Naming and Diagonalization, from Cantor to Godel to Kleene

We trace self-reference phenomena to the possibility of namingfunctions by names that belong to the domain over which thefunctions are defined. A naming system is a structure of theform (D, type( ),{ }), where D is a non-empty set; for everya D, which is a name of a k-ary function, {a}: D^k D is thefunction named by a, and type(a) is the type of a, which tellsus if a is a name and, if it is, the arity of the named function.Under quite general conditions we get a fixed point theorem,whose special cases include the fixed point theorem underlyingGödel's proof, Kleene's recursion theorem and many othertheorems of this nature, including the solution to simultaneousfixed point equations. Partial functions are accommodated byincluding "undefined" values; we investigate different systemsarising out of different ways of dealing with them. Many-sortednaming systems are suggested as a natural approach to generalcomputatability with many data types over arbitrary structures.The first part of the paper is a historical reconstruction ofthe way Gödel probably derived his proof from Cantor'sdiagonalization, through the semantic version of Richard. Theincompleteness proof–including the fixed point construction–resultfrom a natural line of thought, thereby dispelling the appearanceof a "magic trick". The analysis goes on to show how Kleene'srecursion theorem is obtained along the same lines.     

A conditional process model of perfectionism,goal-realization,and post-competition mood

Research has recently begun to examine the relationship between multidimensional perfectionism and athletes’ post-competition mood. However, to date, there have been few attempts to examine the interaction between dimensions of perfectionism or model possible explanatory processes. To address these limitations, in the current study we tested a novel conditional process model whereby the relationship between perfectionistic strivings and post-competition affect was mediated by the degree to which goals were considered to have been met (goal-realization) and that this indirect effect was, in turn, moderated by levels of perfectionistic concerns. We tested this model in a sample of 251 athletes who took part in a “Runmageddon” event - a cross-country obstacle race. Athletes completed measures of perfectionism (perfectionistic strivings and perfectionistic concerns) before the race and measures of goal-realization and mood (tense arousal, energetic arousal, and hedonic tone) between 24 and 48 h after the race. Analyses revealed that perfectionistic strivings were indirectly linked to a more unpleasant post-competition mood (higher tense arousal and lower hedonic tone) via perceptions of lower goal-realization. In addition, these two indirect effects were statistically significant only when perfectionistic concerns were medium and high. The results support the proposed conditional model and suggest the interplay between dimensions of perfectionism is important for athletes’ post-competition mood, and the level of perfectionistic concerns, especially.     

Holding points of view does not amount to knowledge

I argue that knowing and having points of view are fundamentally different epistemic states if we assume that having justified true beliefs is necessary for knowledge. Knowers necessarily possess justified true beliefs, but persons holding points of view may, for example, lack justification, have false beliefs, or both. I examine these differences and expose other crucial differentiating patterns between the structure of knowledge and points of view that make the latter more likely to lead to disagreements. I hypothesize that these patterns remain invariant in alternative views of knowledge like contextualism as long as we preserve the classical structure. Yet there is much research to be done on the multiple and contrasting properties that emerge if we consider non-classical analyses of knowledge and points of view.     

Transdisciplinarity and Conceptual Change

This article tenders an inaugural discussion of how conceptual change theory can contribute to deeper understandings of what is conceptually involved when people attempt (or succeed) to transition from multi- and interdisciplinarity to transdisciplinarity. After explaining the nuances of Newtonian thinking (framed as formal rather than postformal thinking), the article shares a comparison of multi-, inter-, and transdisciplinarity along four dimensions. Special attention is given to Nicolescuian transdisciplinarity, an approach predicated on the new sciences of quantum physics, chaos theory, and living systems theory (rather than Newtonian and Cartesian thinking). Nicolescuian transdisciplinarity is a new methodology for creating knowledge and it comprises three axioms: multiple Levels of Reality and the Hidden Third; the Logic of the Inclusive Middle; and, knowledge as complex, emergent, and embodied. The discussion then turns to an overview of three basic approaches to conceptual change theory: knowledge as theory, knowledge as elements, and knowledge as context. The author then applies conceptual change theory to understand what is involved in moving toward transdisciplinary thinking, including four elements necessary for conceptual change to occur (intelligibility, plausibility, fruitfulness, and dissatisfaction with existing conceptualizations and mental models). The article concludes with the idea that transdisciplinary thinking is a form of postformal thinking (especially paradigmatic order thinking) and suggests that future conceptual shifts toward transdisciplinarity involve achieving a transdisciplinary conceptual tipping point.     

