In attempting to understand personal identity, it is common practice to imagine a person existing at some time t and a person existing at a time t* , and then to ask, What does it take for person x at t to be the same person as person y at t*?The Psychological Continuity Approach answers: there is a relation, R, of psychological continuity such that person x at t is the same person as person y at t* if (...) and only if x at t bears R to y at t*.But maybe the question above is not the right one to ask when trying to understand personal identity. Olson calls this the narrow question of personal identity, which he distinguishes from the broad question: What does it take for person x at t to be the same individual as y at t*? (shrink)
Deep brain stimulation is a well-accepted treatment for movement disorders and is currently explored as a treatment option for various neurological and psychiatric disorders. Several case studies suggest that DBS may, in some patients, influence mental states critical to personality to such an extent that it affects an individual’s personal identity, i.e. the experience of psychological continuity, of persisting through time as the same person. Without questioning the usefulness of DBS as a treatment option for various serious and treatment (...) refractory conditions, the potential of disruptions of psychological continuity raises a number of ethical and legal questions. An important question is that of legal responsibility if DBS induced changes in a patient’s personality result in damage caused by undesirable or even deviant behavior. Disruptions in psychological continuity can in some cases also have an effect on an individual’s mental competence. This capacity is necessary in order to obtain informed consent to start, continue or stop treatment, and it is therefore not only important from an ethical point of view but also has legal consequences. Taking the existing literature and the Dutch legal system as a starting point, the present paper discusses the implications of DBS induced disruptions in psychological continuity for a patient’s responsibility for action and competence of decision and raises a number of questions that need further research. (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)
The life–mind continuity thesis is difficult to study, especially because the relation between life and mind is not yet fully understood, and given that there is still no consensus view neither on what qualifies as life nor on what defines mind. Rather than taking up the much more difficult task of addressing the many different ways of explaining how life relates to mind, and vice versa, this paper considers two influential accounts addressing how best to understand the life–mind (...) class='Hi'>continuity thesis: first, the theory of autopoiesis developed in biology and in enactivist theories of mind; and second, the recently formulated free energy principle in theoretical neurobiology, with roots in thermodynamics and statistical physics. This paper advances two claims. The first is that the free energy principle should be preferred to the theory of AT, as classically formulated. The second is that the FEP and the recently formulated framework of autopoietic enactivism can be shown to be genuinely continuous on a number of central issues, thus raising the possibility of a joint venture when it comes to answering the life–mind continuity thesis. (shrink)
The view that an account of personal identity can be provided in terms of psychological continuity has come under fire from an interesting new angle in recent years. Critics from a variety of rival positions have argued that it cannot adequately explain what makes psychological states co-personal (i.e. the states of a single person). The suggestion is that there will inevitably be examples of states that it wrongly ascribes using only the causal connections available to it. In this paper, (...) I describe three distinct attacks on the psychological continuity theory along these lines. While I acknowledge that a number of interesting issues arise, I argue that the theory can withstand all three attacks. (shrink)
Marya Schechtman has raised a series of worries for the Psychological Continuity Theory of personal identity (PCT) stemming out of what Derek Parfit called the ‘Extreme Claim’. This is roughly the claim that theories like it are unable to explain the importance we attach to personal identity. In her recent Staying Alive (2014), she presents further arguments related to this and sets out a new narrative theory, the Person Life View (PLV), which she sees as solving the problems as (...) well as bringing other advantages over the PCT. I look over some of her earlier arguments and responses to them as a way in to the new issues and theory. I argue that the problems for the PCT and advantages that the PLV brings are all merely apparent, and present no reason for giving up the former for the latter. (shrink)
The life–mind continuity thesis holds that mind is prefigured in life and that mind belongs to life. The biggest challenge faced by proponents of this thesis is to show how an explanatory framework that accounts for basic biological processes can be systematically extended to incorporate the highest reaches of human cognition. We suggest that this apparent ‘cognitive gap’ between minimal and human forms of life appears insurmountable largely because of the methodological individualism that is prevalent in cognitive science. Accordingly, (...) a twofold strategy is used to show how a consideration of sociality can address both sides of the cognitive gap: (1) it is argued from a systemic perspective that inter-agent interactions can extend the behavioral domain of even the simplest agents and (2) it is argued from a phenomenological perspective that the cognitive attitude characteristic of adult human beings is essentially intersubjectively constituted, in particular with respect to the possibility of perceiving objects as detached from our own immediate concerns. These two complementary considerations of the constitutive role of inter-agent interactions for mind and cognition indicate that sociality is an indispensable element of the life–mind continuity thesis and of cognitive science more generally. (shrink)
