An axiom system for orthomodular quantum logic

Logical matrices for orthomodular logic are introduced. The underlying algebraic structures are orthomodular lattices, where the conditional connective is the Sasaki arrow. An axiomatic calculusOMC is proposed for the orthomodular-valid formulas.OMC is based on two primitive connectives — the conditional, and the falsity constant. Of the five axiom schemata and two rules, only one pertains to the falsity constant. Soundness is routine. Completeness is demonstrated using standard algebraic techniques. The Lindenbaum-Tarski algebra ofOMC is constructed, and it is shown to be an orthomodular lattice whose unit element is the equivalence class of theses ofOMC.This research was supported by National Science Foundation Grant Number SOC76-82527.     

Plain Semi-Post algebras as a poset-based generalization of post algebras and their representability

Semi-Post algebras of any type T being a poset have been introduced and investigated in [CR87a], [CR87b]. Plain Semi-Post algebras are in this paper singled out among semi-Post algebras because of their simplicity, greatest similarity with Post algebras as well as their importance in logics for approximation reasoning ([Ra87a], [Ra87b], [RaEp87]). They are pseudo-Boolean algebras generated in a sense by corresponding Boolean algebras and a poset T. Every element has a unique descending representation by means of elements in a corresponding Boolean algebra and primitive Post constants which form a poset T. An axiomatization and another characterization, subalgebras, homomorphisms, congruences determined by special filters and a representability theory of these algebras, connected with that for Boolean algebras, are the subject of this paper.To the memory of Jerzy SupeckiResearch reported here has been supported by Polish Government Grant CPBP 01.01     

Some Results on Modal Axiomatization and Definability for Topological Spaces

We consider two topological interpretations of the modal diamond—as the closure operator (C-semantics) and as the derived set operator (d-semantics). We call the logics arising from these interpretations C-logics and d-logics, respectively. We axiomatize a number of subclasses of the class of nodec spaces with respect to both semantics, and characterize exactly which of these classes are modally definable. It is demonstrated that the d-semantics is more expressive than the C-semantics. In particular, we show that the d-logics of the six classes of spaces considered in the paper are pairwise distinct, while the C-logics of some of them coincide. Mathematics Subject Classifications (2000): 03B45, 54G99. Presented by Michael Zakharyaschev     

A second-order relevance logic with modality

In this paper a system, RPF, of second-order relevance logic with S5 necessity is presented which contains a defined, notion of identity for propositions. A complete semantics is provided. It is shown that RPF allows for more than one necessary proposition. RPF contains primitive syntactic counterparts of the following semantic notions: (1) the reflexive, symmetrical, transitive binary alternativeness relation for S5 necessity, (2) the ternary Routley-Meyer alternativeness relation for implication, and (3) the Routley-Meyer notion of a prime intensional theory, as well as defined syntactic counterparts, of the semantic notions of a possible world and the Routley-Meyer ^* operator.     

Place and World: On Jeff Malpas’ Second Edition of Place and Experience

ABSTRACT

Jeff Malpas’ book Experience and Place has become a significant landmark in philosophy. I take the publication of the revised and extended second edition of the book in 2018 as an opportunity to reflect on some key issues in Malpas’ thought. After briefly outlining Malpas’ commitment to topophilia and topoanalysis, I address, in the first part of my essay, the relation of place to subjectivity and normativity, pointing out certain shortcomings or ambiguities in Malpas’ account. I also critically discuss the omission of an account of migration, or, rather, immigration, which seems called for, especially if we realize that the inhabited place always comes with its limit or border, which implies that there is also a view from outside, and that we have moral obligations to the stranger and/or immigrant coming into our place from outside. In the second part of my essay, I engage Malpas’ argument according to which Heidegger ‘derived’ space from time. By an analysis of relevant texts in Heidegger, I show that this argument does not hold.     

Functional Monadic Bounded Algebras

The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator ${\exists} reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomorphic to ones whose elements are propositional functions.     

The adequacy of the theories of deductive systems with respect to sentential calculi

Summary The sentential calculiR, under discussion, are axiomatizable and implication is among their primitive terms. The modus ponens and the rule of substitution are their primitive rules. ByS _r is denoted the set of sentences obtained from the formulae of the calculusR by substituting sentences of a given language for all variables. The variablesx, y, z ... represent the elements of the setS _r , the variablesX, Y, Z ... represent the subsets ofS _R . The formulacxy designates an implication withx as its antecedent andy as its consequent,cxy is always an element ofS _R δ(X) means, thatX is closed with respect to the modus ponens rule.A _R designates the class of allS _R -substitutions of the axioms of the sentential calculusR.     

