This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is (...) of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures. (shrink)

This paper distinguishes four major types of futility (physiological, imminent demise, lethal condition, and qualitative) that have been advocated in the literature either in a patient dependent or a patient independent fashion. It proposes five criteria (precision, prospective, social acceptability, significant number, and non-agreement) that any definition of futility must satisfy if it is to serve as the basis for unilaterally limiting futile care. It then argues that none of the definitions that have been advocated meet the criteria, primarily because (...) their proponents have not paid sufficient attention to the problematic nature of the data supporting the use of their definitions. (shrink)