HUMAN WHOLENESS IN LIGHT OF FIVE TYPES OF PSYCHIC DUALITY

Abstract. Five types of psychic duality are distinguished: bipolarity, bimodality, contrariety, dualism, and the coincidentia op–positorurn. Bipolarity is the basic division of the psyche into egoic and nonegoic (physico–dynamic) poles. Bimodality is the division of egoic functioning into active and receptive modes. Contrariety is the division of the nonegoic sphere into opposing sympathetic and parasympathetic systems. Dualism is the organization imposed upon the bipolar structure by primal repression. And the coincidentia opositorum is the condition of psychic integration that would emerge were dualism to be transcended and the bipolar structure (together with the bimodal and contrarietal structures) unified into a higher whole.     

Semilattice-based dualities

The paper discusses regularisation of dualities. A given duality between (concrete) categories, e.g. a variety of algebras and a category of representation spaces, is lifted to a duality between the respective categories of semilattice representations in the category of algebras and the category of spaces. In particular, this gives duality for the regularisation of an irregular variety that has a duality. If the type of the variety includes constants, then the regularisation depends critically on the location or absence of constants within the defining identities. The role of schizophrenic objects is discussed, and a number of applications are given. Among these applications are different forms of regularisation of Priestley, Stone and Pontryagin dualities.     

Birkhoff-like sheaf representation for varieties of lattice expansions

Given a variety we study the existence of a class such that S1 every A can be represented as a global subdirect product with factors in and S2 every non-trivial A is globally indecomposable. We show that the following varieties (and its subvarieties) have a class satisfying properties S1 and S2: p-algebras, distributive double p-algebras of a finite range, semisimple varieties of lattice expansions such that the simple members form a universal class (bounded distributive lattices, De Morgan algebras, etc) and arithmetical varieties in which the finitely subdirectly irreducible algebras form a universal class (f-rings, vector groups, Wajsberg algebras, discriminator varieties, Heyting algebras, etc). As an application we obtain results analogous to that of Nachbin saying that if every chain of prime filters of a bounded distributive lattice has at most length 1, then the lattice is Boolean.We wish to thank Lic. Alfredo Guerin and Dr. Daniel Penazzi for helping us with linguistics aspects. We are indebted to the referee for several helpful suggestions. We also wish to thank Professor Mick Adams for providing us with several reprints and useful e-mail information on the subject.Suported by CONICOR and SECyT (UNC).     

Duality for algebras of relevant logics

This paper defines a category of bounded distributive lattice-ordered grupoids with a left-residual operation that corresponds to a weak system in the family of relevant logics. Algebras corresponding to stronger systems are obtained by adding further postulates. A duality theoey piggy-backed on the Priestley duality theory for distributive lattices is developed for these algebras. The duality theory is then applied in providing characterizations of the dual spaces corresponding to stronger relevant logics.The author gratefully acknowledges the support of the National Sciences and Engineering Research Council of Canada.     

Three Dual Ontologies

In this paper we give an example of intertranslatability between an ontology of individuals (nominalism), an ontology of properties (realism), and an ontology of facts (factualism). We demonstrate that these three ontologies are dual to each other, meaning that each ontology can be translated into, and recaptured from, each of the others. The aim of the enterprise is to raise the possibility that, at least in some settings, there may be no need for considerations of ontological primacy. Whether the world is made up of things, or properties, or facts, may be no more than a matter of how we look at it.     

Mereological nihilism: quantum atomism and the impossibility of material constitution

Mereological nihilism is the philosophical position that there are no items that have parts. If there are no items with parts then the only items that exist are partless fundamental particles, such as the true atoms (also called philosophical atoms) theorized to exist by some ancient philosophers, some contemporary physicists, and some contemporary philosophers. With several novel arguments I show that mereological nihilism is the correct theory of reality. I will also discuss strong similarities that mereological nihilism has with empirical results in quantum physics. And I will discuss how mereological nihilism vindicates a few other theories, such as a very specific theory of philosophical atomism, which I will call quantum abstract atomism. I will show that mereological nihilism also is an interpretation of quantum mechanics that avoids the problems of other interpretations, such as the widely known, metaphysically generated, quantum paradoxes of quantum physics, which ironically are typically accepted as facts about reality. I will also show why it is very surprising that mereological nihilism is not a widely held theory, and not the premier theory in philosophy.     

Canonical Extensions and Relational Representations of Lattices with Negation

This work is part of a wider investigation into lattice-structured algebras and associated dual representations obtained via the methodology of canonical extensions. To this end, here we study lattices, not necessarily distributive, with negation operations.We consider equational classes of lattices equipped with a negation operation ¬ which is dually self-adjoint (the pair (¬,¬) is a Galois connection) and other axioms are added so as to give classes of lattices in which the negation is De Morgan, orthonegation, antilogism, pseudocomplementation or weak pseudocomplementation. These classes are shown to be canonical and dual relational structures are given in a generalized Kripke-style. The fact that the negation is dually self-adjoint plays an important role here, as it implies that it sends arbitrary joins to meets and that will allow us to define the dual structures in a uniform way.Among these classes, all but one—that of lattices with a negation which is an antilogism—were previously studied by W. Dzik, E. Or?owska and C. van Alten using Urquhart duality.In some cases in which a given axiom does not imply that negation is dually self-adjoint, canonicity is proven with the weaker assumption of antitonicity of the negation.     

人的存在的历史性及其现代境遇

This article argues that the problem of modernity concerns the circumstances of existence and human destiny in modern times. To understand the nature of this problem and find the corresponding solution, we need to reinterpret the thought of Karl Marx regarding the contradictions of human existence and its historical dimensions. Following Marx’s line of thinking, this article reviews his critical sequence, creative transformation, and development of duality of thought on man and the world in Western history, focusing on the following four issues: (1) how Marx, on the basis of man’s sensuous objective activities, observes the duality of man and the world as well as the relationship between man’s internal and external activities; (2) how Marx discloses the true connotation and real significance of man’s historical existence, history, and historicity; (3) how Marx reveals the inherent contradictions of modern capitalist society and the destiny of modern man based on historic thought concerning man’s existence; and (4) by praising Marx’s views on material production and the eternal significance of ancient Greek culture, the article reveals another dimension of Marx’s thought, a dimension that tends to be ignored. This article holds that in this era of globalization, it is extremely important and urgent to have an in-depth understanding of Marx’s historical thoughts regarding human existence and of the feasibility of his theory. Moreover, it is imperative to further develop this understanding to create a clearer picture of our own path of development and our outlook on humanity. Translated by Cui Hui from Zhongguo Shehuikexue Wenzhai 中国社会科学文摘 (China Social Science Digest), 2005, (3): 44–46     

Principal Congruences on Semi-De Morgan Algebras

In this paper we use Hobby's duality for semi-De Morgan algebras, to characterize those algebras having only principal congruences in the classes of semi-De Morgan algebras, demi-pseudocomplemented lattices and almost pseudocomplemented lattices. This work extends some of the results reached by Beazer in [3] and [4].