The widely accepted “continuing bonds” model of grief tells us that rather than bereavement necessitating the cessation of one’s relationship with the deceased, very often the relationship continues instead in an adapted form. However, this framework appears to conflict with philosophical approaches that treat reciprocity or mutuality of some form as central to loving relationships. Seemingly the dead cannot be active participants, rendering it puzzling how we should understand claims about continued relationships with them. In this article, we resolve this (...) tension by highlighting two fundamental aspects of paradigmatic loving relationships that can, and often do, continue in an adapted form following bereavement: love and mutual shaping of interests, choices, and self-concepts. Attention to these continuing features of relationships helps to capture and clarify the phenomenological and behavioral features of continuing bonds. However, love and mutual shaping must also change in important ways following bereavement. Love becomes unreciprocated, and although the dead continue to shape our interests, choices, and self-concepts, we predominantly shape their legacies and memories in return. These changes place important constraints upon the nature of our interpersonal connections with the dead. (shrink)

Reasoning about bedrock abstract concepts such as time, number, and valence relies on spatial metaphor and often on multiple spatial metaphors for a single concept. Previous research has documented, for instance, both future-in-front and future-to-right metaphors for time in English speakers. It is often assumed that these metaphors, which appear to have distinct experiential bases, remain distinct in online temporal reasoning. In two studies we demonstrate that, contra this assumption, people systematically combine these metaphors. Evidence for this combination was found (...) in both directly elicited and spontaneous co-speech gestures about time. These results provide first support for the hypothesis that the metaphorical representation of time, and perhaps other abstract domains as well, involves the continuous co-activation of multiple metaphors rather than the selection of only one. (shrink)

The status of continuity in Deleuze’s metaphysics is a subject of debate. Deleuze calls the virtual, in Difference and Repetition, an Ideal continuum, and the differential relations that constitute the Ideal imply the continuity of this field. But, Deleuze does not hesitate to formulate the same field by the affirmation of divergence (incompossibility) that can be regarded as a form of discontinuity. It is, hence, unclear how these two ostensibly contradictory accounts might reconcile. This article attempts to reconstitute (...) a Deleuzian theory of continuity through Leibniz whose philosophy is equally subject to a tension between the law of continuity, prevalent in his mathematics and metaphysics, and the discontinuity or absolute individuality of monads. By reorienting The Fold around the motif of continuity a new conceptual space is opened for continuity qua heterogeneity-and-inseparability. Then, enfolding the conceptual personae of The Fold onto Difference and Repetition reveals the tacit though decisive presence of different types of continuity operational in Deleuze’s metaphysics that will be called divergent, intensive, torsional, and tenorsional continuities. (shrink)

A comprehensive and systematic reconstruction of the philosophy of Charles S. Peirce, perhaps America's most far-ranging and original philosopher, which reveals the unity of his complex and influential body of thought. We are still in the early stages of understanding the thought of C. S. Peirce (1839-1914). Although much good work has been done in isolated areas, relatively little considers the Peircean system as a whole. Peirce made it his life's work to construct a scientifically sophisticated and logically rigorous philosophical (...) system, culminating in a realist epistemology and a metaphysical theory ("synechism") that postulates the connectedness of all things in a universal evolutionary process. In The Continuity of Peirce's Thought, Kelly Parker shows how the principle of continuity functions in phenomenology and semeiotics, the two most novel and important of Peirce's philosophical sciences, which mediate between mathematics and metaphysics. Parker argues that Peirce's concept of continuity is the central organizing theme of the entire Peircean philosophical corpus. He explains how Peirce's unique conception of the mathematical continuum shapes the broad sweep of his thought, extending from mathematics to metaphysics and in religion. He thus provides a convenient and useful overview of Peirce's philosophical system, situating it within the history of ideas and mapping interconnections among the diverse areas of Peirce's work. This challenging yet helpful book adopts an innovative approach to achieve the ambitious goal of more fully understanding the interrelationship of all the elements in the entire corpus of Peirce's writings. Given Peirce's importance in fields ranging from philosophy to mathematics to literary and cultural studies, this new book should appeal to all who seek a fuller, unified understanding of the career and overarching contributions of Peirce, one of the key figures in the American philosophical tradition. (shrink)

