The notion of superhigh computably enumerable (c.e.) degrees was first introduced by (Mohrherr in Z Math Logik Grundlag Math 32: 5–12, 1986) where she proved the existence of incomplete superhigh c.e. degrees, and high, but not superhigh, c.e. degrees. Recent research shows that the notion of superhighness is closely related to algorithmic randomness and effective measure theory. Jockusch and Mohrherr proved in (Proc Amer Math Soc 94:123–128, 1985) that the diamond lattice can be embedded into the c.e. tt-degrees preserving 0 (...) and 1 and that the two atoms can be low. In this paper, we prove that the two atoms in such embeddings can also be superhigh. (shrink)

The potential health risks of vegan diets specifically for women and children are discussed. Women and children are at higher risk of malnutrition from consumption of unsupplemented vegan diets than are adult males. Those who are very young, pregnant, lactating, elderly, or who suffer from poverty, disease or other environmentally induced disadvantages are at special risk. The size of these risks is difficult to quantify from existing studies. Fortunately the risk of dietary deficiency disease can be avoided and the potential (...) health benefits of vegan diets can be realized when diets for these groups are planned in line with theRecommended Dietary Allowances so that nutrient intakes reach or exceed recommended levels, and access to preventive and curative health services is assured. (shrink)

Review by: Johanna N. Y. Franklin The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 115-118, March 2013.

We give several characterizations of Schnorr trivial sets, including a new lowness notion for Schnorr triviality based on truth-table reducibility. These characterizations allow us to see not only that some natural classes of sets, including maximal sets, are composed entirely of Schnorr trivials, but also that the Schnorr trivial sets form an ideal in the truth-table degrees but not the weak truth-table degrees. This answers a question of Downey, Griffiths and LaForte.

We study the connection between Schnorr triviality and genericity. We show that while no 2-generic is Turing equivalent to a Schnorr trivial and no 1-generic is tt-equivalent to a Schnorr trivial, there is a 1-generic that is Turing equivalent to a Schnorr trivial. However, every such 1-generic must be high. As a corollary, we prove that not all K-trivials are Schnorr trivial. We also use these techniques to extend a previous result and show that the bases of cones of Schnorr (...) trivial Turing degrees are precisely those whose jumps are at least 0". (shrink)

We show that van Lambalgen's Theorem fails with respect to recursive randomness and Schnorr randomness for some real in every high degree and provide a full characterization of the Turing degrees for which van Lambalgen's Theorem can fail with respect to Kurtz randomness. However, we also show that there is a recursively random real that is not Martin-Löf random for which van Lambalgen's Theorem holds with respect to recursive randomness.

We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune free degrees, lowness for isomorphism is entirely independent of computable traceability.

We investigate the relationship between lowness for Schnorr randomness and Schnorr triviality. We show that a real is low for Schnorr randomness if and only if it is Schnorr trivial and hyperimmune free.

The weakly random reals contain not only the Schnorr random reals as a subclass but also the weakly 1-generic reals and therefore the n -generic reals for every n . While the class of Schnorr random reals does not overlap with any of these classes of generic reals, their degrees may. In this paper, we describe the extent to which this is possible for the Turing, weak truth-table, and truth-table degrees and then extend our analysis to the Schnorr random and (...) hyperimmune reals. (shrink)

We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures with degrees (...) of categoricity is $\Pi_{1}^{1}$-complete. (shrink)

A real is Martin-Löf (Schnorr) random if it does not belong to any effectively presented null ${\Sigma^0_1}$ (recursive) class of reals. Although these randomness notions are very closely related, the set of Turing degrees containing reals that are K-trivial has very different properties from the set of Turing degrees that are Schnorr trivial. Nies proved in (Adv Math 197(1):274–305, 2005) that all K-trivial reals are low. In this paper, we prove that if ${{\bf h'} \geq_T {\bf 0''}}$ , then h (...) contains a Schnorr trivial real. Since this concept appears to separate computational complexity from computational strength, it suggests that Schnorr trivial reals should be considered in a structure other than the Turing degrees. (shrink)

We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and several other problems related to computing isomorphisms. These other problems include Scott analysis (in the form of back-and-forth relations), jump hierarchies, and computing descending sequences in linear orders.

