Matthias Schröder has asked the question whether there is a weakest discontinuous problem in the topological version of the Weihrauch lattice. Such a problem can be considered as the weakest unsolvable problem. We introduce the discontinuity problem, and we show that it is reducible exactly to the effectively discontinuous problems, defined in a suitable way. However, in which sense this answers Schröder’s question sensitively depends on the axiomatic framework that is chosen, and it is a positive answer if we (...) work in Zermelo–Fraenkel set theory with dependent choice and the axiom of determinacy $\mathsf {AD}$. On the other hand, using the full axiom of choice, one can construct problems which are discontinuous, but not effectively so. Hence, the exact situation at the bottom of the Weihrauch lattice sensitively depends on the axiomatic setting that we choose. We prove our result using a variant of Wadge games for mathematical problems. While the existence of a winning strategy for Player II characterizes continuity of the problem (as already shown by Nobrega and Pauly), the existence of a winning strategy for Player I characterizes effective discontinuity of the problem. By Weihrauch determinacy we understand the condition that every problem is either continuous or effectively discontinuous. This notion of determinacy is a fairly strong notion, as it is not only implied by the axiom of determinacy $\mathsf {AD}$, but it also implies Wadge determinacy. We close with a brief discussion of generalized notions of productivity. (shrink)

Liminaires--Le livre du temps--Spatiologie--Succession et discontinuité--Le discontinu et le géométrie--Pour l'atomisme.

In this paper we continue, from [2], the development of provably recursive analysis, that is, the study of real numbers defined by programs which can be proven to be correct in some fixed axiom system S. In particular we develop the provable analogue of an effective operator on the set C of recursive real numbers, namely, a provably correct operator on the set P of provably recursive real numbers. In Theorems 1 and 2 we exhibit a provably correct operator on (...) P which is discontinuous at 0; we thus disprove the analogue of the Ceitin-Moschovakis theorem of recursive analysis, which states that every effective operator on C is (effectively) continuous. Our final theorems show, however, that no provably correct operator on P can be proven (in S) to be discontinuous. (shrink)

The more interest philosophers take in memory, the less agreement there is that memory exists—or more precisely, that remembering is a distinct psychological kind or mental state. Concerns about memory’s distinctiveness are triggered by observations of its similarity to imagination. The ensuing debate is cast as one between discontinuism and continuism. The landscape of debate is set such that any extensive engagement with empirical research into episodic memory places one on the side of continuism. Discontinuists concerns are portrayed as almost (...) exclusively conceptual and a priori. As philosophers of memory become increasingly interested in memory science, this pushes continuism into an apparent lead. The aim of this paper is to challenge this characterization of the continuism debate—namely, that a naturalistic approach to the philosophy of mind and memory favors continuism. My response has two components. First, I argue for weakening the alignment between naturalism and continuism. Second, I defend a naturalistically oriented, empirically-informed discontinuism between memory and imagination. I do so by introducing seeming to remember, which I argue is distinct from other mental attitudes—most importantly, from imagining. (shrink)

Continuists maintain that, aside from their distinct temporal orientations, episodic memory and future-oriented mental time travel (FMTT) are qualitatively continuous. Discontinuists deny this, arguing that, in addition to their distinct temporal orientations, there are qualitative metaphysical or epistemological differences between episodic memory and FMTT. This chapter defends continuism by responding both to arguments for metaphysical discontinuism, based on alleged discontinuities between episodic memory and FMTT at the causal, intentional, and phenomenological levels, and to arguments for epistemological discontinuism, based on alleged (...) discontinuities with respect to the epistemic openness of the past and future, the directness or indirectness of our knowledge of past and future, and immunity to error through misidentification. The chapter concludes by sketching a positive argument for continuism. (shrink)

Several clinical cases are presented to illustrate the phenomenon of discontinuity of personal narrative. These discontinuities are markedly and overtly present in the cases described, which include cases of bipolar disorder, incipient schizophrenia, dissociative disorder, and others. One of the patients suggests that they are also ubiquitous in people without psychiatric diagnoses.

