A reduction rule for Peirce formula

A reduction rule is introduced as a transformation of proof figures in implicational classical logic. Proof figures are represented as typed terms in a -calculus with a new constant P ⁽⁽⁾⁾. It is shown that all terms with the same type are equivalent with respect to -reduction augmented by this P-reduction rule. Hence all the proofs of the same implicational formula are equivalent. It is also shown that strong normalization fails for P-reduction. Weak normalization is shown for P-reduction with another reduction rule which simplifies of (( ) ) into an atomic type.This work was partially supported by a Grant-in-Aid for General Scientific Research No. 05680276 of the Ministry of Education, Science and Culture, Japan and by Japan Society for the Promotion of Science. Hiroakira Ono     

Dowód aksjomatyzowalności pewnychn-wartościowych rachunków zdań

Praca ta zostaa wykonana pod kierunkiem prof. drJerzego Supeckiego. Jej szczególny przypadek dotyczcyn-wartociowego rachunku zda o jednej wartoci wyrónionej by referowany w Warszawie na zjedzie Grupy Logiki Instytutu Filozofii i Socjologii PAN. Streszczenie tego referatu [5] zostao wydrukowane w Sprawozdaniach Wydziau Nauk Spoecznych PAN.Allatum est die 19 Aprilis 1963     

The responsive order: A new empiricism

The uniqueness of logic is upheld and contrasted with twenty roles of a wider responsive order that includes us and our procedures. Empirical responses are precise, but different in different approaches. Procedures and findings are independent of (not separable from) their concepts. Two-way feedback obviates a top-down derivation of findings from assumptions, hypotheses, history, or language. The postmodern problems of interpretation, conditions of appearances and relativism involve the ancient error of making perception the model-instance of experience. Instead, bodily interaction functions in language and precedes perception and interpretation. Logic, space time locations and individuated referents involve positional relations derived from comparing. Beyond Kuhn, Feyerabend, Newton and Einstein, if we can give interaction priority over comparing, the responsive objectivity of both can be upheld. A new empiricism, neither naive nor constructivist, uses the words order, explication, truth, and exactly to build on Wittgenstein and on Dilthey's hermeneutic. Natural language is metaphor-like, originally crossed. Logic must ignore its assumptions. It must render everything as a machine and drop humans and animals out. A new discipline is proposed, to move between the logical and the responsive orders, to deal with the machine/human interface and the social uses of science such as bioengineering.     

Theorizing Gender for Experimental Game Theory: Experiments with “Sex Status” and “Merit Status” in an Asymmetric Game

In experimental game-theoretic research, to the extent that sex has been considered at all, the approach has been to focus on the individual level of analysis. This paper reports the results of experiments designed to focus on sex/gender and to expand the level of analysis to include the institutional level. An asymmetric game was designed such that players in the male and female institutional locations had 3 and 2 alternatives, respectively. Players earned the institutional locations based on a test, so that top and bottom scorers respectively merited the 3- and 2-alternatives locations. Game-theoretic understandings of sex-of-player were compared to the expectations states theory concept of sex status; that is, men expect and are expected to perform more competently than women. Results indicated that top-scorer men and women behave similarly; bottom-scorer men resist their low merit status (behaving the most rationally of all player groups); bottom-scorer women accept their low merit status (behaving the most irrationally of all player groups). Whereas game theory cannot provide a coherent understanding of these findings, the concept of sex status helps to interpret the behavior of all four player groups and shows how judgments about rationality and irrationality depend critically on the interpretive framework used.     

Theological and Biblical Interpretations of Current Movements and Emerging Paradigms Within Bereavement Studies

Among the predominant themes in the last few years of bereavement studies have been those around disenfranchised grief, masculine grief, spirituality and grief, and the movement from medical/hierarchical models of grief work/counseling to a more non-hierarchical model that emerges internally, inherently, and intrinsically within the bereaved. In the latter model the grief counselor becomes a facilitator or, as Alan Wolfelt noted at the Chicago ADEC conference, a companioning presence. The intent of this article is to take this conversation into the realm of theology, and/or biblical theology. The following offers theological analysis of what is already good clinical theory. Integrating theories from anthropology and theology, this article will explore the concepts of voice, etic and emic theory, and incarnational theology as they relate to emerging patterns in bereavement studies. It will also relate a model of the Kingdom of God to disenfranchised grief, as well as offer support for the theory of masculine grief from biblical sources and complementary fields of study.     

