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 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     

Richard Zaner’s Phenomenology of the Clinical Encounter

The clinical ethics propounded by Richard Zaner is unique. Partly because of his phenomenological orientation and partly because of his own daily practice as a clinical ethicist in a large university hospital, Zaner focuses on the particular concrete situations in which patients and their families confront illness and injury and struggle toward workable ways for dealing with them. He locates ethical reality in the clinical encounter. This encounter encompasses not only patient and physician but also the patients family and friends and indeed the entire lifeworld in which the patient is still striving to live. In order to illuminate the central moral constituents of such human predicaments, Zaner discusses the often-overlooked features of disruption and crisis, the changed self, the patients dependence and the physicians power, the violation of personal boundaries and their necessary reconfiguring, and the art of listening.     

“Anchor-range” results with “same” and “different” responses and similar and dissimilar stimuli

Summary Blocks of pairs of dissimilar (anchor-like) circles were unexpectedly followed by single pairs of similar circles and vice versa. The dissimilar circles were 3 and 10 mm in diameter, and the similar circles were 3 and 5 mm, 5 and 7 mm, and 7 and 10 mm in diameter. In a second experiment, the dissimilar and similar circles did not overlap in size (e.g., they were 1.5 and 5 mm and 7 and 10 mm, respectively). The same responses to the unexpected same pairs of similar circles were faster than the same responses to the identical pairs in the blocks. In contrast, the different responses to the unexpected different pairs of similar circles were slower than the different responses to the identical pairs in the blocks. Similar stimuli accelerate same responses and slow down different responses. So the time results (and the error results as well) suggest that the context of the block dissimilar circles increased the perceived similarity of the unexpected similar circles. These anchor-range results are not explained by Thurstonian theories, which are based on the absolute properties of stimuli. Instead, they imply that the relation between the similar circles in the context of the relation between the dissimilar circles affected performance.     

Iconic memory — an artifact of perceptual reconstruction processes?

Summary Two experiments, using a partial vs. whole report procedure to isolate iconic from short-term memory loss, are reported. In the first experiment 10 Ss had to judge the difference between two line lengths in a display of three pairs of lines (in rows). Results showed no significant variation in d' with cue delay in spite of a medium overall performance, and in contrast to preliminary partial/whole report experiments. To counter the possibility that the short-term memory load was too small in this experiment, a second experiment was performed with displays containing nine instead of three pairs, i.e., three pairs per row. Equivalence of performance for all conditions was about the same as before. This was true for both hit- and false-alarm rates. The results are interpreted as evidence against the view of iconic memory as a high capacity store containing a lot of information. An alternative reconstructive theory is put forward to explain both conventional iconic loss and our results. According to this account, partial report measures processed material rather than reflecting an iconic store of uninterpreted sensory events. Some consequences of this model are discussed in the context of some weak effects in our data; and suggestions are put forward for further investigation of visual processing.The experiments to be reported here were made possible by grant Schu 421/1–2 of the Deutsche Forschungsgemeinschaft. The main results of Experiment II have already been reported at the European Conference on Visual Perception at Nordwijkerhout, October 1979. I am indebted to Mrs. R. Ledebur, cand. phil, and Dipl.-Psych. G. Gros who collected the data. I also wish to thank Dr. A. Reeves (Dortmund) for helpful comments on an earlier version of this paper. Dr. P. Wolff (Osnabrück) and two anonymous reviewers contributed valuable suggestions concerning the final draft     

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).     

Логистическая система, исходными связками которой являются эквивалентность и дизъюнкция

- Allatum est die 5 Martii 1970     

Distance and fusion in Robinson Jeffers' “the purse-seine” and other poems

Distance and fusion are fundamental ideas in Bowenian thinking, especially as expressed in the dynamic of distancing and pursuing. In this paper I have used these ideas as a means to briefly examine a short selection of Robinson Jeffers' poetry, which provides us with a literary example of these concepts in action.My thanks to M. K. Lane and the anonymous reviewers of an earlier draft of this article for their many suggestions, especially to the reviewer who helped me better distinguish between distance and fusion, and intimacy and autonomy.     

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.     

A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic

Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.     

