We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.

Let us show how property is grasped as an institutional fact. If Jones steals a computer, he does not own it in the sense of property, but only exercises control towards it. If he buys the computer, he controls it too, and moreover owns it in the sense of property. In other words, simply exercising control towards something is a brute fact. This control counts asproperty only in a certain context: the computer counts as Jones’s property only if he got (...) it through a licit transfer. This is why property is not a brute fact, and is therefore an institutional fact. The same kind of reasoning applies to privacy. When a personal information P about Jones is openly diffused, it seems that P becomes public. From this point of view, a violation of privacy equates to a publication. The problem about this account is the following: who would call “publication of a book” the hacking of it on its author’s computer? No one, because the word “publication” is an institutional word that only refers to a licit diffusion. Considering this answer, we may conclude as follows: if the diffusion of P is illicit, P still countsas private, even if everyone knows about it. If that conclusion is true, privacy is an institutional fact. (shrink)

Is the societal-level of analysis sufficient today to understand the values of those in the global workforce? Or are individual-level analyses more appropriate for assessing the influence of values on ethical behaviors across country workforces? Using multi-level analyses for a 48-society sample, we test the utility of both the societal-level and individual-level dimensions of collectivism and individualism values for predicting ethical behaviors of business professionals. Our values-based behavioral analysis indicates that values at the individual-level make a more significant contribution to (...) explaining variance in ethical behaviors than do values at the societal-level. Implicitly, our findings question the soundness of using societal-level values measures. Implications for international business research are discussed. (shrink)

When we talk about Presocratic philosophy, we are speaking about the origins of Greek philosophy and Western rationality itself. But what exactly does it mean to talk about “Presocratic philosophy” in the first place? How did early Greek thinkers come to be considered collectively as Presocratic philosophers? In this brief book, André Laks provides a history of the influential idea of Presocratic philosophy, tracing its historical and philosophical significance and consequences, from its ancient antecedents to its full crystallization in (...) the modern period and its continuing effects today. Laks examines ancient Greek and Roman views about the birth of philosophy before turning to the eighteenth-century emergence of the term “Presocratics” and the debates about it that spanned the nineteenth and twentieth centuries. He analyzes the intellectual circumstances that led to the idea of Presocratic philosophy—and what was and is at stake in the construction of the notion. The book closes by comparing two models of the history of philosophy—the phenomenological, represented by Hans-Georg Gadamer, and the rationalist, represented by Ernst Cassirer—and their implications for Presocratic philosophy, as well as other categories of philosophical history. Other figures discussed include Plato, Aristotle, Cicero, Diogenes Laertius, Schleiermacher, Hegel, Nietzsche, Max Weber, and J.-P. Vernant. Challenging standard histories of Presocratic philosophy, the book calls for a reconsideration of the conventional story of early Greek philosophy and Western rationality. (shrink)

This paper reviews the origin of inertia according to Mach's principle and Weber's law of gravitation. The resulting theory is based on simultaneous nonlocal gravitational interactions between particles in the solar system and others in the remote universe beyond the Milky Way galaxy. It explains the precession of the perihelion of Mercury. A most important implication of the Mach-Weber theory of the force of inertia is the necessity for a large amount of uniformly distributed matter in the galactic (...) universe. This matter could be the source of the cosmic background radiation. Nonlocal inertia forces are compatible with a static universe and also with an expanding universe but the latter would demand slow changes in the mass of particles and the gravitational constant. (shrink)

Le développement conjoint, au cours du XVIIIe siècle, de la méthode historico-critique et du perspectivisme est à l'origine d'une tension nouvelle dans le traitement de l'histoire de la philosophie. L'article analyse brièvement quelques réactions, plus ou moins radicales, à cette configuration féconde. Zeller, Dilthey, Yorck, Nietzsche, Weber, Heidegger, Rorty, sont les principaux témoins. Il est aussi suggéré que la « doxographie », en dépit de la réputation détestable dont elle jouit, aussi bien chez les historiens que chez les philosophes, (...) demeure une composante importante de toute réflexion sur la relation de la philosophie à son passé. The joint development, in the course of the XVIIIth century, of the historico-critical method on the one hand and of a self-conscious perspectivism on the other hand, created a new tension in the handling of the history of philosophy. In the following, I sketch some characteristic ways, hard or more compromising, of dealing with this lasting and, I suggest, productive tension. Zeller, Dilthey, Yorck, Nietzsche, Weber, Heidegger, Rorty are my main witnesses. In the wake of an analysis made by M. Frede, I also suggest, in the light of this tension, that « doxography », despite the detestable reputation the genre has among philosophers and historians of philosophy alike, remains an important component of any reflexion about the relationship between philosophy and its past. (shrink)

