This paper provides an analysis of contrary-to-duty reasoning from the proof-theoretical perspective of category theory. While Chisholm’s paradox hints at the need of dyadic deontic logic by showing that monadic deontic logics are not able to adequately model conditional obligations and contrary-to-duties, other arguments can be objected to dyadic approaches in favor of non-monotonic foundations. We show that all these objections can be answered at one fell swoop by modeling conditional obligations within a deductive system defined as an instance of (...) a symmetric monoidal closed category. Using category theory as a foundational framework for logic, we show that it is possible to model conditional normative reasoning and conflicting obligations within a monadic approach without adding further operators or considering deontic conditionals as primitive. (shrink)
In psychology, measurement instruments are constructed from scales, which are obtained on the grounds of exploratory and confirmatory factor analysis. Looking at the literature, one can find various recommendations regarding how these techniques should be used during the scale construction process. Some authors suggest to use exploratory factor analysis on the entire data set while others advice to perform an internal cross-validation by randomly splitting the data set in two and then either perform exploratory factor analysis on both parts or (...) exploratory factor analysis on the first part and confirmatory factor analysis on the other. In spite of all these divergent recommendations, there is no consensus on which method yields the best result. In this paper, we analyze this issue in light of the prediction versus accommodation debate and argue that the answer to this question depends on one’s conception of the criteria that should be used to achieve the goals of the scientific enterprise. (shrink)
Monoidal logics were introduced as a foundational framework to analyse the proof theory of deontic logic. Building on Lambek’s work in categorical logic, logical systems are defined as deductive systems, that is, as collections of equivalence classes of proofs satisfying specific rules and axiom schemata. This approach enables the classification of deductive systems with respect to their categorical structure. When looking at their proof theory, however, one can see that there are similarities between monoidal and substructural logics. The purpose of (...) the present paper is to address this issue and highlight the differences between these two approaches. We argue that monoidal logics provide a more flexible foundational framework that enables a finer analysis of the relationship between negation and other logical connectives. We show that the elimination of double negation is independent from the de Morgan dualities, that monoidal deductive systems are not necessarily weakly distributive and that deduc... (shrink)
Realism is generally assumed as the correct position with regards to psychological research and the measurement of psychological attributes in psychometrics. Borsboom et al., 203–219 2003), for instance, argued that the choice of a reflective measurement model necessarily implies a commitment to the existence of psychological constructs as well as a commitment to the belief that empirical testing of measurement models can justify their correspondence with real causal structures. Hood :739–761 2013) deemphasized Borsboom et al.’s position and argued that the (...) choice of a reflective measurement model does not necessarily require ontological commitments, though, in his view, it does necessitate a commitment to minimal epistemic realism. Although these arguments are formulated with regard to psychological research, they can actually be generalized to other disciplines in social sciences that use similar methodologies and statistical techniques. In Hood’s opinion, empiricism does not suffice to provide an adequate account of the choice of reflective measurement models given that this choice requires an appeal to causal explanations. In this paper, we argue against Hood and answer this challenge, providing epistemic foundations for social science research that do not appeal to realism. (shrink)
This research article revisits Hempel’s logic of confirmation in light of recent developments in categorical proof theory. While Hempel advocated several logical conditions in favor of a purely syntactical definition of a general non-quantitative concept of confirmation, we show how these criteria can be associated to specific logical properties of monoidal modal deductive systems. In addition, we show that many problems in confirmation logic, such as the tacked disjunction, the problem of weakening with background knowledge and the problem of irrelevant (...) conjunction, are also associated with specific logical properties and, incidentally, with some of Hempel’s logical conditions of adequacy. We discuss the raven paradox together with further objections against Hempel’s approach, showing how our analysis enables a clear understanding of the relationships between Hempel’s conditions, the problems in confirmation logic, and the properties of deductive systems. (shrink)
Cet article se veut une critique de la thèse défendue par [Cleland 1993], laquelle soutient que la thèse de Church doit être rejetée puisque les limites du calcul dépendent de la structure physique du monde. Dans un premier temps, nous offrons un (très) bref aperçu de la thèse de Church puis nous présentons l argument de Cleland. Par la suite, nous proposons une analyse critique de son argument, ce qui nous amènera à faire quelques distinctions conceptuelles par rapport aux notions (...) qui concernent la calculabilité. Finalement, nous montrons que les limites du calcul ne sont pas physiques mais bien logiques. En résumé, notre argument est que les limites du calcul sont déterminées en partie par le fait qu’une procédure effective doit pouvoir être décrite de manière finie. (shrink)
