What are symbols symbols of? Situated action,mythological bootstrapping and the emergence of the Self

This paper addresses the question of how symbols should be understood in analytical psychology and psychoanalysis. The point of view examined focuses on the recent turn to more cognitive and developmental models in both disciplines and briefly reviews and critiques the evolutionary and cognitive arguments. The paper then presents an argument based on dynamic systems theory in which no pre-existing template or structure for either mind or behaviour is assumed. Within the dynamic systems model the Self is viewed as an emergent phenomenon deriving from the dynamic patterns existing in a complex system that includes the physiological characteristics of the infant, the intentional attributions of the caregiver and the cultural or symbolic resources that constitute the environment. The symbol can then be seen as a discrete, and in important ways an autonomous, element in the dynamic system. Conclusions are drawn for further research into the nature of the symbol with implications for both theory and practice in analytical psychology and psychoanalysis.     

Experience and inference: how far will science carry us?

This paper begins with a view of the remarkable understanding of infant and child development that has evolved from research and observation. The limitations of this contribution from science to the multi-dimensional context-based individuality of each human in his or her intersubjective realm are then considered. For a contemporary view we must recognize the influence of the variability of experiences and the inferences drawn from them. Inferences involve symbolization and culturally derived archetypes as illustrated in a clinical example.     

On Modal μ-Calculus and Non-Well-Founded Set Theory

A finitary characterization for non-well-founded sets with finite transitive closure is established in terms of a greatest fixpoint formula of the modal -calculus. This generalizes the standard result in the literature where a finitary modal characterization is provided only for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and non-well-founded sets.     

Categorical Abstract Algebraic Logic Metalogical Properties

Metalogical properties that have traditionally been studied in the deductive system context (see, e.g., [21]) and transferred later to the institution context [33], are here formulated in the -institution context. Preservation under deductive equivalence of -institutions is investigated. If a property is known to hold in all algebraic -institutions and is preserved under deductive equivalence, then it follows that it holds in all algebraizable -institutions in the sense of [36].     

Nonparametric IRT: Testing the bi-isotonicity of isotonic probabilistic models (ISOP)

Nonparametric tests for testing the validity of polytomous ISOP-models (unidimensional ordinal probabilistic polytomous IRT-models) are presented. Since the ISOP-model is a very general nonparametric unidimensional rating scale model the test statistics apply to a great multitude of latent trait models. A test for the comonotonicity of item sets of two or more items is suggested. Procedures for testing the comonotonicity of two item sets and for item selection are developed. The tests are based on Goodman-Kruskal's gamma index of ordinal association and are generalizations thereof. It is an essential advantage of polytomous ISOP-models within probabilistic IRT-models that the tests of validity of the model can be performed before and without the model being fitted to the data. The new test statistics have the further advantage that no prior order of items or subjects needs to be known.     

Dynamic analyses of mother-child interactions in functional and dysfunctional dyads: a synergetic approach

Describes the application of a new analytical approach (derived from synergetics, a complex dynamic systems theory) to home observational data of mother–child interactions in average dyads and dyads with children referred for disruptive behavior problems at home and school (n = 11 in each group). Results show that (1) the two groups differed in their daily interactions in predictable ways, and (2) the most frequent patterns of interactions observed in the two groups brought them back repeatedly to behave in similar ways toward each other. The findings are in keeping with a body of literature on mother–child interactions. However, they add to it by providing multivariate, graphical representations of these interactions and by offering a conceptual framework within which to move from an observational to an inferential level of analysis. At that level, the transactional processes that are characteristic of functional and dysfunctional relationships may become apparent.     

What the Liar Taught Achilles

Zeno's paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno's paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.     

Severe Withdrawal (and Recovery)

The problem of how to remove information from an agent's stock of beliefs is of paramount concern in the belief change literature. An inquiring agent may remove beliefs for a variety of reasons: a belief may be called into doubt or the agent may simply wish to entertain other possibilities. In the prominent AGM framework for belief change, upon which the work here is based, one of the three central operations, contraction, addresses this concern (the other two deal with the incorporation of new information). Makinson has generalised this work by introducing the notion of a withdrawal operation. Underlying the account proffered by AGM is the idea of rational belief change. A belief change operation should be guided by certain principles or integrity constraints in order to characterise change by a rational agent. One of the most noted principles within the context of AGM is the Principle of Informational Economy. However, adoption of this principle in its purest form has been rejected by AGM leading to a more relaxed interpretation. In this paper, we argue that this weakening of the Principle of Informational Economy suggests that it is only one of a number of principles which should be taken into account. Furthermore, this weakening points toward a Principle of Indifference. This motivates the introduction of a belief removal operation that we call severe withdrawal. We provide rationality postulates for severe withdrawal and explore its relationship with AGM contraction. Moreover, we furnish possible worlds and epistemic entrenchment semantics for severe withdrawals.     

A Systems/Dialectical Model of Supervision: A Symbolic Process

Although there has been a proliferation of models of supervision in the marriage and family therapy literature recently, most tend to focus on methods rather than on the process of supervision. The model presented here is grounded in developmental concepts and focuses on student learning through a dialectical process of cognitive and emotional growth and incorporates three stages: 1) developing relationships; 2) breaking impasses, and 3) orchestrating changes. Students discover that supervision becomes isomorphic with relationship issues that arise in their therapy sessions. Dialectical in nature in that each stage is characterized by the resolution of contradictory emotions, the supervision process helps supervisees experience emotional shifts in their interactions with others, referred to as emotional restructuring.     

Proof-Theoretic Modal PA-Completeness III: The Syntactic Proof

This paper is the final part of the syntactic demonstration of the Arithmetical Completeness of the modal system G; in the preceding parts [9] and [10] the tools for the proof were defined, in particular the notion of syntactic countermodel. Our strategy is: PA-completeness of G as a search for interpretations which force the distance between G and a GL-LIN-theorem to zero. If the GL-LIN-theorem S is not a G-theorem, we construct a formula H expressing the non G-provability of S, so that ⊢_GL-LIN ∼ H and so that a canonical proof T of ∼ H in GL-LIN is a syntactic countermodel for S with respect to G, which has the height θ(T) equal to the distance d(S, G) of S from G. Then we define the interpretation ξ of S which represents the proof-tree T in PA. By induction on θ(T), we prove that ⊢_PA S^ξ and d(S, G) > 0 imply the inconsistency of PA. This revised version was published online in June 2006 with corrections to the Cover Date.