Combinatory logic and lambda-conversion were originally devised in the 1920s for investigating the foundations of mathematics using the basic concept of 'operation' instead of 'set'. They have now developed into linguistic tools, useful in several branches of logic and computer science, especially in the study of programming languages. These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive (...) functions. The key ideas and basic results are presented, as well as a number of more specialised topics, and man), exercises are included to provide manipulative practice. (shrink)

Introduction Combinatory logic deals with a class of formal systems designed for studying certain primitive ways in which functions can be combined to form ...

Because the main difference between combinatory weak equality and λβ-equality is that the rule \begin{equation*}\tag{\xi} X = Y \vdash \lambda x.X = \lambda x.Y\end{equation*} is valid for the latter but not the former, it is easy to assume that another way of defining combinatory β-equality is to add rule (ξ) to the postulates for weak equality. However, to make this true, one must choose the definition of combinatory abstraction in (ξ) very carefully. If one tries to use one of the (...) more common abstraction algorithms, the result will be an equality, = ξ , that is either equivalent to βη-equality (and so strictly stronger than β-equality) or else strictly weaker than β-equality. This paper will study the relations = ξ for several commonly used abstraction algorithms, distinguish between them, and axiomatize them. (shrink)

This paper raises questions about the epistemological foundations of evidence-based medicine . We argue that EBM is based upon reliabilist epistemological assumptions, and that this is appropriate - we should focus on identifying the most reliable processes for generating and collecting medical knowledge. However, we note that this should not be reduced to narrow questions about which research methodologies are the best for gathering evidence. Reliable processes for generating medical evidence might lie outside of formal research methods. We also question (...) the notion of the knower that is assumed by EBM. We argue that EBM assumes an enlightenment conception of knowers as autonomous, substitutable individuals. This conception is troubled by the way that clinicians learn the role of anecdote in health care and the role of patient choice, all of which bring into play features of clinicians and patients as situated individuals with particular backgrounds and experiences. EBM's enlightenment conception of the knower is also troubled by aspects of the way evidence is produced. Given these limitations, we argue that EBM should retain its reliabilist bent, but should look beyond formal research methodologies in identifying processes that yield reliable evidence for clinical practice. We suggest looking to feminist epistemology, with its focus on the standpoints of individual situated knowers, and the role of social context in determining what counts as knowledge. (shrink)

Although little noticed by practicing theorists, narrative voice influences theoretical work. This essay presents a demonstration of voice as method, concentrating on brief segments of works by Garfinkel and Goffman. We attend to two methodological themes: how theorists use voice to establish intellectual autonomy, and how the use of voice influences credibility with readers. Garfinkel maximizes his autonomy by using narrative techniques that isolate him from his readers, and produce little common context with them as a result. Goffman maintains a (...) context for credibility with his readers by using a personal voice, but he uses this voice to request their indulgence as he follows his autonomous muse. Goffman's narrative self-indulgence prevents him from fashioning a coherent theoretical program for his readers, something Garfinkel's distant voice enables him to achieve. (shrink)

(Report assembled for the Workshop of the AMIA Working Group on Formal Biomedical Knowledge Representation in connection with AMIA Symposium, Washington DC, 2005.) Best practices in ontology building for biomedicine have been frequently discussed in recent years. However there is a range of seemingly disparate views represented by experts in the field. These views not only reflect the different uses to which ontologies are put, but also the experiences and disciplinary background of these experts themselves. We asked six questions related (...) to biomedical ontologies to what we believe is a representative sample of ontologists in the biomedical field and came to a number conclusions which we believe can help provide an insight into the practical problems which ontology builders face today. (shrink)

Each title in the "Key Issues" series aims to set the work in its historical context. In this collection of contemporary responses to "Leviathan", attention is focused on its critics who attacked Hobbes's moral, political and religious ideas in a series of pamphlets and short books.

Variations in levels of apolipoprotein E have been tied to the risk and progression of Alzheimer's disease . Our group has previously compared and contrasted the promoters of the mouse and human ApoE gene promoter sequences and found notable similarities and significant differences that suggest the importance of the APOE promoter's role in the human disease. We examine here three specific single-nucleotide polymorphisms within the human APOE promoter region, specifically at -491 , -427 , and at -219 upstream from the (...) +1 transcription start site. The -219 and -491 polymorphic variations have significant association with instance of AD, and -491AA has significant risk even when stratified for the APOEepsilon4 allele. We also show significant effects on reporter gene expression in neuronal cell cultures, and, notably, these effects are modified by species origin of the cells. The -491 and -219 polymorphisms may have an interactive effect in addition to any independent activity. DNA-protein interactions differ between each polymorphic state. We propose SP1 and GATA as candidates for regulatory control of the -491 and -219 polymorphic sites. This work's significance lies in drawing connection among APOE promoter polymorphisms' associations with AD to functional promoter activity differences and specific changes in DNA-protein interactions in cell culture-based assays. Taken together, these results suggest that APOE expression levels are a risk factor for AD irrespective of APOEepsilon4 allele status. (shrink)

This book assesses how Vatican II opened up the Catholic Church to encounter, dialogue, and engagement with other world religions. Opening with a contribution from the President of the Pontifical Council for Interreligious Dialogue, Cardinal Jean-Louis Tauran, it next explores the impact, relevance, and promise of the Declaration Nostra Aetate before turning to consider how Vatican II in general has influenced interfaith dialogue and the intellectual and comparative study of world religions in the postconciliar decades, as well as the contribution (...) of particular past and present thinkers to the formation of current interreligious and comparative theological methods. Additionally, chapters consider interreligious dialogue vis-à-vis theological anthropology in conciliar documents; openness to the spiritual practices of other faith traditions as a way of encouraging positive interreligious encounter; the role of lay and new ecclesial movements in interreligious dialogue; and the development of Monastic Interreligious Dialogue. Finally, it includes a range of perspectives on the fruits and future of Vatican’s II’s opening to particular faiths such as Judaism, Islam, Hinduism, and Buddhism. (shrink)

The word 'hypocrisy' has its root in the classical Greek verb 'hupokrinesthai', 'to answer'. In Attic Greek, the verb could mean 'to speak in dialogue' and hence 'to play a part on the stage'. From here it was a short route to the 'hypokrisia' with which the Pharisees are charge in the Gospel of St. Matthew. Accusations of hypocrisy are surprisingly common in our culture, both at the personal and the political level. Judith Shklar goes so far as to characterise (...) our age as that in which 'hypocrisy...alone is...inexcusable'. But, perhaps equally surprisingly, the nature of hypocrisy is hard to grasp. In this paper, we shall suggest that recent discussion of hypocrisy has foundered through a failure to recognise distinct forms of hypocrisy. We shall outline these different forms, and then consider various views on what they have in common. (shrink)