Some modifications of Scott's theorem on injective spaces

D. Scott in his paper [5] on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.In this paper we prove a generalization of this theorem for the category of , -closure spaces. The main theorem says that, for some cardinal numbers , , absolute extensors for the category of , -closure spaces are exactly , -closure spaces of , -filters in , >-semidistributive lattices (Theorem 3.5).If = and = we obtain Scott's Theorem (Corollary 2.1). If = 0 and = we obtain a characterization of closure spaces of filters in a complete Heyting lattice (Corollary 3.4). If = 0 and = we obtain a characterization of closure space of all principial filters in a completely distributive complete lattice (Corollary 3.3).     

Deflationism and the Normativity of Truth

This paper argues, in response to Huw Price, that deflationism has theresources to account for the normativity of truth. The discussioncenters on a principle of hyper-objective assertibility, that one isincorrect to assert that p if not-p. If this principle doesnt statea fact about truth, it neednt be explained by deflationists. If itdoes, it can be explained.     

Natural deduction rules for English

A system of natural deduction rules is proposed for an idealized form of English. The rules presuppose a sharp distinction between proper names and such expressions as the c, a (an) c, some c, any c, and every c, where c represents a common noun. These latter expressions are called quantifiers, and other expressions of the form that c or that c itself, are called quantified terms. Introduction and elimination rules are presented for any, every, some, a (an), and the, and also for any which, every which, and so on, as well as rules for some other concepts. One outcome of these rules is that Every man loves some woman is implied by, but does not imply, Some woman is loved by every man, since the latter is taken to mean the same as Some woman is loved by all men. Also, Jack knows which woman came is implied by Some woman is known by Jack to have come, but not by Jack knows that some woman came.     

The relationship between perceived surface-lightness and perceived illumination

Summary An attempt was made to specify the relationship between perceived surface lightness and perceived illumination under the stimulus conditions where different combinations of albedo and illuminance gave 10 approximately equal-luminance levels of a test field (TF) on three different (black-, gray- and white-appearing) backgrounds. Two types of category judgments for TF-lightness and overall illumination were made on the total of 94 TFs by 5 Ss. The results indicated that under the condition where achromatic surface colors appear, the perceptual scission which produces two different perceptual dimensions (lightness and perceived illumination) from one sort of stimulation (luminance) was clearly observed. The relation between the two judgments was consistent with the lightness-illumination invariance hypothesis: As lightness judgments (A) changed from darker to lighter, illumination judgments (I) shifted form brighter to dimmer, the sum of A and I being kept nearly invariant for a given luminance of the TF; the psychological relationship between lightness and illumination, A+I, changed as a linear function of the photometric combination of albedo and illuminance, log A+log I. It was also found that the albedo of the background was an important factor determining the extent of perceptual scission between lightness and illumination.     

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.     

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.     

Kenneth Strike on Liberalism,Citizenship and the Private Interest in Schooling

After indicating a number of points of agreement with the argument 0eveloped by Kenneth Strike in his article Liberalism, Citizenship and the Private Interest in Schooling, this article identifies and explores a number of queries and criticisms which arise in relation to that argument. These queries and criticisms relate especially to the nature and extent of the expansiveness involved in Strike's conception of public or common educational influence, and to the implications and justification of the claim that private educational interests enjoy a greater salience and recognition on Strike's view of public or common educational influence than on some alternative views.     

Groups to Resolve Conflicts Between Groups: Diplomacy with a Therapeutic Dimension

The group self, an individual's self-perception as a member of a group, is distinguished from the group's self, a personification of the group as a person with a self. The perceived group's self of an opposing other group is often a repository for attributes group members are not ready to recognize in their own group's self. Theoretically, the need for an adversarial other to hold one's own group's unwanted attributes—and thus to complete one's own group's self—contributes, however unconsciously, to the apparent intractability of intergroup disputes. In dealing with these issues, I compare intergroup conflict resolution (ICR) groups with therapy groups, on the one hand, and advocacy groups on the other. All of this sets the stage for a presentation of two ICR projects and their analysis in group-developmental terms.     

Test of the violation of local realism in quantum mechanics with no use of Bell's inequalities

A novel and versatile polarization-entanglement scheme is adopted to investigate the violation of the EPR local realism for a non-maximally entangled two-photon system according to the recent nonlocality proof by Lucien Hardy. In this context the adoption of a sophisticated detection method allows direct determination of any element of physical reality (viz., determined with probability equal to unity in the words of Einstein, Podolsky and Rosen) for the pair system within complete measurements that are largely insensitive to the detector quantum-efficiencies and noise.