This paper is a contribution toward developing a theory of expansions of semi-Heyting algebras. It grew out of an attempt to settle a conjecture we had made in 1987. Firstly, we unify and extend strikingly similar results of [ 48 ] and [ 50 ] to the (new) equational class DHMSH of dually hemimorphic semi-Heyting algebras, or to its subvariety BDQDSH of blended dual quasi-De Morgan semi-Heyting algebras, thus settling the conjecture. Secondly, we give a criterion for a unary expansion (...) of semi-Heyting algebras to be a discriminator variety and give an algorithm to produce discriminator varieties. We then apply the criterion to exhibit an increasing sequence of discriminator subvarieties of BDQDSH . We also use it to prove that the variety DQSSH of dually quasi-Stone semi- Heyting algebras is a discriminator variety. Thirdly, we investigate a binary expansion of semi-Heyting algebras, namely the variety DblSH of double semi-Heyting algebras by characterizing its simples, and use the characterization to present an increasing sequence of discriminator subvarieties of DblSH . Finally, we apply these results to give bases for “small” subvarieties of BDQDSH , DQSSH , and DblSH. (shrink)

This paper augments Hailperin's substantial efforts to place Boole's algebra of logic on a solid footing. Namely Horn sentences are used to give a modern formulation of the principle that Boole adopted in 1854 as the foundation for his algebra of logic—we call this principle The Rule of 0 and 1.

The purpose of this paper is to define and investigate the new class of quasi-Stone algebras . Among other things we characterize the class of simple QSA's and the class of subdirectly irreducible QSA's. It follows from this characterization that the subdirectly irreducible QSA's form an elementary class and that the variety of QSA's is locally finite. Furthermore we prove that the lattice of subvarieties of QSA's is an -chain. MSC: 03G25, 06D16, 06E15.

A lineage of prominent philosophers who have discussed the second-person relation can be regarded as advancing structural accounts. They posit that the second-person relation effects one transformative change to the structure of practical reasoning. In this paper, I criticise this orthodoxy and offer an alternative, substantive account. That is, I argue that entering into second-personal relations with others does indeed affect one's practical reasoning, but it does this not by altering the structure of one's agential thought, but by changing what (...) reasons can become available. The importance of second-personal thought for action is heterogenous. Second-person relations make possible the emergence of a wide variety of different kinds of practical reasons: creating some, revealing others. Recognising this diminishes the appeal of the traditional, structural accounts of the practical significance of such second-personal relations. Moving away from structural accounts facilitates a more thorough understanding of the intersubjective form of action. (shrink)

This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification.

First published in 1935, The Life and Writings of Giambattista Vico is a succinct biography of the Italian philosopher, Giambattista Vico. Carefully documented, the book comments on Vico's life as well as his oeuvre in a bid to extend his audience to the English-speaking population. From his early childhood to the influence of his writings after his death, the book provides a keen insight into the many facets of his philosophy. This book will be of interest to students of philosophy (...) and history. (shrink)

This paper is about the similarity between the appreciation of a piece of art, such as a cherished music album, and the loving appreciation of a person whom one knows well. In philosophical discussion about the rationality of love, the Qualities View (QV) says that love can be justified by reference to the qualities of the beloved. I argue that the oft-rehearsed trading-up objection fails to undermine the QV. The problems typically identified by the objection arise from the idea that (...) love-worthy qualities could be coarse-grained, when in fact they must be fine-grained. The analogy with appreciation of aesthetic qualities helps to draw out this point. Once the fine-grained nature of love-worthy qualities is properly understood, it is clear that critics of the QV cannot rely on the trading-up objection to motivate its rejection. Moreover, the paper’s core argument helps to illuminate the persistently aesthetic nature of interpersonal affections. (shrink)

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

Poverty violates fundamental human values through its impact on individuals and on human environments, and it goes against the core values of democratic societies. Drawing on numerous scientific studies as well as his own experience witnessing the systematic poverty in his home country of South Africa, H. P. P. [Hennie] Lötter presents a holistic profile of poverty and its effects on human lives all the while accounting for the complexity of each individual case. He argues that shared ethical values must (...) guide the planning and distribution of aid and that our society must reevaluate our notions of justice and reimagine the role of the state in order to enable collective human responsibility for poverty’s successful eradication. (shrink)

Dilthey is a figure of real importance in European philosophy and social theory. He exerted a significant influence on Husserl, Heidegger and Weber through his work on the nature of philosophy and the methodology and epistemology of human and social studies. He was also a distinguished and original historian of ideas and, indeed, many of his philosophical interests arose from the insights and practical difficulties he encountered as a historian. He produced a monumental biography of Schleiermacher, and a series of (...) shorter, but no less striking studies of Hegel, Dickens, Shakespeare, Schiller and many others. (shrink)

The articles published in this volume will bring that knowledge which alone fortifies a student against wrong or fanciful occultism, as against the perils of ...

Summary. — The following theorem is proved.: If the statistical predictions of quantum theory are true in general and. if the macroscopic world is not radically different from what is observed, then what happens macroscopically in one space-time region must in some cases depend on variables that are controlled by experimenters in far-away, space-like-separated. regions. By what happens macroscopically in one space-time region is meant specifically the occurrence or nonoccurrence of a macroscopic event, such as the d.etection and recording of (...) a particle by some macroscopic device. By a variable controlled. by an experimenter in a certain space-time region is meant specifically the experimental setting in that region of some macroscopic device, in which this setting is controlled. by an experimenter acting within that region. The theorem pertains speci6cally to experimental situations in which there .are two far-apart, spacelike-separated. regions in each of which there is a device that can be set at either of two alternative settings by an experimenter acting within ' that region. There. is also a long sequence of experimental results (4.e. events) in each of the two regions. The theorem asserts that, for some such cases, it is mathematically impossible, within the manifold. (shrink)