Nothing seems as certain as death. However, what if life continues digitally after death? Companies and initiatives such as Amazon, Storyfile, Here After AI, Forever Identity and LifeNaut are dedicated to precisely this objective: using avatars, records, and other digital content of the deceased, they strive to enable a digital continuation of life. The deceased live on digitally, and at times, these can even appear very much alive-perhaps too alive? This article explores the ethical implications of these technologies, commonly known (...) as Death Tech. With the advancement of artificial intelligence, Death Tech will inevitably transform mourning practices, our perception of death, and how we cope with its reality in the coming years. In this article, it is demonstrated that Death Tech can contribute to individual grief support, education, and a vibrant culture of remembrance. However, it is crucial to recognise that the Digital Afterlife is not a paradise but necessitates active designing and ethical deliberation. DOI 10.5771/0010-3497-2023-3-427. (shrink)

Technical results about the time dependence of eigenvectors of reduced density operators are considered, and the relevance of these results is discussed for modal interpretations of quantum mechanics which take the corresponding eigenprojections to represent definite properties. Continuous eigenvectors can be found if degeneracies are avoided. We show that, in finite dimensions, the space of degenerate operators has co-dimension 3 in the space of all reduced operators, suggesting that continuous eigenvectors almost surely exist. In any dimension, even when degeneracies are (...) hit, we find conditions under which a theorem due to Rellich can provide continuous eigenvectors. We use this result to formulate an extended version of the modal interpretation. We also discuss eigenvector instability which we argue poses a serious problem for the modal interpretation, even in our extended version. Many examples are given to illustrate the mathematics. (shrink)

Since his Metaphysische Anfangsgründe der Naturwissenschaft was first published in 1786, controversy has surrounded Immanuel Kant’s conception of matter. In particular, the justification for both his dynamical theory of matter and the related dismissal of mechanical philosophy are obscure. In this paper, I address these longstanding issues and establish that Kant’s dynamism rests upon Leibnizian, metaphysical commitments held by Kant from his early pre-Critical texts on natural philosophy to his major critical works. I demonstrate that, throughout his corpus and inspired (...) by Leibniz, Kant endorses the a priori law of continuity of alteration as a truth of metaphysics, according to which all alterations in experience must occur gradually through all intervening degrees. The principle thus legislates against mechanical philosophy’s absolutely impenetrable atoms, as they would would involve instantaneous changes of velocity in impact. This reveals the metaphysical incoherencies in mechanical philosophy and leaves Kant’s own dynamical theory of matter, grounded on material forces, as the only viable approach to physical explanation. Subsequently, I demonstrate that Kant nevertheless made conceptual space in his system for the theoretical consideration of mechanical explanations, which makes manifest one of the positive roles that the faculty of reason can play with respect to natural science. (shrink)

This book takes concepts developed by researchers in theoretical computer science and adapts and applies them to the study of natural language meaning. Summarizing over a decade of research, Chris Barker and Chung-chieh Shan put forward the Continuation Hypothesis: that the meaning of a natural language expression can depend on its own continuation.

The relatively new practice of continuous sedation at the end of life (CS) is increasingly being debated in the clinical and ethical literature. This practice received much attention when a U.S. Supreme Court ruling noted that the availability of CS made legalization of physician-assisted suicide (PAS) unnecessary, as CS could alleviate even the most severe suffering. This view has been widely adopted. In this article, we perform an in-depth analysis of four versions of this ?argument of preferable alternative.? Our goal (...) is to determine the extent to which CS can be considered to be an alternative to PAS and to identify the grounds, if any, on which CS may be ethically preferable to PAS. (shrink)

In this paper a solution of Whitehead’s problem is presented: Starting with a purely mereological system of regions a topological space is constructed such that the class of regions is isomorphic to the Boolean lattice of regular open sets of that space. This construction may be considered as a generalized completion in analogy to the well-known Dedekind completion of the rational numbers yielding the real numbers . The argument of the paper relies on the theories of continuous lattices and “pointless” (...) topology.