Best and Worst Professors: Gender Patterns in Students' Choices

Over 100 primarily White students described their best and worst professor. For best, female professors were chosen more by their female students and less by their male students than expected. There were no gender differences in choice of worst professors. The qualities that students criticize are similar for their male and female professors, mainly a lack of organization and clarity. Best professors most often are described as caring and knowledgeable, but other qualities vary as a function of professor or student gender. These findings suggest that more attention should be paid to gender dynamics in classroom teaching and in student evaluations.     

Modal Logics of Succession for 2-Dimensional Integral Spacetime

We consider the problem of axiomatizing various natural successor logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages, and prove completeness theorems. We also establish that the irreflexive successor logic in the standard modal language (i.e. the language containing and ) is not finitely axiomatizable.     

The artist as transgressor in Mandel'štam's poetry

In Mandel'tam's writing, artistic creativity is described as based on the indispensable yet contradictory modes of compliance and deviation. The artist, by his artistic nature, must be an obedient disciple to the tradition that inspires him, and, at the same time, a violator who renders what inspires him in an individual form. Thus, art implies iterability through novelty. In the totalitarian state, this double nature of art acquires a sinister context and brings the artist to an unavoidable conflict with the state. He has a choice between a servile compliance with the state's command and artistic independence. If the artist complies, he loses his ingenuity; if, on the other hand, he has the courage to break away from the established order, his fate is martyrdom. The criteria of truth and falsehood, the issue of loyalty, of compromise and collaboration or resistance become most relevant. Such words as outcast or non-contemporary acquire the meaning of non-collaborationist or enemy of the people. In the totalitarian state a genuine artist is viewed as a law-breaker, and his art leads him to crime. The notions of compliance and deviation cease being merely aesthetic terms and assume in Mandel'tam's poetry complex, subtle and tragic overtones.I would like to express my gratitude to John Barnstead, Thomas Blakeley, James Doull, Elena Glazov-Corrigan, Gregory Glazov, Leonard Kazdan, Peter Kussmaul, Malcolm Ross, Detlev Steffen, and Ieva Vitins for their valuable criticism, suggestions, and revisions of my English.     

Partially-Ordered (Branching) Generalized Quantifiers: A General Definition

Following Henkins discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or cardinality quantifiers, e.g., most, few, finitely many, exactly , where is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first to a general definition of monotone-increasing (M) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwises 1979 analysis of the basic case of M POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional 1st-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages.     

A longitudinal study of the marriage role expectations of college women: 1961–1984

The marriage role expectations of female university students enrolled in an introductory marriage and family course at the University of Kentucky in 1961 (N=72), 1972 (N=58), 1978 (N=115), and 1984 (N=81) were compared. The 1972 group was found to be significantly more egalitarian than the 1961 group in overall marriage role expectations and on all subscales except authority. The 1978 and 1984 groups were significantly more egalitarian than the 1961 group on overall marriage role expectations and on all seven of the subscales: authority, homemaking, child care, personal characteristics, social participation, education, and employment and support. The 1978 group was significantly more egalitarian than the 1972 group only on authority and homemaking, with no significant differences on the other five subscales or on overall role expectation score. The 1984 group was significantly more egalitarian than the 1972 group only on authority, homemaking, and child care, and was slightly (not satistically significant) more traditional on personal characteristics and social participation. There were no significant differences between the 1978 and 1984 groups on overall expectation or on any of the subscales. In fact, the 1984 group was slightly more traditional on homemaking, personal characteristics, social participation, employment and support, and overall expectations. The data from this study showed the greatest gain in egalitarian trends to be between 1961 and 1972, with a continuation of the trends at a somewhat slower rate of change between 1972 and 1978, and a discontinuation of the trend toward more egalitarian expectations between 1978 and 1984.The data were collected in February 1961, January 1972, September 1978, and September 1984. Special acknowledgement and appreciation are expressed to Jessie Ringo (retired), University of Kentucky, for making the 1961 data available for this study.     