Os oitenta anos de Jürgen Habermas deram lugar a um grande númerode publicações, sublinhando a influência profunda e extensa de sua obra emvários domínios do pensamento contemporâneo: epistemologia, ética, filosofiapolítica, filosofia do direito, sociologia, psicologia social. Essas influências vêmtambém do fato de que o percurso intelectual de Habermas cruzou muitosoutros caminhos, seja em relação à história da filosofia (Kant, Hegel ouMarx, por exemplo), seja com respeito aos pensadores contemporâneos comquem ele travou diálogos fecundos e que marcaram momentos de sua própriaproblemática (...) (a Escola de Frankfurt, Apel, Putnam, Rorty...). Neste volume,encontraremos as figuras importantes de Rousseau, Kant, Peirce, Weber,Mead, Rawls, Foucault, Giddens e Pettit, e várias perspectivas disciplinares.O conjunto dá uma boa ideia da riqueza do pensamento de um filósofo quenunca deixou de dialogar, pondo em prática sua teoria do agir comunicativo. (shrink)

The key to understanding ourselves and the disenchantment of our world, is in fact the age-old logic of religion. This thesis is at the heart of the thought of Marcel Gauchet. For Gauchet, the growing departing from religion that characterises contemporary Western culture is made possible by the logic of religion itself, through its different historical re-articulations, in close interplay with the logic of the political it has given rise to. In a sense, this logic continues to shape our social (...) universe, but now in a way exactly opposite to its original form. The disenchantment of the world is thus not a movement againstreligion, but on the contrary a movement made possible by religion itself. Christianity especially has played a central rôle in all this: it is, in the famous formulation of Gauchet, “the religion for the departing from religion”. In this article, this whole complex movement is reconstructed in its essential steps: the rise of the state and its revolutionary implications for religion, the growth of the ‘higher religions’ and the dynamics of transcendence, the specificity of Christianity , opening up the possibility of a radically new and now disenchanted articulation of autonomy and heteronomy. Further, the background is examined from which Gauchet’s theory has taken shape , as well as the relation between Gauchet and other ‘theories of secularisation’, such as those of Weber, Blumenberg or Löwith. A critical assessment is made of Gauchet’s ‘political’ reading of religion, of its methodological presuppositions, and of his definition of ‘religion’ itself. Finally, the question is raised as to the future of religion according to this theory, and especially the future of Christianity. (shrink)

Proceedings of the conference 'A Clearing _of_ the German Forest: Mysticism, Idealism and Romanticism', with contributions by Jens Halfwassen, Johann Kreuzer, Glenn A. Magee, Christian Danz, et al., concerning the relationship of Fichte, Hegel, Hölderlin and Schelling with the most important German mystics. Akten der Tagung 'Eine Lichtung _des_ deutschen Waldes: Mystik, Idealismus und Romantik', mit Beiträgen von Jens Halfwassen, Johann Kreuzer, Glenn A. Magee, Christian Danz, usw., das Verhältnis von Fichte, Hegel, Hölderlin und Schelling zu den zentralen Autoren der (...) deutschen Mystik betreffend. (shrink)

We comment on and translate Gustav Kirchhoff's important paper of 1857 entitled On the motion of electricity in conductors. The significance of this paper is that Kirchhoff proved with action at a distance that electric disturbances travel along wires of negligible resistance with the velocity of light. He accomplished this with the laws of Newtonian electrodynamics (Coulomb, Ampere, F. Neumann and Weber) before Maxwell had formulated his equations.

