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     

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.     

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.     

Difficult Patients in Group Analysis: The Personification of (ba) I:A/M

Following a discussion of the treatment of difficult patients in group analysis, two theories are proposed concerning a fourth basic assumption in the unconscious life of groups, called Incohesion: Aggregation/Massification or (ba) I:A/M and the personification of basic assumption processes, in particular that of (ba) I:A/M by difficult patients. These theories are illustrated with clinical data. Special attention is given to crustacean and amoeboid forms of encapsulation as a defence against the fear of annihilation within the context of the traumatogenic process. It is suggested that for difficult patients the treatment of choice is dyadic psychotherapy/psychoanalysis followed by group analysis.     

Intuitionistic uniformity principles for propositions and some applications

This note deals with the prepositional uniformity principlep-UP: p x N A (p, x) x N p A (p, x) ( species of all propositions) in intuitionistic mathematics.p-UP is implied by WC and KS. But there are interestingp-UP-cases which require weak KS resp. WC only. UP for number species follows fromp-UP by extended bar-induction (ranging over propositions) and suitable weak continuity. As corollaries we have the disjunction property and the existential definability w.r.t. concrete objects. Other consequences are: there is no non-trivial countable partition of;id is the only injective function from to; there are no many-place injective prepositional functions; card () is incomparable with the cardinality of all metric spaces containing at least three elements.     

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.     

Self and others in “private language”

The aim of this paper is to restore the interdependent or complementary relationship between self and others against the universalistic one (as I call it) that Kant, for example, once insisted on, by reexamining the concept of so-called private language. I shall consider some views in speech act theory and pragmatics, since there has often been discussion about such a private occurrence as the speaker's sincerity. For example, Jürgen Habermas situates it in the speaker's internal nature as will be seen later. In my opinion, alter ego is an ego because we can empathize (einfühlen) with it, and yet it is alter ego because it has some private experiences which we cannot perfectly comprehend.     

Proof-Theoretic Modal PA-Completeness I: A System-Sequent Metric

This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we calculate a canonical characteristic fomula H of S (char(S)) so that _G H (S) and _GL-LIN H, and the complexity of H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of H with H = char(S) and ( H) = d(S, G).     

Clocks,Creation and Clarity: Insights on Ethics and Economics from a Feminist Perspective

This essay discusses the origins, biases, and effects on contemporary discussions of economics and ethics of the unexamined use of the metaphor an economy is a machine. Both neoliberal economics and many critiques of capitalist systems take this metaphor as their starting point. The belief that economies run according to universal laws of motion, however, is shown to be based on a variety of rationalist thinking that – while widely held – is inadequate for explaining lived human experience. Feminist scholarship in the philosophy of science and economics has brought to light some of the biases that have supported the mechanistic worldview. Possible alternatives to the an economy is a machine include an economy is a creative process and an economy is an organism. Such metaphors are intellectually defensible as guides to scientific inquiry and provide a richer ground for moral imagination.     

John Dewey's impact on Turkish education

Conclusion The cultural characteristics of any country generally give shape to the educational system. However, no country can assert its own educational system to be wholly indigenous. All the systems come into being as a synthesis of various ingredients of the home country and other countries. And it is quite natural to make use of the experiences and stock of knowledge of the others. This fact is indispensable especially when education is concerned. The curicial problem is to what extent the borrowing process should be used. When the process of borrowing ideas become to take the form of imitation or copy, unexpected results and failure are unavoidable.     

A game-based formal system for Ł∞

A formal system for , based on a game-theoretic analysis of the ukasiewicz prepositional connectives, is defined and proved to be complete. An Herbrand theorem for the predicate calculus (a variant of some work of Mostowski) and some corollaries relating to its axiomatizability are proved. The predicate calculus with equality is also considered.     

