Sickle cell haemoglobin polymerization reduces erythrocyte deformability, causing deleterous vaso-occlusions. The double-nucleation model states that polymers grow from HbS aggregates, the nuclei, in solution , onto existing polymers . When linearized at initial HbS concentration, this model predicts early polymerization and its characteristic delay-time :591–610, 611–631, 1985). Addressing its relevance for describing complete polymerization, we constructed the full, non-linearized model . Here, we compare the simulated outputs to experimental progress curves . Within 10% from start, average root mean square deviation (...) between simulated and experimental curves is 0.04 ± 0.01 . Conversely, for complete progress curves, averaged rms is 0.48 ± 0.04. This figure is improved to 0.13 ± 0.01 by adjusting heterogeneous pathway parameters : the nucleus stability , and the fraction of polymer surface available for nucleation , from 5e−7, to 13 . Similar results are obtained at 37°C. We conclude that the physico-chemical description of heterogeneous nucleation warrants refinements in order to capture the whole HbS polymerization process. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Mary as the Exemplar of the Body's PovertyAngela FranksRecent MariologyFollowing the trajectory of Mariology and Marian devotion for the last century or so is enough to give one whiplash. On the one hand, the declaration of the doctrine of Mary's Assumption in 1950 by Pope Pius XII represents a strand of Mariology that emphasizes her divinely granted prerogatives and glory. In popular piety, this dogmatic emphasis was mirrored by (...) devotional practices that stressed Mary's mediatorial power.1 On the other hand, many theologians were concerned that such teaching and practice obscured the centrality of Christ, the Church, and the liturgy in Christian life.2 One could see the placing of Mary within chapter 8 of Lumen Gentium less than fifteen years after the declaration of the Assumption as a rebalancing of Mariology. Lumen Gentium (LG) resituated Mary within the doctrine of the Church, echoing patristic equations of Our Lady with the Church.3 One unintended effect of the conciliar move, however, was to make devotion to Mary seem unnecessary, despite the efforts of [End Page 1097] post-conciliar popes to encourage Marian piety—in particular, John Paul II, with his Marian motto Totus Tuus.John Paul II is in many ways an exemplar of conciliar Marian devotion. His Mariology integrates Mary into ecclesiology by emphasizing her role as the paradigmatic follower of Christ.4 This discipleship is, he is careful to say, due to her maternal role and the extraordinary graces that followed from it.5 But these graces did not eliminate her need to follow her son closely; rather, they made such discipleship possible.This interplay between Mary's need and the unique graces granted to meet that need is perhaps clearest in John Paul II's presentation of Mary's faith.6 This attitude of faith is "central" to John Paul II's presentation of Mary in the encyclical Redemptoris Mater (RM), according to Joseph Ratzinger.7 Because of her faith, which is based on the prior action of God in her life (§38, quoting LG §60), she is due "a wealth of praise" that "is more than ever necessary today" (RM §34). In John Paul II, the seeming either-or of twentieth-century Mariology is dissolved, but through the introduction of a causal relationship between the two. In other words, [End Page 1098] Mary's poverty—her need for and receptivity to God—is what makes her able to be rich, to be worthy of a wealth of praise.Perhaps surprisingly, John Paul Il's presentation of Mary as transparent to the mystery of Christ echoes his theology of the body. There, he repeats a hylomorphic maxim: "The body reveals the person." In this revelation, the poverty and the wealth of the body coincide. The body is of great dignity: it can reveal the person. But it is also poor, because it does not reveal itself but rather is transparent to the inner personal mystery. In this, it resembles Mary.This essay will pick up the trail laid down by John Paul II by examining Mary under the rubric of her poverty. Her poverty, I will argue, is exemplary for the poverty of the body, and neither Mary nor the body can be understood properly without understanding poverty. In this essay, I will explore these topics by looking at the Mariology of John Paul II and Hans Urs von Balthasar, before turning to what this Mariology means for the body and for creation in general.Mary's PovertyRedemptoris Mater presents Mary as a model of pilgrim faith, one who "goes before" us on the pilgrimage (RM §§5–6 and 25–28). Mary's reliance upon faith places her among the anawim, the poor of the Lord. John Paul II quotes §55 of Lumen Gentium to note that Mary "stands out among the poor and humble of the Lord, who confidently await and receive salvation from him" (RM §§8 and 11). As the Congregation for the Doctrine of the Faith under Joseph Ratzinger wrote around the time of the Marian encyclical, she is "totally dependent upon God and completely directed towards him, and at the side of her Son, she is... (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)

