We present here a direct elementary construction of continuous utility functions on perfectly separable totally preordered sets that does not make use of the well-known Debreu’s open gap lemma. This new construction leans on the concept of a separating countable decreasing scale. Starting from a perfectly separable totally ordered structure, we give an explicit construction of a separating countable decreasing scale, from which we show how to get a continuous utility map.

THERE ARE TWO CONCEPTS OF MIRACLE: AS (A) THE VIOLATION OF A NATURAL LAW, AND AS (B) A STRIKING COINCIDENCE WITHIN NATURAL LAW. DIFFICULTIES IN (A) HAVE BEEN WIDELY DISCUSSED, E.G., BY R SWINBURNE. THOSE IN (B) HAVE NOT. I ARGUE THAT IF DIFFICULTIES IN (A) FORCE A RETREAT TO (B), THEN A PLACE MUST BE FOUND FOR A GOD TO ACT TO PRODUCE (B). SEVERAL POSSIBILITIES ARE CONSIDERED; NONE ARE FOUND SATISFACTORY EXCEPT POSSIBLY THE GOD INFLUENCING UNNOTICED AN ANIMATE (...) OBJECT. I CONCLUDE WITH A NEW AND FAVORABLE LOOK AT HUME’S CONTRARY MIRACLES ARGUMENT. (shrink)

This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.

The term "stakeholder engagement" has gained increasing prominence over the last few years. This prominence is fueled by a range of issues such as an increased dissatisfaction with business's focus on stockholder/shareholder interests and the demands for greater transparency from business following major business scandals. A perceived response to this issue in South Africa has been the inclusion of guidelines on stakeholder engagement in the King II Report on Corporate Governance. Despite this growing interest, there has not been clarity on (...) how companies engage with their stakeholders and specifically with how they identify and prioritize their stakeholders. The study sought to establish the reporting practices of South African business in relation to stakeholder identification and prioritization through a content analysis of their annual reports. The findings are discussed and recommendations on the two aspects of stakeholder engagement presented. (shrink)

Conventional accounts of the development of the Enlightenment in the English-speaking world posit an evolution. Over time, it is argued, dominant ideas of the “divine attributes,” the characteristics of the First Person of the Trinity, moved from Calvinist images of God as a stern avenger to Latitudinarian reliance on God as an indulgent parent and Deist understandings of God as a First Cause, increasingly synonymous with Nature. This chapter argues that this view is mistaken. All the chief ways of conceiving (...) God had long been available; and powerful and sustained debates in the long eighteenth century about God’s nature followed no single direction. The classic model of the Enlightenment as the advance of secularization is untenable. (shrink)

In the Rhetoric Aristotle frequently illustrates the points he is making with examples drawn both from oratory and from other literary genres. Although some of these citations have been used to date the work, they have never been systematically examined. It is the contention of this article that, when Aristotle gives examples from speeches, he quotes exclusively from epideictic works, and that this fact tells us much both about the circulation of written speeches at Athens and about the preoccupations of (...) Aristotle and his pupils. (shrink)