Clayton Peterson - Profile on Academia.edu (original) (raw)

Papers by Clayton Peterson

L'objectif du présent texte est de discuter de la portée épistémique de la méthode axiomatiqu... more 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.

Formal Philosophy and Legal Reasoning: The Validity of Legal Inferences

Logique Et Analyse, 2016

The aim of the present paper is to introduce a method to test the validity of legal inferences. W... more 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...

revueithaque.org

Résumé Ce texte porte sur les principales objections faites à la logique déontique, notamment le ... more 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 ...

International Workshop on Artificial Intelligence and Cognition, 2014

Monoidal logics are logics that can be seen as specific instances of monoidal categories. They ar... more Monoidal logics are logics that can be seen as specific instances of monoidal categories. They are constructed using specific rules and axiom schemata that allow to make explicit the monoidal structure of the logics. Among monoidal logics, we find Cartesian logics, which are instances of Cartesian categories. As it happens, many paradoxes in epistemic, deontic and action logics can be related to the Cartesian structure of the logics that are used. While in epistemic and deontic logics the source of the paradoxes is often found within the principles that govern the modal operators, our framework enables us to show that many problems can be avoided by adopting a proper monoidal structure. Thus, the usual modal rules and axiom schemata do not necessarily need to be discarded to avoid the paradoxes. In this respect, monoidal logics o↵er an alternative way to model knowledge, actions and normative reasoning. Furthermore, it provides us with new avenues to analyze modalities.

Synthese Library, 2019

Explanation of human and social phenomena is often formulated using unobservable constructs, othe... more 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...

Chapitre 3. La proposition

A Logic for Human Actions

The present paper introduces an action logic able to model human actions. We begin by providing a... more 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.

A comparison between monoidal and substructural logics

Journal of Applied Non-Classical Logics, 2016

Monoidal logics were introduced as a foundational framework to analyse the proof theory of deonti... more 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.

The categorical imperative: Category theory as a foundation for deontic logic

Journal of Applied Logic, 2014

ABSTRACT

Logica Universalis, 2015

This paper provides an analysis of contrary-to-duty reasoning from the proof-theoretical perspect... more 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.

revueithaque.org

Résumé Ce texte porte sur l'analyse sémantique de la logique déontique. Nous analyserons de ... more 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 ...

When workload predicts exposure to bullying behaviours in nurses: The protective role of social support and job recognition

Journal of Advanced Nursing

In Canadian common or civil law treatises on evidence, truth is identified as at the core of our ... more 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 applie... more 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 ...

How to Act? Reasoning with Conflicting Obligations

From linguistics to deontic logic via category theory

The present paper aims to bridge the gap between deontic logic, categorial grammar and category t... more 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.

Cet ouvrage a ete redige en LaTeX, ce qui permet d'atteindre directement certaines sections, ... more Cet ouvrage a ete redige en LaTeX, ce qui permet d'atteindre directement certaines sections, notes ou references bibliographiques par le biais des hyperliens.

Ce texte se veut une analyse critique de l'approche de Thomason (1981) quant a la logique deo... more 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.

Conditional Normative Reasoning with Substructural Logics

This paper extends the results presented in [22,20] and explores how new paradoxes arise in vario... more 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.

L'objectif du présent texte est de discuter de la portée épistémique de la méthode axiomatiqu... more 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.

Formal Philosophy and Legal Reasoning: The Validity of Legal Inferences

Logique Et Analyse, 2016

The aim of the present paper is to introduce a method to test the validity of legal inferences. W... more 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...

revueithaque.org

Résumé Ce texte porte sur les principales objections faites à la logique déontique, notamment le ... more 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 ...

International Workshop on Artificial Intelligence and Cognition, 2014

Monoidal logics are logics that can be seen as specific instances of monoidal categories. They ar... more Monoidal logics are logics that can be seen as specific instances of monoidal categories. They are constructed using specific rules and axiom schemata that allow to make explicit the monoidal structure of the logics. Among monoidal logics, we find Cartesian logics, which are instances of Cartesian categories. As it happens, many paradoxes in epistemic, deontic and action logics can be related to the Cartesian structure of the logics that are used. While in epistemic and deontic logics the source of the paradoxes is often found within the principles that govern the modal operators, our framework enables us to show that many problems can be avoided by adopting a proper monoidal structure. Thus, the usual modal rules and axiom schemata do not necessarily need to be discarded to avoid the paradoxes. In this respect, monoidal logics o↵er an alternative way to model knowledge, actions and normative reasoning. Furthermore, it provides us with new avenues to analyze modalities.

Synthese Library, 2019

Explanation of human and social phenomena is often formulated using unobservable constructs, othe... more 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...

Chapitre 3. La proposition

A Logic for Human Actions

The present paper introduces an action logic able to model human actions. We begin by providing a... more 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.

A comparison between monoidal and substructural logics

Journal of Applied Non-Classical Logics, 2016

Monoidal logics were introduced as a foundational framework to analyse the proof theory of deonti... more 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.

The categorical imperative: Category theory as a foundation for deontic logic

Journal of Applied Logic, 2014

ABSTRACT

Logica Universalis, 2015

This paper provides an analysis of contrary-to-duty reasoning from the proof-theoretical perspect... more 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.

revueithaque.org

Résumé Ce texte porte sur l'analyse sémantique de la logique déontique. Nous analyserons de ... more 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 ...

When workload predicts exposure to bullying behaviours in nurses: The protective role of social support and job recognition

Journal of Advanced Nursing

In Canadian common or civil law treatises on evidence, truth is identified as at the core of our ... more 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 applie... more 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 ...

How to Act? Reasoning with Conflicting Obligations

From linguistics to deontic logic via category theory

The present paper aims to bridge the gap between deontic logic, categorial grammar and category t... more 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.

Cet ouvrage a ete redige en LaTeX, ce qui permet d'atteindre directement certaines sections, ... more Cet ouvrage a ete redige en LaTeX, ce qui permet d'atteindre directement certaines sections, notes ou references bibliographiques par le biais des hyperliens.

Ce texte se veut une analyse critique de l'approche de Thomason (1981) quant a la logique deo... more 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.

Conditional Normative Reasoning with Substructural Logics

This paper extends the results presented in [22,20] and explores how new paradoxes arise in vario... more 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.

De la logique des obligations, des permissions et des interdictions: De von Wright à aujourd'hui

Pensée rationnelle et argumentation

Review of Jean-Pierre Marquis 'From a Geometrical point of view: A study of the history and philosophy of category theory'

Université de Montréal