An Infinitary Extension of Jankov’s Theorem

It is known that for any subdirectly irreducible finite Heyting algebra A and any Heyting algebra B, A is embeddable into a quotient algebra of B, if and only if Jankov’s formula χ _A for A is refuted in B. In this paper, we present an infinitary extension of the above theorem given by Jankov. More precisely, for any cardinal number κ, we present Jankov’s theorem for homomorphisms preserving infinite meets and joins, a class of subdirectly irreducible complete κ-Heyting algebras and κ-infinitary logic, where a κ-Heyting algebra is a Heyting algebra A with # ≥  κ and κ-infinitary logic is the infinitary logic such that for any set Θ of formulas with # Θ ≥  κ, ∨Θ and ∧Θ are well defined formulas.     

An Ecological Approach to Explaining Women’s Adjustment in the Initial Stage of Marriage

In this study, we focused on marital adjustment among a sample of 101 Israeli women who had been married up to 3 years and did not have children. We examined the contribution of variables from three ecological systems to marital adjustment: the ontogenic system (attachment dimensions, and women’s perceptions of differentiation in the family of origin); the microsystem (strategies for resolving marital conflicts); and the exosystem (characteristics of the husband’s employment). The findings revealed that the higher the women’s levels in the two dimensions of attachment, the lower their levels of marital adjustment. By contrast, the more the women used conflict resolution strategies of integration, concession, and compromise, the higher their levels of marital adjustment. Conflict resolution strategies mediated the effects of attachment avoidance and family differentiation on marital adjustment. To conclude, we offer practical recommendations for identifying couples at risk in the first stage of marital life, and for professional interventions to improve marital adjustment at that stage.     

Knowing One’s Own Self: An Analysis of Vivekananda’s Approach to One’s Identity

A successful declaration of one’s identity in saying “ahaṃ Brahmāsmi” is a result of knowing one’s own self as indistinguishable from Brahman. The non-difference between oneself and the Brahman is one’s true identity, and it goes without saying, knowledge of one’s true identity constitutes the correct knowing of one’s own self. That the said non-difference is upheld by vedānta, and we need to put this ideal non-difference into practice is the crux of Vivekananda’s practical vedānta. Vivekananda gives certain reasons for the practicability of vedānta. This paper’s part I is an exposition of Vivekananda’s practical vedānta, focussing on those reasons for practical vedānta and orienting each towards an analytical understanding. In part II, a linguistic analysis of Vivekananda’s approach to one’s identity has been carried out after introducing J. Hintikka’s interpretation of Descartes’ “I think, therefore, I am” and G. Misra’s interpretation of sat (existence, reality or being) cit (consciousness, knowledge or cognition) ānanda (bliss, intense happiness or felicity). The latter’s interpretation displays a positivist’s linguistic analysis of vedānta, whereas the former’s does a speech act theorist’s analysis of Descartes’ cogito principle. The present analysis indicates that practical vedānta can be read in the light of analytic philosophy and Vivekananda’s approach to one’s identity can be understood in terms of speech acts.

     

An Approach to Emerson’s Writing Style from a Daoist Perspective

There is a clear and controlling philosophical concern that governs Ralph Waldo Emerson’s essays: freedom from limitation and self-reliance from external authority. What makes it difficult to understand his essays, however, is his style, which is characterized by disconnection, paradox, and negation. These rhetorical techniques make the meaning of his writings elusive and slippery. Though many scholars have analyzed Emerson’s style, none have approached it through the writings of Laozi, an ancient Chinese philosopher. There are two reasons I compare Emerson and Laozi. First, in spite of their differences, there are important parallel themes and stylistic innovations in their writings. Second, attentiveness to a key figure in the Eastern philosophical tradition can help to explain how Emerson’s thoughts disappoint Western readers, precisely because they employ techniques beyond the method of habitual intellect in the Western frame. This essay tries to approach several features in Emerson’s writing style from a Daoist perspective to show that both philosophers purposefully use linguistic strategies such as disconnection, paradox, and negation to provoke readers into participating in understanding truth, instead of telling them directly what truth is.     

An Introduction to Kristof’s Theorem for Solving Least-Square Optimization Problems Without Calculus

Kristof’s Theorem (Kristof, 1970 Kristof, W. (1970). A theorem on the trace of certain matrix products and some applications. Journal of Mathematical Psychology, 7(3), 515–530. https://doi.org/10.1016/0022-2496(70)90037-4[Crossref], [Web of Science ®] , [Google Scholar]) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof’s Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof’s (1964 Kristof, W. (1964). Die beste orthogonale Transformation zur gegenseitigen Uberfiihrung zweier Faktorenmatrizen. Diagnostica, 10, 87–90. [Google Scholar], 1970 Kristof, W. (1970). A theorem on the trace of certain matrix products and some applications. Journal of Mathematical Psychology, 7(3), 515–530. https://doi.org/10.1016/0022-2496(70)90037-4[Crossref], [Web of Science ®] , [Google Scholar]) writings. In this article, I describe the underlying logic of Kristof’s Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem’s proof. I then show how Kristof’s Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 R Core Team (2017). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from https://www.R-project.org/ [Google Scholar]) code to perform the calculations described in the text.     

