Higman essentially showed that if A is any language then SUBSEQ(A) is regular, where SUBSEQ(A) is the language of all subsequences of strings in A. Let s1, s2, s3, . . . be the standard lexicographic enumeration of all strings over some finite alphabet. We consider the following inductive inference problem: given A(s1), A(s2), A(s3), . . . . learn, in the limit, a DFA for SUBSEQU). We consider this model of learning and the variants of it that are usually (...) studied in Inductive Inference: anomalies, mind-changes, teams, and combinations thereof. This paper is a significant revision and expansion of an earlier conference version [10]. (shrink)

We define and study a new notion called k-immunity that lies between immunity and hyperimmunity in strength. Our interest in k-immunity is justified by the result that θ does not k-tt reduce to a k-immune set, which improves a previous result by Kobzev [7]. We apply the result to show that Φ′ does not btt-reduce to MIN, the set of minimal programs. Other applications include the set of Kolmogorov random strings, and retraceable and regressive sets. We also give a new (...) characterization of effectively simple sets and show that simple sets are not btt-cuppable. (shrink)

There is a family of questions in relativized complexity theory--weak analogs of the Friedberg Jump-Inversion Theorem--that are resolved by 1-generic sets but which cannot be resolved by essentially any weaker notion of genericity. This paper defines aw2-generic sets. i.e., sets which meet every dense set of strings that is r.e. in some incomplete r.e. set. Aw2-generic sets are very close to 1-generic sets in strength, but are too weak to resolve these questions. In particular, it is shown that for any (...) set X there is an aw2-generic set G such that $\mathbf{NP}^G \cap co-\mathbf{NP}^G \nsubseteq \mathbf{P}^{G \oplus X}$ . (On the other hand, if G is 1-generic, then $\mathbf{NP}^G \cap co-\mathbf{NP}^G \subseteq \mathbf{P}^{G \oplus \mathrm{SAT}}$ . where SAT is the NP-complete satisfiability problem [6].) This result runs counter to the fact that most finite extension constructions in complexity theory can be made effective. These results imply that any finite extension construction that ensures any of the Friedberg analogs must be noneffective, even relative to an arbitrary incomplete r.e. set. It is then shown that the recursion theoretic properties of aw2-generic sets differ radically from those of 1-generic sets: every degree above O' contains an aw2-generic set: no aw2-generic set exists below any incomplete r.e. set; there is an aw2-generic set which is the join of two Turing equivalent aw2-generic sets. Finally, a result of Shore is presented [30] which states that every degree above 0' is the jump of an aw2-generic degree. (shrink)

A set A is m-reducible to B if and only if there is a polynomial-time computable function f such that, for all x, x∈ A if and only if f ∈ B. Two sets are: 1-equivalent if and only if each is m-reducible to the other by one-one reductions; p-invertible equivalent if and only if each is m-reducible to the other by one-one, polynomial-time invertible reductions; and p-isomorphic if and only if there is an m-reduction from one set to the (...) other that is one-one, onto, and polynomial-time invertible. In this paper we show the following characterization. Theorem The following are equivalent: P = PSPACE. Every two 1-equivalent sets are p-isomorphic. Every two p-invertible equivalent sets are p-isomorphic. (shrink)

In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little (...) attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects. (shrink)

ontology metaontology wright platonism fregean existence epistemology.

The real distinction between mind and body -- Is conceivability a guide to possibility? -- Textbook kripkeanism and the open texture of concepts -- Coulda, woulda, shoulda -- No fool's cold : notes on illusions of possibility -- Beyond rigidification : the importance of being really actual -- How in the world? -- Mental causation -- Singling out properties -- Wide causation -- Causal relevance : mental, moral, and epistemic.

Part/whole is said in many ways: the leg is part of the table, the subset is part of the set, rectangularity is part of squareness, and so on. Do the various flavors of part/whole have anything in common? They may be partial orders, but so are lots of non-mereological relations. I propose an “upward difference transmission” principle: x is part of y if and only if x cannot change in specified respects while y stays the same in those respects.

