical notions as invariant under permutations of the domain. The outcome, according to Tarski, is that our logic, which is commonly said to be a logic of extension rather than intension, is not even a logic of extension - it is a logic of cardinality (or, more accurately, of "isomorphism type"). In this paper, I make this idea precise. We look at a scale inspired by Ruth Barcan Marcus of various levels of meaning: extensions, intensions and hyperintensions. On this scale, the lower the level of meaning, the more coarse-grained and less "intensional" it is. I propose to extend this scale to accommodate a level of meaning appropriate for logic. Thus, below the level of extension, we will have a more coarse-grained level of form. I employ a semantic conception of form, adopted from Sher, where forms are features of things "in the world''. Each expression in the language embodies a form, and by the definition we give, forms will be invariant under permutations and thus Tarskian logical notions. I then define the logical terms of a language as those terms whose extension can be determined by their form. Logicality will be shown to be a lower level analogue of rigidity. Using Barcan Marcus's principles of explicit and implicit extensionality, we are able to characterize purely logical languages as "sub-extensional", namely, as concerned only with form, and we thus obtain a wider perspective on both logicality and extensionality

Constantes lógicas y la armonía de las reglas de inferencia

All through the literatura, the question about what is a logical constant has recieved many answers, from model-theoretic aproaches (Tarski; 1966), (Sher; 1991), (Bonnay; 2007) to answers that focus in the inferential practice as meaning (Dummett; 1991), (Prawitz; 1965), (Lorenzen; 1955). Detractors of the second tradition presented many ineludible incovenients, in particular, the logical constant named ‘tonk’ (Prior; 1960). Inferentialist tryed many solutions, in particular they presented the concept of ‘harmony’. The goal of this paper is to show that the different criteria of ‘harmony’ used in the proof-theoretic semantics to determine what is and what is not a logical constant fail to be necessary or sufficient.  I will show the philosophical reasons that make this concept appear and then i will describe the different ways in wich the literatura understads the concept of ‘harmony’. Then I will show that they subgenerate or overgenerate connectives with some counterexamples. Finaly, I will explain some philosophical reasons that should delimitate where to go towards a satisfactory definition of ‘harmony’.A lo largo de la literatura la pregunta por qué es una constante lógica ha recibido distintas respuestas desde los acercamientos de la teoría de modelos (Tarski; 1966), (Sher; 1991), (Gómez Torrente; 2003), (Bonnay; 2007) hasta las respuestas que centran el significado en las reglas de uso (Dummett; 1991), (Prawitz; 1965). Frente a la segunda corriente filosófica se han presentado algunos inconvenientes ineludibles, en particular la constante ‘tonk’ (Prior; 1960 ) frente a la que los defensores del inferencialismo en lógica han presentado varias soluciones, en particular la armonía. El objetivo de este artículo es mostrar que los distintos criterios de ‘armonía’ que se utilizan en semántica de la prueba para establecer qué es una constante lógica no cumplen con su objetivo ya que no son necesario o suficientes. Presentaré las razones filosóficas por las que surge el concepto de ‘armonía’ y luego describiré las distintas formas en las que la literatura suele entender el concepto de ‘armonía’. Luego mostraré que o bien sobregeneran o bien subgeneran conectivas en base a una serie de contraejemplos. Finalmente, desarrollaré algunas razones filosóficas que deberían delimitar por dónde continuar la búsqueda de una definición satisfactoria del concepto de ‘armonía’

Historia natural y normatividad: las críticas de Peirce a la lógica de Dewey

El carácter normativo de la lógica fue una preocupación permanente para Peirce. En 1904 publica una reseña de la obra de Dewey, “Studies in Logical Theory”, en la que discute la concepción de éste. Mi propósito en esta ocasión será analizar los argumentos empleados por Peirce para criticar la idea de lógica propuesta por Dewey, a la luz de su propia concepción tal como es reformulada en esa época. Dicha crítica supone una concepción de la lógica como ciencia normativa que se ocupa de nuestras prácticas de investigación, a la vez que ofrece una explicación de la corrección lógica que reconfigura la demarcación entre verdad material y verdad formal, y provee una base objetiva a nuestras evaluaciones lógicas.Facultad de Humanidades y Ciencias de la Educació