We prove that the continuous function${\rm{\hat \Omega }}:2^\omega \to $ that is defined via$X \mapsto \mathop \sum \limits_n 2^{ - K\left} $ for all $X \in {2^\omega }$ is differentiable exactly at the Martin-Löf random reals with the derivative having value 0; that it is nowhere monotonic; and that $\mathop \smallint \nolimits _0^1{\rm{\hat{\Omega }}}\left\,{\rm{d}}X$ is a left-c.e. $wtt$-complete real having effective Hausdorff dimension ${1 / 2}$.We further investigate the algorithmic properties of ${\rm{\hat{\Omega }}}$. For example, we show that the maximal (...) value of ${\rm{\hat{\Omega }}}$ must be random, the minimal value must be Turing complete, and that ${\rm{\hat{\Omega }}}\left \oplus X{ \ge _T}\emptyset \prime$ for every X. We also obtain some machine-dependent results, including that for every $\varepsilon > 0$, there is a universal machine V such that ${{\rm{\hat{\Omega }}}_V}$ maps every real X having effective Hausdorff dimension greater than ε to a real of effective Hausdorff dimension 0 with the property that $X{ \le _{tt}}{{\rm{\hat{\Omega }}}_V}\left$; and that there is a real X and a universal machine V such that ${{\rm{\Omega }}_V}\left$ is rational. (shrink)

Does the universe embody beautiful ideas? Artists as well as scientists throughout human history have pondered this "beautiful question." With Nobel laureate Frank Wilczek as your guide, embark on a voyage of related discoveries, from Plato and Pythagoras up to the present. Wilczek's groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. In fact, every major advance in his career came from this intuition: to assume that the universe (...) embodies beautiful forms, forms whose hallmarks are symmetry--harmony, balance, proportion--and economy. There are other meanings of "beauty," but this is the deep logic of the universe--and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring. As he reveals here, this has been the heart of scientific pursuit from Pythagoras, the ancient Greek who was the first to argue that "all things are number," to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentieth-century physics. Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. Yes: the world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.--From publisher description. (shrink)

One of our great contemporary scientists presents ten insights that illuminate what every thinking person needs to know about what the world is and how it works. Nobel Prize winner Frank Wilczek's Fundamentals is built around a simple but profound idea: the models of the world we construct as children are practical and adequate for everyday life, but they do not bring in the surprising and mind-expanding revelations of modern science. To do that, we must look at the world (...) anew, combining clear thinking with an openness to wonder. This "born again" world is in many ways larger, fuller, and much stranger than it appears. Through an exploration of space, time, matter, and ideas--and equipped with facts, questions, and brilliant speculations--Wilczek guides us through the past, present, and future of fundamental science. Readers will emerge with an expanded vision of our universe. Author Bio: Frank Wilczek won the Nobel Prize in Physics in 2004 for work he did as a graduate student. He was among the earliest MacArthur fellows, and has won many awards both for his scientific work and his writing. He is the author of A Beautiful Question, The Lightness of Being, Fantastic Realities, Longing for the Harmonies, and hundreds of articles in leading scientific journals. His "Wilczek's Universe" column appears regularly in the Wall Street Journal. Wilczek is the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology, founding director of the T. D. Lee Institute and chief scientist at the Wilczek Quantum Center in Shanghai, China, and a distinguished professor at Arizona State University and Stockholm University. (shrink)

Die {raquo}Revolution der Denkart{laquo} hat nicht nur den Anlauf genommen, welchem sie ihren Namen verdankt.! Gezahlt werden noch weitere Umstellungen der Theorie bildung als bloG die kopernikanische Kants. Hier interessieren gleich zwei. Die eine liefert den Gegenstand, die entsprechende, RevolutionPhanomenologie.

**** Reprint of the Indiana U. Press edition of 1966--which is cited in BCL3. Annotation copyright by Book News, Inc., Portland, OR.

