If r is a reducibility between sets of numbers, a natural question to ask about the structure ? r of the r-degrees containing computably enumerable sets is whether every element not equal to the greatest one is branching (i.e., the meet of two elements strictly above it). For the commonly studied reducibilities, the answer to this question is known except for the case of truth-table (tt) reducibility. In this paper, we answer the question in the tt case by showing that (...) every tt-incomplete computably enumerable truth-table degree a is branching in ? tt . The fact that every Turing-incomplete computably enumerable truth-table degree is branching has been known for some time. This fact can be shown using a technique of Ambos-Spies and, as noticed by Nies, also follows from a relativization of a result of Degtev. We give a proof here using the Ambos-Spies technique because it has not yet appeared in the literature. The proof uses an infinite injury argument. Our main result is the proof when a is Turing-complete but tt-incomplete. Here we are able to exploit the Turing-completeness of a in a novel way to give a finite injury proof. (shrink)

Lattice representations are an important tool for computability theorists when they embed nondistributive lattices into degree-theoretic structures. In this expository paper, we present the basic definitions and results about lattice representations needed by computability theorists. We define lattice representations both from the lattice-theoretic and computability-theoretic points of view, give examples and show the connection between the two types of representations, discuss some of the known theorems on the existence of lattice representations that are of interest to computability theorists, and give (...) a simple example of the use of lattice representations in an embedding result. (shrink)

A recursively enumerable splitting of an r.e. setAis a pair of r.e. setsBandCsuch thatA=B∪CandB∩C= ⊘. Since for such a splitting degA= degB∪ degC, r.e. splittings proved to be a quite useful notion for investigations into the structure of the r.e. degrees. Important splitting theorems, like Sacks splitting [S1], Robinson splitting [R1] and Lachlan splitting [L3], use r.e. splittings.Since each r.e. splitting of a set induces a splitting of its degree, it is natural to study the relation between the degrees of (...) r.e. splittings and the degree splittings of a set. We say a setAhas thestrong universal splitting property if each splitting of its degree is represented by an r.e. splitting of itself, i.e., if for degA=b∪cthere is an r.e. splittingB, CofAsuch that degB=band degC=c. The goal of this paper is the study of this splitting property.In the literature some weaker splitting properties have been studied as well as splitting properties which imply failure of the SUSP. (shrink)

Downey and Lempp 1215–1240) have shown that the contiguous computably enumerable degrees, i.e. the c.e. Turing degrees containing only one c.e. weak truth-table degree, can be characterized by a local distributivity property. Here we extend their result by showing that a c.e. degree a is noncontiguous if and only if there is an embedding of the nonmodular 5-element lattice N5 into the c.e. degrees which maps the top to the degree a. In particular, this shows that local nondistributivity coincides with (...) local nonmodularity in the computably enumerable degrees. (shrink)

We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable elements are (...) disjoint. We formulate general criteria that allow one to conclude that a distributive upper semi-lattice has a decidable two-quantifier theory. These criteria are applied not only to the weak truth-table degrees of the recursively enumerable sets but also to various substructures of the polynomial many-one (pm) degrees of the recursive sets. These applications to the pm degrees require no new complexity-theoretic results. The fact that the pm-degrees of the recursive sets have a decidable two-quantifier theory answers a question raised by Shore and Slaman in [21]. (shrink)

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov function, which (...) assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)

It is argued that causal understanding originates in experiences of acting on objects. Such experiences have consistent features that can be used as clues to causal identification and judgment. These are singular clues, meaning that they can be detected in single instances. A catalog of 14 singular clues is proposed. The clues function as heuristics for generating causal judgments under uncertainty and are a pervasive source of bias in causal judgment. More sophisticated clues such as mechanism clues and repeated interventions (...) are derived from the 14. Research on the use of empirical information and conditional probabilities to identify causes has used scenarios in which several of the clues are present, and the use of empirical association information for causal judgment depends on the presence of singular clues. It is the singular clues and their origin that are basic to causal understanding, not multiple instance clues such as empirical association, contingency, and conditional probabilities. (shrink)

Since the appearance of Plato’s Dialogues, philosophers have been preoccupied with the identity of Socrates and have maintained that successful interpretation of the work hinges upon a clear understanding of what thoughts and ideas can be attributed to him. In Descent of Socrates, Peter Warnek offers a new interpretation of Plato by considering the appearance of Socrates within Plato’s work as a philosophical question. Warnek reads the Dialogues as an inquiry into the nature of Socrates and in doing so (...) opens up the relationship between humankind and the natural world. Here, Socrates appears as a demonic and tragic figure whose obsession with the task of self-knowledge transforms the history of philosophy. In this uncompromising work, Warnek reveals the importance of the concept of nature in the Platonic Dialogues in light of Socratic practice and the Ancient ideas that inspire contemporary philosophy. (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)

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.