Undoubtedly, the topic of discontinuity has got to an extent where it has captured the attention of a good number of researchers. These researchers devote themselves to reflect on the philosophy of the French thinker. Focusing on discontinuity promises to open a new line of analysis that, perhaps, will allow the revaluation of its scope in relation to its philosophical contributions. For such a task, first, we will approach the notion of history in Foucauldian thought to study the (...) development this notion has with the discontinuity; followed by a study of the archaeological method to unravel whether it is possible to analyze discontinuity through an archaeological view. Would it be possible to look at the topic of discontinuity as a characteristic feature of this French philosopher's thinking? This document aims to answer this question. (shrink)

_ Source: _Page Count 22 This is an attempt to discover and clarify the philosophical nature of what Eelco Runia claims to be his new and up-to-date philosophy of history, a programme offered in his 2014 book _Moved by the Past: Discontinuity and Historical Mutation_. His suggestion that his argument is a “dance” is taken seriously, and following an analysis of historical “meaning” and its time-extended nature it is argued that the book’s presentation commits Runia to a conception of (...) meaning that requires more weight than he allows to the centrality of narrative understanding in history. His attempt to reconnect critical and substantive philosophies of history is analysed and criticised. His apparently inconsistent commitments to both Vico’s _verum-factum_ claim, where we can make history, and to Gumbrecht’s “presence”, where history can make us, is clarified in terms of a pragmatic philosophy that permits Runia to have the psychology-based approach that he relies upon. (shrink)

In eukaryotic cells intron sequences are usually spliced out with a high degree of precision from heterogenous nuclear RNA (hnRNA) to give functional mRNA with exons in their right order. Provided with the right substrates, cell extracts can achieve the same. With exotic substrates, on the other hand, the same extracts can cut exons from one RNA and join them to exons from another RNA, a process termed trans‐splicing. In vivo, RNA trans‐splicing could lead to faulty, but also to novel (...) proteins and, through reverse transcription, to genomic rearrangements. So far, in living cells trans‐splicing has only been invoked to occur in trypanosomes. In these unicellular organisms most if not all mRNAs are made discontinuously, so that the mature mRNAs carry, at their 5′ end, a common 35‐nucleotide sequence, called a miniexon, encoded separately in the genome. The miniexon is most likely joined to the body of the mRNA by trans‐splicing. (shrink)

Perturbations of quantum systems ranging from oscillators to fields can be either continuous or discontinuous functions of the coupling. The system under consideration is the familiar harmonic oscillator in one degree of freedom. Previous studies have shown that when the harmonic oscillator is subjected to a perturbation with a power law singularity, a permanent change in the system characteristics is observed for a specific range of power law values. The introduction of a logarithmic singularity into the power law potential fine (...) tunes the singularity power. (shrink)

In this groundbreaking book, Andrea R. English challenges common assumptions by arguing that discontinuous experiences, such as uncertainty and struggle, are essential to the learning process. To make this argument, Dr. English draws from the works of two seminal thinkers in philosophy of education - nineteenth-century German philosopher J. F. Herbart and American Pragmatist John Dewey. English's analysis considers Herbart's influence on Dewey, inverting the accepted interpretation of Dewey's thought as a dramatic break from modern European understandings of education.

Discontinuity refers to the character of many natural language constructions wherein signs differ markedly in their prosodic and semantic forms. As such it presents interesting demands on monostratal computational formalisms which aspire to descriptive adequacy. Pied piping, in particular, is argued by Pollard (1988) to motivate phrase structure-style feature percolation. In the context of categorial grammar, Bach (1981, 1984), Moortgat (1988, 1990, 1991) and others have sought to provide categorial operators suited to discontinuity. These attempts encounter certain difficulties (...) with respect to model theory and/or proof theory, difficulties which the current proposals are intended to resolve.Lambek calculus is complete for interpretation byresiduation with respect to the adjunction operation of groupoid algebras (Buszkowski 1986). In Moortgat and Morrill (1991) it is shown how to give calculi for families of categorial operators, each defined by residuation with respect to an operation of prosodic adjunction (associative, non-associative, or with interactive axioms). The present paper treats discontinuity in this way, by residuation with respect to three adjunctions: + (associative), (.,.) (split-point marking), andW (wrapping) related by the equations 1+s 2+s 3=(s 1,s 3)Ws 2. We show how the resulting methods apply to discontinuous functors, quantifier scope and quantifier scope ambiguity, pied piping, and subject and object antecedent reflexivisation. (shrink)

Relational complexity theory has important virtues, but the present model omits key aspects and evidence. In contrast, skill theory specifies (1) a detailed series of developmental changes in relational complexity from birth to age 30, (2) processes of interaction of content and structure that produce variability in complexity, (3) the role of cortical development, and (4) empirical criteria for complexity levels, including developmental discontinuities. Many findings support these specifications.

