Mr D. H. Mellor, in his article of this title in Religious Studies , Vol. 5 , distinguishes three senses of words such as ‘probable’ which might be used in a religious context, especially in that of attempted theistic proofs: statistical, subjective, and inductive probability. In each case he concludes that it is misleading to use these words in such contexts at all. With his discussion of the second I do not wish to quarrel; but there seem to me to (...) be serious defects in his discussions of the first and third. (shrink)

I propose to begin with some fairly unexciting and uncontroversial remarks about possibility-statements, and then in their light to examine two problems philosophers have raised about certain statements of this kind which might be made in Christian theology where it touches on the doctrine of the Incarnation.

The ‘traditional’ view among philosophical theologians, that God is eternal not merely in the sense of being everlasting but in the sense of being outside time altogether, has come under sharp criticism in recent years, both from biblical theologians and from philosophers. It is against the latter form of attack, particularly as represented by the detailed criticisms of Professor Nelson Pike, that I wish to try and defend the notion of a divine timelessness.

I have come to believe that the whole framework of our current thought is about to begin a long and radical transformation, based on what I shall call a new science of pure consciousness. The content of most of the matters to be considered by this science have hitherto been the concern of some areas of religion, particularly what in our culture we call ‘mysticism’; but the treatment of it would legitimately be called scientific. Thus one aspect of the transformation (...) would be to overcome that apparent conflict between ‘science’ and ‘religion’, which has been so characteristic of our culture over the last few centuries. (shrink)

The notion of autonomy commonly employed in medical ethics literature and practices is inadequate on three fronts: it fails to properly identify nonautonomous actions and choices, it gives a false account of which features of actions and choices makes them autonomous or nonautonomous, and it provides no grounds for the moral requirement to respect autonomy. In this paper I offer a more adequate framework for how to think about autonomy, but this framework does not lend itself to the kinds of (...) practical application assumed in medical ethics. A general problem then arises: the notion of autonomy used in medical ethics is conceptually inadequate, but conceptually adequate notions of autonomy do not have the practical applications that are the central concern of medical ethics. Thus, a revision both of the view of autonomy and the practice of “respect for autonomy” are in order. (shrink)

When philosophers approach philosophy of religion, they typically ask two questions: are there any sound arguments to prove the existence of God; and is talk about God even rationally intelligible? Theologians, for their part, primarily expound the meaning and relevance of Christianity. I am by profession a philosopher, but apart from Secs. VI and VII I am here writing as a puzzled twentieth-century man. My prime worry is whether we philosophers and theologians are beginning with the right questions.

The proposition that a decreasing sequence of ordinals necessarily terminates has been given a new, and perhaps unexpected, importance by the rôle which it plays in Gentzen's proof of the freedom from contradiction of the “reine Zahlentheorie.” Gödel's construction of non-demonstrable propositions and the establishment of the impossibility of a proof of freedom from contradiction, within the framework of a certain type of formal system, showed that a proof of freedom from contradiction could be found only by transcending the axioms (...) and proof processes of that formal system. Gentzen's proof succeeds by utilisingtransfinite inductionto prove that certain sequences of reduction processes, enumerated by ordinals less than ε (the first ordinal to satisfy ε = ὡ) are finite. Were it possible to provethe restricted ordinal theorem, that a descending sequence of ordinals, less thanε, is finite, in Gentzen's “reine Zahlentheorie,” then it would be possible to determine a contradiction in that number system. In his paper, Gentzen proves the theorem of transfinite induction, which he requires, by an intuitive argument. There is also a method of reducing transfinite induction, for ordinals less than ε, to a number-theoretic principle given by Hilbert and Bernays, and a similar method by Ackermann. None of these proofs of transfinite induction isfinitist. (shrink)