A Lewisian Semantics for S2

This paper sets out a semantics for C.I. Lewis's logic S2 based on the ontology of his 1923 paper ‘Facts, Systems, and the Unity of the World’. In that article, worlds are taken to be maximal consistent systems. A system, moreover, is a collection of facts that is closed under logical entailment and conjunction. In this paper, instead of defining systems in terms of logical entailment, I use certain ideas in Lewis's epistemology and philosophy of logic to define a class of models in which systems are taken to be primitive elements but bear certain relations to one another. I prove soundness and completeness for S2 over this class of models and argue that this semantics makes sense of at least a substantial fragment of Lewis's logical theory.     

Demystifying Meaning

Abstract

Some philosophers find linguistic meaning mysterious. Two approaches suggest themselves for removing the felt mystery, or demystifying meaning. One involves providing a substantive account of meaning in meaning-free terms. Although this approach has come under serious attack in recent years, Paul Horwich has recently presented a version of the approach that might be thought impervious. A preliminary attempt is made to argue that Horwich's version is vulnerable to the considerations felt to undermine other versions of the substantive approach to demystification. That leaves the second approach, quietism, which involves showing that although meaning is primitive it is un-mysterious. It is suggested that this approach is worthy of exploration.     

The association of physical activity to occipito-temporal processing during face recognition

ObjectivesThis study examined the association between physical activity level and primitive cognitive processing during a face recognition task in young adults, a topic that has received little attention.DesignCross-sectional.MethodsThe face recognition task required participants to respond to famous faces but not respond to unfamiliar faces. Task performance and several occipito-temporal event-related brain potentials reflecting the various stages of face processing, from perceptual encoding (N170) to recognition (N250 and face-N400), were assessed during the face recognition task.ResultsAlthough analyses revealed no significant group differences in behavioral performance measures, neuroelectric data showed different time courses of face recognition processes between groups. Active individuals exhibited larger N250 amplitude, reflecting an early stage of facial recognition, for famous relative to unfamiliar faces, whereas inactive individuals did not exhibit such a difference.ConclusionsThese findings are suggestive of a possible association between physical activity and relatively early, primitive cognitive processes.     

Emotions–Adaptive Standards And/Or Primitive Constructs: A Reply to Mascolo and Mancuso

Abstract

In replying to Mascolo & Mancuso's paper, I have contrasted their functionalist approach to emotional states and experience with my position on emotions as epigenetically-available primitive constructs. Biologically, Mascolo & Mancuso treat emotions as mobilizaiton in the face of discrepancies. My proposal of a four-dimensional model provides a biological grounding for the marvellous diverisyt of human emotional experience. Where Mascolo & Mancuso treat emotions as discrete entities and highlight emotion knowledge, J have suggested emotions operate as bipolar constructs, and I have highlighted experience. We should attend to emotions in terms of both knowledge and experience, but it is important to maintain the distinction     

Multimo dal Logics of Products of Topologies

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies. AMS subject classification : 03B45, 54B10 The last author’s research was supported by a Social Sciences and Humanities Research Council of Canada grant number: 725-2000-2237. Presented by Melvin Fitting     

A new stable icosahedral quasicrystal in the Cd-Mg-Dy system

A new stable icosahedral quasicrystal has been found in annealed Cd-Mg-Dy alloys. The composition of the icosahedral phase was determined to be approximately Cd₆₆Mg₂₁Dy₁₃. Powder X-ray and electron diffraction patterns revealed that the phase has a primitive icosahedral lattice with a quasilattice parameter a_R = 0.5634 nm. The electron diffraction study confirmed that the phase has a well ordered primitive icosahedral structure.     

The Logic of the Ontological Square

The Ontological Square is a categorial scheme that combines two metaphysical distinctions: that between types (or universals) and tokens (or particulars) on the one hand, and that between characters (or features) and their substrates (or bearers) on the other hand. The resulting four-fold classification of things comprises particular substrates, called substances, universal substrates, called kinds, particular characters, called modes or moments, and universal characters, called attributes. Things are joined together in facts by primitive ontological ties or nexus. This article describes a logic that is meant to capture the basic intuitions behind the Ontological Square. Given a minimal correspondence between atomic logical form and ontological structure, the commitment to nexus as a distinct ontological category entails a rehabilitation of copulae as ties of predication. Thus, the Logic of the Ontological Square is a copula calculus rather than a predicate calculus; its soundness and completeness can be established with respect to a model akin to a so-called first-order semantics for standard second-order logic. Presented by Hannes Leitgeb     

Secular Buddhism and Justice

Abstract

Starting point: The core idea of secular Buddhism is to grasp the spirit of early Buddhism and transpose it into the present. The best known approach to implement this idea is Stephen Batchelor’s Buddhism Without Beliefs, an approach which advocates an agnostic stance with regard to the doctrine of rebirth and denies its relevance for daily practice.

