This volume is not restricted to papers presented at the 1988 Colloquium, but instead aims to provide the reader with a (relatively) coherent reading on Algebraic Logic, with an emphasis on current research. To help the non-specialist reader, the book contains an introduction to cylindric and relation algebras by Roger D. Maddux and an introduction to Boolean Algebras by Bjarni Joacute;nsson.

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 23 (2003) 197-201 [Access article in PDF] An Interview with Donald Mitchell and James Wiseman The 2002 Fred Streng Book Award has been given to Donald W. Mitchell and James Wiseman for their edited collection, The Gethsemani Encounter: A Dialogue on the Spiritual Life by Buddhist and Christian Monastics. Donald W. Mitchell is professor of comparative philosophy at Purdue University and a (...) member of the editorial advisory board of Buddhist-Christian Studies. James Wiseman is a member of the Benedictine community of St. Anselm's Abbey in Washington, D.C., and is an associate professor of theology at the Catholic University of America. Following is an edited interview with both.DONALD MITCHELL How long have Buddhist and Christian monastics been in dialogue? In 1978 the Benedictine Confederation founded what is now named the Monastic Interreligious Dialogue (MID) in order to develop intermonastic dialogue, especially with Buddhism. MID has been in dialogue with Buddhism in Europe, Asia, Australia, and North America. Numerous MID spiritual exchanges and hospitality programs have taken place between Buddhist and Christian monastics over the years. How did the Dalai Lama get involved? His Holiness the Dalai Lama met with Thomas Merton in 1968, and from then on has been interested in Christian monasticism. He first got involved with MID when several of their members spoke with him at an East-West conference at the Naropa Institute in Boulder, Colorado, in 1981. This was the beginning of a series of intermonastic hospitality exchanges, with Tibetan Buddhist monks and nuns visiting Christian monasteries in the United States and Christian monastics being hosted at Tibetan Buddhist sites in India. Years later, at the Parliament of World's Religions in 1993, MID hosted a Buddhist-Christian dialogue on "Emptiness and Kenosis." The Dalai Lama took part in the dialogue and afterward told MID that he felt its dialogue with Buddhism had matured to the point [where] it would be helpful to have a weeklong retreat dialogue on the spiritual life in Buddhism and Christianity. Where did Gethsemani enter the picture? The Dalai Lama asked if it would be possible to hold the spiritual dialogue at Gethsemani Abbey, home of his friend Thomas Merton. In 1994 MID sent a delegation [End Page 197] to Dharamsala to discuss the proposal in more depth with the Dalai Lama. An agreement was reached to hold a retreat dialogue at Gethsemani Abbey with Buddhist and Christian teachers of spirituality coming from around the world. You're not a monk. How did you get involved? Good question. A year later, Sister Mary Margaret Funk, executive director of MID, met with me to request that I help organize the encounter as a lay advisor to MID. MID had used my book, Spirituality and Emptiness: The Dynamics of Spiritual Life in Buddhism and Christianity, to prepare for the Parliament dialogue on kenosis and emptiness. I agreed to help with inviting the Buddhist participants, crafting the program, and editing the proceedings. What developments in the dialogue have you seen occurring over the years? Many developments. As you can imagine, the Gethsemani Encounter in 1996 was itself a spiritual experience. As Ewert Cousins put it, there seemed to be two treasure boxes—Buddhism and Christianity—set before us in a spiritual atmosphere that enabled us to appreciate the gems of spiritual living shared by the participants. So the encounter itself brought the dialogue to a new stage of trust, understanding, and appreciation. This development can be seen in the fact that Buddhist participants suggested a project be undertaken to produce a Buddhist commentary on the Rule of St. Benedict. The result is Benedict's Dharma: Buddhists Reflect on the Rule of Saint Benedict, edited by Patrick Henry and published by Riverhead Books in 2001. What else? A small group of American Buddhist leaders and MID members met in 1999 to discuss the possibility of holding a Gethsemani Encounter II. It was decided to bring the dialogue ahead by focusing on one of the major topics that came up again and again at Gethsemani I—namely, the... (shrink)

" There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book.

Donald R. Gregory has recently argued that the monk Gaunilo's response to St Anselm's ontological argument succeeds in showing what is fundamentally wrong with any ontological argument, including modern modal versions. He holds that the Gaunilo strategy in fact demonstrates what it alleges, that reasoning which parallels the form and intent ofAnselm's reductio argument can ‘prove’ a priori the existence of quite unacceptable entities.

For cardinals we let be the smallest size of a subset B of unbounded in the sense of ; that is, such that there is no function such that has size less than for all . Similarly for , the general dominating number, which is the smallest size of a subset B of such that for every there is an such that the above set has size less than . These cardinals are generalizations of the usual ones for . When (...) all three are the same regular cardinal, the relationships between them have been completely described by Cummings and Shelah. We also consider some variants of the functions, following van Douwen, in particular the version of in which B is required to consist of strictly increasing functions. Some of the main results of this paper are: (1) ; (2) for , always exists; (3) if , then ; (4) . For background see Section 1 of the paper. Several open problems are stated. (shrink)

