We study the proof-theoretic strength and effective content of the infinite form of Ramsey's theorem for pairs. Let RT n k denote Ramsey's theorem for k-colorings of n-element sets, and let RT $^n_{ denote (∀ k)RT n k . Our main result on computability is: For any n ≥ 2 and any computable (recursive) k-coloring of the n-element sets of natural numbers, there is an infinite homogeneous set X with X'' ≤ T 0 (n) . Let IΣ n and BΣ (...) n denote the Σ n induction and bounding schemes, respectively. Adapting the case n = 2 of the above result (where X is low 2 ) to models of arithmetic enables us to show that RCA 0 + IΣ 2 + RT 2 2 is conservative over RCA 0 + IΣ 2 for Π 1 1 statements and that $RCA_0 + I\Sigma_3 + RT^2_{ , is Π 1 1 -conservative over RCA 0 + IΣ 3 . It follows that RCA 0 + RT 2 2 does not imply BΣ 3 . In contrast, J. Hirst showed that $RCA_0 + RT^2_{ does imply BΣ 3 , and we include a proof of a slightly strengthened version of this result. It follows that $RT^2_{ is strictly stronger than RT 2 2 over RCA 0. (shrink)

The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly $\Delta (...) _\alpha ^0 $ orbit (from the proof). (shrink)

We show that the double jump is definable in the computably enumerable sets. Our main result is as follows: let [Formula: see text] is the Turing degree of a [Formula: see text] set J ≥T0″}. Let [Formula: see text] such that [Formula: see text] is upward closed in [Formula: see text]. Then there is an ℒ property [Formula: see text] such that [Formula: see text] if and only if there is an A where A ≡T F and [Formula: see text]. (...) A corollary of this is that, for all n ≥ 2, the high n computably enumerable degrees are invariant in the computably enumerable sets. Our work resolves Martin's Invariance Conjecture. (shrink)

The purpose of this communication is to announce some recent results on the computably enumerable sets. There are two disjoint sets of results; the first involves invariant classes and the second involves automorphisms of the computably enumerable sets. What these results have in common is that the guts of the proofs of these theorems uses a new form of definable coding for the computably enumerable sets.We will work in the structure of the computably enumerable sets. The language is just inclusion, (...) ⊆. This structure is called ε.All sets will be computably enumerable non-computable sets and all degrees will be computably enumerable and non-computable, unless otherwise noted. Our notation and definitions are standard and follow Soare [1987]; however we will warm up with some definitions and notation issues so the reader need not consult Soare [1987]. Some historical remarks follow in Section 2.1 and throughout Section 3.We will also consider the quotient structure ε modulo the ideal of finite sets, ε*. ε* is a definable quotient structure of ε since “Χ is finite” is definable in ε; “Χ is finite” iff all subsets of Χ are computable. We use A* to denote the equivalent class of A under the ideal of finite sets. (shrink)

A result of Soare and Stob asserts that for any non-recursive r.e. setC, there exists a r.e.[C] setA such thatA⊕C is not of r.e. degree. A setY is called [of]m-REA (m-REA[C] [degree] iff it is [Turing equivalent to] the result of applyingm-many iterated ‘hops’ to the empty set (toC), where a hop is any function of the formX→X ⊕W e X . The cited result is the special casem=0,n=1 of our Theorem. Form=0,1, and any (m+1)-REA setC, ifC is not ofm-REA (...) degree, then for alln there exists an-r.e.[C] setA such thatA ⊕C is not of (m+n)-REA degree. We conjecture that this holds also form≥2. (shrink)

We show that if A and $\widehat{A}$ are automorphic via Φ then the structures $S_{R}(A)$ and $S_{R}(\widehat{A})$ are $\Delta_{3}^{0}-isomorphic$ via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.

Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us to better understand the${\cal D}$-maximal (...) sets, we use them to show that several classes of${\cal D}$-maximal sets break into infinitely many orbits. (shrink)

Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us to better understand the${\cal D}$-maximal (...) sets, we use them to show that several classes of${\cal D}$-maximal sets break into infinitely many orbits. (shrink)

We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for Gδ sets. Our constructions essentially settle the reverse mathematical classification of this principle.

We show there is a non-recursive r.e. set A such that if W is any low r.e. set, then the join W $\oplus$ A is also low. That is, A is "almost deep". This answers a question of Jockusch. The almost deep degrees form an definable ideal in the r.e. degrees (with jump.).

In this article we establish the existence of a number of new orbits in the automorphism group of the computably enumerable sets. The degree theoretical aspects of these orbits also are examined.

The main result of this paper is to show that for every recursive ordinal α ≠ 0 and for every nonrecursive r.e. degree d there is a r.e. set of rank α and degree d.