In their recent book Radicalizing Enactivism. Basic minds without content, Dan Hutto and Erik Myin make two important criticisms of what they call autopoietic enactivism. These two criticisms are that AE harbours tacit representationalists commitments and that it has too liberal a conception of cognition. Taking the latter claim as its main focus, this paper explores the theoretical underpinnings of AE in order to tease out how it might respond to H&M. In so doing it uncovers some reasons which not (...) only appear to warrant H&M’s initial claims but also seem to point to further uneasy tensions within the AE framework. The paper goes beyond H&M by tracing the roots of these criticisms and apparent tensions to phenomenology and the role it plays in AE’s distinctive conception of strong life-mind continuity. It is highlighted that this phenomenological dimension of AE contains certain unexamined anthropomorphic and anthropogenic leanings which do not sit comfortably within its wider commitment to life-mind continuity. In light of this analysis it is suggested that AE will do well to rethink this role or ultimately run the risk of remaining theoretically unstable. The paper aims to contribute to the ongoing theoretical development of AE by highlighting potential internal tensions within its framework which need to be addressed in order for it to continue to evolve as a coherent paradigm. (shrink)
Abstract: Those who endorse the Psychological Continuity Approach (PCA) to analyzing personal identity need to impose a non-branching constraint to get the intuitively correct result that in the case of fission, one person becomes two. With the help of Brueckner's (2005) discussion, it is shown here that the sort of non-branching clause that allows proponents of PCA to provide sufficient conditions for being the same person actually runs contrary to the very spirit of their theory. The problem is first (...) presented in connection with perdurantist versions of PCA. The difficulty is then shown to apply to endurantist versions as well. -/- . (shrink)
Analyses of singular (token-level) causation often make use of the idea that a cause in- creases the probability of its effect. Of particular salience in such accounts are the values of the probability function of the effect, conditional on the presence and absence of the putative cause, analyzed around the times of the events in question: causes are characterized by the effect’s probability function being greater when conditionalized upon them. Put this way it becomes clearer that the ‘behavior’ (continuity) (...) of probability functions in small intervals about the times in question ought to be of concern. In this paper I make an extended case that causal theorists employing the ‘probability raising’ idea should pay attention to the continuity question. Specifically, if the probability functions are ‘jumping about’ in ways typical of discontinuous functions, then the stability of the relevant probability increase is called into question. The rub, however, is that sweeping requirements for either continuity or discontinuity are problematic, and as I argue, this constitutes a ‘continuity bind’. Hence more subtle considerations and constraints are needed, two of which I consider: (1) utilizing discontinuous first derivatives of continuous probability functions, and (2) abandoning point probability for imprecise (interval) probability. (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)
If persons endure, personal identity cannot be analyzed in terms of psychological continuity. That is one conclusion defended in my “Endurance, Psychological Continuity, and the Importance of Personal Identity’ . Rea and Silver claim that my argument for that conclusion is sound only if a parallel argument is sound. The parallel argument concludes that if persons perdure, personal identity cannot be analyzed in terms of psychological continuity. In this paper, I show that Rea and Silver are mistaken. (...) My argument is sound but the parallel argument is not. (shrink)
A widely accepted view in the discussion of personal identity is that the notion of psychological continuity expresses a one--many or many--one relation. This belief is unfounded. A notion of psychological continuity expresses a one--many or many--one relation only if it includes, as a constituent, psychological properties whose relation with their bearers is one--many or many--one; but the relation between an indexical psychological state and its bearer when first tokened is not a one--many or many--one relation. It follows (...) that not all types of psychological continuity may take a one--many or many--one form. This conclusion casts doubt on the Lockean approach to the issue, by showing that the notion of psychological continuity Lockeans rely on may not be available. (shrink)
In a recent article, Trenton Mericks argues that psychological continuity analyses of personal identity over time are incompatible with endurantism. We contend that if Merricks’s argument is valid, a parallel argument establishes that PC-analyses of personal identity are incompatible with perdurantism; hence, the correct conclusion to draw is simply that such analyses are all necessarily false. However, we also show that there is good reason to doubt that Merricks’s argument is valid.