While developments of a shared intellectual tradition, the enactivist approach and the organizational account proffer importantly different accounts of organismic normativity. Where enactivists tend to follow Hans Jonas, Andres Weber, and Francisco Varela in grounding intrinsic affordance norms in existential concern, organizational theorists such as Alvaro Moreno, Matteo Mossio, and Leonardo Bich seek a more deflationary account of these normative phenomena. Critiques directed at both of these accounts of organismic normativity motivate the introduction of the precedential account of organismic (...) normativity, which I nevertheless locate within the enactivist approach, broadly construed. After detailing empirical evidence that would seem to vindicate the precedential account, I explore some of its implications. (shrink)

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts (...) and methods originating from randomness enrich computability theory.The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory. (shrink)

There is evidence of persistent inequalities in household financial protection of health and drugs spending in Latin America. Despite the expansion of coverage, strong inequalities persist in access to health and family spending on drugs in the region. Out-of-pocket spending in medicines is regressive in greater need for affordable medicines.

In honour of Detlef Dürr, we report on a mathematical rigorous computation of the electric vacuum polarisation current and extract the well-known expression for the second order perturbation. Intermediate steps in the presented calculation demonstrate, to the knowledge of the authors for the first time, mathematical rigorous versions of the combined dimensional and Pauli-Villars regularisation schemes. These are employed as computational tools to infer convenient integral representations during the computation. The said second order expression is determined up to a remaining (...) degree of freedom of a real number–without ill-defined terms from start to end. (shrink)

IN the last decade deliberative democracy has developed rapidly from a “theoretical statement” into a “working theory.”1 Scholars and practitioners have launched numerous initiatives designed to put deliberative democracy into practice, ranging from deliberative polling to citizen summits.2 Some even advocate deliberation as a new “revolutionary now.”3 Deliberative democracy has also experienced the beginning of an empirical turn, making significant gains as an empirical (or positive) political science. This includes a small, but growing body of literature tackling the connection between (...) the normative standards of deliberation, how well they are met, and the empirical consequences of meeting them.4 This trend has, for instance, included the use of methods and frameworks borrowed from other fields, such as political and social psychology. Such studies suggest that cases approaching ideal deliberation are rare, but that group interaction sometimes works surprisingly well according to such ideals.5. (shrink)

Moral reasoning typically informs environmental decision-making by measuring the possible outcomes of policies or actions in light of a preferred ethical theory. This method is subject to many problems. Environmental pragmatism tries to overcome them, but it suffers also from some pitfalls. This paper proposes a new method of environmental pragmatism that avoids the problems of both the traditional method of environmental moral reasoning and of the general versions of environmental pragmatism. We call it 'justificatory moral pluralism' - it develops (...) the intuition that normative ethical theories need not be mutually exclusive. This leaves room for important forms of pluralist environmental ethics that do not require a once-and-for-all prior commitment to an ethical theory when deciding about policies or courses of action related to the protection of the environment. Justificatory moral pluralism offers a viable solution to the recurrent conflicts between efficient environmental decisions and the need for moral reasoning. (shrink)

The Antecedent-Behavior-Consequence (ABC)-analysis is a tool for analyzing behavior and stems from the field of psychology where it is used as a tool for the understanding of behavior in general and organizational behavior in particular. In this paper the ABC-analysis is implemented as a tool to understand why people behave ethically in organizations, through the identification of key environmental factors that cause such behavior. This analysis can be the first step to recognizing the complexity of circumstances determining ethical behavior, as (...) well as trigger for changing that behavior. This will be elaborated in the implementation process of an ethical code. The working of the ABC-analysis will be illustrated with an example derived from field research concerning the reorganization of a department of a chemical company. (shrink)

We explore the notion that culture influences people’s values, and their subsequent ideologies and ethical behaviors. We present the idea that culture itself changes with time, and explore the influence of culture and generational markers on consumer ethics by examining differences in these ethical dimensions between Australians, Indonesians, and Indonesian Migrants in Australia, as well as differences between Generation X versus Generations Y and Z. The present study addresses the need to investigate the role that culture plays in consumer ethics, (...) and the interaction between culture and generational attitudes in determining consumer ethics. Results established a distinct multiculturality in our three cultural samples, including a generational cohort differences. This suggests that culture and generational markers influence ethical beliefs, ideologies, and consumer ethics. It further indicates that Indonesian Migrants have acculturated to Australian society both in terms of their values and consumer behaviors, illustrating a crossvergence effect; scores indicate that these Migrants have the highest cultural intelligence among our samples. Implications of the findings for consumer ethics theory and practice are considered and future directions identified. (shrink)