According totransmissiontheories of testimony, a listener's belief in a speaker's testimony can be supported by the speaker's justification for what she says. The most powerful objection to transmission theories is Jennifer Lackey'spersistent believercase. I argue that important features about the epistemology of testimony reveal how transmission theories can account for Lackey's case. Specifically, I argue that transmission theorists should hold that transmission happens only if a listener believes a speaker's testimony based on the presumption that the speaker has justification for (...) what she says. If this does not happen in thepersistent believercase, then the case is no counterexample to transmission. If this does happen in thepersistent believercase, then there is an available framework for rejecting the idea that the listener's belief is in fact justified. (shrink)

According to some theories of testimonial knowledge, testimony can allow you, as a knowing speaker, to transmit your knowledge to me. A question in the epistemology of testimony concerns whether or not the acquisition of testimonial knowledge depends on the speaker's testimony being sincere. In this paper, I outline two notions of sincerity and argue that, construed in a certain way, transmission theorists should endorse the claim that the acquisition of testimonial knowledge requires sincerity.

In a dense and fascinating article of some ten years ago, Toomas Karmo adds his voice to the chorus of philosophers who deny the possibility of soundly deriving ‘ought’ from ‘is.’ According to Karmo, no derivation containing an ethical conclusion and only non-ethical premises can possibly be sound, where ‘sound’ describes a deductively valid derivation all of whose premises are true. He also suggests that the only valid derivations of ‘ought’ from ‘is’ will be trivial ones. His argument has, to (...) my knowledge, gone unrebutted; on the contrary, it has won recent endorsements, some philosophers evidently believing that he has finally put to rest the issue of the logical autonomy of ethics. Against that trend, I intend to rebut his argument, both by falsifying the taxonomy on which his argument relies and by offering a nontrivial and potentially sound ‘is’-‘ought’ derivation of my own. (shrink)

Genetic testing technology has brought the ability to predict the onset of diseases many years before symptoms appear and the use of such predictive testing is now widespread. The medical fraternity has met the application of this practice to children with caution. The justification for their predominantly prohibitive stance has revolved around the lack of a readily identifiable medical benefit in the face of potential psychological harms to the child. We argue that predictive testing can have important psychosocial benefits and (...) that the interests of the child have been construed too narrowly. Proponents of a prohibitive stance also argue that testing in childhood breaches the child's future right to make the same decision as an autonomous adult and to maintain this information as confidential. We argue that predictive genetic testing of children is not necessarily a violation of the child's future autonomy. Indeed, in some cases, such testing may facilitate the development of autonomy in the maturing child. We argue that parents are generally best placed to judge what is in their own child's overall interests, and that a parental request for testing after appropriate genetic counselling should be respected unless there is clear evidence that the child will be harmed in an overall sense as a result of testing. (shrink)

