Was Hugh MacColl a logical pluralist or a logical monist? A case study in the slow emergence of metatheorising

Dans la seconde moitié des années 1900, Bertrand Russell et Hugh MacColl échangèrent sans s’entendre sur les questions de l’implication et de l’existence, dans le cadre d’un débat plus général sur la nature de la logique. Il est tentant de voir dans cet échange une opposition entre le moniste logique Russell et le pluraliste MacColl. Dans cet article, j’affirme que cette interprétation est inexacte, et que les deux hommes étaient tous deux monistes, bien qu’ayant des allégeances différentes. La transition du monisme au pluralisme ne s’effectue en réalité qu’à partir du début des années 1910, peu après la mort de MacColl en 1909. Les premiers signes de cette transition sont à trouver particulièrement chez le philosophe américain C. I. Lewis, le mathématicien néerlandais L. E. J. Brouwer, et le logicien polonais Jan Łukasiewicz. Ces auteurs sont des exemples de l’avènement graduel de la métalogique.In the mid- and late 1900s Bertrand Russell and Hugh MacColl had a non-discussion about implication and existence, as parts of a dispute over the nature of logic. We are tempted to see this debate in terms of logical monist Russell against logical pluralist MacColl, but I argue that this interpretation is inaccurate; each man was a logical monist, but with different allegiances. The transition from monism to pluralism began to occur from the early 1910s onwards, soon after MacColl’s death in 1909; early traces will be found especially in the American philosopher C. I. Lewis, the Dutch mathematician L. E. J. Brouwer, and the Polish logician Jan Łukasiewicz. They form examples of the gradual rise of metalogic

MacColl’s elusive pluralism

MacColl a été récemment l’objet de trois intéressantes thèses. D’abord, il serait le probable père du pluralisme en logique. Ensuite, son pluralisme porterait un instrumentalisme sous-jacent. Enfin, les deux thèses précédentes expliqueraient l’oubli dans lequel il serait tombé après 1909. Bien qu’il soit à la fois pluraliste et instrumentaliste à certains égards, je suggèrerai qu’il est difficile de trouver dans les écrits de MacColl un pluralisme qui puisse satisfaire les trois thèses précédentes en apparaissant pour la première fois chez MacColl, en trouvant ses sources dans un instrumentalisme adapté à la logique, et en étant l’explication à l’oubli dans lequel était tombé son auteur.MacColl is the recent subject of three interesting theses. One is that he is the probable originator of pluralism in logic. The other is that his pluralism expresses an underlying instrumentalism. The third is that the first two help explain his post-1909 neglect. Although there are respects in which he is both a pluralist and an instrumentalist, I will suggest that it is difficult to find in MacColl’s writings a pluralism which honours the threefold attribution of having been originated by him, having been rooted in an instrumentalism adapted to logic, and being the occasion of his neglect

Semantic penumbra? Concept similarity in logic

It is widely accepted by formal and informal logicians alike that a formal logic which, by the lights of English, gets the connectives wrong, nevertheless conspires to get entailment right—right that is, modulo English. There is a vexing problem occasioned by this semantic alienation of formal logic. It is next to impossible for formal logic to meet the expectations of realism. What, then, of informal logic

Some arguments for propositional logic: MacColl as a philosopher

L’article examine les raisons philosophiques, plutôt que mathématiques ou logiques, pour lesquelles MacColl a pu vouloir développer une logique propositionnelle. Nous trouvons des éléments de réponse dans le refus discret d’endosser une logique des choses, dans l’anti-psychologisme nuancé de MacColl, et dans une subtile épistémologie de la certitude liée à un usage méthodique de la grammaire.The paper considers the philosophical, rather than mathematical or logical, reasons why MacColl decided to develop a propositional logic. We find some answers in a discrete refusal to countenance a logic of things, in MacColl’s qualified anti-psychologism, and in a subtle epistemology of certainty linked to the methodical use of grammar

Some remarks on Hugh MacColl’s notion of symbolic existence

L’approche la plus influente de la logique des non-existences est celle provenant de la tradition Frege-Russell. L’un des plus importants dissidents à cette tradition, à ses débuts, était Hugh MacColl. C’est en relation avec la notion d’existence et avec les arguments impliquant des fictions, que le travail de MacColl montre une grande différence avec celui de ses contemporains. En effet, MacColl fut le premier à implémenter dans un système formel l’idée qu’introduire des fictions dans le domaine de la logique revient à fournir un langage muni de sous-domaines avec différents types d’objets. Dans cet article, nous avançons quelques remarques sur la portée de la logique de MacColl sur les non-existences. Plus précisément, nous suggérons qu’il y a un lien conceptuel fort entre la notion de subsistance chez Russell et la notion d’existencesymbolique chez MacColl.The most influential approach to the logic of non-existents is certainly the one stemming from the Frege-Russell tradition. One of the most important early dissidents to that tradition was Hugh MacColl. It is in relation to the notions of existence and arguments involving fictions that MacColl’s work shows a deep difference from the work of his contemporaries. Indeed, MacColl was the first to attempt to implement in a formal system the idea that to introduce fictions in the context of logic amounts to providing a many-sorted language. The main aim of the paper is to add some brief remarks that should complete the scope of MacColl’s logic of non-existence. More precisely, I will suggest that there seems to be a strong conceptual link between Russell’s notion of subsistence and MacColl’s notion of symbolic existence