Murder in the family: An analysis of two Poe short stories

Learning to be possessed has been described elsewhere by the writer as a form of pathogenic relating begun when children are taught by adults that they will receive a lesser penalty for misbehavior if they can show they were not responsible, such as if it were caused by an evil agent or the Devil. It was suggested that learning to be possessed can be an underlying cause of psychopathology, the delusion of persecution in particular. Two short stories by the distinguished American writer Edgar Allan Poe are examined to develop the formulation of learning to be possessed, especially when it has passed to a delusion of persecution. Two propositions are offered: (1) Where it appears that a family member is murdered by a delusional assailant by accident, it is not an accident; and (2) the delusion of persecution entails a memory loss so that the murderer not only can claim lack of personal responsibility for the act, but also spares himself the guilt of having broken a fundamental taboo. Further comparison is made between learning to be possessed as a cause of delusion, and the psychoanalytic theory in which the defense mechanism of projection is central. In the latter theory, interpretation of the delusion is critical; whereas in the former, interpretation is counterproductive because it merely reinforces the delusion.Probably a note of appreciation is due the writer's daughter Cary, who at age 14 is an expert at badgering her father for help with homework assignments. For several weeks the writer was alternatively pestered and cajoled to help Cary with her Poe Project for high school English which required an essay analyzing the work of a great American writer denigrated by the author as weird by his recollection formed decades earlier. Cary's persistence required the author to consider Poe anew, to recognize his unwarranted earlier prejudice, and to recognize that Poe offered him a gift of understanding regarding a topic about which the author had been thinking for several years, namely that form of pathogenic relating named learning to be possessed.     

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.     

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.     

On the logic of conscious belief

In this paper we are discussing a version of propositional belief logic, denoted by LB, in which so-called axioms of introspection (B BB and B B B) are added to the usual ones. LB is proved to be sound and complete with respect to Boolean algebras equipped with proper filters (Theorem 5). Interpretations in classical theories (Theorem 4) are also considered. A few modifications of LB are further dealt with, one of which turns out to be S5.     

Micro-economic models of problem choice in basic science

This paper describes the way in which a certain representation of basic scientific knowledge can be coupled with traditional microeconomic analysis to provide an analysis of rational research planning or agenda setting in basic science. Research planning is conceived as a resource allocation decision in which resources are being allocated to activities directed towards the solution of basic scientific problems. A structuralist representation of scientific knowledge is employed to provide a relatively precise characterization of a basic scientific problem.The research reported here was partially supported by a grant from the EXXON Foundation.     

Inverses for Normal Modal Operators

Given a 1-ary sentence operator , we describe L - another 1-ary operator - as as a left inverse of in a given logic if in that logic every formula is provably equivalent to L. Similarly R is a right inverse of if is always provably equivalent to R. We investigate the behaviour of left and right inverses for taken as the operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended by the addition of such inverses, as well as to the question of when, in such extensions, the inverses behave as normal modal operators in their own right.     

Variations in use of the term “or”

Two studies showed that adults' responses to questions involving the term or varied markedly depending upon the type of question presented. When presented with various objects (A's and B's) and asked to circle all things which are A or B subjects tended to circle A's as well as B's, whereas when asked to circle all the A's or B's subjects showed a relatively stronger tendency to circle one or the other. Moreover the nature of the sets of objects (As and Bs) influenced behavior as well. There was also evidence that the effects due to question wording or set type transferred.     

Discrete tense logic with infinitary inference rules and systematic frame constants: A Hilbert-style axiomatization

The paper deals with the problem of axiomatizing a system 1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 (immediate successor) and -1 (immediate predecessor). 1 is like the Segerberg-Sundholm system W1 in working with so-called infinitary inference rules; on the other hand, it differs from W1 with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a now operator, and, most importantly, with respect to (iii) the presence in of so-called systematic frame constants, which are meant to hold at exactly one point in a temporal structure and to enable us to express the irreflexivity of such structures. Those frame constants will be seen to play a paramount role in our axiomatization of 1.The present contribution reports research done under the auspices of the Swedish Council for Research in the Humanities and the Social Sciences (HSFR), project On the Legal Concepts of Rights and Duties: an Analysis Based on Deontic and Causal Conditional Logic. I wish to thank the anonymous referee for his/her extremely patient and accurate revision work, and Krister Segerberg for his helpful suggestions.     

A measure of stereotyping in fear-of-success cues

Prior studies suggest that sex-role stereotypes influence responses to Horner's fear-of-success cue. This study investigates stereotypes about both sex roles and achievement settings. One hundred sixty college males and females wrote stories to different cues, then rated the masculinity-femininity of their characters. Both John and Anne were rated more masculine as medical students than in a neutral setting. Anne was rated more feminine than John in the neutral setting but equally masculine as a medical student. However, Anne's success was not regarded as maladaptive, but competent. Clearly Horner's cue reflects stereotypes; a more ambiguous cue might assess motives more effectively.Portions of this article were presented at the annual meeting of the American Psychological Association in Washington, D.C., 1976. Special thanks to Professor Charles P. Smith for his advice and encouragement throughout this research.