Pierre André,Michel Bourban | : Dans un contexte d’urgence, les philosophes ne peuvent plus se contenter d’élaborer des théories idéales de la justice climatique fondées sur des motivations purement morales. Il est désormais nécessaire d’envisager des approches non idéales. Nous proposons ici de prendre au sérieux le problème de la motivation à l’action et nous mettons en avant certains motifs prudentiels pour lutter contre le changement climatique, en vue non pas de remplacer, mais de renforcer les motivations morales existantes, (...) mais insuffisantes. Nous commençons par présenter trois grandes approches idéales qui ont prévalu jusqu’ici dans la recherche sur la justice climatique et sont fondées respectivement sur l’éthique déontologique, sur l’éthique des vertus et sur l’utilitarisme. Nous mettons en évidence leurs limites pratiques, en ciblant le problème de la motivation à l’action. Nous proposons ensuite quelques pistes pour résoudre ce problème en esquissant une approche non idéale de la justice climatique. Cette approche est centrée sur les motivations amorales ressortant de l’examen attentif des perturbations systémiques globales et des contextes nationaux et locaux spécifiques. Elle est à notre sens incontournable pour motiver les États-nations, les entreprises et les individus. Il s’agit cependant moins de la substituer totalement aux théories idéales de la justice climatique que de compléter celles-ci pour établir une vision plus compréhensive qui distingue le problème de la justification morale de celui de la motivation. | : In a situation of urgency, philosophers can no longer rely exclusively on ideal theories of climate justice grounded on purely moral motives. It has become necessary to build nonideal approaches. We propose to give serious consideration to the problem of motivation to act by putting forward some prudential reasons for tackling climate change—with the aim not of replacing existing but inadequate moral motivations, but of strengthening them. First, we identify three major ideal approaches that have so far prevailed in climate justice research, grounded respectively on deontological ethics, on virtue ethics, and on utilitarianism. We highlight their practical limitations, particularly with regards to the problem of motivation to act. Second, we open the way for an alternative nonideal approach to climate justice based on amoral motivations issuing from a careful examination of global systemic disruptions as well as of specific national and local situations. This approach cannot be ignored if one wishes to motivate nation-states, corporations, and individuals to act. However, our goal is not to replace ideal theory with nonideal theory, but rather to complete the former with the latter for a more comprehensive account of climate justice that distinguishes the problem of moral justification from the problem of motivation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Was Hume An Atheist? Shane Andre Hume's philosophy of religion, as expressed in the Dialogues Concerning Natural Religion, the Natural History of Religion, and sections 10 and 11 ofthe Enquiry ConcerningHuman Understanding,1 invites a number of diverse interpretations. At one extreme are those who see Hume as an "atheist"2 or "anti-theist."3 At the other extreme are those who see Hume as some kind of theist, though not a classical (...) or orthodox one.4 In between are others for whom Hume is an "agnostic* or "ironic skeptic."6 Still a fourth interpretation can be found, according to which Hume "seems to vacillate hopelessly" in his view ofreligion;7 in other words, no coherent philosophy ofreligion can be found in his work and so it is futile to look for one. Ofthe four alternatives, it seems to me that the fourth, being less interesting philosophically and less to Hume's credit as a major philosopher, should be rejected unless by default no coherent case can be made for one of the other three. Since I believe that Hume's views about the nature and existence of God are complex, somewhat unconventional, but still coherent, I will concentrate on the title question. Before tackling that question directly, however, we need to clarify the meaning of the term "atheist" and its cognates. While an atheist is popularly defined as one who does not believe in God, this definition is inadequate for two reasons. First, while the absence of belief is sometimes treated as a synonym for disbelief, it is clear that the two are not the same. An infant does not believe in God, but that does not make him an atheist,8 for, as yet, he does not have the linguistic competence to reflect on the question, Does God exist? Neither is the agnostic an atheist, for, though he has reflected on the question, he has not found reason to answer it affirmatively, Uke the theist, or negatively, like the atheist. For this reason, the atheist must be characterized more strongly, as one who disbelieves that God exists. But even this stronger characterization is insufficient, for, as is well-known but perhaps less widely takeninto account, there are many different conceptions ofGod, ranging from monotheism to polytheism, from beUef in a perfect being to belief in a being who shares some human limitations, from deism to pantheism, and so on. Accordingly, it has become commonplace in philosophy to recognize at least two senses ofthe term "God": a narrow sense, signifying "a supremely good being, creator of but separate from and independent of the world, omnipotent, omniscient, eternal and self-existent";9 and a wide sense, Volume XLX Number 1 141 SHANE ANDRE signifying one or more divine beings, personal or otherwise, manifesting extraordinarybut perhaps not superlative properties. For short, we could call the narrow sense the standard concept ofGod, and beliefin the existence ofsuch a being standard theism.10 And we could call the broad sense, applicable to any concept of the divine, the extended concept of God, and belief in the existence of such a being(s) extendedtheism. On this account, standard theists will alsobe extended theists, but of course someone could be an extended theist without being a standard theist. Let us call such a person (for example, Epicurus, who denied, not that the Gods exist, but that they intervene in human affairs) a limited theist. It is important to note that the limited theist rejects standard theism but is not an atheist simpliciter. How does recognition of these different forms oftheism affect our understanding of atheism? There seem to be two major possibilities. One is to characterize atheism in the narrow sense as disbeUef in standard theism; the other is to characterize it in the broad sense as disbeliefin any form of theism, including limited theism. While either option is open, it seems to me that the latter is preferable. For ifwe say that anyone who rejects standard theism is an atheist, we will end up with the paradoxical result that many distinguished theists will turn out to be atheists. For example, while Charles Hartshorne is not a standard theist, insofar as he rejects the... (shrink)

