This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element (...) subsets for each natural number n ≥ 2. Moreover, series ∑β<αf are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic. (shrink)

This paper examines whether the modern bioethical principles of respect for autonomy, beneficence, non-maleficence, and justice proposed by Beauchamp and Childress are existent in, compatible with, or acceptable to the leading Chinese moral philosophy—the ethics of Confucius. The author concludes that the moral values which the four prima facie principles uphold are expressly identifiable in Confucius’ teachings. However, Confucius’ emphasis on the filial piety, family values, the “love of gradation”, altruism of people, and the “role specified relation oriented ethics” will (...) inevitably influence the “specification” and application of these bioethical principles and hence tend to grant “beneficence” a favourable position that diminishes the respect for individual rights and autonomy. In contrast, the centrality of respect for autonomy and its stance of “first among equals” are more and more stressed in Western liberal viewpoints. Nevertheless, if the Confucian “doctrine of Mean” and a balanced “two dimensional personhood” approach are properly employed, this will require both theorists and clinicians, who are facing medical ethical dilemmas, of searching to attain due mean out of competing moral principles thus preventing “giving beneficence a priority” or “asserting autonomy must triumph”. (shrink)

Children, because of age-related reasons, are a vulnerable population, and protecting their health is a social, scientific and emotional priority. The increased susceptibility of children and fetuses to environmental agents has been widely discussed by the scientific community. Children may experience different levels of chemical exposure than adults, and their sensitivity to chemical toxicities may be increased or decreased in comparison with adults. Such considerations also apply to unborn and newborn children. Therefore, research on children is necessary in both clinical (...) and environmental fields, to provide age-specific relevant data regarding the efficacy and safety of medical treatments, and regarding the assessment of risk from unintended environmental exposure. In this context, the stakeholders are many, including children and their parents, physicians and public health researchers, and the society as a whole, with its ethical, regulatory, administrative and political components. The important ethical issues are information of participants and consent to participate. Follow-up and protection of data should be discussed in the context of biobanks, where children obtain individual rights when they become adults. It is important to realise that there are highly variable practices within European countries, which may have, in the past, led to differences in practical aspects of research in children. A number of recommendations are provided for research with children and environmental health. Environmental research with children should be scientifically justified, with sound research questions and valid study protocols of sufficient statistical power, ensuring the autonomy of the child and his/her family at the time of the study and later in life, if data and samples are used for follow-up studies. When children are enrolled, we recommend a consent dyad, including parental informed consent and the child’s assent and/or informed consent from older minors. For evaluation of the studies including children, a paediatrician should always be involved in the research ethics committee. (shrink)

I have argued in other work that emotion, attentional functions, and executive functions are three interpenetrant global state variables, essentially differential slices of the consciousness pie. This paper will outline the columnar architecture and connectivities of the PAG (periaqueductal gray), its role in organizing prototype states of emotion, and the re-entry of PAG with the extended reticular thalamic activating system (“ERTAS”). At the end we will outline some potential implications of these connectivities for possible functional correlates of PAG networks that (...) are just starting to be mapped. Overall, we will look at many lines of evidence that PAG should be conceptualized as a peri-reticular structure that has a foundational role in emotion, in generating the meaningful organization of behavior by the brain through prototype emotional states, and in allowing the various emotional systems to globally influence and tune both the forebrain and brainstem. Finally, we address implications of these concepts for what is currently understood about consciousness, underlining the need for somewhat more humility within consciousness studies about our current level of understanding of consciousness in the brain, combined with a deeper appreciation of the intrinsic connections between emotion and consciousness. One hopes that more concerted empirical interest in structures underneath the thalamus, combined with a deeper appreciation for the fundamental role that organismic and social value must have in bootstrapping awareness in the developing brain, would begin more widely to influence the fundamental lines of neuroscientific research in both emotion studies and consciousness studies. (shrink)