Hoyningen-Huene develops an account of what science is, distinguishing it from common sense. According to Hoyningen-Huene, the key distinguishing feature is that science is more systematic. He identifies nine ways in which science is more systematic than common sense. I compare Hoyningen-Huene’s view to a view I refer to as the “Continuity Thesis.” The Continuity Thesis states that scientific knowledge is just an extension of common sense. This thesis is associated with Quine, Planck, and others. I argue that (...) Hoyningen-Huene ultimately rejects the Continuity Thesis, and I present further evidence to show that the Continuity Thesis is false. I also argue that it is the systematicity of science that ultimately grounds the epistemic authority of science. Hoyningen-Huene thus draws attention to an important feature of science that explains the place of science in contemporary society. (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.
In this paper, I focus on an internal tension within James’s "Principles" and suggest that its formal structure provides useful insight into James’s subsequent evolution. Specifically,through a close reading of James’s account of ‘conceptions’ in the "Principles," I examine the tension between these ‘conceptions' construed as discrete and self-identical and James’s famous phenomenological description of consciousness as a continuous stream. Such a tension primarily involves the intersection of an epistemic need (or condition of possibility) with a quasi-metaphysical intuition or postulate (...) (continuity). Importantly, this tension is intensified by the methodological constraints of bracketing metaphysical questions that James sets for himself in the "Principles." James’s decision to deny the cogency of this methodological bracketing can therefore be read as his response to the tension I examine and his speculative turn to “radical empiricism” as an attempt to resolve epistemological difficulties by going more radical ontologically. Doing so raises questions about the status of speculative metaphysics in intersection with empirical inquiry. (shrink)
Left-continuous t-norms are much more complicated than the continuous ones, and obtaining a complete classification of them seems to be a very hard task. In this paper we investigate some aspects of left-continuous t-norms, with emphasis on their continuity points. In particular, we are interested in left-continuous t-norms which are isomorphic to t-norms which are continuous in the rationals. We characterize such a class, and we prove that it contains the class of all weakly cancellative left-continuous t-norms.
This paper explores the relationship between temporal continuity in nursing and temporal features of sickness. It is based on phenomenological and hermeneutical philosophy, empirical studies of sickness time, and the nursing theories of Nightingale, of Benner and of Benner and Wrubel. In the first part, temporal continuity is defined as distinct from interpersonal continuity. Tensions between temporal continuity and discontinuity are discussed in the contexts of care management, of conceptualisations of disease and of time itself. Temporal (...) limitations to the methodological concept of situation are discussed. The main part of this paper explores nurses' possibilities to relate to their patients' time, and how temporal features of sickness may warrant temporal continuity of nursing. Three temporal characteristics of sickness are discussed: the immediacy of patients' suffering, the basic continuity of life through sickness and health care, and the indeterminism and precariousness of sickness. The timing of nursing acts is discussed. The paper explores how sickness is both part of the continuity of life, and threatens this continuity. It concludes that this tension is implicitly recognised in the temporal continuity of nursing, which allows for discontinuous and continuous aspects of sickness time. Nurses accordingly perceive the sick person's time at several levels of temporality, and distinguish highly complex temporal processes in their patients' trajectory. Temporal continuity provides the time, flexibility, and closeness for nurses to perceive and act into time dimensions of individual sickness. The paper shows that temporal continuity of nursing is grounded in temporal characteristics of severe sickness. It suggests that temporal continuity is an important theoretical concept in nursing. (shrink)
This paper examines Husserl’s fascination with the issues raised by Hume’s critique of the philosophy of the ego and the continuity of consciousness. The path taken here follows a continental and phenomenological approach. Husserl’s 1905 lecture course on the temporalization of immanent time-consciousness is a phenomenological-eidetic examination of how the continuity of consciousness and the consciousness of continuity are possible. It was by way of Husserl’s reading of Hume’s discussion of “flux” or “flow” that his discourse on (...) temporal phenomena led to the classification of a point-like now as a “fiction” and opened up a horizonal approach to the present that Hume’s introspective analyses presuppose but that escaped the limitations of the language that was available to him. In order to demonstrate the radicality of Husserl’s temporal investigations and his inspiration in the work of Hume, I show how his phenomenological discourse on the living temporal flow of consciousness resolves the latter’s concern about the problem of continuity by re-thinking how, in the absence of an abiding impression of Self, experience is continuous throughout the flux of its running off impressions. (shrink)
