On Extensions of Intermediate Logics by Strong Negation

In this paper we will study the properties of the least extension n() of a given intermediate logic by a strong negation. It is shown that the mapping from to n() is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n (). This summarizes results that can be found already in [13,14] and [4]. Furthermore, we determine the structure of the lattice of extensions of n(LC).     

Varieties of Monadic Heyting Algebras. Part III

This paper is the concluding part of [1] and [2], and it investigates the inner structure of the lattice (MHA) of all varieties of monadic Heyting algebras. For every n , we introduce and investigate varieties of depth n and cluster n, and present two partitions of (MHA), into varieties of depth n, and into varieties of cluster n. We pay a special attention to the lower part of (MHA) and investigate finite and critical varieties of monadic Heyting algebras in detail. In particular, we prove that there exist exactly thirteen critical varieties in (MHA) and that it is decidable whether a given variety of monadic Heyting algebras is finite or not. The representation of (MHA) is also given. All these provide us with a satisfactory insight into (MHA). Since (MHA) is dual to the lattice NExtMIPC of all normal extensions of the intuitionistic modal logic MIPC, we also obtain a clearer picture of the lattice structure of intuitionistic modal logics over MIPC.     

O pojęciu zdania analitycznego

Rezultaty przedstawione w pracy niniejszej pokrywaj si czciowo z wynikami osignitymi przezR. Wójcickiego w pracy:Analityczne komponenty definicji arbitralnych. Studia Logica, t. XIV. Dotyczy to gównie rezultatów zawartych w czci pierwszej. Chciabym podkreli, i wyniki R. Wójcickiego uzyskane zostay cakowicie niezalenie od rezultatów przedstawionych w pracy obecnej.Allatum est die 16 Aprilis 1962     

Some properties of two measures of multivariate association

Two kinds of measures of multivariate association, based on Wilks' and the Bartlett-Nanda-Pillai trace criterionV, respectively, are compared in terms of properties of the univariateR ² which they generalize. A unified set of derivations of the properties is provided which are self-contained and not restricted to decompositions in canonical variates. One conclusion is that asymmetric index based on allows generalization of the multiplicative decomposition ofR ² in terms of squared partial correlations, but not the additive decomposition in terms of squared semipartial correlations, while the reverse is true for anasymmetric index based onV.We are indebted to Jos M. F. ten Berge for some fruitful discussions.     

Treating the “Wise Baby”

In a previous examination of Ferenczis concept of the Wise Baby (1996), I had noted both its applications and its limitations in the analytic treatment of an unusually intelligent adult. Ferenczis concepts of the origin of intellect in trauma and of the wise baby have often left the indistinct impression of being interrelated phenomena. In this paper, I regard as arguable the notion that very high intelligence is pathological when it is precocious. This return visit to the territory of the wise baby extends Ferenczis ideas about the origin and use of the intellect to include a consideration of what may constitute effective treatment for those who suffer from giftedness.Judith E. Vida, M.D. edits On the Arts for this journal. She is a Founding Member and Faculty of the Institute of Contemporary Psychoanalysis in Los Angeles, CA, a member of both American and International Psychoanalytic Associations, and of the Sándor Ferenczi Society of Budapest. Her private practice is in Pasadena, CA.Address correspondence to Judith E. Vida, 301 S. Fair Oaks Ave., Suite 406A, Pasadena, CA 91105, USA; e-mail: jvida@spence.net     

Mel Gibson’s Big Gamble: <Emphasis Type="Italic">The Passion of Christ</Emphasis>

Mel Gibsons film is a creative reworking of opportunities provided by migrating to Australia as a boy and a life-long desire to be reconciled to his father, Hutton Gibson. If the film is read as a study in psychology and biography, then biblical and theological critiques, along with contemporary politically correct stances towards what Gibson did, can be set temporarily aside in search of a larger trajectory of meaning implicit in the film. The embodied nature of the film, along with other violent films in which Gibson starred in the past three decades, points to wellsprings of power in the blood. Violence becomes an idiom of reconciliation with authority. Gibsons relationship to his father plays a major role in such a reading of the film. A continuous reconciliation with his father is evident not only in thematic continuities over the course of Mel Gibsons professional acting career and starring roles. It also structures the directors construction of Christs Passion. A desire not to be forsaken gives rise to this idiosyncratic and controversial film, itself a cinematic statement about Gibsons own personal spiritual torment.Richard A. Hutch is Director of Studies of the Faculty of Arts and Reader in Religion and Psychological Studies in the School of History, Philosophy, Religion, and Classics at the University of Queensland in Brisbane, Australia 4072.     