Systematizing Toulmin’s Warrants: An Epistemic Approach

Relevance of premises to conclusion can be explicated through Toulmin’s notion of warrant, understood as an inference rule, albeit not necessarily formal. A normative notion of relevance requires the warrant to be reliable. To determine reliability, we propose a fourfold classification of warrants into a priori, empirical, institutional, and evaluative, with further subdivisions possible. This classification has its ancestry in classical rhetoric and recent epistemology. Distinctive to each type of warrant is the mode by which such connections are intuitively discovered and the grounds on which we ultimately justify them. The classification of warrants is thus epistemic. We illustrate the difference by contrasting empirical physical with institutional intuition, and argue for the advantages of this approach over Toulmin’s conception of field dependence.     

The Logics of Discovery in Popper’s Evolutionary Epistemology

Popper is well known for rejecting a logic of discovery, but he is only justified in rejecting the same type of logic of discovery that is denied by consequentialism. His own account of hypothesis generation, based on a natural selection analogy, involves an error-eliminative logic of discovery and the differences he admits between biological and conceptual evolution suggest an error-corrective logic of discovery. These types of logics of discovery are based on principles of plausibility that are used in the generation as opposed to the preliminary evaluation of hypotheses. The normative relevance of these principles is grounded in the distinction between strategic and definitory rules.

Survey of Confucius’s Approach to Expediency

Confucius held that expediency means adjusting to changing circumstances, not necessarily going along with or against anything, having a sense of propriety about times and measures, and doing things in their proper time and manner. However, expediency does not mean doing whatever one likes without any principle; instead, it means taking benevolence and righteousness as criteria and acting accordingly. In Confucius’s opinion, one should cultivate benevolence internally and act with righteousness externally, weigh importance and unimportance, measure advantages and disadvantages, and not “set the mind either for anything, or against anything,” pursuing “what the heart desires, without transgressing what is right.” In this way, he would keep to benevolence without deviating from it, act expediently without despising any principles, and attain a dialectical unification of expediency and principles.     

Moment/History Duality in Prior’s Logics of Branching-Time

The basic notions in Prior’s Ockhamist and Peircean logics of branching-time are the notion of moment and that of history (or course of events). In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical (and ontological) dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of a non-Archimedean topology on the set of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories.     

Another Approach to Spinoza’s De Intellectus Emendatione

This paper examines Spinoza’s De Intellectus Emendatione from the standpoint of its place in the rationalist canon, and also with respect to certain lines of feminist thought. It concludes that Spinoza’s wholism, lack of interest in skepticism, and insistence on simples are not inconsistent with a variety of feminist concerns. The commentary of Genevieve Lloyd and Harald Hoffding is alluded to, and notions taken from works of contemporary feminism are cited.     

Situating Maimonides’s Approach to the Oral Torah in Its Andalusian Context

Maimonides’s readers have long recognized that his presentation of the Oral Torah differed markedly from that of the Baghdadi geonim, particularly Sa‘adya Gaon. Maimonides did not cite any precedent for his disagreements with the geonim. Recent studies, however, have called attention to Andalusian sources that prefigure and parallel Maimonidean claims, suggesting that his views, at least in part, drew on earlier Andalusian thought. This article argues that a uniquely Andalusian understanding of the talmudic adage “A sage is superior to a prophet,” first found in the writings of Isaac Ibn Ghiyāth, demonstrates that Andalusian Rabbanite culture had long approached the Oral Torah differently than did the geonim of Baghdad. After identifying a number of Andalusian antecedents for Maimonides’s approach to the Oral Torah, this article explores possible motives for the divergent pictures of revelation put forward by Rabbanites in Baghdad and Andalusia. It is suggested that the impact of Andalusian Maliki jurists helps explain the divergent positions of Baghdadi and Andalusian Rabbanites.     

Dewey’s Social Ontology: A Pragmatist Alternative to Searle’s Approach to Social Reality

Dewey’s social ontology could be characterized as a habit ontology, an ontology of habit qua second nature that offers us an account of intentionality, social statuses, institutions and norms in terms of habituations. Such an account offers us a promising alternative to contemporary intentionalist and deontic approaches to social ontology such as Searle’s. Furthermore, it could be the basis of a social ontology better suited to explain both the maintenance and the transformation of social reality.     