The main notion dealt with in this article is where A is a Boolean algebra. A partition of 1 is a family ofnonzero pairwise disjoint elements with sum 1. One of the main reasons for interest in this notion is from investigations about maximal almost disjoint families of subsets of sets X, especially X=ω. We begin the paper with a few results about this set-theoretical notion.Some of the main results of the paper are:• (1) If there is a maximal family (...) of size λ≥κ of pairwise almost disjoint subsets of κ each of size κ, then there is a maximal family of size λ of pairwise almost disjoint subsets of κ+ each of size κ.• (2) A characterization of the class of all cardinalities of partitions of 1 in a product in terms of such classes for the factors; and a similar characterization for weak products.• (3) A cardinal number characterization of sets of cardinals with a largest element which are for some BA the set of all cardinalities of partitions of 1 of that BA.• (4) A computation of the set of cardinalities of partitions of 1 in a free product of finite-cofinite algebras. (shrink)

We give some results concerning various generalized continuum cardinals. The results answer some natural questions which have arisen in preparing a new edition of 5. To make the paper self-contained we define all of the cardinal functions that enter into the theorems here. There are many problems concerning these new functions, and we formulate some of the more important ones.

We consider eight special kinds of subalgebras of Boolean algebras. In Section 1 we describe the relationships between these subalgebra notions. In succeeding sections we consider how the subalgebra notions behave with respect to the most common cardinal functions on Boolean algebras.

Recall that a subset X of a Boolean algebra A is independent if for any two finite disjoint subsets F , G of X we have ∏ x∈F x ∏ y∈G −y≠0. The independence of a BA A , denoted by Ind, is the supremum of cardinalities of its independent subsets. We can also consider the maximal independent subsets. The smallest size of an infinite maximal independent subset is the cardinal invariant i , well known in the case A= P (...) / fin . In this article we consider the collection of all cardinalities of infinite maximal independent subsets of a BA A ; we call this set the spectrum of infinite maximal independent subsets , denoted by Spind. Note that infinite maximal independent subsets exist in any BA which is not superatomic. The main result is that any set of infinite cardinals can occur as Spind for some infinite BA A . Beyond this we give results concerning the way that Spind changes under various algebraic operations. However, the basic components of most algebras that we deal with are free algebras. (shrink)

Assume that all algebras are atomless. (1) $Spind(A x B) = Spind(A) \cup Spind(B)$ . (2) $(\prod_{i\inI}^{w} = {\omega} \cup \bigcup_{i\inI}$ $Spind(A_{i})$ . Now suppose that $\kappa$ and $\lambda$ are infinite cardinals, with $kappa$ uncountable and regular and with $\kappa \textless \lambda$ . (3) There is an atomless Boolean algebra A such that $\mathfrak{u}(A) = \kappa$ and $i(A) = \lambda$ . (4) If $\lambda$ is also regular, then there is an atomless Boolean algebra A such that $t(A) = \mathfrak{s}(A) = (...) \kappa$ and $\mathfrak{a}(A) = \lambda$ . All results are in ZFC, and answer some problems posed in Monk [01] and Monk [ $\infty$ ]. (shrink)

Donald Price and James Barrell show how a science of human experience can be developed through a strategy that integrates experiential paradigms with methods from the natural sciences.

For any Boolean Algebra A, let cmm be the smallest size of an infinite partition of unity in A. The relationship of this function to the 21 common functions described in Monk [4] is described, for the class of all Boolean algebras, and also for its most important subclasses. This description involves three main results: the existence of a rigid tree algebra in which cmm exceeds any preassigned number, a rigid interval algebra with that property, and the construction of an (...) interval algebra in which every well-ordered chain has size less than cmm. (shrink)

Afghanistan. In the heat and dust, young British army medic Elinor Nielson watches an Afghan girl walk into a hail of bullets. But when she runs to help, Ellie finds her gone. Who is she? And what's happened to her? What Ellie discovers makes her question everything she believes in - even her feelings for the American lieutenant who takes her side.

Understanding the nature of pain at least partly depends on recognizing its inherent first person epistemology and on using a first person experiential and third person experimental approach to study it. This approach may help to understand some of the neural mechanisms of pain and consciousness by integrating experiential–phenomenological methods with those of neuroscience. Examples that approximate this strategy include studies of second pain summation and its relationship to neural activities and brain imaging-psychophysical studies wherein sensory and affective qualities of (...) pain are correlated with cerebral cortical activity. The experiential paradigm of Price and Barrell offers the possibility of improved designs and methods for investigating neural mechanisms underlying pain and consciousness. (shrink)

In this paper, we explore Peirce's work for insights into a theory of learning and cognition for education. Our focus for this exploration is Peirce's paper The Fixation of Belief (FOB), originally published in 1877 in Popular Science Monthly. We begin by examining Peirce's assertion that the study of logic is essential for understanding thought and reasoning. We explicate Peirce's view of the nature of reasoning itself—the characteristic guiding principles or ‘habits of mind’ that underlie acts of inference, the dimensions (...) of and interaction between doubt and belief, and his four methods of resolving or ‘fixing’ belief (i.e., tenacity, authority, a priori, and experimentation). The four methods are then juxtaposed against current models of teaching and learning such as constructivism, schema theory, situated cognition, and inquiry learning. Finally, we discuss Peirce's modes of inference as they relate educationally to the resolution of doubt and beliefs and offer an example of belief resolution from an experienced teacher in a professional development environment. (shrink)