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Illusions that produce perceptual suppression despite constant retinal input are used to manipulate visual consciousness. Here we report on a powerful variant of existing techniques, Continuous Flash Suppression. Distinct images flashed successively around 10 Hz into one eye reliably suppress an image presented to the other eye. Compared to binocular rivalry, the duration of perceptual suppression increased more than 10-fold. Using this tool we show that the strength of the negative afterimage of an adaptor was reduced by half when it (...) was perceptually suppressed by input from the other eye. The more likely the adaptor was completely suppressed, the larger the reduction of the afterimage intensity. Paradoxically, trial-to-trial visibility of the adaptor did not correlate with the degree of suppression. Our results imply that formation of afterimages involves neuronal structures that access input from both eyes, but that do not correspond directly to the neuronal correlates of perceptual awareness. (shrink)

Are works of music types of performance or are they continuants? Types are unchanging entities that could not have been otherwise; continuants can undergo change through time and could have been different. Picking up on this distinction, Guy Rohrbaugh has recently argued that musical works are continuants rather than performance-types. This paper replies to his arguments and, in the course of so doing, elaborates and defends the conception of musical works as types of performance. I end the article by arguing (...) that the conception of musical works as continuants is under-motivated and, ultimately, obscure. (shrink)

Empirical studies largely support the continuity hypothesis of dreaming. Despite of previous research efforts, the exact formulation of the continuity hypothesis remains vague. The present paper focuses on two aspects: the differential incorporation rate of different waking-life activities and the magnitude of which interindividual differences in waking-life activities are reflected in corresponding differences in dream content. Using a correlational design, a positive, non-zero correlation coefficient will support the continuity hypothesis. Although many researchers stress the importance of emotional (...) involvement on the incorporation rate of waking-life experiences into dreams, Hartmann formulated the hypothesis that highly focused cognitive processes such as reading, writing, etc. are rarely found in dreams due to the cholinergic activation of the brain during dreaming. The present findings based on dream diaries and the exact measurement of waking activities replicated two recent questionnaire studies. These findings indicate that it will be necessary to specify the continuity hypothesis more fully and include factors which modulate the incorporation rate of waking-life experiences into dreams. Whether the cholinergic state of the brain during REM sleep or other alterations of brain physiology are the underlying factors of the rare occurrence of highly focused cognitive processes in dreaming remains an open question. Although continuity between waking life and dreaming has been demonstrated, i.e., interindividual differences in the amount of time spent with specific waking-life activities are reflected in dream content, methodological issues have limited the capacity for detecting substantial relationships in all areas. Nevertheless, it might be concluded that the continuity hypothesis in its present general form is not valid and should be elaborated and tested in a more specific way. (shrink)

One important activity in conceptual ethics and conceptual engineering involves proposing to associate a new semantics with an existing word. Many philosophers think that one important way to evaluate such a proposal concerns whether it preserves the “topic” picked out by the existing word, and several have offered competing proposals concerning what is required to preserve topic. Our paper is focused on the conceptual ethics question of how conceptual engineers should use the term ‘topic continuity’. We provide and defend (...) a context- sensitive answer to this question. Our answer is motivated by the idea that there are several distinct considerations that we can reasonably care about (and which many conceptual engineers already do care about) in thinking about “topic continuity”, and, moreover, that how best to weigh them against each other can vary from context to context. On our proposal, ‘topic continuity’ can function as a useful representational device that enables coordination by inquirers with respect to these concerns. We conclude by locating our account in a broader way of thinking about topic continuity across a range of inquiries. (shrink)

This article presents an edited excerpt from a hitherto unknown fragmentary treatise by Rush Rhees. In the treatise, Rhees gives his account of the problem of continuity that he had started elaborating before he became acquainted with Wittgenstein. The excerpt, which contains Rhees' original distinction between outer and inner surfaces of bodies, builds on Brentano's theory of the continuum and his doctrine of plerosis. This treatment of continuity sheds light on Rhees' early philosophical development and confirms that even (...) though he and Wittgenstein discussed the problem of continuity, Rhees' own approach remained distinct from that of Wittgenstein. (shrink)

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We deal with principles which are equivalent to the statements "every mapping is sequentially nondiscontinuous", "every sequentially nondiscontinuous mapping is sequentially continuous", and "every sequentially continuous mapping is continuous". As corollaries, we show that every mapping of a complete separable space is continuous in constructive recursive mathematics (the Kreisel-Lacombe-Schoenfield-Tsejtin theorem) and in intuitionism.