MacColl’s influences on Peirce and Schröder

Les contributions à la logique de MacColl et Charles Sanders Peirce (1839-1914) ont été les deux plus profondes influences sur le travail de Ernst Schröder (1841-1902) en logique algébrique. Dans son Vorlesungen über dieAlgebra der Logik, Schröder a cité MacColl comme l’un de ses précurseurs les plus importants. Schröder a comparé les travaux de Peirce avec les premières parties de la série d’articles intitulés « The calculus of equivalent statements » que MacColl publie entre 1877 et 1880. Schröder a attribué la priorité à MacColl pour avoir anticipé les résultats de Peirce. Pour Schröder, MacColl était une phase préliminaire à l’algèbre de la logique de Peirce.The contributions to logic of MacColl and Charles Sanders Peirce (1839-1914) were the two most profound influences upon the work of Ernst Schröder (1841-1902) in algebraic logic. In his Vorlesungen über die Algebra der Logik, Schröder referred to MacColl as one of his most important precursors. Schröder compared Peirce’s considerations with the early parts of MacColl’s series of papers “The calculus of equivalent statements” (published between 1877 and 1880), and he attributed to MacColl priority for having anticipated Peirce’s results. For Schröder, MacColl’s calculus was a preliminary stage of Peirce’s algebra of logic

Dialogues as a Dynamic Framework for Logic

Dialogical logic is a game-theoretical approach to logic. Logic is studied with the help of certain games, which can be thought of as idealized argumentations. Two players, the Proponent, who puts forward the initial thesis and tries to defend it, and the Opponent, who tries to attack the Proponent’s thesis, alternately utter argumentative moves according to certain rules. For a long time the dialogical approach had been worked out only for classical and intuitionistic logic. The seven papers of this dissertation show that this narrowness was uncalled for. The initial paper presents an overview and serves as an introduction to the other papers. Those papers are related by one central theme. As each of them presents dialogical formulations of a different non-classical logic, they show that dialogical logic constitutes a powerful and flexible general framework for the development and study of various logical formalisms and combinations thereof. As such it is especially attractive to logical pluralists that reject the idea of “the single correct logic”. The collection contains treatments of free logic, modal logic, relevance logic, connexive logic, linear logic, and multi-valued logic.LEI Universiteit LeidenPhilosoph

Non-Boolean classical relevant logics I

Under embargo until: 2020-12-13Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment Theorem as well as the variable sharing property. In addition it has the same S4-type modal feature as the original relevant logic E as well as the same enthymematical deduction theorem. The variable sharing property was only ever regarded as a necessary property for a logic to have in order for it to not validate the so-called paradoxes of implication. The Entailment Theorem on the other hand was regarded as both necessary and sufficient. This paper shows that the latter theorem also holds for classical logic, and so cannot be regarded as a sufficient property for blocking the paradoxes. The concept of suppression is taken up, but shown to be properly weaker than that of variable sharing.acceptedVersio

