An alternative notion of an existential quantifier on four-valued Łukasiewicz algebras is introduced. The class of four-valued Łukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by \. It is shown that the alternative existential quantifier is interdefinable with the standard existential quantifier on a four-valued Łukasiewicz algebra. Some connections between the new existential quantifier and the existential quantifiers defined on bounded distributive lattices and Boolean algebras are given. Finally, a completeness theorem for the monadic four-valued (...) Łukasiewicz predicate calculus corresponding to the dual of the alternative existential quantifier is proven. (shrink)

It is shown that in a linearly ordered MV-algebra A , the implication is unique if and only if the identity function is the unique De Morgan automorphism on A . Modulo categorical equivalence, our uniqueness criterion recalls Ohkuma's rigidness condition for totally ordered abelian groups. We also show that, if A is an Archimedean totally ordered MV-algebra, then each non-trivial De Morgan automorphism of the underlying involutive lattice of A yields a new implication on A , which is not (...) isomorphic to the original implication. (shrink)

Evangelical Protestant spirituality, under the influence of the Enlightenment, has assumed a somewhat modernist flavor. As a result, traditional forms of religious symbol and piety were demoted in favor of religious affections, true spirituality was now discerned by means of “heart knowledge,” and the assurance of salvation assumed a place of prominence in the emerging market of spiritual autobiography. This essay explores several ways that a non-monastic, non-modern Protestant tradition, which lives according to a community rule, can contribute to the (...) spiritual formation conversation. I begin by introducing the reader to the Amish narrative and discuss how two theological themes shape their approach to spirituality–-the cross of Christ and the relationship between faith and works, justification and sanctification. Next, I question a common view of Jesus’ ministry as being diametrically opposed to that of the Pharisees and suggest that the Sermon on the Mount deserves to be central to the enterprise of spiritual formation. I conclude this essay by revealing how the Amish put spiritual theology into practice, via a locally constructed Ordnung and while seated around the supper table. (shrink)

A family of formal intuitionistic theories is proposed with realizability of proved formulas in several subrecursive classes, e.g. Grzegorczyk classes, polynomial-time computable functions class, etc. xA) Algorithm extraction forxyA is shown for various classes of bounded complexity. The results on polynomial computability are closely connected to work on the Bounded Arithmetic by S. Buss.

Ch. 1. Filosofskoe osmyslenie kulʹtury -- ch. 2. Problemy mnozhestvennosti kulʹtur.

This book constitutes the refereed proceedings of the International Conference on Spatial Information Theory, COSIT 2005, held in Elliottville, NY, USA in September 2005. The 30 revised full papers presented were carefully reviewed and selected from 82 submissions. The papers are organized in topical sections on vagueness, uncertainty, and gradation; paths and routes; ontologies and semantics; ontologies and spatial relations; spatial reasoning: cognitive maps and spatial reasoning; time, change, and dynamics; landmarks and navigation; geographic information, and spatial behaviour.

This paper describes the topological aspect of a logic-based, artificial intelligence approach to formalising the qualitative description of spatial properties and relations, and reasoning about those properties and relations. This approach, known as RCC theory, has been under development for several years at the University of Leeds. The main rationale for this project is that qualitative descriptions of spatial properties and relationships, and qualitative spatial reasoning, are of fundamental importance in human thinking about the world: even where quantitative spatial data (...) are most important, they must be attached to the components of a perceived spatial structure if we are to make use of them. RCC theory covers other qualitative aspects of spatial description and reasoning, but the topological properties and relations of spatially extended entities are fundamental to our work. The topological formalisms used by mathematicians are, in general, not well suited to the task of formalising the kinds of ‘common-sense’ or ‘everyday’ qualitative spatial description and reasoning which are our primary interest. Nevertheless, we must come to grips with the concepts of topology as practised by mathematicians if we are not to risk constantly ‘reinventing wheels’. (shrink)

Question and quotation marks tend to proliferate in articles which ask whether Homer can provide any historical information about early Greek society. In this article ‘Homeric’ society will refer to the society which is portrayed in the Iliad and the Odyssey. ‘The World of Odysseus’ will refer to the recension of ‘Homeric’ society which appears in M. I. Finley's book of that name. Finley claims that ‘The World of Odysseus’ is a faithful account of ‘Homeric’ society and that the latter (...) is a literary portrait of a real society that existed in Greece some time during the dark ages. As a result of Finley's influential book, ‘The World of Odysseus’, or something very like it, has found its way into most of the history books generally available in the classroom. In this article I wish to reconsider ‘Homeric’ society and to question the propriety of identifying it with either ‘The World of Odysseus’ or any real society. (shrink)

At the beginning of the fifth century there was a change in the style of clothing worn by Athenian men.1 When Thucydides speaks of it,2 he first describes how the Greeks of ancient times used to carry weapons in everyday life, just as the barbarians of his own day still did. The Athenians were the first to lay weapons aside and to take up a relaxed and more luxurious way of life.

It was with this bitter intervention from Thrasymachus, occurring halfway through the first of its ten Books, that that work begins to come urgently alive. For the remainder of Book I the Socrates of the Dialogue asks questions and raises objections, while Thrasymachus keeps urging that in fact the just become through their very justice the victims of exploitation–the suckers!

Bateson's belated acceptance of the chromosome theory came in two main stages, and was permanent, although he retained to the end reservations about some implications and extensions of the theory. Coleman's attempt to explain Bateson's resistance in terms of his conservative mode of thought is critically examined, and rejected: the attributes Coleman assigns to Bateson are all either inappropriate, or irrelevant to chromosome theory, or both. Instead, the diverse factors which contributed to Bateson's resistance are enumerated and discussed. These include (...) deficiencies in the evidence then available to support the theory; embryological difficulties; Bateson's aversion to microscopy combined with the lack of a close colleague skilled in cytology; his iconoclastic temperament, and the fact that he found T. H. Morgan, the leader of the Drosophila school, an uncongenial personality. Taken together, these factors suffice to account for his resistance. Bateson's position is contrasted with that of the other most eminent opponent, W. Johannsen, whose organismic outlook was the main obstacle to acceptance. (shrink)

At their extremes, the modernization of ancient mathematical texts (absolute presentism) leaves nothing of the source and the refusal to modernize (absolute antiquarism) changes nothing. The extremes exist only as tendencies. This paper attempts to justify the admissibility of broad modernization of mathematical sources (presentism) in the context of a socio-cultural (non-fundamentalist) philosophy of mathematics.

Suffering patients (when able), grieving families and compassionate physicians have always sought the least detrimental alternative while deciding care in the face of tragedy. Modern medical technology has brought great benefits to patients but has blurred traditional concepts of life and death and created new dilemmas for practising doctors. While this technology has given doctors great control over living and dying, their dominance in critical decision making is being challenged. More and more their decisions are liable to public and legal (...) scrutiny, intense publicity by the news media and exploitation by lobbyists with opposing aims. Increasing pressure of this kind may deflect the physician form his primary responsibility to patients and their families. For infants with gross malformations or a distressing terminal illness we believe that the parents and their doctors must be allowed primary decisional power even if the chosen course of action involves the death of the infant. Choices for death should be permitted but only after suitable family and professional consultation. Some general guidelines are suggested. As these situations are so varied and so complex, much latitude in decision-making should be expected and tolerated. (shrink)