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)

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 ...

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)

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)

Philosophy and Phenomenological Research, EarlyView.

This new book describes the intellectual structure of modern science as a body of knowledge produced by the Cartesian method.

To circumvent objections that the death penalty was “cruel and unusual punishment” and therefore a violation of the Eighth Amendment to the Constitution, advocates proposed lethal injection and the involvement of physicians to overcome the negative perceptions associated with the death penalty, and to increase public acceptability of the practice. Initiated in 1982, lethal injection is now the primary method of execution in 37 of the 38 states with the death penalty. “To be exact, this method has been used to (...) kill 788 of the 956 men and women who have been executed in the United States since 1976, when the death penalty was reinstated by the Supreme Court.” More recently, of the 191 executions performed in the United States since 2001, 189 have been by lethal injection.This “medicalization” of the death penalty has ignited a debate, by those within the medical profession and by others outside it, about the appropriateness of physicians participating in executions. (shrink)

In the last few years, the U.S. health care system has seemingly been gripped by “back to the nineties” fever. But there is a notable change in professional debates about how to better control health care costs. Discussion of health care rationing, which was hotly debated in the nineties, has become much more muted.Is health care rationing passé? I contend that debates about health care rationing have waned not because the need to ration has dwindled nor because ethical debates about (...) how or whether to ration have been resolved. They have declined because the word “rationing,” and unrelated concepts such as cost‐effectiveness analysis, have been replaced by terms—“parsimony,” “value,” and “CER”—that are not burdened by emotional and historical baggage.Sometimes the best way to promote healthy moral debate is to turn to new words that don't carry the burden of past debates. (shrink)

Background: Some members of the general public feel that patients who cause their own organ failure through smoking, alcohol use, or drug use should not receive equal priority for scarce transplantable organs. This may reflect a belief that these patients (1) cause their own illness, (2) have poor transplant prognoses or, (3) are simply unworthy. We explore the role that social acceptability, personal responsibility, and prognosis play in people's judgments about transplant allocation. Methods: By random allocation, we presented 283 prospective (...) jurors in Philadelphia county with one of five questionnaire versions. In all questionnaires, subjects were asked to distribute transplantable hearts between patients with and without a history of three controversial behaviors (eating high fat diets against doctors’ advice, cigarette smoking, or intravenous drug use). Across the five questionnaire versions, we varied the relative prognosis of the transplant candidates and whether their behavior caused their primary organ Results: Subjects were significantly less willing to distribute organs to intravenous drug users than to cigarette smokers or people eating high fat diets (p le; 0.0005), even when intravenous drug users had better transplant outcomes than other patients. Subjects’ allocation decisions were influenced by transplant prognosis, but not by whether the behavior in question was causally responsible for the patients’ organ failure. Conclusion: People's unwillingness to give scarce transplantable organs to patients with controversial behaviors cannot be explained totally on the basis of those behaviors either causing their primary organ failure or making them have worse transplant prognoses. Instead, many people believe that such patients are simply less worthy of scarce transplantable organs. (shrink)

In the past few decades, scholars have offered positive, normative, and most recently, interpretive theories of contract law. These theories have proceeded primarily from deontological and consequentialist premises. In A Theory of Contract Law: Empirical Understandings and Moral Psychology, Professor Peter A. Alces confronts the leading interpretive theories of contract and demonstrates their interpretive doctrinal failures. Professor Alces presents the leading canonical cases that inform the extant theories of Contract law in both their historical and transactional contexts and, argues (...) that moral psychology provides a better explanation for the contract doctrine than do alternative comprehensive interpretive approaches. (shrink)

In their article, “Supported Decision Making with People at the Margins of Autonomy,” Peterson, Karlawish, and Largent point to the fact that the concept of ‘supported decision-making’ has recently...

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)

This paper considers the implications of David Marr's computational theory of vision for the issues of individualism and methodological solipsism. A recent argument that the theory is nonindividualistic is shown to be similar to Gibson's arguments for "direct perception." The paper argues that a complete analysis of Marr's theory must take into account Marr's rejection of Gibson's approach, and that such an analysis shows Marr's theory to be consistent with methodological solipsism as a research strategy.

This book introduces students to the principal issues in the philosophy of mind by tracing the history of the subject from Plato and Aristotle through to the present day. Over forty primary-source readings are included. Extensive commentaries from the editors are provided to guide student readers through the arguments and jargon and to offer necessary historical context for the readings. The new third edition examines some of the most exciting recent developments in the field, including advances in theories about the (...) mind’s relation to action and agency. Previous editions of this book, published under the title _A Historical Introduction to the Philosophy of Mind_, have been praised and widely taught for more than two decades. (shrink)