This article presents an edited excerpt from a hitherto unknown fragmentary treatise by Rush Rhees. In the treatise, Rhees gives his account of the problem of continuity that he had started elaborating before he became acquainted with Wittgenstein. The excerpt, which contains Rhees' original distinction between outer and inner surfaces of bodies, builds on Brentano's theory of the continuum and his doctrine of plerosis. This treatment of continuity sheds light on Rhees' early philosophical development and confirms that even (...) though he and Wittgenstein discussed the problem of continuity, Rhees' own approach remained distinct from that of Wittgenstein. (shrink)

CONTINUOUS MODEL THEORY CHAPTER I TOPOLOGICAL PRELIMINARIES. Notation Throughout the monograph our mathematical notation does not differ drastically from ...

A strongly independent preorder on a possibly in finite dimensional convex set that satisfi es two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfi es two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii') mixture continuity; and (...) (iii') completeness. Applications to decision making under conditions of risk and uncertainty are provided. (shrink)

The usual meaning of the word continuous is “unbroken” or “uninterrupted”: thus a continuous entity —a continuum—has no “gaps.” We commonly suppose that space and time are continuous, and certain philosophers have maintained that all natural processes occur continuously: witness, for example, Leibniz's famous apothegm natura non facit saltus—“nature makes no jump.” In mathematics the word is used in the same general sense, but has had to be furnished with increasingly precise definitions. So, for instance, in the later 18th century (...) continuity of a function was taken to mean that infinitesimal changes in the value of the argument induced infinitesimal changes in the value of the function. With the abandonment of infinitesimals in the 19th century this definition came to be replaced by one employing the more precise concept of limit. (shrink)

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We show that every mapping is sequentially continuous if and only if it is sequentially nondiscontinuous and strongly extensional, and that "every mapping is strongly extensional", "every sequentially nondiscontinuous mapping is sequentially continuous", and a weak version of Markov's principle are equivalent. Also, assuming a consequence of Church's thesis, we prove a version of the Kreisel-Lacombe-Shoenfield-Tsĕitin theorem.

Two experiments were carried out to investigate the role of referential continuity in understanding discourse. In experiment 1, a group of university students listened to stories and descriptive passages presented in three different versions: the original passages, versions in which the sentences occured in a random order, and randomised versions in which referential continuity had been restored primarily by replacing pronouns and other terms with fuller and more appropriate noun phrases. The original stories were remembered better, and rated (...) as more comprehensible, than the random versions, but the restoration of referential continuity ameliorated the effects of randomisation. The descriptive passages had little referential continuity from one sentence to the next, and as expected the effects of randomisation on comprehensibility and memory were negligible. In experiment 2, a group of skilled comprehenders and a group of less skilled comprehenders were selected from a population of 7–8-year-old children. The difference between the groups was known to be largely their inferential ability in reading texts. Both groups read a series of short stories presented in the same three versions as used in the previous experiment. As predicted, the ameliorating effects on memory of restoring referential continuity in a randomised story were confined to the skilled group. The results are discussed in relation to the theories of story grammar, text microstructure, and mental models of discourse. (shrink)

This paper begins with a brief account of how I started out as a young logician studying modal logic with the hope that it would be useful when applied to evaluating real examples of arguments found in natural language texts. The exposition moves on to relate how my interests shifted to the study of argumentation in informal logic, and from there to computational systems combining defeasible argumentation schemes with argument mapping (diagramming). The story ends by leading to recent collaborations with (...) three young logicians and computer scientists who are continuing on the path of my journey. (shrink)