This paper investigates the degree to which corporate philanthropy is influenced by the extent to which a firm is internationalised and/or whether it hasoperations in one or more controversial countries. Utilising data on a sample of large UK firms, we find evidence of a positive effect not for internationalisation per se, but only for a presence in these controversial countries. More specifically, we find evidence that in this connection the salient feature of a country is a lack of political rights (...) and/or civil liberties, rather than a presence of rampant corruption. Furthermore, this positive impact on charitable giving is restricted to a presence in only those countries that are, according to Freedom House indicators, most lacking (and so controversial) in this respect. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 37.1 (2004) 72-91 [Access article in PDF] Passing Theories through Topical Heuristics: Donald Davidson, Aristotle, and the Conditions of Discursive Competence Stephen R. Yarbrough Department of English The University of North Carolina at Greensboro What are the conditions of discursive competence? In "A Nice Derangement of Epitaphs" Donald Davidson explains how it is possible that in practice we can, with little effort, understand and appropriately (...) respond to linguistic anomalies such as the malapropism—anomalies because, by definition, the "language" cannot account for how we understand them. Such anomalies, Davidson concludes, are the exceptions that do not prove but refute the traditional rule that antecedent linguistic systems govern discursive meaning. If that is so, then meanings are not a property of a linguistic system and are not "governed by learned conventions or regularities" (1986, 436); therefore, learning and sharing such conventions, what we traditionally call "language," is not a necessary condition of successful communication. He shows this by arguing that two conditions must be met for successful interlocution and that meeting these sufficiently allows successful interlocution to take place. A third condition—that the interlocutors share a language, an organized set of learned conventions or regularities "learned in advance of occasions of interpretation" (436) for which phenomena such as malapropisms would be anomalous—is neither a necessary nor sufficient condition of discursive competence.What I hope to show in this paper is that the two conditions Davidson argues interlocution must meet in order to succeed both involve the interlocutor's implicit knowledge of what since Aristotle the rhetorical tradition has called topical heuristics. Although Davidson himself seems unaware of it, his philosophy places invention in a new light, one that allows us to understand that the invention process is not merely a supplement to discourse, useful only for professional speakers and writers, but intrinsic to all intercourse, and that the topics are not merely formal but pragmatic relations that develop from the processes of our interactions with others and with objects of our common concern in a world we can come to share. [End Page 72] Inferential method Davidson argues that the first condition necessary for successful interlocution is that "the interpreter can learn the semantic role of each of a finite number of words or phrases and can learn the semantic consequences of a finite number of modes of expression" (1986, 437). "For this to be possible," says Davidson, "there must be systematic relations between the meanings of utterances" (436). Here he is not talking about grammatical systems but about systematic relations between and among the interlocutors' discursive actions and the world with its objects to which their actions refer. As I'll explain more fully shortly, these are topical relations. What makes these relations possible, Davidson argues, is that the interlocutors share, not a set of learned conventions, but a "recursive characterization of the truth conditions of all possible utterances of the speaker" (437).Such a theory of truth can be something like a Tarski truth definition, the explanation of which can be extremely convoluted (see Davidson 1984), but it boils down to saying that an utterance is true if the anticipations raised by a belief in an interpreted utterance are met by the consequences of believing the utterance; or, to put it another way, if the utterance is an answer to the question that solicited it or a solution to the problem to which it responds. Thus, an example of such a truth definition would be "The grass is green (an utterance made by someone, somewhere, somewhen, under certain conditions) is true if and only if the grass is green (to that person, at that place, at that time, under those conditions)." The force of a Tarski truth definition is that to understand what an utterance means is to understand the conditions that make it true (to the speaker). This, in turn, implies that in order for the interpreter to learn the semantic roles of the speaker's words and phrases and the semantic consequences of her modes of expression, the... (shrink)

In this discussion, the author asks the question if Oakeshott’s famous depiction of a practice might be understood in relation to contemporary cognitive science, in particular connectionism (the contemporary cognitive science approach concerned with the problem of skills and skilled knowing) and in terms of the now conventional view of "normativity" in Anglo-American philosophy. The author suggests that Oakeshott meant to contrast practices to an alternative "Kantian" model of a shared tacit mental frame or set of rules. If cognitive science, (...) in its connectionist forms, allows us to give a naturalistic though nonreductive sense to his words, Oakeshott, like other philosophers who have employed the concept of tradition, expanded his discussion into a broader reconsideration of the nature of theorizing, a metaphilosophy. And this extension can be understood in relation to such recent thinkers as McDowell and, in particular, to the problem of the acquisition of the normative. Key Words: idealism • Oakeshott • connectionism • normativity. (shrink)

Many teachers of bioethics often express concern, in their writings and otherwise, about the theoretical basis (or lack of it) of bioethics and the allied issue of relativism. The companion articles by Tong and Momeyer are in this vein and rightly address such issues within the context of a liberal arts education. This article addresses such issues in a different venue, i.e., bioethics teaching in the clinical sphere of health care institutions. It presumes to suggest that many of these theoretical (...) concerns, as well as the threat of relativism, seldom arise in this sphere. Rather, a broad based, well accepted body of moral truth has been fashioned over the last quarter century and it is this that clinical bioethics regularly keys to and to which most moral dilemmas are referred for resolution. The various forms of this pedagogy, e.g., case consultations or institutional policy statements, are charted out in this regard, as well as the often tactical character of much of this teaching, i.e., not "what should we do?", but "how might we best do it?". The article then goes on to conclude with a reflection on the use and abuse of power in clinical bioethics teaching and consultation. (shrink)

Although long touted as an ethical and legal requirement, some clinicians still seem to offer less than fully adequate informed consent processes; similarly the counseling of patients and families, particularly about post-intervention scenarios, is often perfunctory at best. Keyed to a narrative of a patient's experience with surgery for a deviated septum, this article reflects on why such less than adequate clinician behaviors tend to occur and what might be done about them. Certain legal misconceptions about informed consent are highlighted (...) in this reflection, as well as why certain clinicians seem to take such a narrow view of their responsibilities to patients. Further reference in this regard is also made to a recently constructed module on informed consent for medical residents. In it, though legal requirements for informed consent are reviewed, the basic perspective taken regards informed consent as a clinical intervention that pursues certain basic goods and values, only one of which lies in determining when legal closure for such processes has occurred. (shrink)

