Innovations in computational type theory using Nuprl

For twenty years the Nuprl (“new pearl”) system has been used to develop software systems and formal theories of computational mathematics. It has also been used to explore and implement computational type theory (CTT)—a formal theory of computation closely related to Martin-Löf's intuitionistic type theory (ITT) and to the calculus of inductive constructions (CIC) implemented in the Coq prover.

This article focuses on the theory and practice underpinning our use of Nuprl for much of the last decade. We discuss innovative elements of type theory, including new type constructors such as unions and dependent intersections, our theory of classes, and our theory of event structures.

We also discuss the innovative architecture of Nuprl as a distributed system and as a transactional database of formal mathematics using the notion of abstract object identifiers. The database has led to an independent project called the Formal Digital Library, FDL, now used as a repository for Nuprl results as well as selected results from HOL, MetaPRL, and PVS. We discuss Howe's set theoretic semantics that is used to relate such disparate theories and systems as those represented by these provers.     

Perceptions of married life among single never‐married,single ever‐married,and married adults

With the increasing prevalence of single adults in the United States, perceptions of marriage as the relationship “gold standard” may be diminishing. In this study (N = 6,576), we explored perceptions of married life in three subgroups of participants: Those who have never married, ever married, and currently married. Across subgroups, most did not perceive married life more positively than single life in external/tangible domains (e.g., more friends), but did in emotional experiences and frame of mind (e.g., contentment). These findings suggest conceptualizations of marriage may be changing to be less positive or less discrepant from conceptualizations of single life. However, these findings also suggest that people continue to view marital relationships as a positive source of emotional experience and support.     

Ambiguity and contradiction: the outlines of Jung’s dialectics

This essay explores Jung’s thinking strategies, argumentation patterns, and concept formation processes, and reveals how they distinguish his work from normal present‐day science. Jung doesn’t much appreciate the law of noncontradiction, which is a cornerstone of classical logic, and he doesn’t refrain from using openly ambiguous theoretical terms. It will be pointed out that not only specific archetypes, but the notion of archetype itself, as well as other of Jung’s theoretical notions (energy, including libidinal energy, polarity, integration, wholeness, instinct, symbol, and so on), are consciously ambiguous and thus potentially contradictory. It is shown that this kind of dialectic research strategy and related contradiction‐tolerant and ambiguity‐tolerant methods connect his work to Post‐Kantian German Idealism, Schelling’s and Schopenhauer’s philosophy in particular. However, it was Hegel who, in his Science of Logic, presented a systematic overview of such dialectic principles of reasoning, which were, in the 19^th century, widely applied by German philosophers, theologians, and other scholars. Unfortunately, Jung decided not to study Hegel, but, instead, wrote derogatorily of his work. It will be argued that a Jungian who wants to be conscious of her own argumentation strategies and methods of concept formation should study Hegel’s complex and sophisticated dialectical logic. In addition, it is suggested that Jungian depth psychology might help us to amend the phenomenological deficits of Hegel’s system by providing it with a primal experiential source. This is needed because Hegel’s Geist, due to its intellectual emphasis, is a self‐conscious conceptual totality which advances progressively from stage to stage by guiding itself with the help of dialectical reason (Vernunft). It will be shown that if enriched with a proper kind of experiential givenness, which includes the Jungian unconsciousness (with libidinal energy, instincts, and archetypes), Hegelian metaphysics would be able to embrace a seriously aconceptual or preconceptual dimension. Aconceptual experience, which is, for Jung, mainly the instinctual layer of archetypes, remains essentially inaccessible, not only for normal scientific concepts, but for the concepts of any form of dialectics as well.     

Discipleship Training Of Children and Youth

Today, we all face an infinite number of faith choices, especially youth. This makes confirmation ministry as discipleship training most important in our churches. This article explores the confirmation ministry of Lord of Life Lutheran Church in Depew, NY, and critically analyzes the methodology—4 turnings, 6 disciplines, and 19 assets—behind the ministry. This methodology has been developed from researchers such as Jean Piaget, James Fowler, Duffy Robins, and researchers at the Search Institute.     

Martin's Axiom,Omitting Types,and Complete Representations in Algebraic Logic

We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n w via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin's axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey's omitting types theorem fails for L _n, the first order logic restricted to the first n variables when 2 #lt; n#lt;w. L _n has been recently (and quite extensively) studied as a many-dimensional modal logic.     