Whether or not quantum physics can account for molecular structure is a matter of considerable controversy. Three of the problems raised in this regard are the problems of molecular structure. We argue that these problems are just special cases of the measurement problem of quantum mechanics: insofar as the measurement problem is solved, the problems of molecular structure are resolved as well. In addition, we explore one consequence of our argument: that claims about the reduction or emergence of molecular structure (...) cannot be settled independently of the choice of a particular resolution to the measurement problem. Specifically, we consider how three standard putative solutions to the measurement problem inform our under- standing of a molecule in isolation, as well as of chemistry’s relation to quantum physics. (shrink)

Recent discussions of emergence in physics have focussed on the use of limiting relations, and often particularly on singular or asymptotic limits. We discuss a putative example of emergence that does not fit into this narrative: the case of phonons. These quasi-particles have some claim to be emergent, not least because the way in which they relate to the underlying crystal is almost precisely analogous to the way in which quantum particles relate to the underlying quantum field theory. But there (...) is no need to take a limit when moving from a crystal lattice based description to the phonon description. Not only does this demonstrate that we can have emergence without limits, but also provides a way of understanding cases that do involve limits. (shrink)

A predominant ethical view holds that physician‐investigators should conduct their research with therapeutic intent. And since a physician offering a therapy wouldn't prescribe second‐rate treatments, the experimental intervention and the best proven therapy should appear equally effective. "Clinical equipoise" is necessary. But this perspective is flawed. The ethics of research and of therapy are fundamentally different, and clinical equipoise should be abandoned.

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalization group. This article has three aims: to clarify the structure of the explanation of universality, to discuss the physics of such RG explanations, and to examine the extent to which universality is thus explained. The derivation of critical exponents proceeds via a real-space or a field-theoretic approach to the RG. Building on work by Mainwood, this article argues that these approaches ought to (...) be distinguished: while the field-theoretic approach explains universality, the real-space approach fails to provide an adequate explanation. (shrink)

A polemical account of Australian philosophy up to 2003, emphasising its unique aspects (such as commitment to realism) and the connections between philosophers' views and their lives. Topics include early idealism, the dominance of John Anderson in Sydney, the Orr case, Catholic scholasticism, Melbourne Wittgensteinianism, philosophy of science, the Sydney disturbances of the 1970s, Francofeminism, environmental philosophy, the philosophy of law and Mabo, ethics and Peter Singer. Realist theories especially praised are David Armstrong's on universals, David Stove's on logical probability (...) and the ethical realism of Rai Gaita and Catholic philosophers. In addition to strict philosophy, the book treats non-religious moral traditions to train virtue, such as Freemasonry, civics education and the Greek and Roman classics. (shrink)

The leading ethical position on placebo-controlled clinical trials is that whenever proven effective treatment exists for a given condition, it is unethical to test a new treatment for that condition against placebo. Invoking the principle of clinical equipoise, opponents of placebo-controlled trials in the face of proven effective treatment argue that they (1) violate the therapeutic obligation of physicians to offer optimal medical care and (2) lack both scientific and clinical merit. We contend that both of these arguments are mistaken. (...) Clinical equipoise provides erroneous ethical guidance in the case of placebo-controlled trials, because it ignores the ethically relevant distinction between clinical trials and treatment in the context of clinical medicine and the methodological limitations of active-controlled trials. Placebo controls are ethically justifiable when they are supported by sound methodological considerations and their use does not expose research participants to excessive risks of harm. (shrink)