The philosophy problem of identity and the related problem of change go back to the ancient Greek philosophers and fascinated later figures including Leibniz, Locke and Hume. Heraclitus argued that one could not swim in the same river twice because new waters were ever flowing in. When is a river not the same river? If one removes one plank at a time when is a ship no longer a ship? What is the basic nature of identity and persistence? This book (...) introduces and asseses the philosophical puzzles posed by things persisting through time. Beginning with essential historical background to the problem it explores the following key topics and debates: mereology and identity, including 'Leibniz's Law' the constitution view of identity the 'relative identity' argument concerning identity temporary identity four-dimensionalism, counterpart and mulitiple counterpart theory supervenience the problem of temporary intrinsics the necessity of identity presentism ontological and epistemological criteria for persistence and the difference between them. Including chapter summaries, annotated further reading and a glossary this book is essential reading for anyone seeking a clear and informative introduction to and assessement of the metaphysics of identity. (shrink)

The biinterpretability conjecture for the r.e. degrees asks whether, for each sufficiently large k, the [Formula: see text] relations on the r.e. degrees are uniformly definable from parameters. We solve a weaker version: for each k ≥ 7, the [Formula: see text] relations bounded from below by a nonzero degree are uniformly definable. As applications, we show that Low 1 is parameter definable, and we provide methods that lead to a new example of a ∅-definable ideal. Moreover, we prove that (...) automorphisms restricted to intervals [d, 1], d ≠ 0, are [Formula: see text]. We also show that, for each c ≠ 0, can be interpreted in [0, c] without parameters. (shrink)

We investigate the upper semilattice Eq* of recursively enumerable equivalence relations modulo finite differences. Several natural subclasses are shown to be first-order definable in Eq*. Building on this we define a copy of the structure of recursively enumerable many-one degrees in Eq*, thereby showing that Th has the same computational complexity as the true first-order arithmetic.

Most professionals have the arduous task of managing their own dual loyalty: in one contextual relationship, they are members of a profession while simultaneously they are employed as members of a locally established organisation. This sense of a dual loyalty has to be taken into account when professional bureaucracies develop ethics programmes. This article focuses on universities. Accounting for the dual loyalty of academic professionals, it is the objective of the study to contribute to the most appropriate ethics programmes in (...) such an academic context. Based on a review of the literature, we identify which ethical issues commonly emerge in educational and research activities. Then we offer a conceptual analysis of the conditions required for each different strategy of ethics management. We argue that none of the four theoretically derived strategies is applicable solely on its own. For universities it is most promising to design ethics programmes based on the guiding values of the academic community, including integrity measures for universities and corrective measures for students. The argument developed in this article is assumed to be widely applicable in assessing the appropriateness of ethics management strategies in other professional settings. (shrink)