Logical Localism in the Context of Combining Logics

[eng] Logical localism is a claim in the philosophy of logic stating that different logics are correct in different domains. There are different ways in which this thesis can be motivated and I will explore the most important ones. However, localism has an obvious and major challenge which is known as ‘the problem of mixed inferences’. The main goal of this dissertation is to solve this challenge and to extend the solution to the related problem of mixed compounds for alethic pluralism. My approach in order to offer a solution is one that has not been considered in the literature as far as I am aware. I will study different methods for combining logics, concentrating on the method of juxtaposition, by Joshua Schechter, and I will try to solve the problem of mixed inferences by making a finer translation of the arguments and using combination mechanisms as the criterion of validity. One of the most intriguing aspects of the dissertation is the synergy that is created between the philosophical debate and the technical methods with the problem of mixed inferences at the center of that synergy. I hope to show that not only the philosophical debate benefits from the methods for combining logics, but also that these methods can be developed in new and interesting ways motivated by the philosophical problem of mixed inferences. The problem suggests that there are relevant interactions between connectives, justified by the philosophical considerations for conceptualising different logic systems, that the methods for combining logics should allow to emerge. The recognition of this fact is what drives the improvements on the method of juxtaposition that I develop. That is, in order to allow for the emergence of desirable interaction principles, I will propose alternative ways of combining logic systems -specifically classical and intuitionistic logics- that go beyond the standard for combinations, which is based on minimality conditions so as to avoid the so-called collapse theorems.[spa] El localismo lógico es una tesis en filosofía de la lógica según la cual diferentes sistemas lógicos son correctos en función del dominio en el que se aplican. Dicha tesis cuenta, prima facie, con cierta plausibilidad y con varios argumentos que la respaldan como mostraré. Sin embargo, el localismo se presta a un evidente y poderoso contraargumento conocido como ‘el problema de las inferencias mixtas’. El objetivo principal de esta disertación es dar respuesta a ese problema y extender la solución al problema afín de los compuestos mixtos que afecta al pluralismo alético. La manera de abordar el problema de las inferencias mixtas consistirá en analizar casos paradigmáticos en la literatura a la luz de los métodos de combinación de lógicas. En concreto, me centraré en el método de la yuxtaposición, desarrollado por Joshua Schechter. Así, ofreceré una solución al problema de las inferencias mixtas que pasará por realizar un análisis más sutil y una formalización más precisa de las mismas, para después aplicar los mecanismos de combinación como criterio de validez. Además, mostraré que el problema de las inferencias mixtas provee de multitud de ejemplos que invitan a desarrollar los métodos de combinación de lógicas de formas novedosas. Una de las aportaciones más relevantes de la disertación consistirá en modificar el método de la yuxtaposición para obtener mecanismos que van más allá del estándar de las extensiones mínimas conservativas. En concreto, propondré diferentes mecanismos para combinar la lógica clásica y la intuicionista, de manera que se permita la aparición de distintos principios puente para los que tenemos buenas razones que los justifican, sin que ello conduzca al colapso de las lógicas que se combinan

Logical Localism in the Context of Combining Logics

Programa de Doctorat en Ciència Cognitiva i Llenguatge[eng] Logical localism is a claim in the philosophy of logic stating that different logics are correct in different domains. There are different ways in which this thesis can be motivated and I will explore the most important ones. However, localism has an obvious and major challenge which is known as ‘the problem of mixed inferences’. The main goal of this dissertation is to solve this challenge and to extend the solution to the related problem of mixed compounds for alethic pluralism. My approach in order to offer a solution is one that has not been considered in the literature as far as I am aware. I will study different methods for combining logics, concentrating on the method of juxtaposition, by Joshua Schechter, and I will try to solve the problem of mixed inferences by making a finer translation of the arguments and using combination mechanisms as the criterion of validity. One of the most intriguing aspects of the dissertation is the synergy that is created between the philosophical debate and the technical methods with the problem of mixed inferences at the center of that synergy. I hope to show that not only the philosophical debate benefits from the methods for combining logics, but also that these methods can be developed in new and interesting ways motivated by the philosophical problem of mixed inferences. The problem suggests that there are relevant interactions between connectives, justified by the philosophical considerations for conceptualising different logic systems, that the methods for combining logics should allow to emerge. The recognition of this fact is what drives the improvements on the method of juxtaposition that I develop. That is, in order to allow for the emergence of desirable interaction principles, I will propose alternative ways of combining logic systems -specifically classical and intuitionistic logics- that go beyond the standard for combinations, which is based on minimality conditions so as to avoid the so-called collapse theorems.[spa] El localismo lógico es una tesis en filosofía de la lógica según la cual diferentes sistemas lógicos son correctos en función del dominio en el que se aplican. Dicha tesis cuenta, prima facie, con cierta plausibilidad y con varios argumentos que la respaldan como mostraré. Sin embargo, el localismo se presta a un evidente y poderoso contraargumento conocido como ‘el problema de las inferencias mixtas’. El objetivo principal de esta disertación es dar respuesta a ese problema y extender la solución al problema afín de los compuestos mixtos que afecta al pluralismo alético. La manera de abordar el problema de las inferencias mixtas consistirá en analizar casos paradigmáticos en la literatura a la luz de los métodos de combinación de lógicas. En concreto, me centraré en el método de la yuxtaposición, desarrollado por Joshua Schechter. Así, ofreceré una solución al problema de las inferencias mixtas que pasará por realizar un análisis más sutil y una formalización más precisa de las mismas, para después aplicar los mecanismos de combinación como criterio de validez. Además, mostraré que el problema de las inferencias mixtas provee de multitud de ejemplos que invitan a desarrollar los métodos de combinación de lógicas de formas novedosas. Una de las aportaciones más relevantes de la disertación consistirá en modificar el método de la yuxtaposición para obtener mecanismos que van más allá del estándar de las extensiones mínimas conservativas. En concreto, propondré diferentes mecanismos para combinar la lógica clásica y la intuicionista, de manera que se permita la aparición de distintos principios puente para los que tenemos buenas razones que los justifican, sin que ello conduzca al colapso de las lógicas que se combinan