The law values fairness, proportionality, and predictability. Accordingly, in the context of criminal law, punishments should be carefully calibrated to reflect the harm caused by an offense and the culpability of the offender. Yet, while this would suggest the dominance of “smooth” input/output relationships—for example, such that a minuscule increase in culpability would result in a correspondingly small increase in punishment—in fact, the law is laden with “bumpy” input/output relationships. Indeed, a minuscule change in input (be it of harm, culpability, (...) or any number of other measures) may result in a drastic change in output, creating significant discontinuities. Leading scholars have argued that smooth input/output relationships, which feature careful gradation and calibration, better accord with dominant theories of punishment than do bumpy relationships, which lack fine-tuning. Accepting as a starting premise that smooth input/ output relationships are to be preferred in the criminal law, this Article focuses on the significant doctrinal and practical impediments to smoothing out these relationships. This analysis reveals challenges to smoothing out relationships between inputs and outputs, as well as the difficulties associated with addressing discontinuous relationships among inputs and outputs. Specifically, it exposes the law’s classification of inputs and outputs itself as contestable and responsible for a range of hard-to-resolve discontinuities. In doing so, this Article begins the task of laying the groundwork for further analysis and possible reforms. (shrink)

In 2004 in Prague, I met Slovak philosopher Miroslav Marcelli, who had attended Foucault's lectures in Paris in 80s. We talked about the legacy of Foucault and contemporary philosophy. Mr. Marcelli taught me philosophy at Comenius University in 1995.. I never visited his lectures, I only passed the exam.. The most interesting point was his answer to my 'provocations' replicating the common prejudice about impracticability of the philosophy. He answered "Do you think that e.g. Descartes didn't know about it?" In (...) fact, people tend to think that philosophers or mathematicians, are "asocial" without "social" intelligence, while their occasional isolation (e.g. Nietzsche) is a product of social exclusion, rather than their choice. In 2013 I applied Foucault's concept of Discontinuity to short 10 minutes movie: Discontinuity, projected in my exhibition "From Animation" in Holland Park, London. The film has 3 parts, ends as it starts to show the significant historical events in 4 windows, when the same idea appears to disappear to re-appear.. Foucault's philosophy doesn't seem to me so unique now, e.g. the idea that many historical changes or progress itself is often illusionary - masking the power structure, had already been explored 515 BC, in depth by Parmenides who concluded: the change is impossible. (shrink)

L’abîme entre le caractère individuel du discret et le caractère homogène du continu est resté, depuis la philosophie grecque jusqu’à nos jours un des problèmes centraux de la logique et des fondements des mathématiques. On a obtenu des progrès dans la méthode, mais fort peu dans les résultats. Du côté quantitatif, le problème est éclairé par le principe de non-dénombrabilité du continu. De la conception atomistique du continu, par le finitisme de l’école de Paris, le néo-intuitionnisme de Brouwer, la théorie (...) dogmatique des Principia Mathematica, jusqu’à la méthode axiomatique, qui s’appuie sur une preuve de la non-contradiction ou sur un réalisme platonicien, ces écoles introduisent un grand nombre de nuances qui, dans ces dernières années, sont de plus en plus près de s’entendre réciproquement. (shrink)

Assume that M is a transitive model of $ZFC+CH$ containing a simplified $(\omega _1,2)$ -morass, $P\in M$ is the poset adding $\aleph _3$ generic reals and G is P-generic over M. In M we construct a function between sets of terms in the forcing language, that interpreted in $M[G]$ is an $\mathbb R$ -linear order-preserving monomorphism from the finite elements of an ultrapower of the reals, over a non-principal ultrafilter on $\omega $, into the Esterle algebra of formal power series. (...) Therefore it is consistent that $2^{\aleph _0}>\aleph _2$ and, for any infinite compact Hausdorff space X, there exists a discontinuous homomorphism of $C(X)$, the algebra of continuous real-valued functions on X. (shrink)