European Journal of Political Theory, Volume 21, Issue 2, Page 368-389, April 2022. Epistemic impairment has been the decisive yardstick when excluding infants from political agency. One of the suggestions to bypass the epistemic requirement of political agency and to encourage the inclusion of infants in representative democracies is to resort to proxies or surrogates who share or advocate interests which may be coincidental with their interests. However, this solution is far from desirable, given that it privileges the political agency (...) of parents, guardians and trustees over other adult citizens. This article offers an alternative to this conceptual frame of reference by making a case for the political agency of infants. Firstly, it maintains that political agency can be understood in terms of the several facets involved in political representation. Secondly, it claims that the all-affected principle can be reformulated as an ‘infant-affected-interests principle’ in light of which infants are members of the class of the represented. Thirdly, it explores the ways through which this political agency can occur without having to resort to alternative conceptions of representation. The conclusion ascertains that infant enfranchisement is highly undesirable and that there are more viable forms to promote infant political agency, such as virtual representation, infant-beneficial principles of political action and ombudspersons for infants. (shrink)

Em Parmênides 132b-c é afirmado que se as Ideias fossem pensamentos, então as coisas que participam nelas também seriam pensamentos. A afirmação soa estranha dentro da dinâmica,apresentada no corpus platonicum, da “participação” dos entes sensíveis nas Ideias; todavia, não parece simples determinar o motivo desta estranheza. A chave do problema pode ser uma identificação dos tipos de qualidades das Ideias ou Formas nteligíveis que estão implicados na “participação”. Vários especialistas trataram da matéria na segunda metade do século XX (OWEN, 1968; (...) KEYT, 1969 e 1971; VLASTOS, 1972), tendo sempre como ponto de partida a distinção de qualidades das Ideias traçada no texto dos Tópicos de Aristóteles (137b3-13). Nesse sentido, o presente artigo: i) apresenta os conceitos utilizados no tratamento desta matéria pelos exegetas: “atributos ideais”, “atributos próprios”, “Distinção-P”, “Predicação Paulina”, “Predicação Ordinária” e “Autopredicação”; ii) explica a incompatibilidade da distinção aristotélica de qualidades das Ideias (“Distinção-P”) com a ontologia apresentada nos próprios diálogos platônicos (VLASTOS, 1972 e 1973; CHERNISS, 1944); iii) sugere uma nova “Distinção-P”, mostrando sua compatibilidade com essa ontologia; iv) aplica-a ao caso daquela afirmação sobre as Ideias de Parmênides 132b-c, demonstrando a utilidade dessa distinção pela elucidação que ela promove da dinâmica da “participação” nessa passagem. (shrink)

§1. Introduction. Natural sets that can be enumerated by a computable function always seem to be either actually computable or of the same complexity as the Halting Problem, the complete r.e. set K. The obvious question, first posed in Post [1944] and since then called Post's Problem is then just whether there are r.e. sets which are neither computable nor complete, i.e., neither recursive nor of the same Turing degree as K?Let be the r.e. degrees, i.e., the r.e. sets modulo (...) the equivalence relation of equicomputable with the partial order induced by Turing computability. This structure is a partial order with least element 0, the degree of the computable sets, and greatest element 1 or 0′, the degree of K. Post's problem then asks if there are any other elements of.The solution of Post's problem by Friedberg [1957] and Muchnik [1956] was followed by various algebraic or order theoretic results that were interpreted as saying that the structure was in some way well behaved:Theorem 1.1. Every countable partial ordering or even uppersemilattice can be embedded into.Theorem 1.2. For every nonrecursive r.e. degreeathere are r.e. degreesb, c < asuch thatb ∨ c = a.Theorem 1.3. For every pair of nonrecursive r.e. degreesa < bthere is an r.e. degreecsuch thata < c < b. (shrink)

We show that the elementary theory of the recursively enumerable tt-degrees has the same computational complexity as true first-order arithmetic. As auxiliary results, we prove theorems about exact pairs and initial segments in the tt-degrees.