We state and prove the Translation Theorem. Then we apply the Translation Theorem to Soare's Extension Theorem, weakening slightly the hypothesis to yield a theorem we call the Modified Extension Theorem. We use this theorem to reprove several of the known results about orbits in the lattice of recursively enumerable sets. It is hoped that these proofs are easier to understand than the old proofs.

Let b and c be r.e. Turing degrees such that b>c. We show that there is an r.e. degree a such that b>a>c and all lattices containing a critical triple, including the lattice M5, cannot be embedded into the interval [c, a].

A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show that the class of maximal contiguous degrees forms an automorphism base for the c.e. degrees and therefore for the (...) Turing degrees in general. Finally we note that the construction of a maximal contiguous degree can be modified to answer a question of Walk about the array computable degrees and a question of Li about isolated formulas. (shrink)

Medicine and health care generate many bioethical problems and dilemmas that are of great academic, professional and public interest. This comprehensive resource is designed as a succinct yet authoritative text and reference for clinicians, bioethicists, and advanced students seeking a better understanding of ethics problems in the clinical setting. Each chapter illustrates an ethical problem that might be encountered in everyday practice; defines the concepts at issue; examines their implications from the perspectives of ethics, law and policy; and then provides (...) a practical resolution. There are 10 key sections presenting the most vital topics and clinically relevant areas of modern bioethics. International, interdisciplinary authorship and cross-cultural orientation ensure suitability for a worldwide audience. This book will assist all clinicians in making well-reasoned and defensible decisions by developing their awareness of ethical considerations and teaching the analytical skills to deal with them effectively. (shrink)

Waar de een zijn leven geeft voor een goed geweten, haalt de ander zijn schouders erover op. Het geweten: een achterhaald begrip of hard toe aan herwaardering?

In this paper I sketch an account of moral blame and blameworthiness. I begin by clarifying what I take blame to be and explaining how blameworthiness is to be analyzed in terms of it. I then consider different accounts of the conditions of blameworthiness and, in the end, settle on one according to which a person is blameworthy for φ-ing just in case, in φ-ing, she violates one of a particular class of moral requirements governing the attitudes we bear, and (...) our mental orientation, toward people and other objects of significant moral worth. These requirements embody the moral stricture that we accord to these others a sufficient level of respect, one that their moral worth demands. This is a familiar theme which has its roots in P. F. Strawson’s pioneering views on moral responsibility. My development of it leads me to the conclusion that acting wrongly is not a condition of blameworthiness: violating a moral requirement to perform, or refrain from performing, an action is neither necessary nor sufficient for being blameworthy. All we are ever blameworthy for, I will argue, are certain aspects of our mental bearing toward others. We can be said to be blameworthy for our actions only derivatively, in the sense that those actions are the natural manifestations of the things for which we are strictly speaking blameworthy. (shrink)

There is a debate in normative ethics about whether or not our moral obligations depend solely on either our evidence concerning, or our beliefs about, the world. Subjectivists maintain that they do and objectivists maintain that they do not. I shall offer some arguments in support of objectivism and respond to the strongest argument for subjectivism. I shall also briefly consider the significance of my discussion to the debate over whether one’s future voluntary actions are relevant to one’s current moral (...) obligations. (shrink)

Preliminary draft of November 2010—please do not circulate without permission.

This volume, an expanded edition of the philosophy of language issue of the journal Midwest Studies in Philosophy (1977), includes essays by some of the ...

In this lucid and penetrating book, Peter A. Schouls considers Locke's major writings in terms of the closely related ideas of freedom, progress, mastery, reason, and education.

Many health care decisions depend not only upon medical facts, but also on value judgments—patient goals and preferences. Until recent decades, patients relied on doctors to tell them what to do. Then ethicists and others convinced clinicians to adopt a paradigm shift in medical practice, to recognize patient autonomy, by orienting decision making toward the unique goals of individual patients. Unfortunately, current medical practice often falls short of empowering patients. In this article, we reflect on whether the current state of (...) medical decision making effectively promotes patients' health care goals. We base our reflections, in part, on research in which we observed physicians making earnest efforts to partner with patients in making treatment decisions, but still struggling to empower patients—failing to communicate clearly to patients about decision-relevant information, overwhelming patients with irrelevant information, overlooking when patients' emotions made it hard to engage in choices, and making recommendations before discussing patients' goals. (shrink)

If practical reason is concerned with thoughtful normative regulation of action, then theoretical reason might be seen as a matter of thoughtful normative regulation of belief. The conclusion of a piece of practical reasoning, we are told, is an act or intention to act; the conclusion of a piece of theoretical reasoning, by parallel, would be a belief or a belief-tendency. Because theoretical reason is understood to be responsive specifically to epistemic – not merely pragmatic – reasons for belief, the (...) norms involved in heoretical reason are norms pertinent to knowledge, including norms of evidence, justification, and truth. In both the practical and theoretical case we need not exactly agree with the conclusion another person reaches in order to attribute rationality to her – but it seems we do need to find something normatively appropriate about the means by which the other reaches her conclusion, given her capacities and circumstances. (shrink)

David Lewis has offered a reply to the standard argument for the claim that the truth of determinism is incompatible with anyone’s being able to do otherwise than she in fact does. Helen Beebee has argued that Lewis’s compatibilist strategy is untenable. In this paper I show that one recent attempt to defend Lewis’s view against this argument fails and then go on to offer my own defense of Lewis’s view.