This paper critiques the new mechanistic explanatory program on grounds that, even when applied to the kinds of examples that it was originally designed to treat, it does not distinguish correct explanations from those that blunder. First, I offer a systematization of the explanatory account, one according to which explanations are mechanistic models that satisfy three desiderata: they must 1) represent causal relations, 2) describe the proper parts, and 3) depict the system at the right ‘level.’ Second, I argue that (...) even the most developed attempts to fulfill these desiderata fall short by failing to appropriately constrain explanatorily apt mechanistic models. -/- *This paper used to be called "The Emperor's New Mechanisms". (shrink)

: Bioethicists have failed to understand the pervasively paternalistic character of research ethics. Not only is the overall structure of research review and regulation paternalistic in some sense; even the way informed consent is sought may imply paternalism. Paternalism has limits, however. Getting clear on the paternalism of research ethics may mean some kinds of prohibited research should be reassessed.

Blaming (construed broadly to include both blaming-attitudes and blaming-actions) is a puzzling phenomenon. Even when we grant that someone is blameworthy, we can still sensibly wonder whether we ought to blame him. We sometimes choose to forgive and show mercy, even when it is not asked for. We are naturally led to wonder why we shouldn’t always do this. Wouldn’t it be a better to wholly reject the punitive practices of blame, especially in light of their often undesirable effects, and (...) embrace an ethic of unrelenting forgiveness and mercy? In this paper I seek to address these questions by offering an account of blame that provides a rationale for thinking that to wholly forswear blaming blameworthy agents would be deeply mistaken. This is because, as I will argue, blaming is a way of valuing, it is “a mode of valuation.” I will argue that among the minimal standards of respect generated by valuable objects, notably persons, is the requirement to redress disvalue with blame. It is not just that blame is something additional we are required to do in properly valuing, but rather blame is part of what that it is to properly value. Blaming, given the existence of blameworthy agents, is mode of valuation required by the standards of minimal respect. To forswear blame would be to fail value what we ought to value. (shrink)

The universality of critical phenomena is best explained by appeal to the Renormalisation Group (RG). Batterman and Morrison, among others, have claimed that this explanation is irreducible. I argue that the RG account is reducible, but that the higher-level explanation ought not to be eliminated. I demonstrate that the key assumption on which the explanation relies – the scale invariance of critical systems – can be explained in lower-level terms; however, we should not replace the RG explanation with a bottom-up (...) account, rather we should acknowledge that the explanation appeals to dependencies which may be traced down to lower levels. (shrink)

Conventional medical ethics and the law draw a bright line distinguishing the permitted practice of withdrawing life-sustaining treatment from the forbidden practice of active euthanasia by means of a lethal injection. When clinicians justifiably withdraw life-sustaining treatment, they allow patients to die but do not cause, intend, or have moral responsibility for, the patient's death. In contrast, physicians unjustifiably kill patients whenever they intentionally administer a lethal dose of medication. We argue that the differential moral assessment of these two practices (...) is based on a series of moral fictions – motivated false beliefs that erroneously characterize withdrawing life-sustaining treatment in order to bring accepted end-of-life practices in line with the prevailing moral norm that doctors must never kill patients. When these moral fictions are exposed, it becomes apparent that conventional medical ethics relating to end-of-life decisions is radically mistaken. (shrink)

A basic question of medical ethics is whether the norms governing medical practice should be understood as the application of principles and rules of the common morality to medicine or whether some of these norms are internal or proper to medicine. In this article we describe and defend an evolutionary perspective on the internal morality of medicine that is defined in terms of the goals of clinical medicine and a set of duties that constrain medical practice in pursuit of these (...) goals. This perspective is developed by means of a critical examination of the essentialist conception of the internal morality of medicine advocated by Edmund Pellegrino and the critique of internal morality approaches by Robert Veatch and Tom Beauchamp. (shrink)

