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.

The introduction of novel diagnostic techniques in clinical domains such as genomics and radiology has led to a rich ethical debate on how to handle unsolicited findings that result from these innovations. Yet while unsolicited findings arise in both genomics and radiology, most of the relevant literature to date has tended to focus on only one of these domains. In this article, we synthesize and critically assess similarities and differences between “scanning the body” and “sequencing the genome” from an ethical (...) perspective. After briefly describing the novel diagnostic contexts leading to unsolicited findings, we synthesize and reflect on six core ethical issues that relate to both specialties: terminology; benefits and risks; autonomy; disclosure of unsolicited findings to children; uncertainty; and filters and routine screening. We identify ethical rationales that pertain to both fields and may contribute to more ethically sound policies. Considerations of preserving public trust and ensuring that people perceive healthcare policies as fair also support the need for a combined debate. (shrink)

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)

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)

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

The relation between morality and religion has often been discussed. However, it is not always recognized that the relation varies greatly according to the variety of religions. I shall here be concerned solely with Christian theism in its traditional form. I take the latter to signify, essentially, belief in a morally perfect Creator who exists in the threefold form of Father, Son and Holy Spirit and who, in the person of the Son, became man in Christ for our salvation. I (...) thus exclude from consideration all non-theistic accounts of God or the Absolute. Also I shall consider, not simply bare theism of the kind that Christians share with Jews and Muslims, but also the distinctively Christian form of theism that is generated by distinctively Christian revelation. Many otherwise sound descriptions of the relation between morality and theism are defective because they fail to consider the distinctively Christian contribution to the theistic concept of God and of his relation to the world. (shrink)

Many writers often generalise about mysticism without a sufficiently close analysis of texts. Consequently the generalisations are often invalid. My present aim is to analyse one text and, in the light of this analysis, to offer some observations concerning mysticism in general and Christian mysticism in particular.

For over thirty years C. A. Campbell has made major contributions to both ethics and metaphysics. Since these do not correspond to the prevailing fashions in philosophy and theology they are in danger of being under-estimated, if not ignored. I hope to summarise and comment on them as impartially as possible. Inevitably I must be selective. In writing for this journal I have, naturally, chosen to stress those elements in Campbell's thought which are directly or indirectly relevant to religion. Even (...) so, there are many points which I have no space to develop. I shall be content if I say enough to indicate the importance of Campbell's writings for the study of the philosophically crucial topics to which they are devoted. (shrink)

Christianity affirms, with Judaism and Islam, that God is the omnipotent Creator of all things. But it diverges from them in also affirming that the Creator assumed a human nature in one figure of history, Jesus of Nazareth. Christ thus differs from other men in kind, not merely in degree; he is absolutely, not just relatively, unique. Admittedly many Christian theologians have held that the difference between Christ and other men is only one of degree. Yet the Church's traditional claim, (...) as expressed in the Chalcedonian Definition, is that Jesus was both creature and Creator, both fully man and fully God. (shrink)

The purpose of this paper is to resolve two paradoxes, which occur in quantum theory, by using the discussion of the theory of measurement presented in two earlier papers by the author [3], [4], [5]. The two paradoxes discussed will be the Schrödinger cat paradox and the Einstein, Podolski, Rosen paradox [2]. An introductory section will be included which summarizes the relevant results from the author's previous papers. Also a discussion will be made regarding the author's interpretation of the density (...) operator. (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)

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