Can there be a science of the symbolic?

Science means not just 'knowing', but knowing verified by replicability. Science is particularly hard to bring to depth psychology because the individual uniquenesses that can't be repeated are what make people most deeply themselves. Everyone, including the analytic investigator, however, has a science, in the sense of a world-view that is replicated by experience. Jung offered hermeneutics as an alternative mode to science for getting to know the psychological subject. But as Heidegger emphasized, hermeneutics always begins with the projection of a world-view, i.e., the science of the would-be interpreter. In the analytic situation, dialogue is available to test the world-view and enlarge its horizon, in accord with Gadamer's expansion of hermeneutics, 'the classical discipline concerned with the art of understanding texts', into a method of inquiry open to the possibilities of otherness. An example is given from an analytic training seminar, in which the author began by projecting his version of the theory of psychological types onto the dream material a candidate offered in response to the seminar. A dialogue with the candidate ensued which enabled the teacher to correct his original, somewhat rigid, application of his scientific viewpoint. In such a dialogue, psyche emerges as the final interpreter of what is, generating hypotheses that can fruitfully be applied to the understanding of other cases.     

Propositions as Structured Cognitive Event-Types

According to act theories, propositions are structured cognitive act-types. Act theories appear to make propositions inherently representational and truth-evaluable, and to provide solutions to familiar problems with alternative theories, including Frege’s and Russell’s problems, and the third-realm and unity problems. Act theories have critical problems of their own, though: acts as opposed to their objects are not truth evaluable, not structured in the right way, not expressed by sentences, and not the objects of propositional attitudes. I show how identifying propositions with other cognitive event-types, namely thoughts, has the perceived virtues of act theories without the defects.     

Attentional processing of emotional material in types of anxiety and depression

ABSTRACT

The present study was designed to address the hypothesis that differences and similarities in patterns of attentional processing in recently proposed types of anxiety and depression are connected with the dominant (reactive, regulative) function they play in stimulation processing and their structural components. Participants (N?=?1247) filled out the Anxiety and Depression Questionnaire, which assesses types of anxiety and depression, and completed the Emotional Faces Attentional Test one week later. The obtained results confirmed our prediction and suggested that the proposed typology of anxiety and depression is valid in the adaptive meanings of both phenomena.     

Self‐Regulation and Personality Profiles: Empirical Development,Longitudinal Stability and Predictive Ability

We used Latent Profile and Latent Profile Transition Analysis to empirically develop and compare competing models of personality profiles (three‐ and four‐profile models). We do so using data from the New Zealand Attitudes and Values Study, a large longitudinal national probability sample of New Zealanders. Both three‐ and four‐profile solutions demonstrated good fit and longitudinal stability. Trait configurations and predictive outcomes of the four‐profile model were the most interpretable in terms of the theoretical literature, as this solution mirrored the theoretical foundation of self‐regulatory ego‐constructs. This supported the interpretation of a four‐profile model as providing a useful distinction over and above the three‐profile model. We conclude that, compared to the three‐profile model, the four‐profile solution provides a better foundation to serve as a complementary approach to variable‐centre research. Copyright © 2016 European Association of Personality Psychology     

C. G. Jung and intuition: from the mindscape of the paranormal to the heart of psychology

Intuition is central in the work, practice, and philosophical legacy of C. G. Jung. In this paper, I will first discuss the importance of intuition for Jung in the paradigm usually designated the ‘paranormal’. Jung was attracted to intuition as an extra‐ordinary gift or function in the traditional sense, and this is considered here in relation to his 1896‐1899 Zofingia Lectures and 1902 On the Psychology and Pathology of So‐called Occult Phenomena: A Psychiatric Study. A significant development then occurred in 1913, when esotericist intuitions were turned toward psychological use with Jung's Red Book. There, his personal and private use of intuition – and we know how extraordinarily intuitive he was – led Jung to fully incorporate intuition at the core of his psychology. Not only in his practice, in the crucial intuitive form of empathy, but as we will see, also at the very heart of his theory. In 1921, Jung wrote Psychological Types, where intuition became one – the first – of the four fundamental functions and types of the psyche next to thinking, feeling, and sensation. In 1921, Jung proved to the world in rational argument that intuition was no longer a psychologist's hobby for table turning, but the most significant function of the psyche.