Event-causal libertarians maintain that an agent’s freely bringing about a choice is reducible to states and events involving him bringing about the choice. Agent-causal libertarians demur, arguing that free will requires that the agent be irreducibly causally involved. Derk Pereboom and Meghan Griffith have defended agent-causal libertarianism on this score, arguing that since on event-causal libertarianism an agent’s contribution to his choice is exhausted by the causal role of states and events involving him, and since these states and events leave (...) it open which decision he will make, he does not settle which decision occurs, and thus “disappears.” My aim is to explain why this argument fails. In particular, I demonstrate that event-causal libertarians can dismantle the argument by enriching the reductive base in their analysis of free will to include a state that plays the functional role of the self-determining agent and with which the agent is identified. (shrink)

The practice of voluntary physician‐assisted death as a last resort is compatible with doctors' duties to practice competently, to avoid harming patients unduly, to refrain from medical fraud, and to preserve patients' trust. It therefore does not violate physicians' professional integrity.

The Death of the Past argues that critical problems in the philosophy of history, such as the the truth of historical texts, how texts relate to the past that they are about, and the nature of historical explanation, can be successfully investigated if we accept the claim that historical writing is historicist--perspectival (from the standpoint of the historian) rather than purporting to be like an eyewitness account (as in the first-person "presentist" views critiqued by Enzo Traverso). This approach admits all (...) relevant evidence as subject to analysis in order to determine the widest point of view, as opposed to the biased "eyewitness" approach, which observes only partially. The link between the past itself and historical knowledge is radically broken, giving the latter the wisdom of hindsight across a broader temporal field from the events examined up to the present. The truth about the past is only accessible from a later point in time; "the past" itself is not a reality for the historian; it no longer exists. Frank Ankersmit offers a surprising foundation for the historicist notion of history: Leibniz' monadological universe, in which each monad or substance has its own point of view. There is no deeper ontology to which they owe their status--just an infinity of monads and a corresponding infinity of points of view on other monads. So with historical representations, statements about the past that can be either true or false but not depictions of the past itself. In striking contrast to Hayden White's view, Ankersmit insists that historical writing is no less rational than the sciences-- mathematical and scientific writing has its counterpart in the writing of history. (shrink)

This book provides the reader with a detailed and captivating account of the story where, for the first time, physicists ventured into proposing a new force of nature beyond the four known ones - the electromagnetic, weak and strong forces, and gravitation - based entirely on the reanalysis of existing experimental data. Back in 1986, Ephraim Fischbach, Sam Aronson, Carrick Talmadge and their collaborators proposed a modification of Newton's Law of universal gravitation. Underlying this proposal were three tantalizing pieces of (...) evidence: 1) an energy dependence of the CP (particle-antiparticle and reflection symmetry) parameters, 2) differences between the measurements of G, the universal gravitational constant, in laboratories and in mineshafts, and 3) a reanalysis of the Eötvos experiment, which had previously been used to show that the gravitational mass of an object and its inertia mass were equal to approximately one part in a billion. The reanalysis revealed that, contrary to Galileo's position, the force of gravity was in fact very slightly different for different substances. The resulting Fifth Force hypothesis included this composition dependence and also added a small distance dependence to the inverse-square gravitational force. Over the next four years numerous experiments were performed to test the hypothesis. By 1990 there was overwhelming evidence that the Fifth Force, as initially proposed, did not exist. This book discusses how the Fifth Force hypothesis came to be proposed and how it went on to become a showcase of discovery, pursuit and justification in modern physics, prior to its demise. In this new and significantly expanded edition, the material from the first edition is complemented by two essays, one containing Fischbach's personal reminiscences of the proposal, and a second on the ongoing history and impact of the Fifth Force hypothesis from 1990 to the present. <. (shrink)

Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid.