Pompey does not accept defeat at Pharsalus. Rather, in an effort to gain support from powers beyond Rome, he makes for Egypt and, unbeknownst to him, his decapitation. As narrated in Lucan'sBellum ciuile, after deliberating in Cilicia with his senatorial advisers (8.259–455), Pompey stops at the island of Cyprus (8.456–9):tum Cilicum liquere solum Cyproque citatasimmisere rates, nullas cui praetulit arasundae diua memor Paphiae, si numina nascicredimus aut quemquam fas est coepisse deorum.Then they left the Cilician soil and steered their vessels (...) in haste for Cyprus—Cyprus which the goddess, mindful of Paphian waves, prefers to any of her shrines (if we believe that deities have birth, or if it is lawful to hold that any of the gods had a beginning).In Lucan, Pompey's trip to Cyprus is brief and includes a somewhat curious reference to Venus (diua), her origins (undae … Paphiae) and the birth of the gods. Other authors also record Pompey's visit to Cyprus, although the details vary. Some, including Julius Caesar, set his deliberations not in Cilicia but on Cyprus itself (Caes.BCiu.3.102.3.1–8.1; cf. Plut.Vit. Pomp. 77.1.1–2.1). Others, it seems, provide few if any details of Pompey at the island, for example the scanty evidence from Livy,Per. 112.1–10. (shrink)

In The Foundations of Private Law James Gordley argues that the modern private law in common and civil law jurisdictions is best explained on the basis of a neo-Aristotelian theory first developed by a group of 16th century Spanish thinkers known as the ‘late scholastics’. The concepts of distributive and commutative justice that, according to Gordley, lay at core of the scholastics’ theory and that explain, respectively, modern property law and the law of obligations , though ignored and disparaged for (...) much of the 19th and 20th centuries, are today familiar to most private law scholars . Yet Gordley’s understanding of these concepts and, in particular, of their relationship both to one another and to the apex idea of ‘living a distinctively human life’ is unique, setting his account apart not just from utilitarian and other ‘modern’ accounts of private law, but also from other neo-Aristotelian theories . In Gordley’s presentation, commutative justice is derived from distributive justice and distributive justice is derived from the idea of the distinctively human life. Confidently traversing a wide range of historical, comparative and theoretical materials, the book’s argument is at once ambitious, learned, and elegantly presented. But as a theoretical account of the foundations of the modern private law it is unpersuasive. The book’s own account of property law suggests that in practice the idea of distributive justice does little, if any, work in explaining the rules we actually have. Nor is it clear how, if at all, distributive justice flows from the allegedly foundational idea of the ‘distinctively human life’. As for commutative justice, it is not clear why, if is derived from distributive justice in the way Gordley believes, the courts should care about it. Finally, but perhaps most significantly, Gordley’s conception of commutative justice is unable to account for central features of the law of obligations. (shrink)

Sport is a producer of both emotional and aesthetic experiences. But how do these relate? Does a spectator’s emotional engagement in sport enhance or hinder it as an aesthetic experience? And does the aesthetic perception of sport enhance or hinder the emotional experiences? These questions will be addressed with particular reference to the distinction that can be drawn between partisan and purist watchers of sport, and making use of thinking in contemporary aesthetics and philosophy of emotion. There are some reasons (...) to think that emotion and aesthetics pull in opposite directions, in both sport and wider life. Does a purist miss out on the essence of sport if they adopt a detached aesthetic attitude? If that were the case, it would suggest that the sports spectator might have to choose between the two: experiencing one or the other but not both at the same time. Emotions and aesthetics would be a trade-off but I argue for some significant exceptions to this conclusion. (shrink)

This paper discusses why integration is important in doing research for developing policy and practice of sustainable environmental management. The imperative of integration includes environmental, social, economic, and other disciplinary considerations, as well as stakeholder interests. However, what is meant by integration is not always clear. While the imperative is being increasingly enunciated, the challenges it presents are difficult and indicate a long term pursuit. This paper clarifies the different dimensions of integration, as an important preliminary step toward advancing mutual (...) understanding and the development of approaches. The paper identifies the driving forces for integration, discusses when integration is required, categorises forms of integration, and proposes principles to inform research programs and projects. (shrink)