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)
A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current j=ρ ∇ S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may be described by a linear differential equation for a complex-valued state variable (...) χ. Using these assumptions and the simplest possible Ansatz χ(ρ,S), for the relation between χ and ρ,S, Schrödinger’s equation for a particle of mass m in a mechanical potential V(q,t) is deduced. For simplicity the calculations are performed for a single spatial dimension (variable q). Using a second Ansatz χ(ρ,S,q,t), which allows for an explicit q,t-dependence of χ, one obtains a generalized Schrödinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schrödinger’ equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for a non-unique external q,t-dependence of χ, one obtains Schrödinger’s equation with electrodynamic potentials A,φ in the familiar gauge coupling form. This derivation shows a deep connection between non-uniqueness, quantum mechanics and the form of the gauge coupling. A possible source of the non-uniqueness is pointed out. (shrink)
According to the mental continuity claim (MCC), human mental faculties are physical and beneficial to human survival, so they must have evolved gradually from ancestral forms and we should expect to see their precursors across species. Materialism of mind coupled with Darwin’s evolutionary theory leads directly to such claims and even today arguments for animal mental properties are often presented with the MCC as a premise. However, the MCC has been often challenged among contemporary scholars. It is usually argued (...) that only humans use language and that language as such has no precursors in the animal kingdom. Moreover, language is quite often understood as a necessary tool for having representations and forming beliefs. As a consequence, by lacking language animals could not have developed representational systems or beliefs. In response to these worries, we aim to mount a limited defense of the MCC as an empirical hypothesis. First, we will provide a short historical overview of the origins of the MCC and examine some of the motives behind traditional arguments for and against it. Second, we will focus on one particular question, namely whether language as such is necessary for having beliefs. Our goal is to show that there is little reason to think language is necessary for belief. In doing so, we will challenge a view of belief that is widely accepted by those working in animal cognition, namely representational belief, and we will argue that if belief is non-representational, then different research questions and methods are required. We will conclude with an argument that to study the evolution of belief across species, it is essential to begin the study of subjects in their social and ecological environment rather than in contexts that are not ecologically valid along the social and ecological dimensions. Thus, rather than serving as a premise in an argument 3 in favor of animal minds, the MCC can only be defended by empirical investigation, but importantly, empirical investigation of the right sort.. (shrink)
I want to examine the implications of a metaphysical thesis which is presupposed in various objections to Rawls' theory of justice.Although their criticisms differ in many respects, they concur in employing what I shall refer to as the continuity thesis. This consists of the following claims conjointly: (1) The parties in the original position (henceforth the OP) are, and know themselves to be, fully mature persons who will be among the members of the well-ordered society (henceforth the WOS) which (...) is generated by their choice of principles of justice. (2) The OP is a conscious event among others, integrated (compatibly with the constraints on knowledge and motivation imposed on the parties) into the regular continuity of experience that comprises each of their ongoing constitutes lives. (3) The parties in the OP thus are, and regard themselves as, psychologically continuing persons, partially determined in personality and interests by prior experiences, capable of recollection and regret concerning the past, anticipation and apprehensiveness regarding the future, and so on. Although the continuity thesis as stated above is not at odds with any of the conditions that define the OP, its exegetical validity is a matter for discussion. I shall be concerned to argue that if it is indeed contained in or a consequence of Rawls' theory, then it casts into doubt the capacity of the OP to generate or justify any principles of justice at all. On the other hand, if the continuity thesis is viewed as dispensable and unnecessary to the Rawlsian enterprise, then Rawls