From Wittgenstein’s N-operator to a New Notation for Some Decidable Modal Logics

Wittgenstein’s N-operator is a ‘primitive sign’ which shows every complex proposition is the result of the truth-functional combination of a finite number of component propositions, and thus provides a mechanical method to determine logical truth. The N-operator can be interpreted as a generalized Sheffer stroke. In this paper, I introduce a new ‘primitive sign’ that is a hybrid of generalized Sheffer stroke and modality, and give a uniform expression for modal formulas. The general form of modal formula in the new notation is [A₀···A_n?1; B₀···B_m?1], which is semantically equivalent to ¬A₀∨···∨¬ A_n?1∨? (¬B₀∨···∨¬B_m?1). Based on this new notation, I propose several analytic axiomatic systems for some decidable modal logics. Every axiom of these analytic systems is an ‘Atomic-Sheffer’, which is the result of the combination of a finite number of component propositions. The inferential rules are analytic in that the set of elementary propositions that are combined in the premiss overlaps the set of elementary propositions combined in the conclusion, in virtue of which every complex proposition can be reduced to an ‘Atomic-Sheffer’ at the ultimate level. The analytic modal systems have the same classical inferential rules. Different modal systems can be built by adding special modal inferential rules. In an analytic system for modal logic L, valid formulas on L-models can be proved by a purely mechanical method.     

An Introduction to Nicolai Hartmann’s Critical Ontology

Nicolai Hartmann contributed significantly to the revitalization of the discipline of ontology in the early twentieth century. Developing a systematic, post-Kantian critical ontology ‘this side’ of idealism and realism, he subverted the widespread impression that philosophy must either exhaust itself in foundationalist epistemology or engage in system-building metaphysical excess. This essay provides an introduction to Hartmann’s approach in light of the recent translation of his early essay ‘How is Critical Ontology Possible?’ (1923) In it Hartmann criticizes both the pretensions of epistemology as well as the principal errors of classical ontology, and he proposes a series of correctives that lead to his development of a highly original and elaborate stratified categorial ontology. This introduction explains the most important errors of the ‘old’ ontology, his correctives to them, and further fleshes out these correctives with reference to his mature ontological work.     

Frege’s Result: Frege’s Theorem and Related Matters

One of the remarkable results of Frege’s Logicism is Frege’s Theorem, which holds that one can derive the main truths of Peano arithmetic from Hume’s Principle (HP) without using Frege’s Basic Law V. This result was rediscovered by the Neo-Fregeans and their allies. However, when applied in developing a more advanced theory of mathematics, their fundamental principles—the abstraction principles—incur some problems, e.g., that of inflation. This paper finds alternative paths for such inquiry in extensionalism and object theory.     

An Adaptive Logic Based on Jaśkowskiˈs Approach to Paraconsistency

In this paper, I present the modal adaptive logic AJ ^r (based on S5) as well as the discussive logic D ^r ₂ that is defined from it. D ^r ₂ is a (non-monotonic) alternative for Jaśkowski’s paraconsistent system D ₂ . Like D ₂ , D ^r ₂ validates all single-premise rules of Classical Logic. However, for formulas that behave consistently, D ^r ₂ moreover validates all multiple-premise rules of Classical Logic. Importantly, and unlike in the case of D ₂ , this does not require the introduction of discussive connectives. It is argued that this has clear advantages with respect to one of the main application contexts of discussive logics, namely the interpretation of discussions.*Research for this paper was indirectly supported by the Flemish Minister responsible for Science and Technology (contract BIL1/8). The author is indebted to Leon Horsten, Jo?o Marcos, Jerzy Perzanowski, Liza Verhoeven, and especially to the referee and to Diderik Batens for comments and suggestions.     

The Predictive Power of Horney’s Psychoanalytic Approach: An Empirical Study

This study investigated the construct validity of a measure of Karen Horneys (1945) psychoanalytic theory that postulated three neurotic trends: compliant, aggressive, and detached. Her theory was operationalized by the Horney-Coolidge Type Indicator (HCTI). One hundred seventy-two adults completed the HCTI and the short form of the Coolidge Axis II Inventory, a measure of the three DSM-IV personality disorder clusters. Multiple regression and canonical correlation analyses revealed significant and differential patterns of the three HCTI dimensions with the three clusters. Because Paris (1994) has noted that Horneys neurotic trends may today be conceived of as personality disorders, one implication of the present findings is that Horneys dynamic theory can be valid and useful in the general understanding of personality disorders from a cluster perspective.     

Reading Anxiety: An Early Affective Impediment to Children’s Success in Reading

Learning to read is a critical but often challenging academic task for young children. In the current study, we explore the relation between children’s reading affect-–particularly anxiety-–and reading achievement in the early years of reading acquisition. We hypothesized that reading anxiety would relate to reading achievement across the school year and that boys and girls might show differential patterns in the relation between reading anxiety and achievement due to the common stereotype that boys underperform in reading. A sample of first and second grade students completed measures of reading anxiety, positive reading affect, math achievement, and reading achievement in the fall and spring. Results show that reading anxiety and reading achievement share a bi-directional relation in which fall reading anxiety predicts spring reading achievement and vice versa. Furthermore, the pattern of relation between reading anxiety and achievement differs by gender: boys appear more susceptible to the reciprocal damaging effects of reading anxiety on reading achievement across the school year. Finally, reading achievement shares a stronger relation with reading anxiety than with positive reading affect, perhaps because of the phenomenon in which negative relative to positive experiences have a greater psychological impact.