Despite its current popularity, “emergence” is a concept with a venerable history and an elusive, ambiguous standing in contemporary evolutionary theory. This paper briefly recounts the history of the term and details some of its current usages. Not only are there radically varying interpretations about how to define emergence but “reductionist” and “holistic” theorists hold very different views about the issue of causation. However, these two seemingly polar positions are not irreconcilable. Reductionism, or detailed analysis of the parts and their (...) interactions, is essential for answering the “how” question in evolution—how does a complex living system work? But holism is equally necessary for answering the “why” question—why did a particular arrangement of parts evolve? In order to answer the “why” question, a broader, multi-leveled paradigm is required. The reductionist approach to explaining emergent complexity has entailed a search for underlying “laws of emergence.” In contrast, the “Synergism Hypothesis” focuses on the “economics”—the functional effects produced by emergent wholes and their selective consequences in evolutionary change. This paper also argues that emergent phenomena represent, in effect, a subset of a larger universe of cooperative, synergistic effects in the natural world. (shrink)

In April 1999, Dr. Curt Freed of the University of Colorado in Denver and Dr. Stanley Fahn of Columbia Presbyterian Center in New York presented the results of a four-year, $5.7 million government-financed study using tissue from aborted fetuses to treat Parkinson’s disease at a conference of the American Academy of Neurology. The results of the first government-financed, placebo-controlled clinical study using fetal tissue showed that the symptoms of some Parkinson’s patients had been relieved. This research study involved forty subjects, (...) nineteen women and twenty-one men; all suffered from Parkinson’s disease for an average of 13.5 years. In the study, each subject underwent neurosurgery: “four tiny burr holes, drilled through the wrinkle lines above the eyebrows into the skull, to clear a pathway to the brain. But only half received injections of fetal cells into the putamen, the region of the brain that controls movement; the other half received nothing. One year later, three members of the placebo group said their symptoms had improved.” In two-thirds of the transplant recipients, the fetal tissue took hold and seemed to establish a new network to produce the missing neurochemical dopamine. (shrink)

Theorists have hypothesized that skill in critical thinking is positively correlated with the consistent internal motivation to think and that specific critical thinking skills are matched with specific critical thinking dispositions. If true, these assumptions suggest that a skill-focused curriculum would lead persons to be both willing and able to think. This essay presents a researchbased expert consensus definition of critical thinking, argues that human dispositions are neither hidden nor unknowable, describes a scientific process of developing conventional testing tools to (...) measure cognitive skills and human dispositions, and summarizes recent empirical research findings that explore the possible relationship of critical thinking skill and the consistent internal motivation, or disposition, to use that skill. Empirical studies indicate that for all practical purposes the hypothesized correlations are not evident. It would appear that effective teaching must include strategies for building intellectual character rather than relying exclusively on strengthening cognitive skills. (shrink)

A decade ago, we reviewed the field of clinical ethics; assessed its progress in research, education, and ethics committees and consultation; and made predictions about the future of the field. In this article, we revisit clinical ethics to examine our earlier observations, highlight key developments, and discuss remaining challenges for clinical ethics, including the need to develop a global perspective on clinical ethics problems.

ABSTRACTMother‐to‐child transmission of HIV represents a particularly dramatic aspect of the HIV epidemic with an estimated 600,000 newborns infected yearly, 90% of them living in sub‐Saharan Africa. Since the beginning of the HIV epidemic, an estimated 5.1 million children worldwide have been infected with HIV. MTCT is responsible for 90% of these infections. Two‐thirds of the MTCT are believed to occur during pregnancy and delivery, and about one‐third through breastfeeding. As the number of women of child bearing age infected with (...) HIV rises, so does the number of infected children. It is apparent that voluntary testing in Botswana has made some valuable inroads in decreasing perinatal HIV transmission, but the statistics showing the increased rate of HIV infection among women 15–24 years of age are not very promising. After reviewing all the pertinent scientific data it is clear that mandatory HIV testing of all pregnant women in conjunction with the implementation of a full package of interventions would save thousands of lives – mothers, newborns and others who could be infected as a result of these women not being aware of their HIV status. If the protection and preservation of human life is a priority in Botswana, then it is time to allow for mandatory HIV testing of all pregnant women, before it is too late for those who are the most vulnerable. To do less would be medically inappropriate and ethically irresponsible. (shrink)