We consider the question of randomness of the probability ΩU[X] that an optimal Turing machine U halts and outputs a string in a fixed set X. The main results are as follows: ΩU[X] is random whenever X is $\Sigma _{n}^{0}$-complete or $\Pi _{n}^{0}$-complete for some n ≥ 2. However, for n ≥ 2, ΩU[X] is not n-random when X is $\Sigma _{n}^{0}$ or $\Pi _{n}^{0}$ Nevertheless, there exists $\Delta _{n+1}^{0}$ sets such that ΩU[X] is n-random. There are $\Delta _{2}^{0}$ sets (...) X such that ΩU[X] is rational. Also, for every n ≥ 1, there exists a set X which is $\Delta _{n+1}^{0}$ and $\Sigma _{n}^{0}$-hard such that ΩU[X] is not random. We also look at the range of ΩU as an operator. We prove that the set {ΩU[X]: X ⊆ 2<ω} is a finite union of closed intervals. It follows that for any optimal machine U and any sufficiently small real r, there is a set X ⊆ 2<ω recursive in ∅′ ⊕ r, such that ΩU[X] = r. The same questions are also considered in the context of infinite computations, and lead to similar results. (shrink)

Teaching medical ethics by the case method may be enriched by adding to the principles-and-rules approach to practical reasoning modes of inquiry and interpretation that engage the moral imagination.

The complex hexaploid wheat genome offers many challenges for genomics research. Expressed sequence tags facilitate the analysis of gene-coding regions and provide a rich source of molecular markers for mapping and comparison with model organisms. The objectives of this study were to construct a high-density EST chromosome bin map of wheat homoeologous group 2 chromosomes to determine the distribution of ESTs, construct a consensus map of group 2 ESTs, investigate synteny, examine patterns of duplication, and assess the colinearity with rice (...) of ESTs assigned to the group 2 consensus bin map. A total of 2600 loci generated from 1110 ESTs were mapped to group 2 chromosomes by Southern hybridization onto wheat aneuploid chromosome and deletion stocks. A consensus map was constructed of 552 ESTs mapping to more than one group 2 chromosome. Regions of high gene density in distal bins and low gene density in proximal bins were found. Two interstitial gene-rich islands flanked by relatively gene-poor regions on both the short and long arms and having good synteny with rice were discovered. The map locations of two ESTs indicated the possible presence of a small pericentric inversion on chromosome 2B. Wheat chromosome group 2 was shown to share syntenous blocks with rice chromosomes 4 and 7. (shrink)

After distinguishing different species of Legal Moralism I outline and defend a modest, positive Legal Moralism, according to which we have good reason to criminalize some type of conduct if it constitutes a public wrong. Some of the central elements of the argument will be: the need to remember that the criminal law is a political, not a moral practice, and therefore that in asking what kinds of conduct we have good reason to criminalize, we must begin not with the (...) entire realm of wrongdoing, but with conduct falling within the public realm of our civic life; the need to look at the different processes of criminalization, and to ask what kinds of consideration can properly figure in those processes; the need to attend to the relationship, and the essential differences, between criminal law and other modes of legal regulation. (shrink)

He then proceeds with an examination of the picture theory developed by Wittgenstein, Carnap, and Goodman, and concludes with an examination of Patricia Churchland, Ruth Millikan, Robert Cummins, and Mark Rollins. The use of the historical development of representationalism to pose a central problem in contemporary cognitive science is unique.

After an initial discussion (§i) of what a theory of criminal law might amount to, I sketch (§ii) the proper aims of a liberal, republican criminal law, and discuss (§§iii–iv) two central features of such a criminal law: that it deals with public wrongs, and provides for those who perpetrate such wrongs to be called to public account. §v explains why a liberal republic should maintain such a system of criminal law, and §vi tackles the issue of criminalization—of how we (...) should determine the proper scope of the criminal law. (shrink)

How can a system of criminal punishment be justified? In particular can it be justified if the moral demand that we respect each other as autonomous moral agents is taken seriously? Traditional attempts to justify punishment as a deterrent or as retribution fail, but Duff suggests that punishment can be understood as a communicative attempt to bring a wrong-doer to repent her crime. This account is supported by discussions of moral blame, of penance, of the nature of the law's demands, (...) and of the proper meaning and purpose of the criminal process of trial and verdict: it deals both with the ideals that should inform a system of criminal law and the extent to which those ideals are actualised in existing institutions and practices. The conclusion is pessimistic: punishment cannot be justified within our legal system; and this gap between the ideal and the actual presents us with serious moral dilemmas. (shrink)

Aim To study the views of people in a largely Muslim country, Kuwait, of the acceptability of a life-ending action such as physician-assisted suicide (PAS). Method 330 Kuwaiti university students judged the acceptability of PAS in 36 scenarios composed of all combinations of four factors: the patient's age (35, 60 or 85 years); the level of incurability of the illness (completely incurable vs extremely difficult to cure); the type of suffering (extreme physical pain or complete dependence) and the extent to (...) which the patient requests a life-ending procedure, euthanasia or PAS (no request, some form of request, repeated requests). In all scenarios, the patients were women who were receiving the best possible care. The ratings were subjected to cluster analysis and analyses of variance. Results Five clusters were found. For 44%, PAS was always very unacceptable, no matter what the circumstances. For 23%, it was unacceptable, but less so if the patient was older or requested it repeatedly. For 16%, it was unacceptable if the patient was young but was acceptable if the patient was elderly. For 5%, it was unacceptable if the patient had extreme pain but was acceptable if completely dependent. For 11%, it was unacceptable if the patient did not request it but acceptable if she did. Conclusion The majority of the Kuwaiti university students opposed PAS either categorically or with a slight variation according to circumstances. Nonetheless, a minority approved of PAS in some cases, particularly when the patient was elderly. (shrink)

The reputation Theologoumena Arithmeticae has acquired is largely that of being an odd, and frequently opaque, compilation of arithmological lore. As a sourcebook for this aspect of the Pythagorean tradition it is, of course, invaluable. However, its poor reputation is increased, and its historical value lessened, by the depredations time has wrought on the text. ThA was never great prose: it is a compilation, largely from the lost Theologoumena Arithmeticae of Nicomachus of Gerasa and from Anatolius' Peri Dekados; and the (...) text which cannot be safely or conjecturally assigned to these two sources often reads like little more than the written-up notes of some student. However, the treatise contains passages of considerable lucidity, within the context of its peculiar framework. (shrink)

The reputation Theologoumena Arithmeticae has acquired is largely that of being an odd, and frequently opaque, compilation of arithmological lore. As a sourcebook for this aspect of the Pythagorean tradition it is, of course, invaluable. However, its poor reputation is increased, and its historical value lessened, by the depredations time has wrought on the text. ThA was never great prose: it is a compilation, largely from the lost Theologoumena Arithmeticae of Nicomachus of Gerasa and from Anatolius' Peri Dekados; and the (...) text which cannot be safely or conjecturally assigned to these two sources often reads like little more than the written-up notes of some student. However, the treatise contains passages of considerable lucidity, within the context of its peculiar framework. (shrink)