Sets and Classes as Many

In this paper the view is developed that classes should not be understood as individuals, but, rather, as classes as many of individuals. To correlate classes with individuals labelling and colabelling functions are introduced and sets identified with a certain subdomain of the classes on which the labelling and colabelling functions are mutually inverse. A minimal axiomatization of the resulting system is formulated and some of its extensions are related to various systems of set theory, including nonwellfounded set theories.     

Fragmentation and re-integration of experience

Secular and religious counselors require a model of psychotherapy that conceptualizes human beings as conscious, goal-seeking entities. Such a model, based on the construct being in one's own world, is sketched in broad outline in this essay. The building blocks for the model are the intentional modes that lie at the heart of the self-world dialectic in which we live our lives. It is demonstrated how these intentional modes are organized into a gestalt-like whole referred to as the existential gestalt. From the diagram of the existential gestalt the concepts of intentional clarity and modal congruence are derived. These concepts enable us to understand the processes of the fragmentation and re-integration of experience that lie at the heart of psychotherapy. Inclusiveness and purposefulness, two additional factors that are important for assessing the adequacy of the existential gestalt, are also briefly touched upon.     

The treatment of adolescents and their families in cultural transition: Issues and recommendations

Increasing numbers of immigrant families with adolescent children are seeking therapy because of intergenerational conflicts specific to the adolescent separation-individuation phase of the life cycle and transitional problems related to immigration and cultural transition. Three types of adolescent immigrants are identified and discussed: Immigrants (subtypes Reluctants and Optimists), Immigrant-Americans, and Americans. Therapists' issues which can negatively affect therapy with such adolescents and families are also discussed. Effective therapy with immigrant families requires that family therapists become more culturally sensitive, therapeutically flexible, and accepting of family values to which they may be diametrically opposed. Recommendations for therapy are offered.Dr. Baptiste is himself an immigrant. The experiences and observations discussed here are culled from his work with immigrant families and children over the past 19 years in the District of Columbia, Massachusetts, Indiana, and New Mexico.Portions of this article will appear in a chapter Psychotherapy with adolescent immigrants and their families in cultural transition in B. Settles and D. Hanks (Eds.),Families on the move: Emigration, immigration, migration and mobility. Sage Publications, 1990, and are used here with permission.     

Family therapy with one-parent families

In this article the author introduces an integrative approach to family therapy with one-parent families. This includes a diagnostic framework built on the developmental stages of the family, critical areas, and—most importantly—specific settings and therapeutic strategies based on the assumption that one-parent families can raise children as successfully as other families, but in a different manner.The term one-parent families is used in this article, although it is not the correct expression, simply because no child has only one parent. The term binuclear families does not fit with all of them, and single-parent-led families seems to be ambiguous but quite cumbersome to use.     

A paradigm shift in Heidegger research

The Beiträge zur Philosophie mandates a paradigm shift in Heidegger scholarship. In the face of (1) widespread disarray in the current model, the new paradigm (2) abandons Sein as a name for die Sache selbst, (3) understands Welt/Lichtung/Da as that which gives being, (4) interprets Dasein as apriori openedness rather than as being-there, (5) understands the Kehre as the interface of Geworfenheit and Entwurf, not as a shift in Heidegger's thinking, (6) interprets Ereignis as the opening of the Da rather than as appropriation, and (7) understands human finitude as what gives all forms of being and all epochs in the history of being. The conclusion alludes to the function of Mitdasein (co-openness) as die Sache selbst.     