When it comes to the question of what kind of moral claim an intelligent or autonomous machine might have, one way to answer this is by way of comparison with humans: Is there a fundamental difference between humans and other entities? If so, on what basis, and what are the implications for science and ethics? This question is inherently imprecise, however, because it presupposes that we can readily determine what it means for two types of entities to be sufficiently different—what (...) I will refer to as being “discontinuous”. In this paper, I will sketch a formal characterization of what it means for types of entities to be unique with regard to each other. This expands upon Bruce Mazlish’s initial formulation of what he terms a continuity between humans and machines, Alan Turing’s epistemological approach to the question of machine intelligence, and Sigmund Freud’s notion of scientific revolutions dealing blows to the self-esteem of mankind. I will discuss on what basis we should regard entities as (dis-)continuous, the corresponding moral and scientific implications, as well as an important difference between what I term downgrading and upgrading continuities—a dramatic difference in how two previously discontinuous types of entities might become continuous. All of this will be phrased in terms of which scientific levels of explanation we need to presuppose, in principle or in practice, when we seek to explain a given type of entity. The ultimate purpose is to provide a framework that defines which questions we need to ask if we argue that two types of entities ought (not) to be explained (hence treated) in the same manner, as well as what it takes to reconsider scientific and ethical hierarchies imposed on the natural and artificial world. (shrink)

This article discusses some continuous limit cases of Susan Haack’s crossword puzzle metaphor for the coherent development and foundation of science. The main objective of this discussion is to build a bridge between Haack’s foundherentism and the epistemological framework of objective cognitive constructivism, including its key metaphor of objects as tokens for eigen-solutions. The historical development of chemical affinity tables is used to illustrate our arguments.

Using traditional meta-analytic techniques, we compile relevant research to enhance conceptual appreciation of ethical climate theory (ECT) as it has been studied in the descriptive and applied ethics literature. We explore the various treatments of ethical climate to understand how the theoretical framework has developed. Furthermore, we provide a comprehensive picture of how the theory has been extended by describing the individual-level work climate outcomes commonly studied in this theoretical context. Meta-analysis allows us to resolve inconsistencies in previous findings as (...) well as confirm the central tenets of the overall ethical climate framework. In addition, we consider the ethical climate relationships in the larger context of the␣theoretical framework, using path analysis to test the structural relationships. Overall, our results provide evidence of the relationships between ethical climate perceptions and individual-level work outcomes. Based on our analyses, we offer future research directions important for further development of ECT. (shrink)

The paper considers and opposes the view that processes are best thought of as continuants, to be differentiated from events mainly by way of the fact that the latter, but not the former, are entities with temporal parts. The motivation for the investigation, though, is not so much the defeat of what is, in any case, a rather implausible claim, as the vindication of some of the ideas and intuitions that the claim is made in order to defend — and (...) the grounding of those ideas and intuitions in a more plausible metaphysics than is provided by the continuant view. It is argued that in addition to a distinction between events and processes there is room and need for a third category, that of the individual process, which can be illuminatingly compared with the idea of a substance. Individual processes indeed share important metaphysical features with substantial continuants, but they do not lack temporal parts. Instead, it is argued that individual processes share with substantial continuants an important property I call ‘modal robustness in virtue of form’. The paper explains what this property is, and further suggests that the category of individual process, thus understood, might be of considerable value to the philosophy of action. (shrink)

Type 1 diabetes (T1D) is a chronic illness that requires intensive lifelong management of blood glucose concentrations by means of external insulin administration. There have been substantial developments in the ways of measuring glucose levels, which is crucial to T1D self-management. Recently, continuous glucose monitoring (CGM) has allowed people with T1D to keep track of their blood glucose levels in near real-time. These devices have alarms that warn users about potentially dangerous blood glucose trends, which can often be shared with (...) ther people. CGM is consistently associated with improved glycemic control and reduced hypoglycemia and is currently recommended by doctors. However, due to the costs of CGM, only those who qualify for hospital provision or those who can personally afford it are able to use it, which excludes many people. In this paper, I argue that unequal access to CGM results in: (1) unjust health inequalities, (2) relational injustice, (3) injustice with regard to agency and autonomy, and (4) epistemic injustice. These considerations provide prima facie moral reasons why all people with T1D should have access to CGM technology. I discuss the specific case of CGM policy in the Netherlands, which currently only provides coverage for a small group of people with T1D, and argue that, especially with additional considerations of cost-effectiveness, the Dutch government ought to include CGM in basic health care insurance for all people with T1D. (shrink)