is correct in maintaining the irrelevance of the question of personal identity to the construction of his moral theory. In this case, the contract-theoretic, instrumentalist justification for the two principles of justice (henceforth the 2PJ) needs to be supplanted by a modified conception of wide reflective equilibrium. The considerations that form the bulk of this discussion then may be understood as providing a rationale for Rawls' recent revisions in the model of justification on which his theory of justice rests, and for his increasing emphasis on us as moral mediators between the OP and the WOS. Now I want to consider the question of whether or not, given the textual evidence, anything like the continuity thesis is stated or implied by Rawls, and what problems for his theory, if any, turn on a positive or negative answer to this question. -/- . (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)
Berkeley holds that the esse of sensible objects is percipi. So, sensible objects cannot exist unperceived. Naturally, this has invited questions about the existence of sensible objects when unperceived by finite minds. This is sometimes called the Problem of Continuity. It is frequently said that Berkeley solves the problem by invoking God’s ever-present perception to ensure that sensible objects maintain a continuous existence. Problems with this line of response have led some to a phenomenalist interpretation. This paper argues that (...) neither of these are Berkeley’s solutions since he recognizes no such problem. The paper sketches a new interpretation of sensible objects that obviates the need for a “solution” by avoiding the “problem” in the first place. (shrink)
The strong version of the life-mind continuity thesis claims that mind can be understood as an enriched version of the same functional and organizational properties of life. Contrary to this view, in this paper I argue that mental phenomena offer distinctive properties, such as intentionality or representational content, that have no counterpart in the phenomenon of life, and that must be explained by appealing to a different level of functional and organizational principles. As a strategy, and following Maturana’s autopoietic (...) theory of cognition, I introduce a conceptual distinction between mind and cognition. I argue that cognition corresponds to the natural behaviour that every living being exhibits in the realization of its existence, and that, viewed in that way, cognition is a dynamic process of structural coupling that, unlike mental phenomena, involves no representational contents. On the basis of this distinction, I try to show that while life suffices for cognition, it does not suffice for mind. That is, that the strong continuity is not between life and mind but between life and cognition. (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)
The continuity thesis of the Poznań school threshold model of the growth of scientific knowledge is considered in the light of the example of Van der Waals' and Boyle-Mariotte's laws. It is argued - using both traditional logical means and the structuralist reconstruction of the example - that the continuity thesis does not hold. A distinction between 'a historical and a systematic point of view' is introduced and it is argued that the continuity thesis of the threshold (...) model presupposes the systematic point of view. However, looking at matters from the systematic point of view need not yield the original theory, looked at from the historical point of view. Applied to the case of Van der Waals/Boyle-Mariotte laws, it turns out that the latter law is not a true idealizing special case of the former, contrary to the continuity thesis. The structuralist analysis of the example indicates that Boyle-Mariotte's law is a false factual law from the historical point of view. However, viewed from the systematic point of view, Boyle-Mariotte's law turns out to be a law which is expandable, adding the relevant new concepts, to an idealized version of Van der Waals' law. This idealizing version of Van der Waal's law in turn is a structuralist specialization of the (general) Van der Waals' law. (shrink)
The relation between near continuity and sequential continuity for mappings between metric spaces is explored constructively. It is also shown that the classical implications “near continuity implies sequential continuity” and “near continuity implies apart continuity” are essentially nonconstructive.
In the last decade of his life C.S. Peirce began to formulate a purely geometrical theory of continuity to supersede the collection-theoretic theory he began to elaborate around the middle of the 1890s. I argue that Peirce never succeeded in fully formulating the later theory, and that while that there are powerful motivations to adopt that theory within Peirce’s system, it has little to recommend it from an external perspective.
It is shown, within constructive mathematics, that the unit ball B1 of the set of bounded operators on a Hilbert space H is weak-operator totally bounded. This result is then used to prove that the weak-operator continuity of the mapping T → AT on B1 is equivalent to the existence of the adjoint of A.