This paper uses autocatalytic networks to model discontinuous cultural transitions involving cross-domain transfer, using as an illustrative example, artworks inspired by the oldest-known uncontested example of figurative art: the carving of the Hohlenstein-Stadel Löwenmensch, or lion-human. Autocatalytic networks provide a general modeling setting in which nodes are not just passive transmitters of activation; they actively galvanize, or “catalyze” the synthesis of novel nodes from existing ones This makes them uniquely suited to model how new structure grows out of earlier structure, (...) i.e., cumulative, generative network growth. They have been used to model the origin and early evolution of biological life, and the emergence of cognitive structures capable of undergoing cultural evolution. We conducted a study in which six individual creators and one group generated music, prose, poetry, and visual art inspired by the Hohlenstein-Stadel Löwenmensch, and answered questions about the process. The data revealed four through-lines by which they expressed the Löwenmensch in an alternative art form: lion-human hybrid, subtracting from the whole to reveal the form within, deterioration, and waiting to be found with a story to tell. Autocatalytic networks were used to model how these four spontaneously derived through-lines form a cultural lineage from Löwenmensch to artist to audience. We used the resulting data from three creators to model the cross-domain transfer from inspirational source to creative product. These four spontaneously-generated threads of cultural continuity formed the backbone of this Löwenmensch-inspired cultural lineage, enabling culture to evolve even in the face of discontinuity at the level conventional categories or domains. We know of no other theory of cultural evolution that accommodates cross-domain transfer or other forms of discontinuity. The approach paves the way for a broad scientific framework for the origins of evolutionary processes. (shrink)

BackgroundBioethics and law distinguish between the practices of "physician-assisted death" and "allowing the patient to die."DiscussionAdvances in biotechnology have allowed medical devices to be used as destination therapy that are designed for the permanent support of cardiac function and/or respiration after irreversible loss of these spontaneous vital functions. For permanent support of cardiac function, single ventricle or biventricular mechanical assist devices and total artificial hearts are implanted in the body. Mechanical ventilators extrinsic to the body are used for permanent support (...) of respiration. Clinical studies have shown that destination therapy with ventricular assist devices improves patient survival compared to medical management, but at the cost of a substantial alteration in end-of-life trajectories. The moral and legal assessment of the appropriateness and permissibility of complying with a patient's request to electively discontinue destination therapy in a life-terminating act in non-futile situations has generated controversy. Some argue that complying with this request is ethically justified because patients have the right to request withdrawal of unwanted treatment and be allowed to die of preexisting disease. Other commentators reject the argument that acceding to an elective request for death by discontinuing destination therapy is 'allowing a patient to die' because of serious flaws in interpreting the intention, causation, and moral responsibility of the ensuing death.SummaryDestination therapy with cardiac and/or ventilatory medical devices replaces native physiological functions and successfully treats a preexisting disease. We posit that discontinuing cardiac and/or ventilatory support at the request of a patient or surrogate can be viewed as allowing the patient to die if--and only if--concurrent lethal pathophysiological conditions are present that are unrelated to those functions already supported by medical devices in destination therapy. In all other cases, compliance with a patient's request constitutes physician-assisted death because of the pathophysiology induced by the turning off of these medical devices, as well as the intention, causation, and moral responsibility of the ensuing death. The distinction between allowing the patient to die and physician-assisted death is pivotal to the moral and legal status of elective requests for death by discontinuing destination cardiac and/or ventilatory medical devices in patients who are not imminently dying. This distinction also represents essential information that must be disclosed to patients and surrogates in advance of consent to this type of therapy. (shrink)

In arguing for a rules-similarity continuum, Pothos should demonstrate that a single process or mechanism (a neural network model, for example) can handle the entire continuum. Pothos deliberately avoids this exercise as beyond the scope of the current research. In this context, I will present simulation, neuropsychological, neurophysiological, and experimental psychological results, arguing against the continuity hypothesis.

“A Public Domain, once a velvet carpet of rich buffalo-grass and grama, now an illimitable waste of rattlesnake-bush and tumbleweed, too impoverished to be accepted as a gift by the states within which it lies. Why? Because the ecology of the Southwest happened to be set on a hair trigger.”.