A novel theoretical framework for an embodied, non-representational approach to language that extends and deepens enactive theory, bridging the gap between sensorimotor skills and language. -/- Linguistic Bodies offers a fully embodied and fully social treatment of human language without positing mental representations. The authors present the first coherent, overarching theory that connects dynamical explanations of action and perception with language. Arguing from the assumption of a deep continuity between life and mind, they show that this continuity extends (...) to language. Expanding and deepening enactive theory, they offer a constitutive account of language and the co-emergent phenomena of personhood, reflexivity, social normativity, and ideality. Language, they argue, is not something we add to a range of existing cognitive capacities but a new way of being embodied. Each of us is a linguistic body in a community of other linguistic bodies. The book describes three distinct yet entangled kinds of human embodiment, organic, sensorimotor, and intersubjective; it traces the emergence of linguistic sensitivities and introduces the novel concept of linguistic bodies; and it explores the implications of living as linguistic bodies in perpetual becoming, applying the concept of linguistic bodies to questions of language acquisition, parenting, autism, grammar, symbol, narrative, and gesture, and to such ethical concerns as microaggression, institutional speech, and pedagogy. (shrink)

In the mid-eighteenth century, it was usually taken for granted that all curves described by a single mathematical function were continuous, which meant that they had a shape without bends and a well-defined derivative. In this paper I discuss arguments for this claim made by two authors, Emilie du Châtelet and Roger Boscovich. I show that according to them, the claim follows from the law of continuity, which also applies to natural processes, so that natural processes and mathematical functions (...) have a shared characteristic of being continuous. However, there were certain problems with their argument, and they had to deal with a counterexample, namely a mathematical function that seemed to describe a discontinuous curve. (shrink)

I examine the reasons Aristotle presents in Physics VIII 8 for denying a crucial assumption of Zeno’s dichotomy paradox: that every motion is composed of sub-motions. Aristotle claims that a unified motion is divisible into motions only in potentiality (δυνάμει). If it were actually divided at some point, the mobile would need to have arrived at and then have departed from this point, and that would require some interval of rest. Commentators have generally found Aristotle’s reasoning unconvincing. Against David Bostock (...) and Richard Sorabji, inter alia, I argue that Aristotle offers a plausible and internally consistent response to Zeno. I defend Aristotle’s reasoning by using his discussion of what to say about the mobile at boundary instants, transitions between change and rest. There Aristotle articulates what I call the Changes are Open, Rests are Closed Rule: what is true of something at a boundary instant is what is true of it over the time of its rest. By contrast, predications true of something over its period of change are not true of the thing at either of the boundary instants of that change. I argue that this rule issues from Aristotle’s general understanding of change, as laid out in Phys. III. It also fits well with Phys. VI, where Aristotle maintains that there is a first boundary instant included in the time of rest, but not a “first in which the mobile began to change.” I then show how this rule underlies Aristotle’s argument that a continuous motion cannot be composed of actual sub-motions. Aristotle distinguishes potential middles, points passed through en route to a terminus, from actual middles. The Changes are Open, Rests are Closed Rule only applies to actual middles, because only they are boundaries of change that the mobile must arrive at and then depart from. On my reading, Aristotle argues that the instant of arrival, the first instant at which the mobile has come to be at the actual middle, cannot belong to the time of the subsequent motion. If it did, the mobile would already be moving towards the next terminus and thus, per Phys. VI 6, would have already left. But it cannot have moved away from the midpoint at the very same moment it has arrived there. This means that the instant of arrival must be separated from the time of departure by an interval of rest. I show how Aristotle’s reasoning applies generally to rule out any continuous reflexive motion or continuous complex rectilinear motion. On my interpretation, however, the argument does not apply to every change of direction. When, as in the case of projectile motion, multiple movers and their relative powers explain why the mobile changes directions, distinct sub-motions are not involved. Aristotle holds that such motions cannot be continuous, not because they involve intervals of rest, but because they involve multiple causes of motion. My interpretation of the Changes are Open, Rests are Closed Rule allows us to make better sense of Aristotle’s argument than any previous interpretation. (shrink)

If is a Polish metric space of dimension 0, then by Wadge’s lemma, no more than two Borel subsets of X are incomparable with respect to continuous reducibility. In contrast, our main result shows that for any metric space of positive dimension, there are uncountably many Borel subsets of that are pairwise incomparable with respect to continuous reducibility. In general, the reducibility that is given by the collection of continuous functions on a topological space \\) is called the Wadge quasi-order (...) for \\). As an application of the main result, we show that this quasi-order, restricted to the Borel subsets of a Polish space \\), is a well-quasiorder if and only if \\) has dimension 0. Moreover, we give further examples of applications of the construction of graph colorings that is used in the proofs. (shrink)