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.     

An almost general splitting theorem for modal logic

Given a normal (multi-)modal logic a characterization is given of the finitely presentable algebras A whose logics L A split the lattice of normal extensions of . This is a substantial generalization of Rautenberg [10] and [11] in which is assumed to be weakly transitive and A to be finite. We also obtain as a direct consequence a result by Blok [2] that for all cycle-free and finite A L A splits the lattice of normal extensions of K. Although we firmly believe it to be true, we have not been able to prove that if a logic splits the lattice of extensions of then is the logic of an algebra finitely presentable over ; in this respect our result remains partial.     

Fitting the factor analysis model

When the covariance matrix (p×P) does not satisfy the formal factor analysis model for m factors, there will be no factor matrix (p×m) such that =(-) is diagonal. The factor analysis model may then be replaced by a tautology where is regarded as the covariance matrix of a set of residual variates. These residual variates are linear combinations of discarded common factors and unique factors and are correlated. Maximum likelihood, alpha and iterated principal factor analysis are compared in terms of the manner in which is defined, a maximum determinant derivation for alpha factor analysis being given. Weighted least squares solutions using residual variances and common variances as weights are derived for comparison with the maximum likelihood and alpha solutions. It is shown that the covariance matrix defined by maximum likelihood factor analysis is Gramian, provided that all diagonal elements are nonnegative. Other methods can define a which is nonGramian even when all diagonal elements are nonnegative.A modified version of this paper forms part of a Ph.D. thesis submitted to the University of South Africa.Presently at the National Institute for Personnel Research, South Africa.     

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).     

Three prepositional calculi of probability

Attempts are made to transform the basis of elementary probability theory into the logical calculus.We obtain the propositional calculus NP by a naive approach. As rules of transformation, NP has rules of the classical propositional logic (for events), rules of the ukasiewicz logic ₀ (for probabilities) and axioms of probability theory, in the form of rules of inference. We prove equivalence of NP with a fragmentary probability theory, in which one may only add and subtract probabilities.The second calculus MP is a usual modal propositional calculus. It has the modal rules x x, x y x y, x x, x y (y x), (y x), in addition to the rules of classical propositional logic. One may read x as x is probable. Imbeddings of NP and of ₀ into MP are given.The third calculus P is a modal extension of ₀. It may be obtained by adding the rule ((xy)y) xy to the modal logic of quantum mechanics Q [5]. One may read x in P as x is observed. An imbedding of NP into P is given.     

Protoalgebraic logics

There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include almost all (non-pathological) systems of prepositional logic that have occurred in the literature. The relationship between the metatheory of a protoalgebraic logic and its matrix models is studied. The following results are obtained for any finite matrix model U of a filter-distributive protoalgebraic logic : (I) The extension _U of is finitely axiomatized (provided has only finitely many inference rules); (II) _U has only finitely many extensions.     

Once More into the Breach of Self-Ownership: Reply to Narveson and Brenkert

In reply to Narveson, I distinguish his no-proviso argument from his liberty argument, and I show that both fail. I also argue that interference lacks the strategic status he assigns to it, because it cannot be appropriately distinguished, conceptually and morally, from prevention; that natural resources do enjoy the importance he denies they have; that laissez-faire economies lack the superiority he attributes to them; that ownership can indeed be a reflexive relation; that anti-paternalism does not entail libertarianism; and that he misrepresents the doctrines of a number of philosophers, including John Locke, Ronald Dworkin, and myself. In reply to Brenkert, I show that he seriously misconstrues my view of the nature of freedom, and of its relationship to self-ownership. I then refute his criticisms of my treatment of the contrasts between self-ownership, on the one hand, and autonomy and non-slavery, on the other. I also show that his attempt to exorcize the demon of self-ownership is multiply flawed.     