Lyme disease is one of the most controversial illnesses in the history of medicine. In 2006 the Connecticut Attorney General launched an antitrust investigation into the Lyme guidelines development process of the Infectious Diseases Society of America (IDSA). In a recent settlement with IDSA, the Attorney General noted important commercial conflicts of interest and suppression of scientific evidence that had tainted the guidelines process. This paper explores two broad ethical themes that influenced the IDSA investigation. The first is the growing (...) problem of conflicts of interest among guidelines developers, and the second is the increasing centralisation of medical decisions by insurance companies, which use treatment guidelines as a means of controlling the practices of individual doctors and denying treatment for patients. The implications of the first-ever antitrust investigation of medical guidelines and the proposed model to remediate the tainted IDSA guidelines process are also discussed. (shrink)

The literature on public perceptions of, and attitudes towards, nanotechnology used in the agrifood sector is reviewed. Research into consumer perceptions and attitudes has focused on general applications of nanotechnology, rather than within the agrifood sector. Perceptions of risk and benefit associated with different applications of nanotechnology, including agrifood applications, shape consumer attitudes, and acceptance, together with ethical concerns related to environmental impact or animal welfare. Attitudes are currently moderately positive across all areas of application. The occurrence of a negative (...) or positive incident in the agri-food sector may crystallise consumer views regarding acceptance or rejection of nanotechnology products. •Acceptance of agrifood nanotechnology based on perceptions of risk, benefit and ethics.•Attitudes towards nanotechnology in general are currently moderately positive.•Occurrence of a major nanotechnology-related "event" may crystallise consumer attitude. (shrink)

Famous for the number-theoretic first-order statement known as Goodstein's theorem, author R. L. Goodstein was also well known as a distinguished educator. With this text, he offers an elementary treatment that employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. The text begins with an informal introduction to the algebra of classes, exploring union, intersection, and complementation; the commutative, associative, and distributive laws; difference and symmetric difference; and Venn diagrams. Professor Goodstein proceeds to a detailed (...) examination of three different axiomatizations, and an outline of a fourth system of axioms appears in the examples. The final chapter, on lattices, examines Boolean algebra in the setting of the theory of partial order. Numerous examples appear at the end of each chapter, with full solutions at the end. (shrink)

Background Central to the involvement of children in health research is the notion of risk. In this paper we present one of the factors, a matter of trust, that shaped Canadian parents' and children's perceptions and assessments of risk in child health research. Participants and methods Part of a larger qualitative research study, 82 parents took part an in-depth qualitative interview, with 51 parents having children who had participated in health research and 31 having children with no research history. 51 (...) children ranging from 6 to 19 years of age were also interviewed, with 28 having a history of participation in child health research and 23 having no history. Children also took part in 3 focus groups interviews. Themes emerged through a grounded theory analysis of coded interview transcripts. Findings The presence or absence of trust was not only perceived by parents and children as a contributing factor to involving children in health research, but also shaped their perceptions and assessments of risk. Three interrelated subthemes identified were: (1) relationships of trust; (2) placing trust in symbols of authority; and (3) the continuum of trust. Conclusions Our study reinforces that trust is an important factor when parents assess risk in child health research and shows that children use the language of trust in relation to risk. More discussion regarding trust in training researchers is warranted given the trust in researchers and institutions evident in this study. We also recommend further study of the continuum of trust in child health research. (shrink)

In this paper, the structure of a southeastern Spanish population was studied for the first time with respect to its inbreeding patterns and its relationship with demographic and geographic factors. Data on consanguineous marriages from 1900 to 1969 were taken from ecclesiastic dispensations. Our results confirm that the patterns and trends of inbreeding in the study area are consistent with those previously observed in most non-Cantabrian Spanish populations. The rate of consanguineous marriages was apparently stable between 1900 and 1935 and (...) then sharply decreased since 1940, which coincides with industrialization in Spain. A marked departure from Hardy-Weinberg expectations in the ratio of first cousin to second cousin marriages in the study population was observed. The high levels of endogamy and its significant steadiness throughout the twentieth century is noteworthy. Accordingly, our results show that exogamous marriages were not only poorly represented but also that this reduced mobility suggests that the choice of a mate was preferentially local. We found higher mobility in M22 with respect to M33 cousin mating. The relationships between population size and consanguinity rates and inbreeding fit power-law distributions. A significant positive correlation was observed between inbreeding and elevation. Many Spanish populations have experienced a prolonged and considerable isolation across generations, which has led to high proportions of historical and local endogamy that is associated, in general, with high \ values. Thus, assessing genomic inbreeding using runs of homozygosity in current Spanish populations could be an additional pertinent strategy for obtaining a more refined perspective regarding the population history inferred from the extent and frequency of ROH regions. (shrink)

This detailed 1990 book describes the light and dark adaptation of receptoral and post-receptoral mechanisms from a number of perspectives. The authors emphasise the importance of the study of achromatopsia, a rare congenital condition in which the visual mechanisms that mediate day vision are absent whilst those that mediate night vision remain intact.