The Bottoming‐Out Experience and the Turning Point: A Phenomenology of the Cognitive Shift From Drinker to Nondrinker

The bottoming‐out experience (BOE) is commonly considered the catalyst to sobriety. A phenomenological study was conducted to gain an understanding about this occurrence for alcoholics. Results indicated two distinct experiences: the BOE and the turning point.     

Leverage Points,Paradigms, and Grounded Action: Intervening in Educational Systems

This article discusses connections between grounded action, leverage points, and paradigm transformation and transcendence. Part one provides background on Meadows' (1999) Meadows, D. H. 1999. Leverage points: Places to intervene in a system, The Sustainability Institute. www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf (Accessed 22 June, 2006) [Google Scholar] approach to leverage points as well as the concept of paradigms. Part two argues that grounded action is inherently suited for leverage points analysis and paradigm-based interventions. Part three offers an example of individual paradigm transformation in the educational context vis-à-vis Olson's (2006) Olson, M. M. 2006. Driven Succeeding—The serpentine path of adult learning: A grounded action study in adult education, Ed.D. dissertation Fielding Graduate University.  [Google Scholar] grounded theory of driven succeeding. The article concludes with considerations of how the application of grounded action in one classroom might leverage system-wide paradigm transformation.     

Malleable conjoint partworths: How the breadth of response scales alters price sensitivity

In one laboratory study and one field study conducted with a large, representative sample of respondents, we show that seemingly innocuous questions that precede a conjoint task, such as demographic and usage-related screening questions can alter the price sensitivities recovered from the main conjoint task. The findings demonstrate that whether these prior questions use broad response categories (i.e., few scale points) or narrow response categories (i.e., many scale points) systematically influences consumers' price sensitivity in a CBC (Choice Based Conjoint) study. We suggest that this may occur because the narrow (vs. broad) response categories in the prior questions lead to consideration of a greater (vs. fewer) number of attributes during the key conjoint task. Since both groups of consumers readily consider the naturally salient price attribute, responding to previous questions with narrow (vs. broad) response categories leads to a greater (vs. fewer) number of non-price attributes being considered, and consequently, decrease the weight afforded to price and reduce price sensitivity.     

The discovery and comparison of symbolic magnitudes

Humans and other primates are able to make relative magnitude comparisons, both with perceptual stimuli and with symbolic inputs that convey magnitude information. Although numerous models of magnitude comparison have been proposed, the basic question of how symbolic magnitudes (e.g., size or intelligence of animals) are derived and represented in memory has received little attention. We argue that symbolic magnitudes often will not correspond directly to elementary features of individual concepts. Rather, magnitudes may be formed in working memory based on computations over more basic features stored in long-term memory. We present a model of how magnitudes can be acquired and compared based on BARTlet, a representationally simpler version of Bayesian Analogy with Relational Transformations (BART; Lu, Chen, & Holyoak, 2012). BARTlet operates on distributions of magnitude variables created by applying dimension-specific weights (learned with the aid of empirical priors derived from pre-categorical comparisons) to more primitive features of objects. The resulting magnitude distributions, formed and maintained in working memory, are sensitive to contextual influences such as the range of stimuli and polarity of the question. By incorporating psychological reference points that control the precision of magnitudes in working memory and applying the tools of signal detection theory, BARTlet is able to account for a wide range of empirical phenomena involving magnitude comparisons, including the symbolic distance effect and the semantic congruity effect. We discuss the role of reference points in cognitive and social decision-making, and implications for the evolution of relational representations.     

Moderate structural realism about space-time

This paper sets out a moderate version of metaphysical structural realism that stands in contrast to both the epistemic structural realism of Worrall and the—radical—ontic structural realism of French and Ladyman. According to moderate structural realism, objects and relations (structure) are on the same ontological footing, with the objects being characterized only by the relations in which they stand. We show how this position fares well as regards philosophical arguments, avoiding the objections against the other two versions of structural realism. In particular, we set out how this position can be applied to space-time, providing for a convincing understanding of space-time points in the standard tensor formulation of general relativity as well as in the fibre bundle formulation.     

The question of the training analysis system. Notes from the debate in Oslo

The Norwegian discussion of the training analyst system and the pro et contra arguments are shortly presented. When this note is written, the Board is contemplating to propose a revision of the by-laws, making it somewhat easier to fulfil the criteria for being approved as training analyst.