A Dichotomic Analysis of the Surprise Examination Paradox

This paper presents a dichotomic analysis of the surprise examination paradox. In section 1, I analyse the surprise notion in detail. I introduce then in section 2, the distinction between a monist and dichotomic analysis of the paradox. I also present there a dichotomy leading to distinguish two basically and structurally different versions of the paradox, respectively based on a conjoint and a disjoint definition of the surprise. In section 3, I describe the solution to SEP corresponding to the conjoint definition. Lastly, I expose in section 4, the solution to SEP based on the disjoint definition

An Analytic View of Delusion

The present article proposes a logical account of delusions, which are regarded as conclusions resulting from fallacious arguments. This leads to distinguish between primary, secondary, ..., n-ary types of delusional arguments. Examples of delusional arguments leading to delusion of reference, delusion of influence, thought-broadcasting delusion and delusion of grandeur are described and then analyzed. This suggests finally a way susceptible of improving the efficiency of cognitive therapy for delusions

Theory of Cognitive Distortions: Over-Generalisation and Mislabeling

In a previous paper (Compléments pour une théorie des distorsions cognitives, Journal de Thérapie Comportementale et Cognitive, 2007), we introduced some elements aimed at contributing to a general theory of cognitive distortions. Based on the reference class, the duality and the system of taxa, these elements allow to define the general cognitive distortions as well as the specific cognitive distortions. This model is extended here to the description of two other classical cognitive distortions: over-generalisation and mislabelling. The definition of the two latter cognitive distortions is based on preliminary distinction between three levels of reasoning: primary, secondary and ternary pathogenic arguments. The latter analysis also leads to define two other cognitive distortions which insert themselves into this framework: ill-grounded inductive projection and confirmation bias

A Dichotomic Analysis of the Surprise Examination Paradox

This paper proposes a new framework to solve the surprise examination paradox. I survey preliminary the main contributions to the literature related to the paradox. I introduce then a distinction between a monist and a dichotomic analysis of the paradox. With the help of a matrix notation, I also present a dichotomy that leads to distinguish two basically and structurally different notions of surprise, which are respectively based on a conjoint and a disjoint structure. I describe then how Quine's solution and Hall's reduction apply to the version of the paradox corresponding to the conjoint structure. Lastly, I expose a solution to the version of the paradox based on the disjoint structure

A Logical Defence of Maher's Model of Polythematic Delusions

We proceed to describe a model for the formation and maintenance of polythematic delusions encountered in schizophrenia, which is in adequacy with Brendan Maher's account of delusions. Polythematic delusions are considered here as the conclusions of arguments triggered by apophenia that include some very common errors of reasoning such as post hoc fallacy and confirmation bias. We describe first the structure of reasoning which leads to delusions of reference, of telepathy and of influence, by distinguishing between the primary, secondary, tertiary and quaternary types of delusional arguments. These four levels of arguments correspond to a stage the nature of which is respectively instantial, inductive, interpretative at a monothematic level and interpretative at a polythematic level. We also proceed to identify accurately the fallacious steps in the corresponding reasoning. We expose then the role of apophenia in the elaboration of delusional ideas. Lastly, we describe the role played by the hallucinations in the present model

The Problem of the Relationships of Love, Hate and Indifference

In Franceschi (2002), I presented a theory based on the matrices of concepts aiming at providing an alternative to the classification proposed by Greimas, in the field of paradigmatic analysis. The problem of specifying the relationships of the concepts of love, hate and indifference, arises in this construction. I attach myself to describe the problem of the love-hate-indifference relationships in detail, and several solutions that have been proposed to solve it. Finally I expose a solution to this problem, based on an extension of the theory of matrices of concepts

A characterization of the one-sidedness fallacy within the framework of the cognitive distortions

In this paper, I propose an accurate description of the cognitive process involved in the one-sidedness fallacy, a widespread type of fallacy. I describe first several characterizations of the one-sidedness fallacy, that are either inductive or deductive, or occurring at a meta-philosophical level. I recall, second, the framework of the cognitive distortions described in Franceschi (2007). I give then a definition of the one-sidedness fallacy, by describing it as a general cognitive distortion: the disqualification of one pole. I show finally how the one-sidedness fallacy distinguishes itself from the confirmation bias

Theory of cognitive distortions: personalisation

In a previous paper (Compléments pour une théorie des distorsions cognitives, Journal de Thérapie Comportementale et Cognitive, 2007), we did present some elements aimed at contributing to a general theory of cognitive distortions. Based on the reference class, the duality and the system of taxa, these elements led to distinguish between the general cognitive distortions (dichotomous reasoning, disqualification of one pole, minimisation, maximisation) and the specific cognitive distortions (disqualifying the positive, selective abstraction, catastrophism). By also distinguishing between three levels of reasoning - the instantiation stage, the interpretation stage and the generalisation stage - we did also define two other cognitive distortions: over-generalisation and mislabelling (Théorie des distorsions cognitives : la sur-généralisation et l'étiquetage, Journal de Thérapie Comportementale et Cognitive, 2009). We currently extend this model to another classical cognitive distortion: personalisation

Tutte's invariant approach for Brownian motion reflected in the quadrant

We consider a Brownian motion with drift in the quarter plane with orthogonal reflection on the axes. The Laplace transform of its stationary distribution satisfies a functional equation, which is reminiscent from equations arising in the enumeration of (discrete) quadrant walks. We develop a Tutte's invariant approach to this continuous setting, and we obtain an explicit formula for the Laplace transform in terms of generalized Chebyshev polynomials.Comment: 14 pages, 3 figure