“Minimax length links” of a dissimilarity matrix and minimum spanning trees

A theorem is proved stating that the set of all minimax links, defined as links minimizing, over paths, the maximum length of links in any path connecting a pair of objects comprising nodes in an undirected weighted graph, comprise the union of all minimum spanning trees of that graph. This theorem is related to methods of fitting network models to dissimilarity data, particularly a method called Pathfinder due to Schvaneveldt and his colleagues, as well as to single linkage clustering, and results concerning the relationship between minimum spanning trees and single linkage hierarchical trees.Acknowledgments: The author thanks Phipps Arabie, Lawrence J. Hubert, and K. Christoph Klauer for a number of helpful suggestions and comments on various aspects of this paper.     

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.     

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.     

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.     

Frege,Boolos, and Logical Objects

In this paper, the authors discuss Frege's theory of logical objects (extensions, numbers, truth-values) and the recent attempts to rehabilitate it. We show that the eta relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the eta relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for Logical Objects and banishes encoding (eta) formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstract objects are described, involving: (a) the theory of extensions, (b) the theory of directions and shapes, and (c) the theory of truth values.     

The Self Psychology of Heinz Kohut: What's It All About Theologically?

As a psychoanalytic thinker who offered by means of his self psychology a new paradigm of psychological development and functioning, Heinz Kohut was also a theologian manqué. With the help of the method of interpretation devised by Paul Tillich and David Tracy, Kohut's limit-concepts of tragic man, the self-object, and empathy, all set within his theory of narcissism, are elucidated as theological constructs. These are critiqued for adequacy from a Christian perspective. The conclusion is that Kohut's understanding of the human dilemma and of the way of salvation correlates well with Christianity, while his view of empathy as the means of salvation has created some confusion. Kohut has thus left an unfinished, profoundly important, agenda for theologians and clinicians.     

The endorsement of irrational beliefs in a general clinical population

Burgess' Attitude and Belief Scale, a measure of Ellis' irrational beliefs, was administered to a large sample of outpatients. All 13 subscales demonstrate very adequate internal consistency. A factor analysis yielded one factor accounting for 83% of the variance, which was labeled irrationality. Clients endorsed focused items more than overgeneralized items, self-referential items more than non-self-referential items, and preferential items more than irrational items. Clients also received higher scores on the irrational process of demandingness than they did on the irrational process of awfulizing, self-worth and low frustration tolerance. The results were consistent with new formulations in Rational-Emotive theory. Suggestions were made for the construction of measures of irrational beliefs.     

Логистическая система, исходными связками которой являются эквивалентность и дизъюнкция

- Allatum est die 5 Martii 1970     

On Ultrafilter Logic and Special Functions

Logics for generally were introduced for handling assertions with vague notions,such as generally, most, several, etc., by generalized quantifiers, ultrafilter logic being an interesting case. Here, we show that ultrafilter logic can be faithfully embedded into a first-order theory of certain functions, called coherent. We also use generic functions (akin to Skolem functions) to enable elimination of the generalized quantifier. These devices permit using methods for classical first-order logic to reason about consequence in ultrafilter logic.Presented by André Fuhrmann     

Yes,Virginia, Lemons are Yellow

This paper discusses a number of themes and arguments in The Quest for Reality: Stroud's distinction between philosophical and ordinary questions about reality; the similarity he finds between the view that coloris unreal and the view that it is subjective; his argument against thesecondary quality theory; his argument against the error theory; and the disappointing conclusion of the book.     

“Soul-making” in a schizophrenic saint

Soul-making (cf. Jung and Hillman) is the process of integrating spiritual and bodily imagery into an intimated wholeness transcending conscious comprehension. Pierre Janet's case of the psychotic mystic, Madeleine, reveals that the patient had been making her own-soul even though his theory had no provision for soul. Janet's soul-stripping theory is contrasted with a soul-making approach, primarily in their respective interpretations of Madeleine's altered states of consciousness. Religious ecstasy is a stretching of soul, an expansion into the realm of spirit, which requires a subsequent descent into and reconciliation with tradition, society, outer world, and body.     

Modifying Violent Communities by Enhancing Altruism: A Vision of Possibilities

A model for diagnosing and treating violent communities is outlined. The treatment consists of enhancing a form of pragmatic altruism by building relationships and mutual understanding between community leaders who are derived from task groups called community stabilizing systems, defined as groups essential for peaceful, creative stability in a community. Two examples of an intervention derived from this theory are described.     

