For a set A of non-negative integers, let D be the set of non-negative differences of elements of A. Clearly, if A is computable, then D is computably enumerable. We show that every simple set which contains 0 is the difference set of some computable set and that every computably enumerable set is computably isomorphic to the difference set of some computable set. Also, we prove that there is a computable set which is the difference set of the complement of (...) some computably enumerable set but not of any computably enumerable set. Finally, we show that every arithmetic set is in the Boolean algebra generated from the computable sets by the difference operator D and the Boolean operations. (shrink)

TheK-trivial sets form an ideal in the Turing degrees, which is generated by its computably enumerable members and has an exact pair below the degree of the halting problem. The question of whether it has an exact pair in the c.e. degrees was first raised in [22, Question 4.2] and later in [25, Problem 5.5.8].We give a negative answer to this question. In fact, we show the following stronger statement in the c.e. degrees. There exists aK-trivial degreedsuch that for all (...) degreesa, bwhich are notK-trivial anda > d, b > dthere exists a degreevwhich is notK-trivial anda > v, b > v. This work sheds light to the question of the definability of theK-trivial degrees in the c.e. degrees. (shrink)

We study inversions of the jump operator on ${\mathrm{\Pi }}_{1}^{0}$ classes, combined with certain basis theorems. These jump inversions have implications for the study of the jump operator on the random degrees—for various notions of randomness. For example, we characterize the jumps of the weakly 2-random sets which are not 2-random, and the jumps of the weakly 1-random relative to 0′ sets which are not 2-random. Both of the classes coincide with the degrees above 0′ which are not 0′-dominated. A (...) further application is the complete solution of [24, Problem 3.6.9]: one direction of van Lambalgen's theorem holds for weak 2-randomness, while the other fails. Finally we discuss various techniques for coding information into incomplete randoms. Using these techniques we give a negative answer to [24, Problem 8.2.14]: not all weakly 2-random sets are array computable. In fact, given any oracle X, there is a weakly 2-random which is not array computable relative to X. This contrasts with the fact that all 2-random sets are array computable. (shrink)

The human immune system can directly lyse invading micro‐organisms and aberrant host cells by generating pores in the cell envelope, called membrane attack complexes (MACs). Recent studies using single‐particle cryoelectron microscopy have revealed that the MAC is an asymmetric, flexible pore and have provided a structural basis on how the MAC ruptures single lipid membranes. Despite these insights, it remains unclear how the MAC ruptures the composite cell envelope of Gram‐negative bacteria. Recent functional studies on Gram‐negative bacteria elucidate (...) that local assembly of MAC pores by surface‐bound C5 convertase enzymes is essential to stably insert these pores into the bacterial outer membrane (OM). These convertase‐generated MAC pores can subsequently efficiently damage the bacterial inner membrane (IM), which is essential for bacterial killing. This review summarizes these recent insights of MAC assembly and discusses how MAC pores kill Gram‐negative bacteria. Furthermore, this review elaborates on how MAC‐dependent OM damage could lead to IM destabilization, which is currently not well understood. A better understanding on how MAC pores kill bacteria could facilitate the future development of novel strategies to treat infections with Gram‐negative bacteria. (shrink)

Effectiveness is a key criterion in assessing the justification of antibiotic resistance interventions. Depending on an intervention’s effectiveness, burdens and costs will be more or less justified, which is especially important for large scale population-level interventions with high running costs and pronounced risks to individuals in terms of wellbeing, integrity and autonomy. In this paper, we assess the case of routine hospital screening for multi-drug-resistant Gram-negative bacteria (MDRGN) from this perspective. Utilizing a comparison to screening programs for Methicillin-Resistant Staphylococcus aureus (...) (MRSA) we argue that current screening programmes for MDRGN in low endemic settings should be reconsidered, as its effectiveness is in doubt, while general downsides to screening programs remain. To accomplish justifiable antibiotic stewardship, MDRGN screening should not be viewed as a separate measure, but rather as part of a comprehensive approach. The program should be redesigned to focus on those at risk of developing symptomatic infections with MDRGN rather than merely detecting those colonised. (shrink)

The pathogenic, Gram‐negative bacteria, Neisseria gon‐orrhoeae, Neisseria meningitidis and Haemophilus influenzae, secrete immunoglobulin A1 proteases into their extracellular surroundings. An extraordinary feature in the secretory pathway of these putative virulence factors is a self‐directed outer membrane transport step allowing the proteins to be secreted autonomously, even from foreign Gram‐negative host cells like Escherichia coli. Here we summarize recent achievements in the understanding of IgA protease outer membrane translocation.