It has been presumed within bioethics that the benefits and risks of treatments can be assessed independently of information disclosure to patients as part of the informed consent process. Research on placebo and nocebo effects indicates that this is not true for symptomatic treatments. The benefits and risks that patients experience from symptomatic treatments can be shaped powerfully by information about these treatments provided by clinicians. In this paper we discuss the implications of placebo and nocebo research for risk–benefit assessment (...) and informed consent. (shrink)

Calibration, the use of a surrogate signal to standardize an instrument, is an important strategy for the establishment of the validity of an experimental result. In this paper, I present several examples, typical of physics experiments, that illustrate the adequacy of the surrogate. In addition, I discuss several episodes in which the question of calibration is both difficult to answer and of paramount importance. These episodes include early attempts to detect gravity waves, the question of the existence of a 17–keV (...) neutrino, and the question of the existence of a Fifth Force in gravity. I argue that in these more complex cases, the adequacy of calibration, in an extended sense, was both considered and established. (shrink)

This paper sketches a causal account of scientific explanation designed to sustain the judgment that high-level, detail-sparse explanations—particularly those offered in biology—can be at least as explanatorily valuable as lower-level counterparts. The motivating idea is that complete explanations maximize causal economy: they cite those aspects of an event’s causal run-up that offer the biggest-bang-for-your-buck, by costing less (in virtue of being abstract) and delivering more (in virtue making the event stable or robust).

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by the (...) ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem. (shrink)

Surgical clinical trials have seldom used a "sham" or placebo surgical procedure as a control, owing to ethical concerns. Recently, several ethical commentators have argued that sham surgery is either inherently or presumptively unethical. In this article I contend that these arguments are mistaken and that there are no sound ethical reasons for an absolute prohibition of sham surgery in clinical trials. Reflecting on three cases of sham surgery, especially on the recently reported results of a sham-controlled trial of arthroscopic (...) surgery for arthritis of the knee, I present an ethical analysis that focuses on the methodological rationale for use of sham surgery, risk-benefit assessment, and informed consent. (shrink)

Cosmetic surgery is a fast-growing medical practice. In 1997 surgeons in the United States performed the four most common cosmetic procedures443,728 times, an increase of 150% over the comparable total for 1992. Estimated total expenditures for cosmetic surgery range from $1 to $2 billion. As managed care cuts into physicians' income and autonomy, cosmetic surgery, which is not covered by health insurance, offers a financially attractive medical specialty.

Multiple realisation prompts the question: how is it that multiple systems all exhibit the same phenomena despite their different underlying properties? In this paper I develop a framework for addressing that question and argue that multiple realisation can be reductively explained. I illustrate this position by applying the framework to a simple example – the multiple realisation of electrical conductivity. I defend my account by addressing potential objections:contra Polger and Shapiro, Batterman, and Sober, I claim that multiple realisation is commonplace, (...) that it can be reductively explained, but that it requires asui generisreductive explanatory strategy. (shrink)

Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio of two heights, for example, is (...) a perceivable and measurable real relation between properties of physical things, a relation that can be shared by the ratio of two weights or two time intervals. Ratios are an example of continuous quantity; discrete quantities, such as whole numbers, are also realised as relations between a heap and a unit-making universal. For example, the relation between foliage and being-a-leaf is the number of leaves on a tree,a relation that may equal the relation between a heap of shoes and being-a-shoe. Modern higher mathematics, however, deals with some real properties that are not naturally seen as quantity, so that the “science of quantity” theory of mathematics needs supplementation. Symmetry, topology and similar structural properties are studied by mathematics, but are about pattern, structure or arrangement rather than quantity. (shrink)

Seth Shabo has presented a new argument that attempts to codify familiar worries about indeterminism, luck, and control. His ‘Assimilation Argument’ contends that libertarians cannot distinguish overtly randomized outcomes from exercises of free will. Shabo claims that the argument possesses advantages over the Mind Argument and Rollback Argument, which also purport to establish that indeterminism is incompatible with free will. I argue first that the Assimilation Argument presents no new challenges over and above those presented by the Rollback Argument, and (...) second that the Rollback Argument itself neither presents a deep challenge to, nor raises the cost of, accepting libertarianism. (shrink)