Against Continuity is the first book to demonstrate that the beating heart of Gilles Deleuze's philosophy is a systematic ontology of irreducible, singular entities. This requires a radical break with decades of Deleuzian orthodoxy, according to which Deleuze's metaphysics revolves around the dissolution of discrete entities into a continuous world of flows and events.With reference to all of Deleuze's work, including published and untranslated seminars, as well as the recently published 'Lettres et autres textes', Arjen Kleinherenbrink critically compares Deleuze's (...) ontology to seven related contemporary thinkers: Levi Bryant, Maurizio Ferraris, Markus Gabriel, Manuel DeLanda, Graham Harman, Tristan Garcia and Bruno Latour. These comparisons establish Deleuze as an important precursor to object-oriented speculative realism and open up exciting new avenues of thought for critics and supporters of Deleuze alike. (shrink)

Any theory that analyses personal identity in terms of phenomenal continuity needs to deal with the ordinary interruptions of our consciousness that it is commonly thought that a person can survive. This is the bridge problem. The present paper offers a novel solution to the bridge problem based on the proposal that dreamless sleep need not interrupt phenomenal continuity. On this solution one can both hold that phenomenal continuity is necessary for personal identity and that persons can (...) survive dreamless sleep. (shrink)

The concepts of a spatially continuous substance, of spatial dimension and of spatial boundary are here "analyzed out" of the concepts of individual thing, of constituent and of coincidence. The analysis is based upon the theory of spatial coincidence that was developed by Brentano. Its presuppositions are essentially these: (1) if there are spatial objects of any kind, then there are continuous spatial substances. (2) such substances are possibly such that they are not constituents of any individual thing; and (3) (...) they contain constituents (namely, boundaries) which are necessarily such that they are constituents of spatial substances. (shrink)

Uniform sequential continuity, a property classically equivalent to sequential continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.

The development of rigorous foundations of differential calculus in the course of the nineteenth century led to concerns among physicists about its applicability in physics. Through this development, differential calculus was made independent of empirical and intuitive notions of continuity, and based instead on strictly mathematical conditions of continuity. However, for Boltzmann and Poincaré, the applicability of mathematics in physics depended on whether there is a basis in physics, intuition or experience for the fundamental axioms of mathematics—and this (...) meant that to determine the status of differential equations in physics, they had to consider whether there was a justification for these mathematical continuity conditions in physics. For this reason, their ideas about continuity and discreteness in nature were entangled with epistemology and philosophy of mathematics. They reached opposite conclusions: Poincaré argued that physicists must work with a continuous representation of nature, and thus with differential equations, while Boltzmann argued that physicists must ultimately take nature to be discrete. (shrink)

The objective of this paper is to balance two major conceptual tendencies in science policy studies, continuity and discontinuity theory. While the latter argue for fundamental and distinct changes in science policy in the late 20th century, continuity theorists show how changes do occur but not as abrupt and fundamental as discontinuity theorists suggests. As a point of departure, we will elaborate a typology of scientific governance developed by Hagendijk and Irwin ( 2006 ) and apply it to (...) new empirical material. This makes possible a contextualization of the governance of science related to the codification of the “third assignment” of the Swedish higher education law of 1977. The law defined the relation between university science and Swedish citizens as a dissemination project, and did so despite that several earlier initiatives actually went well beyond such a narrow conceptualisation. Our material reveals continuous interactive and rival arrangements linking the state, public authorities, the universities and private industrial enterprises. We show how different but coexisting modes of governance of science existed in Sweden during the 20th century, in clear contrast with the picture promoted by discontinuity theorists. A close study of the historical development suggests that there were several periods of layered governance when interactions and dynamics associated with continuity as well as discontinuity theories were prevalent. In addition, we conclude that the typology of governance applied in the present paper is fruitful for carrying out historical analyses of the kind embarked upon in spite of certain methodological shortcomings. (shrink)