Type of problem:

? Is there a way to revise the doctrine of rebirth, instead of completely dropping it?

? What is the impact on the notion of justice?

Result: The doctrine of rebirth cannot be revised in a strict sense, but there are some striking similarities between the ancient and modern (biological) view on the topic. Since the stream of genetic and epigenetic information has the power to create consciousness and reflects experiences of past lives, it can be associated with the stream of consciousness (cittasantāna) in the Mahayana model of rebirth. Parents not only determine the genetic constitution of their children, they also transfer character traits by means of epigenetic heredity. If genetic inheritance is associated with karma, then genes become an element of synchronic and diachronic connectedness (pratītya-samutpāda). Instead of an individual learning process across successive lives, there is a collective learning process across successive generations.

Given the biological model of rebirth, the belief in cosmic justice turns into a quest for mundane justice. There is a thought experiment for constructing such a concept, which complies well with the secular Buddhist spirit. John Rawls assumes that the legislative deliberation is taking place ‘behind a veil of ignorance’, so that the participants of the deliberation do not know their future genetic constitution and their future position within the society. If the participants imagine that their future self is contingent and impermanent – in accordance with the Buddhist doctrine of anātman and anitya – then the resulting principles of justice will be impartial.     

An algebraic study of well-foundedness

A foundational algebra ( , f, ) consists of a hemimorphism f on a Boolean algebra with a greatest solution to the condition f(x). The quasi-variety of foundational algebras has a decidable equational theory, and generates the same variety as the complex algebras of structures (X, R), where f is given by R-images and is the non-wellfounded part of binary relation R.The corresponding results hold for algebras satisfying =0, with respect to complex algebras of wellfounded binary relations. These algebras, however, generate the variety of all ( ,f) with f a hemimorphism on ).Admitting a second hemimorphism corresponding to the transitive closure of R allows foundational algebras to be equationally defined, in a way that gives a refined analysis of the notion of diagonalisable algebra.The research reported in this paper was carried out while the author was at the Department of Mathematics and Statistics, University of Auckland, under a teaching exchange with the Victoria University of Wellington.     

How the Good Obligates in Hegel's Conception of Sittlichkeit: A Response to Robert Stern's Understanding Moral Obligation

Abstract

In Understanding Moral Obligation: Kant, Hegel, Kierkegaard, Robert Stern argues that Hegel has a social command view of obligation. On this view, there is an element of social command or social sanction that must be added to a judgment of the good in order to bring about an obligation. I argue to the contrary that Hegel's conception of conscience, and thus the individual's role in obligation, is more central to his account than the social dimension. While agreeing with Stern that Hegel's conception of Sittlichkeit does preserve a role for obligation, and that the social plays an important part in that account, I argue that there is no extra social component that converts the morally good into obligation. Rather, Hegel's conception of Sittlichkeit as the “living good” means that judgments of the moral facts are simultaneously judgments of obligation.     

The Ephesian Megabyzos Priesthood and Religious Diplomacy at the End of the Classical Period

One element consistently cited as evidence that the feminine deities of the poleis of Ionia are aspects of a single Great Mother Goddess of fertility is the Ephesian Megabyzos priest, whose eunuch status is paralleled with the Greco-Roman eunuch priests of Cybele, the Galli. The practice of eunuchism is usually regarded as a pre-Greek or primitive element in Ephesian worship, dating back to the earliest phases of religious activity at the site. This contention is, however, a construction of the evidence coloured by nineteenth-century thinking about the development of religions and the nature of so-called ‘primitive’ societies. The evidence itself makes no claim for any great antiquity for this priesthood but rather suggests an institution of brief duration in the latter portion of the classical period. This article re-examines the evidence for the Megabyzos priesthood in terms of the political changes in and around the city of Ephesos in the fourth century B.C.E. and finds a context for the Megabyzos in the religious diplomacy between Ephesos and the Persian satrapal capital, Sardis, during the shift from Persian to Macedonian control.     

Towards a topological philosophy

This article examines the use of mathematical concepts in philosophy, focusing on topology, which may be viewed as a modern supplement to geometry. We show that Plato and Parmenides were already employing geometric ideas in their research, and discuss three examples of the application of topology to philosophical problems: the first concerns the analysis of the Cartesian distinction between res extensa and res cogitans, the second the ontology of possible worlds of Wittgenstein's Tractatus, and the third Leibniz's monadology. We also consider the role of topology in mathematical explanations of the sort found in science, arguing that it can perform a role in philosophy that is of comparable importance.