An important question for bacterial cell division is how the invaginating septum can overcome the turgor force generated by the high osmolarity of the cytoplasm. I suggest that it may not need to. Several studies in Gram‐negative bacteria have shown that the periplasm is isoosmolar with the cytoplasm. Indirect evidence suggests that this is also true for Gram‐positive bacteria. In this case the invagination of the septum takes place within the uniformly high osmotic pressure environment, and does not have (...) to fight turgor pressure. A related question is how the V‐shaped constriction of Gram‐negative bacteria relates to the plate‐like septum of Gram‐positive bacteria. I collected evidence that Gram‐negative bacteria have a latent capability of forming plate‐like septa, and present a model in which septal division is the basic mechanism in both Gram‐positive and Gram‐negative bacteria. (shrink)

Laura Grams - Language and Learning: Philosophy of Language in the Hellenistic Age - Journal of the History of Philosophy 45:1 Journal of the History of Philosophy 45.1 153-154 Muse Search Journals This Journal Contents Reviewed by Laura Grams University of Nebraska at Omaha Dorothea Frede and Brad Inwood, editors. Language and Learning: Philosophy of Language in the Hellenistic Age. Cambridge-New York: Cambridge University Press, 2005. Pp. xi + 353. Cloth, $90.00. This collection of papers on Hellenistic philosophy of language (...) resulted from the ninth Symposium Hellenisticum, held in Hamburg in July 2001. It makes an important contribution to the secondary literature on this topic and will be valuable to anyone who studies Hellenistic philosophy. Because some chapters discuss broader issues in the philosophy of language or connect.. (shrink)

Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.

a vigorous and challenging defence of direct realism in which one gets not only a clear overview of what precisely the problems are, but also a forceful and ...

In Part 1 the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, (...) time, processes, knowledge and belief, obligation and permission. Accessible, authoritative, and assured, Modal Logics and Philosophy requires no more background than the completion of a standard introductory logic course. It will be welcomed not only by students looking for a bridge between introductory logic texts and the high-level technical literature but as a guide to, and exploration of, work at the forefront of logic and philosophy. (shrink)

The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, "Modal Logics and Philosophy" (...) places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission. (shrink)

Robert I. Soare, Automorphisms of the Lattice of Recursively Enumerable Sets. Part I: Maximal Sets.Manuel Lerman, Robert I. Soare, $d$-Simple Sets, Small Sets, and Degree Classes.Peter Cholak, Automorphisms of the Lattice of Recursively Enumerable Sets.Leo Harrington, Robert I. Soare, The $\Delta^0_3$-Automorphism Method and Noninvariant Classes of Degrees.

From the myths of the ancient world to the Middle Ages to Darwin and beyond, Preece captures the most telling and fascinating accounts of humankind's ...

Construed broadly as interpretation theory, hermeneutics could be understood to encompass all modes of interpretation (textual or otherwise), including any kind of literary criticism, from Aristotle's poetics to the New Criticism of the 1950s, as well as the French tradition of structuralism and even perhaps Derridean poststructural thought. Although Gadamer and Ricoeur both recognize the poetic work or, at least, lyric poetry, as belonging to a special class of literature, they do display somewhat different attitudes toward it. For Gadamer, one (...) of the hallmarks of the eminent text is its un‐translatability. That is, all literary works resist translation to one degree or another, but lyric poetry defies it altogether. In Part I of Truth and Method, Gadamer lays out the history of aesthetics and takes issue with the kind of “aesthetic consciousness” that takes the work of art as an object of study. (shrink)

We argue that the Soros account of reflexivity does not provide a clear-cut distinction between a social science such as economics and the physical sciences. It is pointed out that the participants who attempt to learn from refutations of conjectures in the Soros world are likely to be haunted by the Duhem–Quine problem of conjointness of hypotheses and unfocused refutation. On a more constructive note, we argue that models of inductive learning, in which participants form conjectures on the basis of (...) strictly limited information sets, can capture the basic thrust of the Soros position. The conjectures are in motion, as the participants attempt to avoid those that are systematically wrong, and there is something vague and uncertain about what can be learned from experience and refutations. The only notion of market efficiency in this world is one contingent on the strictly limited and varied information sets in play. Finally we present a mathematical model and numerical simulations that help justify the causal relationship between reflexivity and far-from-equilibrium dynamics postulated by Soros. (shrink)