Although declarations of the death of God seem to be provocations announcing the end of the era of theology, this announcement is actually central to the Christian revelation in its most classic forms, as well as to its reworkings in contemporary religious thought. Indeed provocative new possibilities for thinking theologically open up precisely in the wake of the death of God. Already Hegel envisaged a revolutionary new realization of divinity emerging in and with the secular world through its establishment of (...) a total order of immanence. However, in postmodern times this comprehensive order aspired to by modern secularism implodes or cracks open towards the wholly Other. A hitherto repressed demand for the absolute difference of the religious, or for “transcendence”, returns with a vengeance. This difference is what could not be stated in terms of the Hegelian System, for reasons that poststructuralist writers particularly have insisted on: all representations of God are indeed dead. Yet this does not mean that they cannot still be powerful, but only that they cannot assign God any stable identity. Nietzsche’s sense of foreboding concerning the death of God is coupled with his intimations of the demise of representation and “grammar” as epistemologically bankrupt, but also with his vision of a positive potential for creating value in the wake of this collapse of all linguistically articulated culture. He points the way towards the emergence of a post-secular religious thinking of what exceeds thought and representation. (shrink)

Der Übergang vom Verhältnisbewußtsein zum Selbstbewußtsein kann unmöglich nur vom Verhältnisbewußtsein aus gedacht werden, weil wir uns eine Welt, in der das Bewubtsein unserer selbst verteilt ist auf die Dimensionen der Handlung vor deren Zentrierung in uns, gar nicht vorstellen können. Jedes Tableau der Handlungsmöglichkeiten, so abstrakt es auch abgefaßt sein mag, ist gebunden an Vorstellungen möglicher Handlungssubjekte, denen wir Handlungsmöglichkeiten zuschreiben. Handlungstheorie ist daher notwendig Reflexion unserer Praxis, in der wir uns selbst als Selbstbewußtsein erfahren, das seinem Verhältnisbewubtsein enthoben (...) ist, ohne dieses dadurch selbst schon aufzuheben zu können. Daß uns Freiheit im Handeln unaufhebbar prekär und problematisch bleiben mub, ist die Grundvoraussetzung dafür, dab wir Handlungstheorien historisch und bereichsbezogen ständig neu entwerfen müssen. Das Verhältnis von Handlungsphilosophie zu Handlungstheorien kann daher so gefaßt werden, daß Handlungsphilosophie die Grundbegrifflichkeit in kritischer Absicht bereitstellt, die den bereichsorientierten, mehr oder weniger deskriptiven Handlungstheorien abgehen muß. Dazu muß die ontologische Differenz von Handlung und Interpretation methodologisch ernst genommen werden. Die radikale Andersheit der hier zu begründenden Konzeption liegt vor allem in der Ansicht, daß Handlungen nicht als isolierbare Ereignis-Entitäten aufgefaßt werden können, die gegenüber der »Welt der Tatsachen des Bewußtseins« eine kausale, d.h. von der Welt des Bewußtseins abgetrennte Rolle übernehmen. (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Some properties are causally relevant for a certain effect, others are not. In this paper we describe a problem for our understanding of this notion and then offer a solution in terms of the notion of a program explanation.

In this paper, I consider the relationship between Inference to the Best Explanation and Bayesianism, both of which are well-known accounts of the nature of scientific inference. In Sect. 2, I give a brief overview of Bayesianism and IBE. In Sect. 3, I argue that IBE in its most prominently defended forms is difficult to reconcile with Bayesianism because not all of the items that feature on popular lists of “explanatory virtues”—by means of which IBE ranks competing explanations—have confirmational import. (...) Rather, some of the items that feature on these lists are “informational virtues”—properties that do not make a hypothesis \ more probable than some competitor \ given evidence E, but that, roughly-speaking, give that hypothesis greater informative content. In Sect. 4, I consider as a response to my argument a recent version of compatibilism which argues that IBE can provide further normative constraints on the objectively correct probability function. I argue that this response does not succeed, owing to the difficulty of defending with any generality such further normative constraints. Lastly, in Sect. 5, I propose that IBE should be regarded, not as a theory of scientific inference, but rather as a theory of when we ought to “accept” H, where the acceptability of H is fixed by the goals of science and concerns whether H is worthy of commitment as research program. In this way, IBE and Bayesianism, as I will show, can be made compatible, and thus the Bayesian and the proponent of IBE can be friends. (shrink)

