Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo (1993, 2004) showed that this was not so by displaying an infinite series of sentences none of which is self-referential but which, taken together, are paradoxical. Yablo's paradox consists of a countable series of linearly ordered sentences s(0), s(1), s(2),... , where each s(i) says: For each k > i, s(k) is false (or equivalently: For no k > i is s(k) true). We (...) generalize Yablo's results along two dimensions. First, we study the behavior of generalized Yablo-series in which each sentence s(i) has the form: For Q k > i, s(k) is true, where Q is a generalized quantifier (e.g., no, every, infinitely many, etc). We show that under broad conditions all the sentences in the series must have the same truth value, and we derive a characterization of those values of Q for which the series is paradoxical. Second, we show that in the Strong Kleene trivalent logic Yablo's results are a special case of a more general fact: under certain conditions, any semantic phenomenon that involves self-reference can be emulated without self-reference. Various translation procedures that eliminate self-reference from a non-quantificational language are defined and characterized. An Appendix sketches an extension to quantificational languages, as well as a new argument that Yablo's paradox and the translations we offer do not involve self-reference. (shrink)

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 is the twenty-sixth volume in the Library of Living Philosophers, a series founded by Paul A. Schilpp in 1939 and edited by him until 1981, when the editorship was taken over by Lewis E. Hahn. This volume follows the design of previous volumes. As Schilpp conceived this series, every volume would have the following elements: an intellectual autobiography of the philosopher, a series of expository and critical articles written by exponents and opponents of the philosopher's thought, (...) replies to these critics and commentators by the philosopher, and as nearly complete a bibliography of the published work of the philosopher as possible. (shrink)

This volume includes the Sigma XI-RESA National Lectures, 1961; the Sigma XI-Phi Beta Kappa Lecture, 1961; the RESA Proctor Prize Lecture, 1960; and a special Sigma XI Diamond Jubilee presidential article. The latter three are non-technical articles on such topics as trends in and growth of science in this decade, and the interrelations of science and government. The other articles discuss recent experimental and theoretical results in such areas as climatology, magnetic interaction of atomic nuclei, the effects of solar disturbances (...) on terrestrial magnetism, human genetics and evolution, the biophysics of chemoreceptors, astrophysics and cosmogony, and the physics of the plasma state of matter.--K. P. F. (shrink)

Over the past two decades applied macroeconomics has been transformed by the widespread adoption of a set of new statistical techniques: unit-root tests, vector autoregressions, Granger causality and cointegration. Although these techniques were developed to answer statistical questions, they diffused very rapidly through applied economics because they were thought to be able to answer important theoretical questions in macroeconomics. This paper argues that these techniques have not delivered on the early promises; not because they were not useful - they are (...) very useful for many purposes - but because economists expected too much: they wanted to believe that a statistical summary of the data (an estimate or test statistic) could answer an economic question without interpretation. The paper sets out the statistical motivation for the procedures; the economic questions they were supposed to answer; and the issues that arise in trying to answer economic questions about the sources of trends and cycles, ausality and the nature of equilibrium from statistical summaries. (shrink)

Objective Compare outcome of dogs that did and did not receive fresh frozen plasma (FFP) for treatment of pancreatitis. Design Retrospective case series between 1995 and 2005. Setting University referral hospital. Animals Seventy-four dogs were enrolled with a total of 77 Cases as 2 dogs had repeat episodes of pancreatitis. Diagnosis of pancreatitis was based on clinical signs, physical examination, and abdominal ultrasonographic examination. Interventions The medical database was searched for dogs with a diagnosis of pancreatitis. Information collected included (...) signalment, vital signs, CBC, use of FFP, length of stay, use of antimicrobials and supplemental nutrition, surgical intervention, preexisting illness, evidence of a coagulopathy and outcome. Outcome was compared between those patients that did and did not receive FFP. Measurements and Main Results Fifty-nine dogs survived to discharge. Two dogs with repeat pancreatitis survived to discharge after each episode. Thirteen dogs died and 2 were euthanized. FFP was administered to 20 dogs. Two dogs that were hospitalized for repeat pancreatitis did not receive FFP. Seven of 20 (35%) cases that received plasma died or were euthanized compared with 6 of 57 (12%) cases that did not receive plasma. Plasma administration was significantly related to outcome (P<0.001). Severity of illness scores were difficult to assign, however, dogs meeting criteria for systemic inflammatory response syndrome were not more likely to receive FFP. Other therapies included supplemental nutrition, antimicrobials, and surgical intervention, which did not affect outcome. Conclusions Mortality rate for those dogs receiving plasma was higher than those that did not. Severity of illness scores were difficult to assign; however, preexisting illness, evidence of systemic inflammatory response syndrome, and presence of a coagulopathy were not significantly different between the groups that did and did not receive FFP. No benefit for administration of FFP was noted. Additional investigation should be performed to confirm this result. 2009 Veterinary Emergency and Critical Care Society. (shrink)