The paper rebuts a currently popular criticism against a certain take on the referential role of discontinuities and singularities in the physics of first-order phase transitions. It also elaborates on a proposal I made previously on how to understand this role within the framework provided by the distinction between data and phenomena.

This article explores recent questions regarding the interpretation of Vatican II by examining the council's theological and historical relation to what John O'Malley has called ‘the long nineteenth century’. This period, which O'Malley dates from the French Revolution until the end of the pontificate of Pius XII , connotes a time when political and philosophical developments ‘traumatized’ the Church. This sustained trauma left the Church in a defensive position which deeply informed its view of itself and its relation to the (...) world. While a great deal of attention has been directed at examining the council's degree of continuity or discontinuity with the conciliar tradition, not enough has been done to understand its relationship to developments within this more immediate setting. This study argues that a more contextualized appreciation of the Church's efforts to respond to the challenges of the long nineteenth century, expressed especially in the teachings of Vatican I, can illumine key elements of the meaning of Vatican II's documents and the continuity and/or discontinuity that they represent. (shrink)

This paper investigates the role of visual experience in Wittgenstein's work. The specific thesis is that visual experience provides not only diverse illustrative examples of what could be an explanation of meaning, but that it also provides a recurrent metaphor for the whole process of meaning and understanding. Wittgenstein uses a great number of visual examples in his texts. Their diversity may be accounted for by the great diversity of ways in which he attempts to describe the relationship between a (...) word and its meaning. The resultant variety of visual examples may be summarised by what I call the Visual Discontinuity Thesis. However, beneath this diversity there lies a thread of continuity. This is provided by the persistent use of visual experience in the description of the word-meaning relation. This use underlies the projection relationship of the Tractatus and the "seeing-as" relationship of the Investigations. This recurrent visual metaphor may be summarised by what I call the Visual Continuity Thesis. This paper presents the latter thesis in the context of a description of the former. (shrink)

Starting from recent formulas of EU bureaucracy for subordinating scientific and educational apparatuses to the needs of the capital and to the requests of its political representatives, the article analyses the interconnection between the historical transformation of the ideological state apparatuses and the epistemological discontinuity provoked by the triumph of technosciences. The hypothesis to be tested is the following: While the crisis of West European-North American capitalism requires an ever tighter submission of ideological state apparatuses, and especially of scientific (...) and academic apparatuses to the needs of the capital, theoretical practices in the humanities and social sciences have come to the point where they entered into an open conflict with the domination of the capital and have, as a consequence, started to subvert their own institutional supports in the ideological apparatuses of the capitalist state. For this purpose, the article reconsiders social sciences as a compromise formation and, eventually, reassesses the historical materialism as a non-Cartesian modern science. Polazeci od skorasnjih formula EU birokratije putem kojih se naucni i obrazovni aparati podredjuju potrebama kapitala i zahtevima njegovih politickih predstavnika, ovaj rad analizira uzajamnu povezanost istorijske transformacije ideoloskih aparata drzave i epistemoloskog diskontinuiteta koji je izazvan trijumfom tehno-nauka. Ispitivacemo sledecu hipotezu: iako kriza kapitalizma u Zapadnoj Evropi i Severnoj Americi zahteva sve cvrsce podredjivanje ideoloskih aparata drzave - narocito onih akademskih i naucnih - teorijske prakse u humanistickim i drustvenim naukama su dosegle tacku otvorenog sukoba sa dominacijom kapitala, cime su sledstveno pocele da podrivaju sopstvena institucionalna uporista u ideoloskim aparatima kapitalisticke drzave. U tu svrhu, rad preispituje drustvene nauke kao jednu kompromisnu formaciju i, naposletku, iznova razmatra istorijski materijalizam kao ne-kartezijansku modernu nauku. (shrink)