Frank Ramsey was the greatest of the remarkable generation of Cambridge philosophers and logicians which included G. E. Moore, Bertrand Russell, Ludwig Wittgenstein and Maynard Keynes. Before his tragically early death in 1930 at the age of twenty-six, he had done seminal work in mathematics and economics as well as in logic and philosophy. This volume, with a new and extensive introduction by D. H. Mellor, contains all Ramsey's previously published writings on philosophy and the foundations of mathematics. The (...) latter gives the definitive form and defence of the reduction of mathematics to logic undertaken in Russell and Whitehead's Principia Mathematica; the former includes the most profound and original studies of universals, truth, meaning, probability, knowledge, law and causation, all of which are still constantly referred to, and still essential reading for all serious students of these subjects. (shrink)

In this paper, I offer an analysis of the radical disagreement over the adequacy of string theory. The prominence of string theory despite its notorious lack of empirical support is sometimes explained as a troubling case of science gone awry, driven largely by sociological mechanisms such as groupthink (e.g. Smolin 2006). Others, such as Dawid (2013), explain the controversy by positing a methodological revolution of sorts, according to which string theorists have quietly turned to nonempirical methods of theory assessment given (...) the technological inability to directly test the theory. The appropriate response, according to Dawid, is to acknowledge this development and widen the canons of acceptable scientific methods. As I’ll argue, however, the current situation in fundamental physics does not require either of these responses. Rather, as I’ll suggest, much of the controversy stems from a failure to properly distinguish the “context of justification” from the “context of pursuit”. Both those who accuse string theorists of betraying the scientific method and those who advocate an enlarged conception of scientific methodology objectionably conflate epistemic justification with judgements of pursuit-worthiness. Once we get clear about this distinction and about the different norms governing the two contexts, the current situation in fundamental physics becomes much less puzzling. After defending this diagnosis of the controversy, I’ll show how the argument patterns that have been posited by Dawid as constituting an emergent methodological revolution in science are better off if reworked as arguments belonging to the context of pursuit. (shrink)

We develop a Bayesian framework for thinking about the way evidence about the here and now can bear on hypotheses about the qualitative character of the world as a whole, including hypotheses according to which the total population of the world is infinite. We show how this framework makes sense of the practice cosmologists have recently adopted in their reasoning about such hypotheses.

In the context of discovery-oriented hypothesis testing research, behavioral scientists widely accept a convention for false positive (α) and false negative error rates (β) proposed by Jacob Cohen, who deemed the general relative seriousness of the antecedently accepted α = 0.05 to be matched by β = 0.20. Cohen’s convention not only ignores contexts of hypothesis testing where the more serious error is the β-error. Cohen’s convention also implies for discovery-oriented hypothesis testing research that a statistically significant observed effect is (...) four times more probable to be a mistaken discovery than for a statistically significant true observed effect to be independently replicable. In the long run, Cohen’s convention thus is epistemically harmful to the development of a progressive science of human behavior, making its acceptance crucial in explaining the replication crisis in behavioral science. The balance between α- and β-errors generally ought to be struck using both epistemic and practical considerations. Yet epistemic considerations alone imply that making a genuine contribution to the body of knowledge in behavioral science requires error rates that are not only small but also symmetrical. (shrink)

This article rebuts Ramsey's earlier theory, in 'Universals of Law and of Fact', of how laws of nature differ from other true generalisations. It argues that our laws are rules we use in judging 'if I meet an F I shall regard it as a G'. This temporal asymmetry is derived from that of cause and effect and used to distinguish what's past as what we can know about without knowing our present intentions.

An introduction to informal logic, critical thinking and rhetoric utilizing actual public discourse .

" In the generations since, its influence has grown-today it is accepted as a classic of general jurisprudence.The work is a bold and persuasive attack on the ...

In this article, I consider an important challenge to the popular theory of scientific inference commonly known as ‘inference to the best explanation’, one that has received scant attention.1 1 The problem is that there exists a wide array of rival models of explanation, thus leaving IBE objectionably indeterminate. First, I briefly introduce IBE. Then, I motivate the problem and offer three potential solutions, the most plausible of which is to adopt a kind of pluralism about the rival models of (...) explanation. However, I argue that how ranking explanations on this pluralistic account of IBE remains obscure and pluralism leads to contradictory results. In light of these objections, I attempt to dissolve the problem by showing why IBE does not require a ‘model’ of explanation and by giving an account of what explanation consists in within the context of IBE. (shrink)

We attempt to extend the nominalistic project initiated in Hartry Field's Science Without Numbers to modern physical theories based in differential geometry.