Hierarchical clustering schemes

Techniques for partitioning objects into optimally homogeneous groups on the basis of empirical measures of similarity among those objects have received increasing attention in several different fields. This paper develops a useful correspondence between any hierarchical system of such clusters, and a particular type of distance measure. The correspondence gives rise to two methods of clustering that are computationally rapid and invariant under monotonic transformations of the data. In an explicitly defined sense, one method forms clusters that are optimally connected, while the other forms clusters that are optimally compact.I am indebted to R. N. Shepard and J. D. Carroll for many stimulating discussions about this work, and for aid in preparing this paper.     

Semantic activation during object naming

Summary The study deals with the processes of semantic activation which accompany the response of naming an object. A general model of semantic activation is presented, characterized by the proposal of the existence of different components of the semantic representations that constitute the conceptual nodes corresponding to objects. Within these, a distinction is made between elements corresponding to physical properties of the stimulus objects, and more abstract, functional elements. Two distinct routes are proposed for the activation of the concept node, a direct and an indirect one. A further distinction made in the present study is between categories characterized predominantly in terms of perceptual properties, and primarily conceptual categories.The study reports two sets of experiments, the first one offering support to the distinction of two activation routes, the second to the notion of the existence of two types of categories. This latter distinction also allows a convincing explanation for various facts reported in the literature, in particular for the difference in categorization and in naming latencies for objects and for words.     

Six-year-old children's understanding of sentences adjoined with time adverbs

The adjoining of clauses with temporal links is the basis for many sentences that convey sequence of events. The present study attempts to delineate 6-year-old children's (N=30) understanding of the meaning sequences imparted by sentences adjoined with after, before, and until. Their performance of the meaning sequence for each of 24 carefully constructed sentences is compared to an adult model. Analysis of the results (using a Wilcoxon Matched Pairs Signed Rank Test) indicated that: (1)Ss understood sentences adjoined with after according to an adult model more frequently than before adjoined sentences (P<0.01); (b) Until adjoined sentences with a negative marker in the main clause were understood according to an adult model more often than until adjoined sentences with no such negative element, but the difference was not significant at a=0.01; (3)Ss understood before adjoined sentences according to an adult model more often than until adjoined sentences, but the difference was not significant at a=0.01. In general, the results indicated that 6-year-olds have not yet completed development of an adult grammar with respect to adjoining clauses with temporal links, after, before, and until.     

Thomas Kuhn revisited: Near-death studies and paradigm shifts

Near-death studies can be viewed within a theoretical framework of paradigms and paradigm shifts as explicated by Thomas Kuhn (1962). Assuming the validity of Kuhn's model, I hypothesize that the paradigm of today's normal science is shifting to a new paradigm to accommodate data from near-death studies.     

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.     

Care and the dynamics of social world

The concept of social world is formulated for the purpose of deepening our understanding of the dynamics of inclusion, exclusion, and care in interpersonal interaction. World is defined as an irreducible subject-object polarity.Social world is the extremely fragile environment within which people meet, and is easily destroyed. With special attention to family and church life, the conditions for maintaining or losing this environment are examined. Three levels of social world are defined. On the highest level, mutual care, rather than shared opinion, is seen as the factor that facilitates the preservation of social world in the face of world-threatening issues.     

The Primacy of the “Shoulds”: Where Is the Evidence?

A central tenet of rational emotive behaviour therapy (REBT) has always been that irrational beliefs which express demands through absolutistic shoulds, musts or oughts are the basic cause of emotional disturbance. This premise is characteristic of Ellis' theory but is not always supported by other REBT writers or other writers within the cognitive therapy field. This paper reviews a range of research findings which appear to call into question Ellis' tenet of the primacy of the shoulds and which, in turn, raise theoretical and methodological difficulties in the measurement of beliefs. This along with the current theoretical debate regarding irrational belief processes may preclude the possibility of testing the proposition that demandingness is the primary irrational or dysfunctional belief.     

Depression and Anxiety in Persons with Parkinson's Disease With and Without “On–Off” Phenomena

On–off phenomena in Parkinson's disease (PD) are unpredictable motor fluctuations associated with long-term levodopa use. Mood fluctuations have been found to coincide with the motor fluctuations in that depression and anxiety increase while the person with PD is in the off state. What has been relatively unexplored is whether those persons with PD who have on–off phenomena differ psychologically in fundamental ways from those who do not have on–off phenomena. In the present study, depression and anxiety symptoms were assessed in 36 persons with PD (n = 14 with on–off phenomena, n = 22 without on–off phenomena). All those with on–off phenomena were assessed in their on state. Those persons with PD with on–off phenomena had significantly higher levels of anxiety than those without on–off phenomena. However, both groups, regardless of on–off status, were mildly depressed. Neurobiological interpretations of the results implicate the locus coeruleus in the pathogenesis of both on–off phenomena and anxiety, whereas psychological interpretations of the results involve the issues of learned helplessness and control over health symptoms in PD.