Since the discovery of incommensurability in ancient Greece, arithmeticism and geometricism constantly switched roles. After ninetieth century arithmeticism Frege eventually returned to the view that mathematics is really entirely geometry. Yet Poincaré, Brouwer, Weyl and Bernays are mathematicians opposed to the explication of the continuum purely in terms of the discrete. At the beginning of the twenty-first century ‘continuum theorists’ in France (Longo, Thom and others) believe that the continuum precedes the discrete. In addition the last 50 years witnessed the (...) revival of infinitesimals (Laugwitz and Robinson—non-standard analysis) and—based upon category theory—the rise of smooth infinitesimal analysis and differential geometry. The spatial whole-parts relation is irreducible (Russell) and correlated with the spatial order of simultaneity. The human imaginative capacities are connected to the characterization of points and lines (Euclid) and to the views of Aristotle (the irreducibility of the continuity of a line to its points), which remained in force until the ninetieth century. Although Bolzano once more launched an attempt to arithmetize continuity, it appears as if Weierstrass, Cantor and Dedekind finally succeeded in bringing this ideal to its completion. Their views are assessed by analyzing the contradiction present in Grünbaum’s attempt to explain the continuum as an aggregate of unextended elements (degenerate intervals). Alternatively a line-stretch is characterized as a one-dimensional spatial subject, given at once in its totality (as a whole) and delimited by two points—but it is neither a breadthless length nor the (shortest) distance between two points. The overall aim of this analysis is to account for the uniqueness of discreteness and continuity by highlighting their mutual interconnections exemplified in the nature of a line as a one-dimensional spatial subject, while acknowledging that points are merely spatial objects which are always dependent upon an extended spatial subject. Instead of attempting to reduce continuity to discreteness or discreteness to continuity, a third alternative is explored: accept the irreducibility of number and space and then proceed by analyzing their unbreakable coherence. The argument may be seen as exploring some implications of the view of John Bell, namely that the “continuous is an autonomous notion, not explicable in terms of the discrete.” Bell points out that initially Brouwer, in his dissertation of 1907, “regards continuity and discreteness as complementary notions, neither of which is reducible to each other.”. (shrink)

Analytische annotatie: Rechtsfilosofische beschouwing.

This comment calls attention to the nature of the Aristotelian and classical logics, and the difficulty of representing their judgments and inferences by means of Venn diagrams. The meaning of ‘all’ in the different calculi produces problems. A second problem is that the specification of existence in Venn diagrams for statements and arguments cannot be restricted to a single class, overlooked by Wiebe. This problem is further complicated by his adoption of classical (Renaissance) syllogistic, which is inconsistent. Aristotle’s term logic (...) is consistent. So also is the medieval extension, though the inclusion of singular premisses renders it less perspicuous though more flexible. (shrink)

MARXISM AND LIBERALISM edited by Ellen Frankel Paul, Fred D. Miller, Jr., Jeffrey Paul and John Ahrens New York: Basil Blackwell, 1986. 223 pp., $14?95 (paper) LIBERALISM by John Gray Minneapolis: University of Minnesota Press, 1986. 106 pp., $9.95 (paper).

The dispositional analysis of sentences ascribing powers and abilities to things and people runs into many difficulties. The situation is especially complex and confusing when such ascriptions are brought to bear on particular occasions, and carry some implication about the opportunities available on those occasions. Some of these difficulties are produced by superficial confusions, but I shall concentrate on those that beset any version of the dispositional analysis. Three difficulties will be examined, one presented by Lehrer, and two by Austin.Lehrer (...) presents his difficulty as a refutation of Moore's dispositional analysis of “X could have acted otherwise”, which was “If X had chosen, he would have acted otherwise”. I shall introduce his objection by relating it to the distinctions drawn in Part I.· Expressed in my terminology, his point is that Moore's analysis presupposes that choosing is not an S-factor, and yet it might conceivably be an S-factor. (shrink)