Supererogation in Deontic Logic: Metatheory for DWE and Some Close Neighbours

In "Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator It is supererogatory that. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation, . For worlds u, v and w, we say that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete over three versions of the semantics. We call the strongest of these logics DWE for Doing Well Enough.     

The Suspended Aesthetic: Slavoj Žižek on Eastern European Film

Slavoj iek's writings on Krzysztof Kies´lowski and Andrej Tarkovskij represent direct challenges to the Central and Eastern European tradition of spiritual art and to dominant aesthetic concepts as such. He refuses to separate the solemn films of Kies´lowski and Tarkovskij from popular culture and stresses their import as ethical statements by their directors. Despite this ethical emphasis, iek makes an important contribution to philosophical aesthetics. He implicitly defines art as a suspension of reality which reveals time in its fragility and potentiality. Defining iek's aesthetics in terms of suspension helps to explain his partiality for Kies´lowski and Tarkovskij and bears comparison to the Russian tradition of philosophical aesthetics, in particular Aleksej Losev and Alexander Bakshy.     

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     

Логистическая система, исходными связками которой являются эквивалентность и дизъюнкция

- Allatum est die 5 Martii 1970     

Dichotic sequence discrimination: The effect of continued practice

Summary Dichotic sequence discrimination was studied by means of a three-alternative forced-choice method. Two of the alternatives (same) consisted of a single pair of dichotic clicks with the stimulus at one ear preceding the stimulus at the other ear by a given temporal separation (e.g., R-t-L). One of the alternatives consisted of a single pair of clicks with the opposite sequence (e.g., L-t-R). The subjects' task was to discriminate between the different and the same dichotic pairs. The results indicate that discrimination is a nonmonotonic function of t, i.e., V- or U-shaped, with high levels at both short and long temporal separations (t=2 and 4 ms and t=64 and 96 ms) and with lower levels of discrimination for intermediate ts. A second experiment was performed to study the effect of continued practice by subjects trained in dichotic sequence discrimination for ts 4 and 64 ms (high discrimination levels) and for t=16 ms (low discrimination level). There was no systematic trend towards improvement over 8 blocks of 50 trials for each t. Discrimination levels of these ts did not differ between Experiments 1 and 2.Dr. Babkoff is spending the 1979–1981 academic year at the Walter Reed Army Institute of Research, Department of Military Medical Psychophysiology, Forest Glen Annex, Building 189, Washington, D.C. 20012, USAThe experiments were conducted at the Bar-Ilan University, Ramat-Gan, Israel. The authors would like to thank the Bar-Ilan Research Committee for making funds available to conduct the experimentsThis material has been reviewed by the Walter Reed Army Institute of Research, and there is no objection to its presentation and/or publication. The opinions or assertions contained herein are the private views of the authors and are not to be construed as official or as reflecting the views of the Department of the Army or the Department of Defense     

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.     

Praxis and Agency in Foucault’s Historiography

This paper examines the consequences for agency that Foucaults historiographical approach constructs. The analysis begins by explaining the difference between legislative history and exemplary history, drawing parallels to similar theoretical distinctions offered in the works of Max Weber, J.L. Austin, and Zygmunt Bauman. The analysis continues by reading Habermass critique of Foucault through the tropological lenses suggested by White [Metahistory. Baltimore, MD: Johns Hopkins University Press, 1973]; it argues that Habermass critique misrecognizes the tropes of Foucaultian genealogy. The paper draws implications for education by articulating possibilities for praxis and agency in terms of pedagogy specifically related to the distinction between didactics and modeling. The paper concludes by suggesting that genealogy does not play by Hegels rules, but rather exemplifies agency in ways that are not recognizable from a modernist perspective.