Confusion in philosophy: A comment on Williams (1992)

Patricia Williams made a number of claims concerning the methods and practise of cladistic analysis and classification. Her argument rests upon the distinction of two kinds of hierarchy: a divisional hierarchy depicting evolutionary descent and the Linnean hierarchy describing taxonomic groups in a classification. Williams goes on to outline five problems with cladistics that lead her to the conclusion that systematists should eliminate cladism as a school of biological taxonomy and to replace it either with something that is philosophically coherent or to replace it with pure methodology, untainted by theory (Williams 1992, 151). Williams makes a number of points which she feels collectively add up to insurmountable problems for cladistics. We examine Williams' views concerning the two hierarchies and consider what cladists currently understand about the status of ancestors. We will demonstrate that Williams has seriously misunderstood many modern commentators on this subject and all of her five persistent problems are derivable from this misunderstanding.

Nelson (1989, 67).

     

Adjustment to disability: A cognitive-behavioral model for analysis and clinical management

Profound psychological reactions are frequently seen following the onset of severe disability. Stage models of adjustment, although limiting when used dogmatically, can serve as a helpful guideline for intervention when integrated within a framework that also addresses the sequence of associated irrational beliefs. This article proposes a three phase model for analyzing and facilitating the adjustment process which follows disability. Adjustment is analyzed along cognitive, emotional, and environmental dimensions.The first stage immediately follows the onset of incapacitating disability and is termed the Pre-encounter phase. From a rational emotive perspective, the individual in this phase has not yet acknowledged that an activating, or disabling event has occurred. Acknowledgment is limited to brief contact which is then followed by excessive arousal and extreme distortions in evaluative capabilities. Shock and denial are characteristic of this phase. During this stage, strategies for clinical management are specified with a stronger emphasis on targeting the environment and belief system of the rehabilitation team than the beliefs of the patient.The second stage is referred to as the Post encounter phase during which the disabling condition has been acknowledged as a valid activating event. Periods of anxiety, depression, and expressed anger are common at this time. The final stage is coined the Rational re-encounter phase and is highlighted by repeated re-encounters with various forms of the disabling activating event and anticipated activating events. During this phase the patient is more able to benefit from a traditional psychotherapeutic approach which has been tailored to the specific pattern of irrational beliefs often exhibited in response to life with a disability.     

Rhetoric and Double Hermeneutics in the Human Sciences

Based on an analysis of double hermeneutics in the human sciences, a distinction between a weak and a strong rhetorical analysis of human-scientific research is introduced, taking account of the self-reflective character of hermeneutic interpretation. The paper argues that there are three hermeneutic topics in the research process for human-scientific experience, which are associated with applying specific rhetorical tools. The three topics are described under the following rubrics: (a) bridging the gap between experience-near and experience-distant concepts; (b) achieving integrity of the cultural objects dispersed in different interpretive strategies; and (c) taking into consideration that an important task of hermeneutic interpretation in human-scientific research is to give an account of the object's immanent narrative coherence. The paper is written in the conviction that a kind of re-methodologization of philosophical hermeneutics which does not rehabilitate epistemological foundationalism can provide a new philosophical identity to the human sciences.     

Computer content analysis of sex differences in the language of children

This study presents empirical procedures for the collection and content analysis of the oral language of kindergarten children. The analysis technique used material and machines available to most researchers. The results of the analysis of language samples of 144 randomly selected children from the entire kindergarten class of the Ithaca, New York, school system showed that boys produced significantly more language than did the girls as well as significantly more references to aggression, self, time, space, quantity, fears, good, act of oral communication, negation, and affirmation, and asked more questions of the examiner than did the girls. The girls made significantly more female references than did the boys. Implications for future research are discussed.     

Family therapy for the “Truncated” nuclear family

The truncated nuclear family is the commonest or gardenvariety family psychopathology observed by therapists, and consists of a two-generation group in which heated, prolonged conflict has produced a polarization of values which has generated pathogenic relating, raising the potential for a family member to become scapegoated and react in a disorganized or disoriented manner. Although many so-called intact families are of the truncated variety, the single-parent family is at special risk. Go-between process is a useful family therapy for the truncated nuclear family because it enables the therapist to depolarize sharply conflicted values and is a mechanism for reducing pathogenic relating.This article was originally an invited presentation for the Third Annual Research Symposium of the Eastern Pennsylvania Psychiatric Institute, held in Philadelphia on February 22, 1980.