On finite approximability of ψ-intermediate logics

The aim of this note is to show (Theorem 1.6) that in each of the cases: = {, }, or {, , }, or {, , } there are uncountably many -intermediate logics which are not finitely approximable. This result together with the results known in literature allow us to conclude (Theorem 2.2) that for each : either all -intermediate logics are finitely approximate or there are uncountably many of them which lack the property.     

THE PHENOMENOLOGY OF MATHEMATICAL BEAUTY

It has been observed that whereas painters and musicians are likely to be embarrassed by references to the beauty in their work, mathematicians instead like to engage in discussions of the beauty of mathematics. Professional artists are more likely to stress the technical rather than the aesthetic aspects of their work. Mathematicians, instead, are fond of passing judgment on the beauty of their favored pieces of mathematics. Even a cursory observation shows that the characteristics of mathematical beauty are at variance with those of artistic beauty. For example, courses in art appreciation are fairly common; it is however unthinkable to find any mathematical beauty appreciation courses taught anywhere. The purpose of the present paper is to try to uncover the sense of the term beauty as it is currently used by mathematicians.     

The Deep Structure of Group Life: Unconscious Dimensions

There is a reconsideration and renaissance of interest in expanded conceptions of unconscious processes as they affect individuals and groups (Grotstein, 1999). Recent focus on social unconscious (Hopper, 1996) and cultural unconscious processes (Henderson, 1988) and the nature of intersubjectivity (Harwood and Pines, 1998) raise questions about the location of group analysis. This paper considers the deep structure of group life by examining four functions of the unconscious: repressive, conservative, creative, and mythopoetic (Ellenberger, 1970). On an individual level of analysis, these functions are equated respectively with formative ideas about the: personal–subjective, social–political, intersubjective–cultural and collective–objective unconscious. Group level analogs, as they develop and affect groups and their members, are explored as synthetic, shared, symbolicy and synchronous unconscious processes.     

Is “some-other-time” sometimes better than “sometime” for proving partial correctness of programs?

The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or sometime-logic. We will see that the minor change in this background modal logic increases the program verifying power of Bur. The change can be described either technically as replacing the reflexive version of S5 with an irreflexive version, or intuitively as using the modality some-other-time instead of sometime. Some insights into the nature of computational induction and its variants are also obtained.This project was supported by the Hungarian National Foundation for Scientific Research, Grant No. 1810.     

In and behind a Lenneberg paradigm

Lenneberg suggested that a chimpanzee's linguistic ability could be tested by presenting sentences containing two prepositional phrases joined by a conjunction. This would involve joining two semantic propositions, and thus represents a more complex test of chimpanzee syntactic competence than previously attempted. Jane, a five year-old language trained chimpanzee, was tested on her ability to both produce and comprehend sentences involving a preposition (in or behind) and a conjunction (and). The results from production and comprehension were substantially the same. Jane showed the ability to appropriately deploy and, behind and in, but displayed very little flexibility in their use. It is suggested that a chimpanzee may be able to learn some rules of syntax but is not able to be creative with that syntax.     

Hemingway's Aging Heroes and the Concept of Phronesis

This article explores the concept of phronesis (practical wisdom) in four aging protagonists in Ernest Hemingway's works ranging from the short story A Clean Well-Lighted Place to the novella The Old Man and the Sea. Phronesis represents an understanding of the ways of the world, an acute sensitivity to a critical logic of human existence that can be attained only through extensive experience and suffering. The four aging protagonists are examples of Hemingway's definition of aging productively and profitably by purchasing an inner peace that consists of an intuitive system of continuous adjustment to the exigencies of daily living.     

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.     

Nietzsche's agon with ressentiment: towards a therapeutic reading of critical transvaluation

This paper examines the therapeutic implications of Nietzsche's critique of ressentiment and revenge as our signature malady. §I examines the obstacles to a therapeutic reading of Nietzsche's thought, including his anti-teleological tendencies and the value he places on sickness. Then there is the energetic problem of finding resources to tackle ressentiment, given the volitional exhaustion of modern nihilism. Finally, the self-referential implications of Nietzsche's critique of slave values threaten to trap his thought in a futile ressentiment against ressentiment. If the impulse to cure or redeem us from revenge through critical destruction repeats the logic of revenge, then the challenge for a therapeutic reading is to think through the transformation of revenge on the basis of repetition.An agonal reading of Nietzsche's philosophical practice is proposed to tackle these problems in §II.In Homer's Contest (1872), Nietzsche describes the transference (Übertragung) of Hesiod's evil Eris – goddess of war and destruction – into the good Eris of the contest or agon: destructive impulses are affirmed as stimulants, but also transformed into culture-building forces through an agonal regime of limited aggression. By superimposing this regime, as a model for Nietzsche's textual confrontations, on their unconscious text of embodied ressentiment, a therapeutic perspective emerges, based on three principles: affirmation; mutual empowerment; and externalisation. The agon performs an affirmative transformation of revenge on the basis of a fertile repetition: destructive affects (as in ressentiment) are transferred into constructive deeds of mutual antagonism. Through Nietzsche's agonal discourse, a reactive regime of internalised aggression is externalised in active deeds of limited philosophical aggression – a therapeutic transformation of (self-)destructive into constructive, philosophical impulses.     

Embeddability,syntax, and semantics in accounts of scientific theories

Recently several philosophers of science have proposed what has come to be known as the semantic account of scientific theories. It is presented as an improvement on the positivist account, which is now called the syntactic account of scientific theories. Bas van Fraassen claims that the syntactic account does not give a satisfactory definition of empirical adequacy and empirical equivalence. He contends that his own semantic account does define these notations acceptably, through the concept of embeddability, a concept which he claims cannot be defined syntactically. Here, I define a syntactic relation which corresponds to the semantic relation of embeddability. I suggest that the critical differences between the positivist account and van Fraassen's account have nothing to do with the distinction between semantics and syntax.     

