Clayton Peterson

L'objectif du présent texte est de discuter de la portée épistémique de la méthode axiomatique. Tout d'abord, il sera question du contexte à partir duquel la méthode axiomatique a émergé, ce qui sera suivi d'une discussion des motivations du programme de Hilbert et de ses objectifs. Ensuite, nous exposerons la méthode axiomatique dans un cadre plus moderne afin de mettre en lumière son utilité et sa portée théorique. Finalement, il s'agira d'explorer l'influence de la méthode axiomatique en physique, surtout en ce qui a trait à l'application de la méthode par Hilbert. Nous discuterons de ses objectifs et de l'épistémologie qui accompagnait sa vision du 6e problème, ce qui nous amènera à discuter des limites épistémiques de la méthode axiomatique et de l'entreprise scientifique en général.

The aim of the present paper is to introduce a method to test the validity of legal inferences. We begin by presenting the rationale of our method and then we expose the philosophical foundations of our analysis. If formal philosophy is to be of help to legal discourse, then it must first reflect upon the law's fundamental characteristics that should be taken into account. Our analysis shows that (Canadian) legal discourse possesses three fundamental characteristics which ought to be considered if one wants to represent the formal structure of legal arguments. These characteristics are the presupposed consistency of legal discourse, the fact that there is a hierarchy between norms and obligations to preserve this consistency and the fact that legal inferences are subjected to the principle of deontic consequences. We present a formal deontic logic which is built according to these characteristics and provide the completeness results. Finally, we present a semi-formal method (bas...

Résumé 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 ...

Explanation of human and social phenomena is often formulated using unobservable constructs, otherwise known as latent constructs. In this context, latent constructs are broadly understood as latent characteristics. Formally, latent constructs are interpreted as latent variables that influence the behavior of observed variables (items). Latent constructs are identified through measurement instruments, which are tested in specific samples using measurement models, representing the relationship between the latent variable and the items. Depending on the methodological guidelines that are followed during the development of measurement instruments, these measurement models will be tested using factor analytic techniques such as exploratory and confirmatory factor analysis. Historically, these techniques have been surrounded by various controversies and have generated their share of confusion. This chapter explores the conceptual and philosophical issues related to scale development in h...

The present paper introduces an action logic able to model human actions. We begin by providing an analysis of the proof-theory of action logics from the perspective of category theory. Action logics are classified as different types of monoidal deductive systems with respect to their categorical structure. This enables us to correlate the properties of the logical connectives with the type of deductive system that is used. We then provide a philosophical analysis of action connectives and, in light of our analysis, show which type of deductive system is required to model human actions. According to the usual distinction between actions and propositions in dynamic logic, we distinguish between an action logic, representing the formal structure of actions, and a propositional action logic, expressing the formal structure of the language we use to talk about actions.

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(s) and other logical connectives. We show that the elimination of double negation(s) is independent from the de Morgan dualities, that monoidal deductive systems are not necessarily weakly distributive and that deductive systems satisfying the elimination of double negation(s) and the law of excluded middle are not necessarily classical.

Résumé Ce texte porte sur l'analyse sémantique de la logique déontique. Nous analyserons de façon critique un texte de Schotch (1981) portant sur une interprétation de la logique déontique dans le cadre d'une sémantique non-kripkéenne. Nous laisserons de côté les ...

In Canadian common or civil law treatises on evidence, truth is identified as at the core of our judicial system. Ducharme writes: [translation] “The search of truth is the essential subject of the rules regarding the law of evidence [...]”4 Similarly, Sopinka states that the purpose of a trial “is the search for truth.”5 Others make more modest claims. For instance, Paciocco & Stuesser argue that the rules of evidence are there to “help the trier of fact to come to an accurate factual determination.”6 But still, the notion of an accurate factual determination implies an ideal of truth.

The present thesis develops formal tools relevant to the analysis of legal discourse. When applied to legal reasoning, logic can be used to model the structure of legal inferences and, as such, it provides a criterion to discriminate between good and bad reasonings. But using logic to model normative reasoning comes with some problems, as shown by the various paradoxes one finds within the literature. From a historical point of view, these paradoxes lead to the introduction of different approaches, such as the ones that emphasize the notion of action and those that try to model conditional normative reasoning. In the first part of this thesis, we provide a review of the literature, which is complementary to the one we did in Peterson (2011). The second part of the thesis concerns our theoretical contribution. First, we propose a monadic deontic logic as an alternative to the standard system, answering many objections that can be made against it. This system is then adapted to model ...

The present paper aims to bridge the gap between deontic logic, categorial grammar and category theory. We propose to analyze Forrester's (1984) paradox through the framework of Lambek's (1958) syntactic calculus. We first recall the definition of the syntactic calculus and then explain how Lambek (1988) defines it within the framework of category theory. Then, we briefly present Forrester's paradox in conjunction with standard deontic logic, showing that this paradox contains some features that reflect many problems within the literature. Finally, we analyze Forrester's paradox within the framework of the syntactic calculus and we show how a typed syntax can provide conceptual insight regarding some of the problems that deontic logic faces.

