Many have argued against the claim that Plato posited the mathematical objects that are the subjects of Metaphysics M and N. This paper shifts the burden of proof onto these objectors to show that Plato did not posit these entities. It does so by making two claims: first, that Plato should posit the mathematical Intermediates because Forms and physical objects are ill suited in comparison to Intermediates to serve as the objects of mathematics; second, that their utility, combined with Aristotle’s (...) commentary on Plato’s posit of Intermediates, provides good reason to conclude that Plato did posit them. (shrink)

This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the (...) authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. They provide researchers in algebra and logic with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic. (shrink)

"There are no paradoxes in mathematics," says Kurt Gödel. Moreover, Gödel seems to be right on this count. That is, there are no paradoxes, in the strict sense of the word, internal to the known and available body of mathematical knowledge. But while there are no paradoxes in mathematics, there certainly is an embarrassing bag of difficulties when we come to the application of mathematical concepts to the physical world. Of these, perhaps the most unruly offenders of all are the (...) problems proposed about 2500 years ago by Zeno and which, in modern idiom, have to do with the proper mathematical treatment of phenomena involving change and motion, and the physical meaning—if any—which may be assigned to convergent infinite series. At each stage in the growth of mathematical knowledge since their formulation Zeno's paradoxes have been the subject of some alleged resolution. Now Grünbaum contributes to this tradition, and it must be said that he makes a strong case. The weapons in the intellectual arsenal which Grünbaum brings to bear upon Zeno include such sophisticated devices as measure theory, but the weak link in the argument is in the first chapter where the author presents his somewhat psychologistic theory of temporal becoming. Grünbaum has a great many interesting things to say in later chapters about infinite processes, quantum mechanics, and Hilary Putnam. This is a first-rate contribution to the philosophy of physics.—H. P. K. (shrink)

While it is often argued that U.S. military strategy has gone through substantial changes over the post three decodes, it is not so clear if this is so, or why this should be so. Some changes in the real strategic problem of the west must be considered, including the growth of the Soviet nuclear arsenal. Changes in our perception of the problem may be at least as important, however, amid some possibilities of ‘Finlandisation’. Changes in the West’s opportunities must also (...) be considered, including ‘limited nuclear war’, and a totally conventional defense. Finally to be considered are the bureaucratic motivations of those advocating any such changes in western military postures, all of which suggest that current policies may still be better than the alternatives. (shrink)

The author attempts a dispassionate philosophical evaluation of Ayn Rand's "objectivist" philosophy. Although Professor O'Neill's evaluation is generally negative, he takes great pains to be fair and accurate. For example, there are more than eight hundred footnote references to objectivist literature. The book is divided into two unequal parts. The first and shorter part presents a summary of the cardinal doctrines of objectivism, under three thematic headings: knowing and the knower; personal value and the nature of man; the ethics of (...) objectivism. In presenting the material pertinent to each of these themes, the author employs a great many direct quotations in order to avoid as much as possible the charge of misrepresenting Miss Rand's thought. The major portion of the book is then devoted to criticism of objectivist philosophy. Whenever possible the author employs a method of internal criticism the basic strategy of which is to ask whether objectivist principles are coherent in themselves and in relation to other aspects of the doctrine. Next the author asks whether the various tenets of objectivist theory are true. This means, he says, to ask whether these tenets are empirically verifiable in principle, and whether they are confirmed or disconfirmed by contemporary scientific findings. This book is the only such study available, and thus is useful for anyone interested in its subject matter. The author wisely tries to confine his discussion to basic philosophical issues and to avoid being diverted into arguments about economics and politics. Nevertheless, both of the book's major parts are somewhat unsatisfactory. The presentation of objectivist philosophy tends to be a disjointed collection of quotations and ideas, grouped together under various subheadings. It could be said that this disconnectedness merely reflects the character of objectivism itself, but it should be possible to formulate a more organic statement of the major objectivist tenets. One method would be to approach objectivism through Miss Rand's ethical preoccupation with laissez-faire capitalism, which, as Professor O'Neill recognizes, is her primary concern. Similarly, the evaluative part of the book is more of an arsenal of arguments against various objectivist assertions than an integrated critique.--H. F. (shrink)