We investigate the role of continuous reductions and continuous relativization in the context of higher randomness. We define a higher analogue of Turing reducibility and show that it interacts well with higher randomness, for example with respect to van Lambalgen’s theorem and the Miller–Yu/Levin theorem. We study lowness for continuous relativization of randomness, and show the equivalence of the higher analogues of the different characterizations of lowness for Martin-Löf randomness. We also characterize computing higher [Formula: see text]-trivial sets by higher (...) random sequences. We give a separation between higher notions of randomness, in particular between higher weak 2-randomness and [Formula: see text]-randomness. To do so we investigate classes of functions computable from Kleene’s [Formula: see text] based on strong forms of the higher limit lemma. (shrink)

This paper addresses a question concerning psycho­logical continuity, i.e., which features preserve the same psychological subject over time; this is not the same question as the one concerning the necessary and sufficient conditions for personal identity. Marc Slors defends an account of psychological continuity that adds two features to Derek Parfit’s Relation R, namely narrativity and embodiment. Slors’s account is a significant improvement on Parfit’s, but still lacks an explicit acknowledgment of a third feature that I call relationality. (...) Because they are usually regarded as cases of radical discontinuity, I start my discussion from the experiences of psychological disruption undergone by victims of severe violence and trauma. As it turns out, the challenges we encounter in granting continuity to the experiences of violence and trauma victims are germane to those we encounter in granting continuity to the experiences of subjects in non-traumatic contexts. What is missing in the most popular accounts of psychological continuity is an explicit acknowledgment of the links that tie our psychological lives to other subjects. A more persuasive notion of psychological continuity is not only embodied and narrative, as is Slors’s notion, but also explicitly relational. (shrink)

Understanding the relationship between wilderness outings and the resulting experience has been a central theme in resource-based, outdoor recreation research for nearly 50 years. The authors provide a review and synthesis of literature that examines how people, over time, build relationships with wilderness places and express their identities as consequences of multiple, ongoing wilderness engagements (i.e., continued participation). The paper reviews studies of everyday places and those specifically protected for wilderness and backcountry qualities. Beginning with early origins and working through (...) contemporary research the authors synthesize what diverse social scientists have learned about the long-term and continual nature of wilderness participation and its impact on the formation of identity. The thrust of the paper points researchers, planners, and managers in non-traditional directions and reframes goals and objectives for visitor planning and management in wilderness and other protected areas. (shrink)

We investigate the Ramsey theory of continuous graph-structures on complete, separable metric spaces and apply the results to the problem of covering a plane by functions. Let the homogeneity number[Formula: see text] of a pair-coloring c:[X]2→2 be the number of c-homogeneous subsets of X needed to cover X. We isolate two continuous pair-colorings on the Cantor space 2ω, c min and c max, which satisfy [Formula: see text] and prove: Theorem. For every Polish space X and every continuous pair-coloringc:[X]2→2with[Formula: see (...) text], [Formula: see text] There is a model of set theory in which[Formula: see text]and[Formula: see text]. The consistency of [Formula: see text] and of [Formula: see text] follows from [20]. We prove that [Formula: see text] is equal to the covering number of 2 by graphs of Lipschitz functions and their reflections on the diagonal. An iteration of an optimal forcing notion associated to c min gives: Theorem. There is a model of set theory in which ℝ2 is coverable byℵ1graphs and reflections of graphs of continuous real functions; ℝ2 is not coverable byℵ1graphs and reflections of graphs of Lipschitz real functions. Figure 1.1 in the introduction summarizes the ZFC results in Part I of the paper. The independence results in Part II show that any two rows in Fig. 1.1 can be separated if one excludes [Formula: see text] from row. (shrink)

According to three-dimensionalism, objects persist in time by being wholly present at each time they exist; on the contrary, four-dimensionalism asserts that objects persist by having different temporal parts at different times or that they are instantaneous temporal parts of four-dimensional aggregates. Le Poidevin has argued that four-dimensionalism better accommodates two common assumptions concerning persistence and continuity; namely, that time itself is continuous and that objects persist in time in a continuous way. To this purpose, he has offered two (...) independent arguments, each of which moves from a different understanding of continuity. In this paper, both of Le Poidevin’s arguments will be discussed and rejected. (shrink)