Ce texte se veut une analyse critique de l'approche de Thomason (1981) quant a la logique deontique. Alors que l'auteur defend que celle-ci doit etre formalisee dans le cadre des logiques temporelles, nous soutenons que la temporalite est implicite a l'obligation, et de fait que la logique deontique n'a pas a etre traitee dans la cadre d'une logique temporelle. Nous presenterons 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 modele semantique qu'il propose pour rendre compte de l'obligation. Il sera ensuite sujet d'une critique des exemples de l'auteur et de son modele semantique.

This paper extends the results presented in [22,20] and explores how new paradoxes arise in various substructural logics used to model conditional obligations. Our investigation starts from the comparison that can be made between monoidal logics and Lambek's [17] analysis of substructural logics, who distinguished between four different ways to introduce a (multiplicative) disjunction. While Lambek's analysis resulted in four variants of substructural logics, namely BL1, BL1(a), BL1(b) and BL2, we show that these systems are insufficient to model conditional obligations insofar as either they lack relevant desirable properties, such as some of De Morgan's dualities or the law of excluded middle, or they satisfy logical principles that yield new paradoxes. To answer these concerns, we propose an intermediate system that is stronger than BL1 but weaker than BL1(a), BL1(b) and BL2.

AIMS This study examined the moderating role of two resources (social support and recognition) in the longitudinal relationship between workload and bullying behaviours in nurses. DESIGN A two-wave (12-month) longitudinal study was conducted. METHOD French-Canadian nurses (n = 279) completed an online survey (October 2014 and October 2015) assessing their perceptions of job characteristics within the work environment (workload, social support, job recognition) as well as exposure to negative behaviours at work. RESULTS Workload positively predicted exposure to bullying behaviours over time, but only when job recognition and social support were low. Workload was unrelated to bullying when social support was high and was negatively related to bullying when job recognition was high. CONCLUSION This study aligns with the work environment hypothesis, showing that poorly designed and stressful job environments provide fertile ground for bullying behaviours. IMPACT Bullying is a growing concern in the nursing profession that not only undermines nurses' well-being but also compromises patient safety and care. It is thus important to identify work-related factors that can contribute to the presence of bullying behaviours in nurses in the hopes of reducing their occurrence and repercussions. This study contributes to this endeavour and identifies two key social coping resources that can help manage the stress associated with workload, resulting in less perceived bullying behaviour among nurses.

String diagrams are useful tools in many disciplines, including physics, computer science and linguistics. Their language is closely related to category theory. From an epistemological point of view, category theory offers a foundational framework that enables us to see the common structure shared by these disciplines, namely the structure of a monoidal category. This structure can also be found in other fields of study, for instance in logic. Accordingly, it appears that string diagrams could be applied in logic to model reasonings. In this research article, we apply string diagrams to deontic logic and use them to model conditional normative inferences. Building on previous work, we define a deductive system for conditional normative reasoning CNR and show that it is sound and complete with respect to a string diagrammatic semantics. A decision procedure is provided and string diagrams are used to test the validity of conditional inferences.

Purpose Job demands can contribute to nurses’ turnover intention and this can have an impact on health services among the general population. It appears important to identify the work environment factors associated with turnover intention, as well as the psychological resources liable to act on this relationship. Drawing on self-determination theory (SDT), the purpose of this study (n=1179) is to investigate the relationship between two job demands (role ambiguity and role conflict) and turnover intention, as well as the moderating role of basic need satisfaction (autonomy, competence and relatedness) within these relationships. Design/methodology/approach This cross-sectional study was conducted among nurses (Québec, Canada). Nurses completed an online questionnaire. To test the proposed moderating effect of satisfaction of the three psychological needs (i.e. autonomy, competence and relatedness) in the relationship between job demands (i.e. role ambiguity and role conflict) and tu...

Purpose The purpose of this paper is to investigate the psychological and motivational processes involved in the relationship between two forms of destructive leadership (tyrannical and laissez-faire) and employee health (burnout, affective commitment and job performance). Drawing on self-determination theory, this paper links tyrannical and laissez-faire leadership to employee health through psychological need frustration and poor-quality (controlled) work motivation. Design/methodology/approach A total of 399 Canadian nurses took part in this cross-sectional study. Structural equational modelling analyses were conducted. Findings Results show that tyrannical leadership frustrates nurses’ needs for autonomy, competence and relatedness, whereas laissez-faire leadership frustrates nurses’ need for autonomy only. The frustration of needs for autonomy and competence predicts low-quality (controlled) work motivation, which is consequently associated with impaired health (burnout and low...

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.