The main result of this paper is a weak constructive version of the uniform continuity theorem for pointwise continuous, real-valued functions on a convex subset of a normed linear space. Recursive examples are given to show that the hypotheses of this theorem are necessary. The remainder of the paper discusses conditions which ensure that a sequentially continuous function is continuous. MSC: 03F60, 26E40, 46S30.
Jeff McMahan's impressive recent defence of the embodied mind theory of personal identity in his highly acclaimed work The Ethics of Killing has undoubtedly reawakened belief that physical continuity is a necessary component of the relation that matters in our self-interested concern for the future. My aim in this paper is to resist this belief in a somewhat roundabout way. I want to address this belief in a somewhat roundabout way by revisiting a classic defence of the belief that (...) enormous changes in the contents of a person's psychology does not preclude justified fear of future pain. I have in mind Bernard Williams' The Self and the Future (1970) in which he argues, against the psychological view, that physical continuity is necessary for survival. I examine Williams' second thought experiment which ostensibly supports that intuition and afterwards defend two related claims. First, I argue that a close examination of the second thought experiment reveals that one's prior commitments to a particular criterion of personal identity can influence one's response to that thought experiment. Second, I argue that Williams' second thought experiment is set out in questionbegging terms. I do not claim, however, that the intuition under consideration lacks justification; I only claim that Williams' second thought experiment does not provide the needed support. (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)
The constructive functional calculus for a sequence of commuting selfadjoint operators on a separable Hilbert space is shown to be independent of the orthonormal basis used in its construction. The proof requires a constructive criterion for the absolute continuity of two positive measures in terms of test functions.
Duhem is commonly held to have founded his view of history of science as continuous on the ‘metaphsical assertion’ of natural classification. With the help of a strict distinction between formal and material characterization of natural classification I try to show that this imputation is problematic, if not simply incorrect. My analysis opens alternative perspectives on Duhem's talk of continuity, the ideal form of theories, and the rôle of ‘bon sens’; moreover it emphasizes some aspects of Duhem's realism that (...) play an important part in his philosophy of science. (shrink)
In this paper, I examine the relation between Henri Poincaré’s definition of mathematical continuity and Sartre’s discussion of temporality in Being and Nothingness. Poincaré states that a series A, B, and C is continuous when A=B, B=C and A is less than C. I explicate Poincaré’s definition and examine the arguments that he uses to arrive at this definition. I argue that Poincaré’s definition is applicable to temporal series, and I show that this definition of continuity provides a (...) logical basis for Sartre’s psychological explanation of temporality. Specifically, I demonstrate that Poincaré’s definition allows the for-itself to be understood both as connected to a past and future and as distinct from itself. I conclude that the gap between two terms in a temporal series comprises the present and being-for-itself, since it is this gap that occasions the radical freedom to reshape the past into a distinct and different future. (shrink)
This article is concerned with understanding continuity and stability in teaching, and their significance. It looks particularly at the work of Anthony Giddens on structure and agency, that of Martin Heidegger on the limits of discursive and theoretical analysis, and the communitarian strand within ethics. It applies this discussion to understandings of teachers’ work in the context especially of policy and agendas for change, arguing that continuity and the notion of a community of practitioners is critical to maintaining (...) the distinctive ethical quality of teaching. (shrink)
This is the ﬁrst of two papers that examine Charles Peirce’s denial that human beings have a faculty of intuition. The semiotic and epistemo-logical aspects of that denial are well-known. My focus is on its neglected metaphysical aspect, which I argue amounts to the doctrine that there is no determinate boundary between the internal world of the cognizing subject and the external world that the subject cognizes. In the second paper, I will argue that the “objective idealism” of Peirce’s 1890s (...) cosmological series is a more general iteration of the metaphysical aspect of his earlier denial of intuition. (shrink)
The anti-Specker property, a constructive version of sequential compactness, is used to prove constructively that a pointwise continuous, order-dense preference relation on a compact metric space is uniformly sequentially continuous. It is then shown that Ishihara's principle BD-ℕ implies that a uniformly sequentially continuous, order-dense preference relation on a separable metric space is uniformly continuous. Converses of these two theorems are also proved.