Cet article se veut une critique de la thèse défendue par [Cleland 1993], laquelle soutient que la thèse de Church doit être rejetée puisque les limites du calcul dépendent de la structure physique du monde. Dans un premier temps, nous offrons un bref aperçu de la thèse de Church puis nous présentons l argument de Cleland. Par la suite, nous proposons une analyse critique de son argument, ce qui nous amènera à faire quelques distinctions conceptuelles par rapport aux notions qui (...) concernent la calculabilité. Finalement, nous montrons que les limites du calcul ne sont pas physiques mais bien logiques. En résumé, notre argument est que les limites du calcul sont déterminées en partie par le fait qu’une procédure effective doit pouvoir être décrite de manière finie.Even though Church’s thesis is widely accepted among mathematicians, it is nonetheless controversial. In this paper, we argue against the position of [Cleland 1993], which defends that Church s thesis must be rejected because the limits of computation depend upon the physical structure of the world. We first give a brief overview of Church’s thesis and then we present Cleland s argument. We then propose a critical analysis of Cleland s argument, which will involve some conceptual distinctions regarding the notion of computability, and finally we will show that the limits of computation are not physical but logical. In short, we argue that computation is limited by the fact that an effective procedure must be described in a finite way. (shrink)
Exploratory factor analysis is a statistical method widely used in quantitative psychology for the construction of scales and measurement instruments. It aims to reduce the complexity of a data set and explain the common and unique variance using latent variables. In introductory textbooks, exploratory factor analysis is generally presented in contrast to confirmatory factor analysis as a theory- or a hypothesis-generating process that does not require prior background, theory or hypothesis to be performed. The aim of the present paper is (...) to analyze this claim and clarify in which sense exploratory factor analysis is theory-laden. We provide a careful examination of the concepts it involves and thereby establish a clear limitation of the epistemic scope of exploratory factor analysis. (shrink)
ABSTRACTMonoidal logics were introduced as a foundational framework to analyze the proof theory of logical systems. Inspired by Lambek's seminal work in categorical logic, the objective is to defin...
Ce texte porte sur les principales objections faites à la logique déontique, notamment le dilemme de Jorgensen et les paradoxes de Ross. Pour aborder ces points, nous présenterons d’abord la position de Weinberger quant à la façon dont il considère que la logique doit être appliquée au domaine normatif, ce qui nous permettra d’en arriver à sa critique de la logique déontique. Avant de présenter le dilemme et les paradoxes, nous verrons quelques notions de logique modale afin de faciliter la (...) compréhension des objections et de la critique qui en sera faite. Finalement, nous proposerons une analyse formelle des paradoxes soulevés contre la logique déontique ainsi qu’une critique du présupposé réaliste implicite aux réponses faites au dilemme de Jorgensen. Nous serons alors en mesure de souligner quelques points importants à prendre en compte lors de la formalisation d’un discours. (shrink)
Ce texte se veut une analyse critique de l'approche de Thomason quant à la logique déontique. Alors que l'auteur défend que celle-ci doit être formalisée dans le cadre des logiques temporelles, nous soutenons que la temporalité est implicite à l'obligation, et de fait que la logique déontique n'a pas a être traitée dans la cadre d'une logique temporelle. Nous présenterons d'abord la position de Thomason. Il sera question des exemples dont l'auteur se sert pour justifier son point de vue philosophique (...) et du modèle sémantique qu'il propose pour rendre compte de l'obligation. Il sera ensuite sujet d'une critique des exemples de l'auteur et de son modèle sémantique. (shrink)
Ce texte porte sur l’analyse sémantique de la logique déontique. Nous analyserons de façon critique un texte de Schotch portant sur une interprétation de la logique déontique dans le cadre d’une sémantique non-kripkéenne. Nous laisserons de côté les choix relatifs à la syntaxe de son système afin de se concentrer sur l’analyse sémantique qu’il expose contre la logique déontique et sur celle qu’il propose en retour. Avant de voir le détail de son raisonnement, nous présenterons brièvement quelques notions de logique (...) modale afin de faciliter la compréhension de l’argument de Schotch. Nous présenterons ensuite l’argument de l’auteur contre la logique déontique afin de pouvoir exposer sa solution, ce qui ouvrira la porte à une lecture critique de son analyse. (shrink)
In this paper, we argue that Forrester’s paradox, as he presents it, is not a paradox of standard deontic logic. We show that the paradox fails since it is the result of a misuse of , a derived rule in the standard systems. Before presenting Forrester’s argument against standard deontic logic, we will briefly expose the principal characteristics of a standard system Δ. The modal system KD will be taken as a representative. We will then make some remarks regarding , (...) pointing out that its use is restricted to the standard system’s theorems, and cannot be applied to contingent conditionals. Finally, we will show that Forrester’s paradox is not a paradox of standard deontic logic, at least not in the sense he intended it to be. We show that the paradox cannot arise in KD since its semantical model is not rich enough to represent the intuitive validity of the conditional within Forrester’s paradox. We show that the paradox arises within a system that has a finer semantics. (shrink)