I consider reasons for questioning ‘the laws of logic’, and suggest that these laws do not accord with everyday reality. Either they are rhetorical tools rather than absolute truths, or else Plato and his successors were right to think that they identify a reality distinct from the ordinary world of experience, and also from the ultimate source of reality.

Alberto Cortes, in [1], attempts to show that Leibniz's Principle of The Identity of Indiscernibles is a principle restricted to individuals, and that photons appear to violate L. L is stated by Leibniz as “no two substances are completely similar, or differ solo numero.” In second-order quantification theory with identity L becomes.

L R Perry; Training and Education, Journal of Philosophy of Education, Volume 6, Issue 1, 30 May 2006, Pages 7–29, https://doi.org/10.1111/j.1467-9752.1972.tb00.

The crux of the dispute between formalism and intuitionism, it is held, is not whether certain entities exist or not, but how the term function shall be used in mathematics. The identification of effective definition with general recursion fails because an undefined function lies concealed beneath the requirement of a finite number of substitutions, and a fresh characterization of effective definition is sought in terms of a hierarchy of ordinal recursions.A correspondence exists between primitive recursive properties and direct proofs, of (...) irrationality and transcendence for instance, and between general recursive properties and indirect proofs.Mathematics is a concept creating activity and the distinction between a formal mathematics devoid of meaning, at one level, and a meaningful metamathematics at the next is considered to be untenable.RésuméLa controverse entre les formalistes et les intuitionistes ne repose pas, considére‐t‐on, sur l'existence ou la non‐existence de certaines entités, mail sur l'usage du terme fonction en mathématiques. L'identification de la définition effective avec la récursion générate n'est pas valable parce qu'une fonction indéfinié est dissimulée sous la nécessité d'un nombre fini de substitutions, et une nouvelle caractérisation de définition effective est recherchée sous forme de hiérarchie de récursions ordinates.II existe, d'une part, une correspondance entre les propriétés primitives récursives et les preuves directes, d'irrationalité et de transcendance par exemple, et, d'autre part, entre les propriétés récursives générates et les preuves par l'absurde.Les mathématiques sont une activité créatrice de concepts, et la distinction entre les mathématiques formelles dépourvues de sens et, sur le plan supérieur, une méta‐mathématique chargée de sens, ne semble pas justifiée. (shrink)

‘Jason…chosen leader because his superior declines the honour, subordinate to his comrades, except once, in every trial of strength, skill, or courage, a great warrior only with the help of magical charms, jealous of honour but incapable of asserting it, passive in the face of crisis, timid and confused before trouble, tearful at insult, easily despondent, gracefully treacherous in his dealings with the love-sick Medea but cowering before her later threats and curses, coldly efficient in the time-serving murder of an (...) unsuspecting child , reluctant even in marriage.’ So Carspecken put the case against Jason's heroism. In the face of such an indictment, Lawall's plea in mitigation, ‘it must be admitted that [Jason] often reveals the qualities of a true gentleman’, seems somehow inadequate. Criticism since Carspecken has found various overlapping categories for Jason which both take account of the earlier negative judgements and preserve the centrality of his ‘personality’ and character in the poem: Jason is the quiet diplomat who works through consensus rather than force, his is a heroism of sex-appeal, he is an anti-hero, the embodiment of Sceptic ‘suspension of judgement’, or, alternatively, he is ‘one of us’, credible and lifelike. Carspecken himself tried a different tack: the poem is concerned not with individual heroism but with the heroism of the group. (shrink)