Ever since Saul Kripke and others developed a semantic interpretation for modal logic, 'possible worlds' has been a much debated issue in contemporary metaphysics. To propose the idea of a possible world that differs in some way from our actual world - for example a world where the grass is red or where no people exist - can help us to analyse and understand a wide range of philosophical concepts, such as counterfactuals, properties, modality, and of course, the notions of (...) possibility and necessity. This book examines the ways in which possible worlds have been used as a framework for considering problems in logic and argument analysis. The book begins with a non-technical introduction to the basic ideas of modal logic in terms of Kripke's possible worlds and then moves on to a discussion of 'possible for' and 'possible that'. The central chapters examine questions of meaning, epistemic possibility, temporal logic, metaphysics, and impossibility. Girle also investigates how the idea of a possible world can be put to use in different areas of philosophy, the problems it may raise, and the benefits that can be gained. (shrink)

Ever since Saul Kripke and others developed a semantic interpretation for modal logic, 'possible worlds' has been a much debated issue in contemporary metaphysics. To propose the idea of a possible world that differs in some way from our actual world - for example a world where the grass is red or where no people exist - can help us to analyse and understand a wide range of philosophical concepts, such as counterfactuals, properties, modality, and of course, the notions of (...) possibility and necessity. This book examines the ways in which possible worlds have been used as a framework for considering problems in logic and argument analysis. The book begins with a non-technical introduction to the basic ideas of modal logic in terms of Kripke's possible worlds and then moves on to a discussion of 'possible for' and 'possible that'. The central chapters examine questions of meaning, epistemic possibility, temporal logic, metaphysics, and impossibility. Girle also investigates how the idea of a possible world can be put to use in different areas of philosophy, the problems it may raise, and the benefits that can be gained. (shrink)

First Published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.

In their book, Darwinism Evolving: Systems Dynamics and the Genealogy of Natural Selection, Depew and Weber (1995) argued for the need to address the relationship between self-organization and natural selection in evolutionary theory, and focused on seven “visions” for doing so. Recently, Batten et al. (2008) in a paper in this journal, entitled “Visions of evolution: self-organization proposes what natural selection disposes,” picked up the issue with the work of Depew and Weber as a starting point. While the efforts of (...) both sets of authors are to be commended, there are substantive errors in both the presentations of my work and of my work with colleagues (one of the “visions” discussed) that undermine theirs. My purpose here is to correct the errors in question, thereby removing the undermining effects and in so doing reassert the position my colleagues and I first advanced more than two decades ago, and that I still stand by and argue for today. The central points are as follows: (1) Self-organization or spontaneous ordering is a process of selection; (2) this selection process is governed by a “physical selection principle”; (3) this principle is the law of maximum entropy production; and (4) natural selection is a special case where the components are replicating. (shrink)

We classify the asymptotic densities of the sets according to their level in the Ershov hierarchy. In particular, it is shown that for, a real is the density of an n‐c.e. set if and only if it is a difference of left‐ reals. Further, we show that the densities of the ω‐c.e. sets coincide with the densities of the sets, and there are ω‐c.e. sets whose density is not the density of an n‐c.e. set for any.

In their book, Darwinism Evolving: Systems Dynamics and the Genealogy of Natural Selection, Depew and Weber argued for the need to address the relationship between self-organization and natural selection in evolutionary theory, and focused on seven “visions” for doing so. Recently, Batten et al. in a paper in this journal, entitled “Visions of evolution: self-organization proposes what natural selection disposes,” picked up the issue with the work of Depew and Weber as a starting point. While the efforts of both sets (...) of authors are to be commended, there are substantive errors in both the presentations of my work and of my work with colleagues that undermine theirs. My purpose here is to correct the errors in question, thereby removing the undermining effects and in so doing reassert the position my colleagues and I first advanced more than two decades ago, and that I still stand by and argue for today. The central points are as follows: Self-organization or spontaneous ordering is a process of selection; this selection process is governed by a “physical selection principle”; this principle is the law of maximum entropy production; and natural selection is a special case where the components are replicating. (shrink)