This Article explores settlement incentives under three different burden of proof rules. The conventional burden of proof is a discontinuous step-function, jumping from no damages to full damages at the 0.5 jury confidence level. Continuous burdens of proof, by contrast, would permit sanctions to steadily increase as juror confidence rises from 0 to 1, with no discontinuity. Linear burdens, which have received extensive attention in prior literature, escalate sanctions steadily across the whole range of confidence levels, while the logistic (...) burden takes a nonlinear form. Using a data simulation approach guided by the empirical realities of American civil litigation, I consider the incentives that each of these rules creates for parties contemplating settlement, using a model in which parties make divergent forecasts of their expected outcomes at trial due to optimism bias. Based on this analysis, I conclude that a linear burden would likely raise our settlement rate by a modest amount, except in very large cases and in “easy” cases, in which an unbiased person would predict that a trial factfinder would have a level of confidence in liability quite close to either zero or one. I also compare the expected error rate of the settlements that each rule produces, and find that the linear rule modestly lowers the expected error rate of settlement overall, although this benefit does not hold for easy cases or those with very high damages. Lastly, I conduct a similar analysis for the logistic burden, finding that it induces a similar quality and quantity of settlements as we currently achieve using conventional burdens. (shrink)

Involvement in sport and exercise not only provides participants with health benefits but can be an important aspect of living a meaningful life. The COVID-19 pandemic and the temporary cessation of public life in March/April/May 2020 came with restrictions, which probably also made it difficult, if not impossible, to participate in certain types of sport or exercise. Following the philosophical position that different types of sport and exercise offer different ways of “relating to the world,” this study explored continuity in (...) the type of sport and exercise people practiced during the pandemic-related lockdown, and possible effects on mood. Data from a survey of 601 adult exercisers, collected shortly after the COVID-19 outbreak in Finland, were analyzed. Approximately one third of the participants changed their “worldmaking” and shifted to “I–Nature”-type activities. We observed worse mood during the pandemic in those who shifted from “I–Me,” compared to those who had preferred the “I–Nature” relation already before the pandemic and thus experienced continuity. The clouded mood of those experiencing discontinuity may be the result of a temporary loss of “feeling at home” in their new exercise life-world. However, further empirical investigation must follow, because the observed effect sizes were small. (shrink)

The postulate that a stalled/collapsed replication fork will be generated when the replication complex encounters a UV‐induced lesion in the template for leading‐strand DNA synthesis is based on the model of semi‐discontinuous DNA replication. A review of existing data indicates that the semi‐discontinuous DNA replication model is supported by data from in vitro studies, while the discontinuous DNA replication model is supported by in vivo studies in Escherichia coli. Until the question of whether DNA replicates discontinuously in one or both (...) strands is clearly resolved, any model building based on either one of the two DNA replication models should be treated with caution. BioEssays 27:633–636, 2005. © 2005 Wiley Periodicals, Inc. (shrink)

Ethical issues relating to the withdrawal of dialysis are discussed, comparing dialysis with other life-support systems, particularly artificial ventilation. It is argued that there is no ethical difference between discontinuing treatment in each case. One practical difference between the two is that patients with chronic renal failure are less likely to have reduced autonomy, and so can engage in discussions with their doctors regarding the situations in which their life-supporting treatment might be discontinued. It is argued that doctors caring for (...) patients on dialysis have an ethical duty to discuss with these patients the circumstances in which they may wish to discontinue dialysis. (shrink)

In this paper we examine a class of pairs of recursively enumerable degrees, which is related to the Slaman-Soare Phenomenon.

In research on Augustine, Peter Brown’s paradigm of ‘two Augustines’ has been widely used. According to Brown, Augustine experienced a shift from optimism to pessimism. In his earlier works, Augustine held that humans could achieve happiness in this life by reason. In contrast, in his later works, Augustine emphasised grace, original sin and the imperfection of life. Against Brown’s framework, this paper argues that Augustine does not experience a pessimistic turn. Augustine holds that humans can achieve happiness through faith, hope (...) and love.Contribution: This article explores Augustine’s theory of happiness and revises the ‘two Augustines’ paradigm. On the one hand, Augustine does not deny the freedom of will. On the other hand, Augustine is confident in happiness through faith, hope and love. (shrink)

According to Heidegger’s own testimony, his 1940 essay, “Plato’s Doctrine of Truth,” is derived from a course he first delivered in 1931/32. Yet, while an interpretation of the Theaetetus is central to the argument in 1931/32, this dialogue is not so much as mentioned in the 1940 essay. The reason is that Heidegger’s own careful and insightful reading of the Theaetetus simply does not support his thesis regarding Plato’s “doctrine of truth.” But then the real interest of this reading is (...) that it affords the opportunity for pursuing a genuine dialogue between Heidegger and Plato that was too abruptly discontinued. (shrink)