“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.     

Reflection-impulsivity and information seeking in emotionally disturbed children

Forty-four emotionally disturbed children were administered the Matching Familiar Figures Test by one examiner after which the 13 most impulsive and 13 most reflective were chosen. A second examiner administered the Fixed Alternatives Question-Asking Game in whichSs sought information by asking questions that could be answered either yes or no. These questions were classified on a developmental basis; reflective children were found to employ more mature questions than did impulsive ones. Indirect comparisons between the present results and those obtained with normalSs were made.     

Children's understanding of some temporal terms denoting order,duration, and simultaneity

This study examined the comprehension by children of the concepts of order, duration, and simultaneity as reflected in certain linguistic structures. The children in the study were 3, 5, and 7 years old. Temporal order was examined through children's comprehension of two-clause sentences containing the conjunctions after, before, since, and until. Temporal duration was examined through children's understanding of one-clause sentences containing the progressive aspect and two-clause sentences containing the conjunctions since and until. These two conjunctions signal duration in the main clause when they conjoin two clauses. Simultaneity was studied through children's comprehension of two-clause sentences containing while. The results revealed that the order sentence structures (before and after) were generally comprehended by the children before the duration or simultaneous sentence structures, although at 7 years of age children were still not performing above chance on the order relation in since and until sentences. The duration sentence structures were comprehended by the children before the simultaneous sentence structures. The results support the literature in cognitive psychology and in philosophy which argues that order is simpler than duration is simpler than simultaneity.This report is based on a dissertation submitted to the University of Michigan in partial fulfillment of the requirement for the Ph.D.     

Gender Stereotypes in Japanese Television Advertisements

The aim of this study was to reveal gender portrayal types in Japanese television advertisements through content analysis. Five hundred and thirty-one adult main characters were coded for sex, age, ethnic background, credibility, role, place, dress, background, persuasion type, camera work, camera angle, product type, target, and sex of voice-over. Five types were found by performing quick cluster analysis: beautiful and wise housewives, young ladies attracting people's attention, young celebrities, middle- and old-aged people enjoying private time, and middle-aged worker bee. The first three were mainly women and the latter two were mainly men. The results indicate that in Japanese television advertisements men and women are portrayed differently, and the differences correspond with traditional gender stereotypes.     

The liar: What paradox?

Most philosophers believe that the Liar Paradox is semantical in character, and arises from difficulties in the predicate true. The author argues that the paradox is pragmatic, not semantic, and arises from violations of essential conditions that define statement-making speech acts. The author shows that his solution to the paradox will not only handle the classical Liar sentences that are necessarily or intrinsically paradoxical, but also sets of Kripke-sentences that are contingently paradoxical.     

The family as portrayed on prime-time television, 1947–1990: Structure and characteristics

Successful family series across four decades of American prime-time television were examined. Family portrayals were defined as either conventional or nonconventional. Conventional families were categorized as couples without children and couples with children. Nonconventional families were categorized as single parent or contrived. Additional family characteristics were also recorded including sex of single parent, reason for singleness, social class status, females employed outside the home, live-ins, race, and whether the presentation was dramatic or comedic. The data show a trend toward more equal presentation of conventional and nonconventional families, few divorced or female single parents, and few minority families. Implications of findings are discussed and future research questions suggested.     

Predicate Logics on Display

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem's modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap's display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules.     

O liczbach kardynalnych

Tre: Wstp. I. Niektóre pojcia i prawa teorii klas stosunków. II. O klasach abstrakcji. III. O równoskadnikowoci. IV. O kardynalnych liczbach skadników. V. O. stosowanej teorii równoskadnikowoci. VI. O relacji równej liczby elementów. VII. Stosunek obu poj liczb kardynalnych. Zakoczenie.Allatum est die 30 Augusti 1961     

Analityczne komponenty definicji arbitralnych

Tre: Wstp. I. Definicje arbitralne. II. Syntetyczne konsekwencje definicji arbitralnych III. Analityczne i rzeczowe komponenty definicji arbitralnych. IV. Zdania analityczne.Artyku ten w nieznacznym tylko stopniu róni si od pracy doktorskiej, któr przedstawiem w 1962 r. Jak najuprzejmiej dzikuj Prof. Dr M. Kokoszyskiej-Lutman, Prof. Dr J. Supeckiemu oraz Doc. Dr M. Przeckiemu za szereg uwag i wskazówek, z których tak wiele skorzystaem przygotowujc ostateczn redakcj pracy.     

Formalization of the basic concepts of animal ecology

Summary Formal definitions of the following concepts of animal ecology are given: environment, niche, locality, local population, natural population, community, ecosystem. Five primitive (undefined) notions are used including animal, offspring and habitat, the latter in the sense of Charles Elton. The defining equations for the environment of one animal are first given, then niche (in the Elton sense) is formally defined in terms of the environment. The fifth primitve notion habitat is then introduced in order to define the remaining concepts.     

Faithful Aging and the Development of Character

The author tests the kinship of the concepts faithful aging, the centerpiece of her book, The Art of Growing Old: A Guide to Faithful Aging (1998), and development of character, central to James Hillman's book, The Force of Character and the Lasting Life (1999). Faithful aging is assessed in characters from two plays: Graham Greene's The Potting Shed and Robert Anderson's I Never Sang for My Father. Finally, Saussy reflects on the development of character as a theological issue.