Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the (...) scope of quantifiers reveals a natural way out. (shrink)

In previous work in 2010 we have dealt with the problems arising from Cantor's theorem and the Richard paradox in a definable universe. We proposed indefinite extensibility as a solution. Now we address another definability paradox, the Berry paradox, and explore how Hartogs's cardinality theorem would behave in an indefinitely extensible definable universe where all sets are countable.

This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies (...) in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text. (shrink)

ABSTRACT There is a fierce debate about nonsmokers-only hiring policies, also referred to as no-nicotine hiring policies and “tobacco free” hiring policies. The favorable outcomes of no-nicotine hiring policies include reduced health costs, improved worker productivity, enhanced organizational image, and symbolic messaging. The unfavorable consequences of such policies include violating personal liberty, risking a “slippery slope” to other health-compromising behaviors, exacerbating socio-economic disparities, and discriminating against smokers. No-nicotine hiring policies have not been adequately evaluated and a new approach is warranted. (...) The new conditional employment policy for smokers is described with stipulations for the probationary period. Autonomy and fairness are frequently cited as ethical principles to analyze no-nicotine hiring policies. An analysis of ethical principles is presented for no-nicotine hiring policies and the new conditional employment policy. The ethical principle of fairness is rooted in the effectiveness of any policy. Therefore, an evaluation plan is described for the conditional employment policy to assess effectiveness and efficiency. The proposed policy provides a powerful incentive to overcome smoking addictions, preserve the ethical principles of autonomy and fairness, as well as bridge the divide between personal liberty and personal responsibility. (shrink)

Ethics, architecture and philosophy -- Architecture, ethics and aesthetics -- Architecture and culture -- Experiencing architetcure -- Writing on 'the Wall': memory, monuments and memorials -- Building community: new urbanism, planning and democracy.