A pO -algebra $${(L; f, \, ^{\star})}$$ is an algebra in which ( L ; f ) is an Ockham algebra, $${(L; \, ^{\star})}$$ is a p -algebra, and the unary operations f and $${^{\star}}$$ commute. Here we consider the endomorphism monoid of such an algebra. If $${(L; f, \, ^{\star})}$$ is a subdirectly irreducible pK 1,1 - algebra then every endomorphism $${\vartheta}$$ is a monomorphism or $${\vartheta^3 = \vartheta}$$ . When L is finite the endomorphism monoid of L is (...) regular, and we determine precisely when it is a Clifford monoid. (shrink)

Let (L; f) be a finite simple Ockham algebra and let (X;g) be its dual space. We first prove that every connected component of X is either a singleton or a generalised crown (i.e. an ordered set that is connected, has length 1, and all vertices of which have the same degree). The representation of a generalised crown by a square (0,1)-matrix in which all line sums are equal is used throughout, and a complete description of X, including the number (...) of connected components and the degree of the vertices, is given. We then examine the converse problem of when a generalised crown can be made into a connected component of (X; g). We also determine the number of non-isomorphic finite simple Ockham algebras that belong properly to a given subvariety P 2n,0. Finally, we show that the number of fixed points of (L; f) is 0,1, or 2 according to the nature of X. (shrink)

Let be a class of models with a notion of ‘strong’ submodel and of canonically prime model over an increasing chain. We show under appropriate set-theoretic hypotheses that if K is not smooth , then K has many models in certain cardinalities. On the other hand, if K is smooth, we show that in reasonable cardinalities K has a unique homogeneous-universal model. In this situation we introduce the notion of type and prove the equivalence of saturated with homogeneous-universal.

Retrospective rule-making has few supporters and many opponents. Defenders of retrospective laws generally do so on the basis that they are a necessary evil in specific or limited circumstances, for example to close tax loopholes, to deal with terrorists or to prosecute fallen tyrants. Yet the reality of retrospective rule making is far more widespread than this, and ranges from ’corrective’ legislation to ’interpretive regulations’ to judicial decision making. The search for a rational justification for retrospective rule-making necessitates a reconsideration (...) of the very nature of the rule of law and the kind of law that can rule, and will provide new insights into the nature of law and the parameters of societal order. This book examines the various ways in which laws may be seen as retrospective and analyses the problems in defining retrospectivity. In his analysis Dr Charles Sampford asserts that the definitive argument against retrospective rule-making is the expectation of individuals that, if their actions today are considered by a future court, the applicable law was discoverable at the time the action was performed. The book goes on to suggest that although the strength of this ’rule of law’ argument should prevail in general, exceptions are sometimes necessary, and that there may even be occasions when analysis of the rule of law may provide the foundation for the application of retrospective laws. (shrink)

Background: While religious faith remains one of the most significant features of human life, little is known about its relationship to ordinary belief at the level of the brain. Nor is it known whether religious believers and nonbelievers differ in how they evaluate statements of fact. Our lab previously has used functional neuroimaging to study belief as a general mode of cognition, and others have looked specifically at religious belief. However, no research has compared these two states of mind directly. (...) Methodology/Principal Findings: We used functional magnetic resonance imaging to measure signal changes in the brains of thirty subjects - fifteen committed Christians and fifteen nonbelievers - as they evaluated the truth and falsity of religious and nonreligious propositions. For both groups, and in both categories of stimuli, belief was associated with greater signal in the ventromedial prefrontal cortex, an area important for self-representation, emotional associations, reward, and goal-driven behavior. This region showed greater signal whether subjects believed statements about God, the Virgin Birth, etc. or statements about ordinary facts. A comparison of both stimulus categories suggests that religious thinking is more associated with brain regions that govern emotion, self-representation, and cognitive conflict, while thinking about ordinary facts is more reliant upon memory retrieval networks. Conclusions/Significance: While religious and nonreligious thinking differentially engage broad regions of the frontal, parietal, and medial temporal lobes, the difference between belief and disbelief appears to be content-independent. Our study compares religious thinking with ordinary cognition and, as such, constitutes a step toward developing a neuropsychology of religion. However, these findings may also further our understanding of how the brain accepts statements of all kinds to be valid descriptions of the world. © 2009 Harris et al. (shrink)

The plan for this volume emerged during the international Leipzig conference commemorating the centenary of the death of Gustav Fechner.

The prospect of using cell-based interventions to treat neurological conditions raises several important ethical and policy questions. In this target article, we focus on issues related to the unique constellation of traits that characterize CBIs targeted at the central nervous system. In particular, there is at least a theoretical prospect that these cells will alter the recipients' cognition, mood, and behavior—brain functions that are central to our concept of the self. The potential for such changes, although perhaps remote, is cause (...) for concern and careful ethical analysis. Both to enable better informed consent in the future and as an end in itself, we argue that early human trials of CBIs for neurological conditions must monitor subjects for changes in cognition, mood, and behavior; further, we recommend concrete steps for that monitoring. Such steps will help better characterize the potential risks and benefits of CBIs as they are tested and potentially used for treatment. (shrink)