To localize wheat ESTs on chromosomes, 882 homoeologous group 6-specific ESTs were identified by physically mapping 7965 singletons from 37 cDNA libraries on 146 chromosome, arm, and sub-arm aneuploid and deletion stocks. The 882 ESTs were physically mapped to 25 regions flanked by 23 deletion breakpoints. Of the 5154 restriction fragments detected by 882 ESTs, 2043 were localized to group 6 chromosomes and 806 were mapped on other chromosome groups. The number of loci mapped was greatest on chromosome 6B and (...) least on 6D. The 264 ESTs that detected orthologous loci on all three homoeologs using one restriction enzyme were used to construct a consensus physical map. The physical distribution of ESTs was uneven on chromosomes with a tendency toward higher densities in the distal halves of chromosome arms. About 43% of the wheat group 6 ESTs identified rice homologs upon comparisons of genome sequences. Fifty-eight percent of these ESTs were present on rice chromosome 2 and the remaining were on other rice chromosomes. Even within the group 6 bins, rice chromosomal blocks identified by 1-6 wheat ESTs were homologous to up to 11 rice chromosomes. These rice-block contigs were used to resolve the order of wheat ESTs within each bin. (shrink)

In spite of Stein and Glasier's justifiable conclusion that initial optimism concerning the immediate clinical applicability of neural transplantation was premature, there exists much experimental evidence to support the potential for incorporating this procedure into a therapeutic arsenal in the future. To realize this potential will require continued evolution of our knowledge at multiple levels of the clinical and basic neurosciences.

This comment on the case presented in ‘Cholera and Nothing More’ argues that the physicians at this public-health centre did not have an ordinary clinician's obligations to promote the health of the people who came to them for care, as they were instead set up to serve a laudable and urgent public-health goal, namely, controlling a cholera outbreak. It argues that, nonetheless, these physicians did have some limited moral duties to care for other diseases they encountered—some ancillary-care duties—arising from their (...) voluntarily entering into a kind of intimate relationship with the patients they took in, one in which those patients effectively waive certain rights to bodily and medical privacy. (shrink)

In this paper, perhaps the first of its kind, an attempt is made to elucidate and examine the Vedantic theory of soul constructed on the basis of the experience of dreamless sleep which, being radically and qualitatively different from waking and dreaming states, is considered by the Vedantins as a state of temporarily purified individual soul (atman), a state of pure substantial consciousness. They take the experience of dreamless sleep as a model experience of the soul's final liberation from the (...) body and its internal as well as external faculties. The ultimate liberation, according to the Vedantins, is a state of total identification of the individual soul with the Universal Soul (Brahman), the summum bonum of every Vedantin. The paper also includes a critique of the Vedantic soul theory by the Buddhists who vehemently deny any autonomous and substantial soul whose essence is unchangingly permanent, pure consciousness and self-illuminating knowledge. The soul is instead interpreted by the Buddhists as a product of the functioning of a person's psycho-physical organism and a mere subject of knowing, thinking, desiring, etc. The analysis further shows that the Vedanta, especially the Advaita Vedanta, metaphysics of soul is inadequate in many respects and mainly based on a priori and scriptural arguments and emotive appeals, whereas the Buddhists deny any kind of autonomous and permanent agent of knowing, thinking and desiring by successfully reducing substantial consciousness to mere acts of knowing. (shrink)

IN Physics VIII, 10, Aristotle seems to commit a serious mistake: just before concluding that the first mover required by all motion everywhere remains invariable and without parts or magnitude, Aristotle apparently locates this mover on the circumference of the cosmos.