Let us call an integer part of an ordered field any subring such that every element of the field lies at distance less than 1 from a unique element of the ring. We show that every real closed field has an integer part.

We offer a formal account of the English past tenses. We see the perfect as having reference time at speech time and the preterite as having reference time at event time. We formalize four constraints on reference time, which we bundle together under the term ‘perspective’. Once these constraints are satisfied at the different reference times of the perfect and preterite, the contrasting functions of these tenses are explained. Thus we can account formally for the ‘definiteness effect’ and the ‘lifetime (...) effect’ of the perfect, for the fact that the perfect seems to ‘explain’ something about the present, and that the perfect cannot presuppose a past time point. We explain why perfect and preterite can sometimes be interchangeable, and we offer a solution to the ’present perfect puzzle’. We explain the unacceptability of notorious examples of the perfect such as * Gutenberg has discovered the art of printing . We give greater definition to the familiar notions of ‘current relevance’ and ‘extended now’. (shrink)

Questionnaire studies on the attitudes of Finnish doctors towards euthanasia were conducted in 1993 and 2003, and the results show that they have not become more positive.

In this contribution we investigate the conceptual coherence of penal substitution and its moral validity. After assessing two opposing modern contributions, we turn to Reformed and medieval scholasticism. This scholastic manoeuvre sheds additional light on the analytic questions at issue. Following Owen and Scotus in their use of a relational analysis of guilt and its punishment, we argue that penal substitution is conceptually and morally coherent, albeit not univocally vis-à-vis ordinary punishment. Absent from the case of substitution is personal deservedness; (...) herein we follow Murphy. However, this leaves open the conceptual possibility of representative deservedness. (shrink)

In this historical contribution, we assess Duns Scotus’s analysis of atonement (Commentary on the Sentences bk. III). We also include a partial exploration of his analysis of penance (Sentences bk. IV), because certain topics which we tend to discuss within atonement-theory, for example the analysis of the virtue of punishment, pertained to the subject of penance for Scotus. In recent scholarship, Andrew Rosato has argued that Scotus adapted the Anselmian non-penal view of Christ’s substitutionary satisfaction to the penal understanding of (...) satisfaction operative in penance. In this contribution, however, we argue that Scotus’s understanding remained non-penal: his view of the atonement depends on meritorious supererogatory acts of love. Additionally, we harvest some valuable Scotistic insights for atonement-theory, some of them applicable to penal theories as well. (shrink)